OrangeMath

Book Review - The Death and Life of the Great American School System - Ravitch

2011-02-06T22:23:00.001-08:00

Diane Ravitch, Bill Gate’s number one enemy in his words, doesn’t stoop to blogger-style comments. She is an educational historian! Her critique of education reformers and their emphasis on tests may not rise to Susan Sontage levels, but it is devastating nonetheless. My review that follows tries to supplement her kind words

Perhaps it’s best to read The Death and Life of the Great American School System in reverse order. The last chapter stresses what can be done to improve our schools in ways that are achievable and positive.

The penultimate chapter discusses the non-criticized roles of Gates, Broad, and Walton family (Wal-mart). These foundations have contributed to almost all “elite” ed institutions: dissent has been minimized.

Dr. Ravitch doesn’t discuss particular silencings, but my favorite group, Core Knowledge, which pressures for improved curriculum has become very quiet over test, test, test. The organization merely presses for more integrated content from curriculum to test. Again, she doesn’t stoop to my levels of writing things like why don’t they preach what they practiced: Gates went to a wonderful, liberal high school that allowed him time to work on projects, why does he stress accountability now. He’s like G. Canada of the Harlem Charter School who brags about reading constantly while growing up, but now presses for accountability.

The third to the last chapter focuses on the limitations of testing. No legitimate organization and no country has adopted testing of students as the way to target teachers. Yet we say that we are research-based. Of course, here Dr. Ravitch agrees, but she still pulls back. She shreds the VAT people, because they also advocate for no licensing, no advanced education etc of teachers because it doesn’t correlate to higher test scores. Dr. Ravitch doesn’t state the obvious conclusion: If VAT results don’t correlate to anything, then they are worthless. The key fact that Dr. Ravitch leaves out is that TIMSS scores correlate with the number of demographic questions answered. This implies, or I infer, that test results are a cultural issue, not a teaching issue! The only strange omission in her text is that the unreliability of VAT results is due to “regression to the mean.” She left out that well-know term.

The funniest chapter is the one on “choice.” Who can be against choice? She points out that Schools of Choice were the standard to keep white schools white after 1954 in the South. Choice means segregation. Of course, it will mean the same thing now, but it will be seen differently. Of high importance is that even schools that try to be random in student selection are not in practice. Low achievers are dismissed. This can be seen in my school district Newport-Mesa. Early College High School is meant to have 100 students per class. Only 34 graduated! The other students returned to different schools. The good news was that the test scores of this school were equal to those of a high-SES school for everyone. Are congratulations in order?

In other words, Dr. Ravitch presents evidence quietly and the reader brings the heat to this work. This is clear in that she doesn’t argue, as I would, that all of the attacks on public education are to reap its cash in privatization. This is obvious to me because Gates, Broad, and company refuse to put any money into Catholic schools; even though they have excellent track records in educating poor students. They are in decline because of subsidized competition from charters, which most of whom deliver weak results.

This is the book to read if you value the value of local community schools, see the value in local democracy, and worry about the unchecked power of reformers. If you just think the market should decide things, while ignoring the impact of regulations and foundation money on the market, don’t bother.

Math Games & Competitions @ NCTM 2010

2010-12-28T14:32:00.000-08:00

While the focus at NCTM is on policy and instruction, the vendors displayed some interesting items.

Board/Box Games

Foxmind offers many shape/placement strategy games. Of high interest for symmetry in action is the four game sequence:

Arithmo - paper-based
Khet - laser-mirror table-top game
ISeeCards - simple card games
Delta Education - various math games

Hexagonoes

Math Competitions

MathCounts (Middle School)
American Mathematics Competitions

AMC 8 (14.5 years old and younger)
AMC 10 (grades 9-10)
AMC 12 (high school)

American Regions Math League - also lists all national/state competitions

Power Contest
Local Competions

Mathematical Olympiads (4-6 and 6-8)
Mathathon - fundraiser for St. Jude Hospital (K-8)
Pomona (high school)

Math Compatible Alternatives

The American Contract Bridge League provides a Youth4Bridge afterschool program. Bridge, chess and go are the three most difficult to play games. They take focus and practice. While a bridge club may not succeed by itself, a game club where all three available may be. The club could also offer simpler logic games, both table and construction, such as the Games listed above.

Book Review - Innumeracy - Paulos

2010-12-04T10:30:00.000-08:00

Innumeracy, at a mere 135 pages, jumps in with easy math play. Paulos didn't want a mathematical Cultural Literacy with lists, but an immersion in what being math literate means in attitude and application. Clearly, he sees mental math as fun and the prerequisite to mastering what's necessary; since without some joy, there is little interest in learning enough math to protect one's mind from deception and to gain the tools necessary for interacting with the modern world.

Intermixed with play are quick comments on what should be taught such as Discrete Mathematics (not the conventional push for Calculus), and the very real need for Probability and its Applied Mathematics cousin, Statistics. Paulos, like others such as Mlodinow, realizes the danger in humans seeing patterns where there is only randomness. We need Statistics to detect error within ourselves; not just to detect errors in arguments by others. To put this differently, a mathematical mind isn't about tricks or computation, but how see, how to obtain the heuristics needed for problem solving or merely seeing problems where others have no vision.

Showing how math play leads to value, Paulos proposes models on what having numeracy can exhibit: for example, a logarithmic safety index for rating everyday risk, but he never says "model this." He treats the reader with respect.

Each chapter of the book (1988) presents an area where innumeracy leads to error in different aspects of modern life. This isn't a must read. Those who know, know. Those that don't, probably wouldn't pick it up - sadly.

Quick Clip - Online Education

2010-08-25T22:23:00.001-07:00

Book Review - The Drunkard's Walk - Leonard Mlodinow

2010-08-16T13:03:00.001-07:00

Another book trying to escape a book. Mlodinow desperately wants to push the theme: humans make errors because they are not only not wired to incorporate random outcomes in their analysis, but also are wired to impart patterns to outcomes that are actually random. The law of small numbers is an example of this. This is the double wammy that makes us dumber than rats in some behavioral studies. Unfortunately, the author barely comes close. Instead, 80% of the book covers the history of probabilistic thinking through statistics through the mathematics of error which culminates into the useful math of statistical mechanics.

The stories and anecdotes, Dr. Mlodinow (who has collaborated twice with Hawking!) relates are wonderful and well-told. The progression is thoughtful and coherent and interesting. Yet, the text stops well short of the math of "decision analysis,"which makes the chit-chat on poor human thinking beneath many other authors from both breezy and mathematical perspectives.

The modern editorial decision to exclude even one mathematical expression from a book on mathematics or even an illustration limits the work. While the book might read well on a Kindle(tm), books on this topic should be on an iPad/web with hyperlinks. The irony of an exceptionally intelligent author writing about the limits of human action, using weak tools that he emasculates even further, doesn't bring a smile to my face.

While this review sounds negative, it should be noted that The Drunkard's Walk is better than the average pop science/math book. Learning about Cardano's development of outcomes in a sample space was inspiring and the restatement of the importance of Bayes, without putting him down, was uplifting. This helped counter the exasperation of reading about Bernoulli's golden theorem four times without being told what it was. De Moivre was mentioned and more could have been said of Polya's role in fully proving De Moivre's Central Limit Theorem, but 20th century math doesn't exist in the book!

In summary, Mlodinow's book joins other pop books in providing one very important value: it is a quick read that provides scaffolding for a reader, not to go further intentionally, but to allow advanced work a home in the brain later. For example, decades ago, if I had known of Riemann's great contribution to geometry, I would have realized in the years ahead why I was being taught particular items and they would have stuck better.

More Support for AP and Indirectly Newsweek's Rankings

2010-06-18T19:18:00.000-07:00

Online cheating on graded school work is a real problem. Sites like answers work very well for many assessments taken at home and at school. Even math problems are solved online. My more open students love to take an online class, they claim "[they] finish in a day, get an A. What are friends for?" With more and more students taking online courses, the irregularities in grading remain unresolved.

AP, IB, and Cambridge tests are proctored and are identical to all takers. Their results have integrity, if not validity. As a teacher who has offered courses from many online curriculum providers, I deeply know how believable an A or B is from an online course completed at home. Zip. It is what it is.

Taking an AP test is far, far better than taking an online assessment. Newsweek and Jay Mathews have it right from the standpoint of a beneficiary of a school's rigor, which is what really matters.

Wolfram|Alpha and Online Math - A Wonderfully Unfortunate Fit

2010-06-18T10:48:00.000-07:00

Wolfram|Alpha brings much of Mathematica to everyone. It is a wonder of the 21st century, and it greatly helps doing math homework in Algebra, Algebra 2, Trig and more. As a result, grades must be determined by classroom testing and work alone. Online, distance learning in mathematics is more than compromised - it's obliterated, if grading with credit is an outcome.

Consider StudyIsland, one of the best online programs. One student completed the entire course with an A in a matter of a few class periods by placing each question into WolframAlpha - every possible problem. It takes far longer to type a problem such as Solve 3/(x+6) + 2/(x+1) = x/(x^2+7x+6) than to get the answer. Copy the problem yourself, paste it into Wolfram|Alpha and see. The plot is a bit funny, but the answer is clear. Obviously, this would be grand for instruction, but not evaluation.

In short, teach online, but grade in class. Perhaps regional centers for proctored exam taking with video cameras on students and their computer screens will be the next growth industry.

Costa Mesa High School Ranks in Top 6% of US Schools

2010-06-13T15:34:00.000-07:00

Costa Mesa has joined Corona del Mar and Newport Harbor in the top 6% of US high schools according to Newsweek's easy-to-understand 2010 list based on Summer 2009 data. CdM ranks in the top 1% and Harbor ranks in the top 3%.

For reference, Irvine's exceptional University High School is included in the chart below. The lower the score, the better. Only 1,600 schools out of 27,000 made the cut.

Jay Mathews, an education reporter for the Washington Post and Newsweek, developed the structure of the data. However, the Newport-Mesa Summary, source of the chart above, is solely the responsibility of Dennis Ashendorf.

Thank You - DonorsChoose - Robots

2010-06-12T16:07:00.000-07:00

The following thank you also outlines how a DonorsChoose grant can morph.

Dear Lisa, Michael, Joel, Vicki, Duane, Terry, Christine, Arnie, Maria, Mike, Kristian, George, Shelly, Sy and anonymous donors,

Finding the right level of robotics with programming for continuation students poses challenges. Without your support, the sweet spot wouldn't have been found. Furthermore, your commitment help makes our robot curriculum transferable to conventional schools which may enhance their students's destinations such as First Robotics or VEX. In the future, this effort may lead to summer internships in university labs; where masters of Python, Labview, Matlab, and JMP/Minitab software are in demand.

It would have been easy to start with LEGO Mindstorm robots which use a simplified Labview language. Our continuation students are familiar with LEGO's, but that's about it. None have assembled models or wired electronics. Our school's solar panel installation program would benefit from students who know the difference between open and closed circuits. Parallax Sumobots and BOE-bots provide the needed mechanical and electrical background at low cost. These robots have built-in breadboards that force students to install LED's and speakers, for example.

The tradeoff is that their BASIC software doesn't employ graphics, just text. Students would have to start by puzzling over code, which was an open question before the DonorsChoose grant was submitted. To mitigate this concern, a cardboard robot and several plastic analog robots, OWI Sumobots, "programmed" with variable resistors, were included in the grant. The cardboard robot died a quick death and the analog robots were inconsistent. Students didn't learn much. However the Parallax robots were simple to build and actually easy-to-program: students merely copied other programs and tweaked them to see how robots would respond to modified software. Fun and learning resulted. Showing off robot battles and robot travels impressed friends and teachers.

In the future, two or four students per math lab (3-5 per day) will work on a robotics/software/wiring curriculum. They will start with MIT's Scratch and Microsoft's Small Basic. Next they will work with MIT's Picocricket and inexpensive Parallax microcontroller breadboards. Finally, they will program and fight with the Parallax robots. As an option, they can either venture into greater depth with sensors on the Arrick Arobot platform or move into VEX robots.

None of this would have been possible without your help. You encouraged a few students today and many more at the start of next year. If you have questions, please contact me. Thank you for assisting DonorsChoose in its efforts to assist teachers directly. You made a difference.

With gratitude,
Mr. A

Math Software @ NCTM

2010-05-26T23:37:00.000-07:00

Math software needs to be placed in perspective. One size does not fit all. Various objectives, including cost, must be considered. Please refer to this diagram for areas of concern. At NCTM, several programs were on display. Comments on them and others follow. Text in Bold means that I will attempt to vet the products in 2010-2011.

Please realize that there are many free supplements. Making them work cohesively with a curriculum, not just as an occasional time-filler, is the challenge. It may be wiser to use Heymath, which is designed for teaching. On the other hand, through Lesson Study, combining Wolfram Demonstrations, Gizmos, Wolfram Alpha, VirtualNerd, Brightstorm, Autograph, and Geogebra with an online assessment system; such as Daskala, could yield remarkable results.

General Purpose
Check out thinklinkr! Create and share outlines online.

Elementary

ST Math: K-5 had large crowds. However, it should be noted that neither ALEKS nor Johns Hopkins nor Ascend offer software for K-2.
ThinkFun Education has many math games.
First in Math for K-8.
Thinkport is developing math games.
I Play Math Games has games for k-12 under an unusual format.
Johns Hopkins has furthered development of CTY Online for gifted students.
Guaranteach offers 20,000 video lessons and assessment for K-12 at $15/student.
KendallHunt offers online lessons for K-5: Aha!Math and for the gifted as Project M3.
Math-Whizz sells online tutoring with lessons for 5-13 year-olds.
Tadell sells online assessments in Spanish without text for English Learners in K-8.

Secondary Free Usage

Wolfram Mathematica Demonstrations
Wolfram Alpha
ConceptuaMath has extensive interactives for fractions in the effort to instill number sense for Algebra as the NMAP suggested.
WebMathTutor is a free middle school supplemental program based on Carnegie Tutor.
Brightstorm offers 1800 free online videos for Algebra 1 through Calculus.
Absorb offers numerous free online manipulatives.
VirtualNerd has a basic library of free math videos and a premium, but low cost, extensive library.
MathTV offers online presentations from more than one teacher.
Annenberg Media continues to offer the 20-year-old videos Algebra: In Simplest Terms and Inside Statistics series for instruction, which complements the non-profit's many professional development courses.
STEMCollaborative has several free online games for middle school. They complement other thinkport games such as Labyrinth.

Secondary Paid Usage

ST Math: Secondary Intervention is the software component of Mind Research's Algebra Readiness program
RevolutionK12 offers integrated programs of detailed instruction with assessment for Algebra Readiness, Algebra 1, CAHSEE, and SAT/ACT. Newport-Mesa has used this for CAHSEE and some SAT prep.
CatchupMath, from Hotmath, is an integrated online program with assessment for Algebra only. It has an extremely low cost. It could be considered an homework component for classes without mandatory homework.
Adaptive Math offers a strong, coherent online curriculum.
InternetMath offers an integrated instruction system for K-8 math with random numbers in problems.
DimensionM continues to advertise online math video games. These should be evaluated.
Buzzword created the most buzz at NCTM. It had a strong focus on Middle School math, and is highly compatible with how teachers and students work. It must be evaluated in 2010-2011. While not quite as good as ALEKS. It has more instructional support.
Tutor.com offers online, at home tutoring for students.
Autograph 3.3 graphing software is designed for education: animations can run in slow mode so that students can see change better.
AscendEDU offers online courses through Algebra 1 (116 lessons) that can work in a classroom.
ThinkWell offers Algebra through College Algebra courses.

Programming

Small Basic is a great starting point for 5th grade+.
Depending on the STEM robotics program chosen, variations of Basic and C are learned.
Python is the language of science that would enable students to work in laboratories.
Mathematica and Matlab focus easier on mathematics than Python and are reasonably priced.
Statistics doesn't have a standard. Free R isn't appropriate for high school, but low cost Minitab (Windows only) and JMP are and they can be transferred to college lab environments.
3DVinci offers 3D geometric shapes to enhance Google Sketchup for Math. The Pro version of Sketchup can be purchased at Ed sites for $50.

Book Review - Mathematicians by Mariana Cook

2010-05-23T16:45:00.000-07:00

Each mathematician, accomplished, perhaps famous, has a full page photograph and a facing page containing a brief autobiography or statement. It can be read in a few hours.

Brandon Fradd, a Princeton math major, thought a photo book of Mathematicians would be well-received after seeing Scientists by Mariana Cook. Good idea. Her photographs are striking in black and white. Most of the people were from Princeton (not a big surprise), but individuals from Oxford, Cambridge, Harvard, and a few New York and California schools also made the list - 92 professors in total.

Each reader/viewer will respond differently to the brief personal essays. Timothy Gowers (I have two of his works.) tries to relate his methods to research strategies, the practical rationality of his words shows a cool balance of thought, but Harold Kuhn's reference to all of his teachers by name and the sacrifices made by his parents and the role of chance in meeting people was too easy in which to relate. I cried while reading about him. Of course, Andrew Wiles was photographed. His humility, considering that he proved Fermat's Last Theorem - his childhood dream, was considerable. William Thurston's text may have been the most important. He stressed the pain of everyday public school instruction in math for himself, but he didn't allow it to kill his imagination. He related how internal vision and analysis worked together: paragraphs suggesting the joyful magic in doing mathematics.

And yes, the correlation between mathematicians and the love of music is highly positively correlated.

Two Year Algebra - Reboot

2010-05-13T22:24:00.000-07:00

Struggling students can succeed in Algebra and complete high school.

Approach

Organize a voluntary PLC of math teachers to pursue the pre-selected approach
Consider looping for ninth-tenth grade.
Use a reform math text - dramatically different from the district's standard text
Grade Summative Assessments on a curve of highest eighth = A, offset quartiles = B, C, D. If this is too drastic, then the PLC-advocated college grading scale of 75-100 is an A, 50-75 is a B, and 25-50 is a C may be appropriate.
Bottom eighth can earn a grade or pass by teachers's judgment or completion of alternative work such as ALEKS or StudyIsland or Algebra games like Dimension X/U or re-exam; even if semester has ended.
Bottom eighth cannot be determined until final for student motivation
Course starts with Assessment: Students scoring low that ALEKS Algebra Prep for Six Weeks
"Homework" completed in class as PRACTICE - careful attention paid to technique
Calculators used for most problems (some no calculator to mimic CST)
Supplements such as online formative assessment and/or Gizmos and/or Wolfram|Alpha or Akron.
Cultivate student growth mindset by using Brainology.
Experiment with DimensionU online math video game.

Possible Texts

Its About Time's Math Connections - not enough state standards may be an issue.
CPM - After 20 years, it now has state approval after changes - 1993 attack
Contract with Heymath! - other districts may have done this already.
Kinetic Books or NROC's new program, when available
Supplement current practice with a sequence of online manipulatives (eg Mathematica and Gizmos) coordinated with professional development and a PLC to determine sequence.

Suggested Calculators

Sharp WriteView
Casio Natural Display
TI/Casio Graphing Calculator, if text driven (Connections requires one)

Texts Review Status

More than one text can be selected depending on the number of teachers that volunteer and their interests.
CPM is used by 2-year Algebra programs where students alternate days of doing "homework" in class. CPM claims that no supplementary materials are needed. CPM, a non-profit, has an exceptionally low cost program:

August 2-6 - teacher training in Irvine at No Charge
Teacher text is $95 and each paperback, 3-hole punched, re-usable student text is $18
Classroom set of Algebra tiles is $97
2" loose-leaf binder for text and notes: $1 in volume

CPM has been used at Irvine's Northwood for six years. In one-year classes, CST proficiency has increased from 30% to 80%. In two-year classes, CST proficiency has increased from 6% to 24% and may be higher this year. The main reason Irvine adopted CPM was to give their students a different look at Algebra from the standard texts. CPM is also used by Northwood for Honors Geometry and Honors Algebra 2. I used CPM Geometry briefly at University High as a substitute. The question quality was quite high.
Heymath! has asked us to proceed. We would want to send them the Algebra AB pacing plan. The Massachusetts and Connecticut experiences show this can be fruitful.
For Kinetic Books: To track student progress through the Algebra text and do online homework, you will want copies for the individual students. This would be the Class Set License, which is $49.95 per student.
Putting a Computer Lab License on some of the computers at school would allow them to do online homework while at school, but you wouldn’t be able to track their progress through the book itself.
Online homework is $10.00 per student. Given your situation, I’m not sure you would be doing that on a regular basis.
Given the above you have a few choices:

If the Computer Lab License only, the students can use the text, but you don’t get any scoring information for them.
Use the Computer Lab License with online homework. With this you can track what the students do for homework that you assign.
Get Class Set Licenses for each of the students. This allows you to track their progress through the book and they can work at home.
The Class Set License plus online homework gives you the functionality tracking progress through the text as well as any homework you assign from the online homework system.

Why ALEKS Provides "the Best" Math Software

2010-05-07T20:23:00.000-07:00

Many different online programs for math instruction/assessment exist. ALEKS stands out. If teachers or administrators misunderstand its design, their choice of other programs will be arbitrary. They will be merely victims of marketing, not arbiters of what's best for student learning.

The internal research conducted by ALEKS on its software appears to be extensive. Every topic network is constantly and automatically checked. If less than 90% of students pass any topic, then the network to the question is re-verified. In other words, after a decade of iteration, the learning progression in ALEKS is second-to-none. However, to satisfy the various state standards, additional topics are introduced into standard curricula like Algebra 1 for coverage. These additional standards add redundancy to the network at a price of increased time (more topics) to master a course.

ALEKS uses time more efficiently than any other math program. This is easy to show. First, ALEKS uses constructed responses only, not multiple choice. Fewer correct answers are needed to show mastery; since multiple choice inherently requires more questions to cope with false positives due to random guessing. Second, the ALEKS web of topics and intentional time delay in verifying mastery drive efficiency. No topic is offered until the student has a 90% chance of "passing it" due to completing a network of prerequisites. Also, while usually only four correct answers are necessary to complete a topic, one more topic question is presented days or weeks later to verify mastery. A wrong answer brings the topic back. Third, its artificial intelligence engine further separates ALEKS from most other programs. It appears to use the time-to-answer a sequence of questions correctly to determine how many questions are needed. Sometimes a student only needs to answer two questions to complete a topic (Mastery verification is later.). In short, there is no faster method than ALEKS to develop procedural math mastery.

As part of its interface design, ALEKS doesn't display information that the student doesn't need. For example, neither the time on the question nor the menus of topics is displayed; although ALEKS does record time, when the student is working on a problem. ALEKS wants students focused on the question without distraction. There is research behind this decision. Additionally, ALEKS chose to use Java extensions to provide online protractors, rulers, etc to produce its online manipulatives. This standard software can either be automatically retrieved (www.aleks.com/plugin) or installed. Most other companies use Flash for interactions. These work well, but are losing their position of being an Internet standard. In addition, ALEKS uses natural display of answers and allows for variations in the answer of questions. These features relax students and minimize their frustration - not a small issue.

The last two paragraphs covered Assessment & Interface Design. of the six main aspects of online math software.

ALEKS receives the most criticism on its Instructional Design. In general, the criticisms are ill-considered. First, instruction is offered only when students request it. There are no hints, and students know that they will have to do more work, if they ask for instruction. This motivates students to try to solve problems first and, if unsuccessful, to pay close attention to solutions because they don't want to learn more than once. Second, the instruction is simply text with graphics, no videos. While unappealing initially, they fit how most students actually do math. For example, few students read math textbooks. They attempt problems, then look for examples on how to do them as quickly as possible. ALEKS's instructions quickly suffice. From another perspective, video with sound appears wonderful, but it can distract and requires computers with headphones. ALEKS works quickly and quietly even in dial-up environments. More importantly, videos frequently waste time. Students just look at them in a daze. The low density of information in a video is rarely worth the time to most students. One exception exists. Buzzmath has annotated videos, which allows students to skip sections they don't want to see so that they can go to what they want quickly. ALEKS could offer such a service as an upgrade.

Intermixed with Assessment Design is Database Design. ALEKS satisfies the main math problem criterion: whether through randomization or question quantity, the number of questions per topic is far more than what can be shared between students. In short, cheating by having shared question/answer lists is squelched by ALEKS and several other programs. Another subtle feature is the speed of the database when reports are being generated. ALEKS is so fast, that the browser refresh rate appears slower. Other programs, such as APEX, have slow to generate reports. From a teacher usage perspective, fast reports are critical.

The bars and circle charts in ALEKS's reports are easy to understand. Many have hyperlinks to other reports which greatly saves time. The only program with better reports may be Daskala, which is limited to simple sequences of multiple choice questions. ALEKS reporting could be improved by an all student-class report. This is a small issue, but teachers who have students spread between many classes, have to remember what class a student is in to find the student's status. It would be valuable to have a list report of students and their classes with hyperlinks to the student's report.

The one area in which ALEKS can improve, or at least freshen, is account management. ALEKS works with active licenses, which is the best method, but ALEKS lacks ease in both enrolling students and also in identifying unenrolled users. The information is there, but it is tedious to use. On the other hand, unlike many other active license software vendors, it doesn't lose data on previous students. A simple list with fields would resolve the enrollment issue.

The great issue with ALEKS is that it intentionally rejects rich problems - problems that require strong student insight and drawing from multiple sources to find solutions. This is contentious. Research by ALEKS probably shows what I see in the classroom: many, perhaps the majority, of independent students simply stall out when confronted with problems that stretch them too much. This is sad, but it may just indicate that the desire for math software to do everything - no classroom needed - is a false dream, not research-based. The 90% rule really means a great deal to ALEKS's programmers. Mastery of procedural skills is the goal. The subtleties of applications are left to classroom instruction.

A superb product with richer problems is Carnegie Tutor, CT. Since questions are rich, each question has many objectives built into it. When student cannot solve a problem, the instructional help to get through it; including the teacher, requires considerable time, and is inherently different for each student! CT does have underlying artificial intelligence, but it is results are still linear. If a student is stuck, they must stop. This is a prescription for failure in many computer environments, but CT offers appealing instruction. Another program with rich questions is StudyIsland. Good students are attracted to it. If a student struggles, StudyIsland, like ALEKS, allows students to work on other topics. In short, students stay working - the great benefit of student choice. StudyIsland even incorporates some simple AI to give students easier questions in a topic, if the grade level questions are causing failure. This appears wise, but the ALEKS approach of moving the student through a network of topics, not a flow of topics within the same top-level topic shows far more sophistication in improving the transferable skills of each student.

The more problems that students complete as practice, not experience, each hour, the better! In my observations, only SmartMath and IXL, have higher problem completion rates, with SmartMath having more concentrated practice, but these are K-6 programs! Student choice - for whatever reason, like fatigue or boredom - should be allowed. It keeps students working. Also, in years of ALEKS and SmartMath usage, not one question mistake has been found by me. APEX is riddled with errors, iPass has problems, and StudyIsland has a software link to report mistakes, to which StudyIsland responds promptly. IXL only has a few errors. This issue is missed in software evaluations. Maintaining confidence in the software is an important issue in the value of the software.

In summary, ALEKS does its jobs exceptionally well on three of six categories: Assessment, Interface, and Database. On the two categories Account Management and Reports, ALEKS is very good. Yet, strangely, in Instructional Design, ALEKS is either the best or inadequate, depending on a reviewer's knowledge and/or desires. ALEKS Corporation has decided to focus its software on what they believe works best in software, from a research basis. Others want a full, rich instructional system which is a desirable goal. This may be an example of the best being the enemy of the better. More may be desired in instructional capabilities and in rich problems, but it is not clear whether or not this is valid with more than a few students. ALEKS thinks not; and ALEKS could easily deliver additional features. In the years I've used ALEKS, the company has grown from 20 to 120 employees. More importantly, ALEKS retains its earnings and pours it into development. It is not a cash cow. ALEKS provides the fastest pathway to procedural fluency. Asking software to do more may be unwise or self-delusional.

Lastly, pricing matters. It's easy to forget that software providers are businesses that pay not only for programmers, but also for salespeople, customer service representatives, clerks, brochures, trade shows, etc. Years ago, in a private conversation with an ALEKS executive, I was told that to go below $42 average per user would kill R&D over time. Obviously, large school districts could bargain for a better price and home users, with their many customer service interactions, would have to pay more, but to maintain the average was vital. I never forget this when purchasing other software at 5 -10$ per user, which I frequently do. These programs may not be able to keep improving without venture investments, and programs that cost over $100 per year - many do - may not maintain steady users. ALEKS's pricing allows sustainability and improvement year after year.

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Dennis Ashendorf has extensively used the following:

ALEKS
APEX
iPass
IXL
RevolutionPrep
SmartMath
XLPrep

Dennis Ashendorf has lightly used

Carnegie Tutor
STMath

Threats to Public Education

2010-05-02T20:01:00.000-07:00

The attached chart serves as a starting point for discussing the locus of school criticisms. While not exhaustive; it nonetheless covers the motivations and subsequent grounds for attacks.

APEX Learning Workshop Report - Pomona - 28 April 2010

2010-05-02T15:24:00.000-07:00

From other users:

Add senior summer school with real summer grad ceremony (major life event)
Two week CAHSEE prep @ 2 hours per day yields great improvement in test skills
Develop student flow chart to keep students on track
Due dates must be added for email coach reports
APEX must allow different color code triggers (future component)
Individual school sites and teachers must be allowed to modify rules
Print out math appendix for student use
Use gaggle.net for student email
Alt Ed students don't progress unless pushed continuously
Apex can be used within a Blackboard environment for essays
Locke (a Green Dot school) uses APEX 8-12 & 1-5 daily
Since APEX courses are grade level, one school uses NWEA 8th grade to qualify English
One school moved all study sheets onto online question progra.
APEX changed software for one school so that all inactive licenses after 30 days were archived
Study is available during Quizzes
Use Student Session report

July 1st is the new release date - what's included has not been released to Sales
CAHSEE diagnostic allegedly works well.
APEX suggests "Literacy Advantage" for EL's
AP courses can be offered to small classes using online AP APEX instructors

Calculators @ NCTM

2010-04-29T16:39:00.000-07:00

Graphing Calculators

TI MathForward is a solid way to use graphing calculators in block schedules. Also, the latest revision to TI-84 software allows pretty print display. All TI-84's should be upgraded.

The TI NSpire has been upgraded. Each teacher can send only one to TI to be swapped with a new one by Dec 31, 2010. IMHO, the nine (ten) or more NSpires at Estancia should be sent to TI, one at a time, with a different teachers name; so that the whole small set can be upgraded. Other schools should act similarly.

HP doesn't make new calculators anymore. The division was sold off to a reseller.

Low Cost Classroom Sets

The Sharp EL-W535 ($10) and EL-W516 ($13) deliver the natural display features of the Casio fx-300ES (HP 300s) and Casio fx-115ES, respectively at lower prices with, most importantly, faster input/output of fractions. However, initially the Casio is chosen by students because it's display is the most natural. After showing the faster Sharp output, they switch. The Casio fx-300ES does have a list feature, that the EL-535 doesn't and it's battery may last longer because of a solar panel for power. With the list feature, the W516 can serve a student from Middle School through Statistics. TI's two line calculators aren't as fast or useful sadly.

Only AP Calc and AP Stats require facility with a graphing calculator.

In short, the Sharp W535 would serve well for class sets in middle school. In high school, the 516 would work. These calculators can be used in a variety of STEM classes, where students would/could understand how to use them. Letting everyone use different calculators is similar, but not as big a problem, as letting everyone use a different text. The current standard practice of anything goes with calculators is and has been incorrect.

Primary Curriculum Advances @ NCTM

2010-04-27T23:38:00.000-07:00

The three major vendors and the many NSF spinoffs displayed their wares. For example, the ThinkMath! program seemed relatively balanced between reform and traditional approaches. Also, it uses the number line as its unifying theme - just as the Mind Research Institute does with its Algebra Readiness. It should be noted that several vendors stated 'the math wars were over long ago; except in California. Remember, Everyday Math is the largest selling curriculum in the county.'

A full, rich curriculum from Korea has personalization for problem sets/homework. After a teacher enters formative assessment data into the software, a customized worksheet is printed for each student. Students can progress at their own speed. Numino is an elaborate curriculum in English that should be examined; although the website is 99% in Korean.

However, Singapore Math had the strongest attendance both at its booth and presentations. Furthermore, other Asian countries, particularly South Korea, displayed approaches that varied with conventional (Reform or Traditional) US approaches. Certainly, the emphasis on mental math (common in Europe also) versus the algorithmic approach of US instruction is the most important difference between the cultures.

In brief, Singapore Math blends Number Sense, Word Problem Models, and Mental Math. These areas may be separated to form either an extensive intervention or an American spin. For example, Math With Meaning offers small Word Model texts that can be used for daily instruction for each grade level 1-6. Also, Jongsoo Bae has developed a very rigorous yearly program for mental math. Interestingly, Jongsoo Bae has also developed an exceptional program for home workbooks which trigger video instructions with the voice pen. Combining the products of both vendors with the current prevalence of manipulatives and math software would generate a strong curriculum that would rival Singapore Math and be more accessible to parents.

While the 1995 curriculum has been approved for California, the 2002 revised curriculum has not. While some claim that the newer curriculum hasn't shown success in TIMSS; it is now available from a major US publisher (Harcourt's Great Source imprint): Math in Focus. It now includes "non-Singapore" aspects; such as reteaching.

For more info on Singapore Math: www.singaporemath.com, www.marshallcavendishonline.com, www.singaporemathtraining.com, and www.the-pi-project.com. Professor Ban-Har Yeap, a Singapore leader, spoke three times at NCTM.

Singapore Math people often make fun of elaborate US manipulatives. For example, the beautiful Digi-blocks system is compared with beans glued to popsicle sticks poorly. IMHO Digi-blocks are beautiful things. They cover 0.01 through 1000 and truly do make magnitudes interesting also.

Game vendors were present. Arithmo provided newsprint puzzles that reinforce operational and number sense skills and FoxMind's sequence of 3D games stood out.

Secondary Curriculum Advances @ NCTM

2010-04-27T14:50:00.000-07:00

While elementary school math remains in a quiet turmoil; approaches to high school curriculum are fairly stable.

"Research-based" Curriculum

The Collegeboard has fully released it's pre-AP English/Math curriculum named Springboard. This is researched-based in a different way. It tries to embed not just the math knowledge, but also the communication knowledge that colleges expect students to have. By the time a student starts AP, he or she may not have enough time to develop appropriate academic skills for college. Springboard appears to be considered a hard curriculum that allows a greater chance of college success. It starts in sixth grade and offers either Algebra 1 or "Middle School 3" in eighth grade.

IMHO, Springboard should be carefully examined. Even if there would remain the need to continue using the current texts for students who cannot keep up even with interventions. The effort to use just one text for math courses, while making "Williams" easier, is misguided from an instructional perspective. One size does not fit all. ACT provides a test-based approach to rigorous content called QualityCore that covers more areas and works with current texts.

Furthermore, the Kucera Sequence for eighth graders passing Geometry should be strongly considered:

Accelerated Algebra 2 + Trig in ninth grade
AP Stats in tenth
Accelerated Pre-Calc, followed by Calculus A in eleventh
Calculus BC in twelfth.

Algebra Readiness

UCLA has split its coherent Introduction to Algebra program into packets called Math Links. This helps schools, who don't teach the course for the full year, focus on specific needs in short times.

Its-About-Time offers Aim for Algebra which competes with the coherent Introduction to Algebra. I thought it was better, but the teacher delivery quality to students matters far more.

The Mind Research Institute now offers the software for its Blueprint for Algebra separately. The complete Blueprint program takes about 1 1/2 years to complete - not good. It's possible that the software alone may help enough as a supplement to an eighth grade math course.

High School Preparation for Algebra 1 is a unique ALEKS program. ALEKS suggests that after an assessment at the start of Algebra 1, students who score of 7% or less should be pulled into this program for 6 weeks approximately, 1 hour per day to catch up. This is very rapid.

10th Grade CAHSEE Prep Approaches

Since CAHSEE results strongly affect 10th grade API, it would be wise to offer a deliberate, year-long, not short term preparation approach. Revolution Prep offers a solution online for Math and English; in addition to its Algebra Readiness software. This software could be combined with a tenth grade Business Math course.

Statistics

Texas A&M has an online Statistics program for Teachers to prepare them for AP. Best if visiting A&M.

The second edition of Statistics through Applications is now available.

Four Year Math + Financial Algebra @ NCTM

2010-04-26T16:35:00.000-07:00

Several states have four year math requirements. While California only requires two, the first three years of math applies to the API and the fourth year is needed for smooth transfer to college. In short, four years of math are needed by students from a school viewpoint.

In four-year states, a subtle issue is whether or not passing is required in the fourth year! Also, standards-based math courses are expected. Jokes about arithmetic/formula-based Business Math for students having completed Geometry/Algebra 2 are frequently made. As an alternative, a soon-to-be a-g approved Financial Algebra course (Textbook is available for review) has Algebra 1, Geometry, and Algebra 2 problems. It would work well as a junior course in support of Summative Math.

While many pathways exist, sensible high school pathways would breakdown into the following (yes, my understanding of Business Math is appropriately different than Harbor/Mesa):

Algebra ABCD - Done or advise student to take Geometry, then Algebra
Algebra CD or Algebra 1/Business Math - Done
Algebra CD or Algebra 1/Geometry => Algebra 2, then PreCalc/Stats(AP)/Financial Algebra
Geometry/Algebra 2 => PreCalc/AP Calc or Financial Algebra/Statistics(AP)

Statistics @ NCTM

2010-04-25T22:05:00.000-07:00

AP Statistics 2009 results and rubrics were reviewed and the new lead reader introduced.

AP Stats is now the 8th most popular AP test with an 8% increase after three years of double digit growth.

The main concern in grading to students is that they must be very "communicative" in their answers. For example: if a question says that the "the following values are drawn from a normal distribution," then answers to the question must state that the probability calculated was based on a normal distribution, not just the numeric answer. Otherwise, zip.

Lee Kucera of Capo High mentioned that her school has four sections of AP Stats for tenth graders! 120 students that complete Algebra 1 in 7th grade, Geometry in 8th grade, Accelerated Algebra 2 + Trig in 9th grade, AP Stats in tenth, Accelerated Pre-Calc, followed by Calculus A in eleventh, and Calculus BC in twelfth.

Interpret Capo's approach. Stats is needed more than Calc, but "we" expect top students to take Calc; therefore Capo does both!

TEDxNYED - Dan Meyer - 03/06/10

2010-04-19T20:56:00.000-07:00

Starts out conventionally, but when he gives a real problem, the strength of his approach (Reform Math!) lays the groundwork for people to learn Traditional Math.

The Road to Success

2010-03-13T09:48:00.000-08:00

The TED video of the Director of Disney's Imagineering indirectly relates to Education. It takes off after the "Candle Problem" is played out. This is a must see video that WILL CHANGE YOUR LIFE.

IMHO the dumbing down of education is actually the realignment of topics for simple grading systems. It may be that the increased use of multiple-choice tests drives away the type of problems that really matter. Furthermore, the debates about group work and, perhaps, the Math Wars, were and are distorted by inappropriate, simply false, evaluation methods.

EL's Must Pass Math

2010-03-10T19:51:00.000-08:00

Slide show runs at seven seconds per slide

Comments on Slides

2. Arne Duncan has repeatedly stated that the achievement gap and access are civil rights issues. This will open up school districts to civil rights suits, which will hurt and cost. Yes, it will happen, and there will be a lot less money for teaching.

3. Professor Dweck of Stanford stresses that people who think "Smartness" is just genetic, don't work hard for several simple reasons. She stresses that intelligence is developed and that "learn, learn, learn" can be a normal way for students to think also. This effort to defeat the "internal" squelcher, may also help defeat the "external" squelcher of peer pressure. IMHO this is far more important to get students to understand than ALL other activities. The professor's research is exceptionally strong.

4. Really knowing the vocabulary to pass math tests (not just math vocabulary) must be explicitly taught in context. This is not about posters. This is about seeking "multiplication tables" level of knowledge. Pressing forward with SDAIE strategies in math must be reinforced.

5. The reasonable goal of 9th grade Algebra doesn't make it mandatory for ill-prepared students. Delaying Algebra with different elective math courses until they are ready is wise and doesn't punish them with F's (zero credits) or pointless D's. Naming the courses Math Topics or Algebra Support or General Math helps. The course codes are already present. These courses are really all the same: support Algebra Readiness.

A district could use "grant" money to support special groups, outside or inside of RandR, to entice teachers in this area to use alternative methods and to press for results. This would serve as a model PLC for both school and district and justifies the use of "special" money.

Of course, the state direction must be satisfied with all deliberate effort. There is no reason that bonuses to 7th/8th grade math teachers couldn't be offered for making students Algebra Ready or Algebra Readiness Ready. Teachers could bid for these positions; which would give Management some flexibility. A 9th grade bonus for Algebra Ready for 10th grade may also be wise.

6. Adjusting courses and course titles so that students always earn credit in math would be wise. Failing Algebra 1A may allow Algebra A credit or Algebra Support Credit or General Math. If each math area had one shared computer, for online math; then this adjustment could be handled with minimal scheduling support.

Grading can be done as completion of work and quizzes or Final Test. It may be best to offer Incompletes; instead of F's. Students can use Credit Recovery to earn a grade. Failure is not an option.

7. There are many aspects to motivating students. First, tell them that they can be done with math in 10th grade. It's OK. If they are succeeding, they will stay, and getting them to care about finishing Algebra in 9th or 10th is a big deal. It may motivate them to master Algebra Readiness. Second, tell them that they can "graduate" after 10th grade if they pass the CHSPE which requires Algebra. It's OK. Very, very few will leave school, if they are succeeding.

A Very Short Introduction to Math (Review)

2010-03-01T23:00:00.001-08:00

Professor Timothy Gowers starts with the need for models and ends with the usefulness and necessity of estimation. The body of the book gives the flavor, the value and the connectedness of Proofs, the calm resolutions of infinity and the impact of changes in dimension and Geometry.

No. Not a problem-based course. Not a history lesson. No sexy examples. Little mention of the titans. Yet the point of doing math, its constraints and pathways, would strike anyone who reads the book. Whether high school students would get it. I'm not sure. The maturity in the words and the totality of the immersion within its few pages is sublime. In knowing that exact answers are rarely found, but knowing the boundaries of the answers and their closeness to actual mimics our own lives.

This would be a must read in a non-ADHD world.

Gowers also wrote the Princeton book on Math. The professor is a Fields medal winner.

The Black Hole War

2010-02-22T22:38:00.001-08:00

Leonard Susskind's book is not just a popularization: it's a chronicle of discovery and of the people involved. It echos Watson's Double Helix with Hawking playing the role of Pauling, but it's far more fair, yet unsettling. Scientists stand on the shoulders of previous great scientists, and it's clear that Susskind and the many other scientists he describes stand on the shoulders of Hawking, but also they have surpassed him, and they know it. At times, it is like reading words of physicists who arrived after Einstein like Heisenberg, Dirac, ..., in real time. These are greats who in many ways moved passed Einstein. Susskind and friends are the greats who have moved passed Hawking. If only for this reason, this book allows the reader to be a fly on the wall of science history, and it's fun the read.

But it is much more.

My knowledge of nuclear physics, while not deep, is not trivial. In the 1970's I worked in the Stanford Physics department and was well aware of the whys and hows of the linear accelerator and PEP. Now, I might as well be a worthless witch doctor at Johns Hopkins.

Be ready to be dazzled. Alice in Wonderland doesn't come close to the reality of the Holographic Principle - yes, Virginia, you're a hologram. The wild woollies of string theory or the math of strings (spinning elementary particles) amazes and Susskind makes it fairly clear without any equations. Smart guy holding the endowed Felix Block chair of Physics at Stanford. He is no lightweight. He does briefly state one or two objections to this "Plank Area" world. Basically, string theory has not been proven - it simply works better than anything else. More subtly, it hasn't been shown to be unique. Another mathematical approach may be more "true." Even more importantly, the emphasis on dualism between elementary particles and protons/neutrons etc is questionable. Physicists believe in dualism; perhaps too much.

Consider that recently the Poincare Conjecture was proven - so 19th century! The proof required dealing with scale, getting close to a surface requires different math than being far away. Physicists don't seem to know this issue may actually apply to them in subtle ways that their hubris may preclude. And that's the rub. All talk, no experiments, but for good reason: to test out their theories would a take a linear accelerator the size of the milky way. Oh yeah, one of the ideas of really modern physics is that small things are heavier than big things. When this starts making sense, you become self-aware of your sanity: alt world is the world.

In short, Susskind delivers an accessible tour de force of science today from the view of giants. If you're serious about knowing how the world really works, not in the simple political sense, read this.

Defense of Newsweek's Challenge Index

2010-02-01T16:39:00.000-08:00

Criticism of Newsweek's Challenge Index is misplaced and misdirected. This is due to the limited background of critics who show no knowledge of a valuable analog: evolutionary theory. Consider two of stronger critics of Jay Mathew's work: Sara Mead and Andrew Rotherham. They succinctly write:

"A successful high school should show high levels of student achievement, graduate almost all of its students and not let any demographic subgroup suffer at the expense of others. Most national and local experts and policymakers share these values. To be sure, graduation rates and student achievement are hardly the only indicators of a school's quality. At a minimum, however, America's best high schools should be expected to meet these basic criteria.

"Yet our analysis shows that many schools on Newsweek's list do not meet these minimum standards."

Mead's and Rotherham's words appear well-chosen and difficult with which to disagree, but they are actually irrelevant and misleading for the simple reason that education is an individual achievement. Bureaucratic measures are not only meaningless, but often distorting to individual students. The efforts in education are simply those of multiple single individuals seeking the necessary trade-offs and efficiencies in teaching the many; and there are many types of many. Education is hard, but education is not policy. Forcing education to fit policy is a fool's game. There are many fools.

In 1966, simple Darwinism, which holds that evolution functions primarily at the level of the individual organism, was threatened by opposing concepts such as group selection, a popular idea stating that evolution acts to select entire species rather than individuals. George Williams's famous argument in favor of the Darwinists delivered the decisive response to those in opposing camps. His Adaptation and Natural Selection, now a classic of science literature, is a thorough and convincing essay in defense of Darwinism; its suggestions for developing effective principles for dealing with the evolution debate and its relevance to many fields outside biology ensure the timelessness of this critical work. Almost all Ed wonks ignore this. For example, they think that subgroup success and small "achievement gaps" on tests matter. Well it does for them and it sounds compassionate, but what does it matter to an individual student? Is it realistic to think that someone picks the a school because it has a small achievement gap, without asking "how much achievement or why does that matter to me?" Do Hispanic parents chose a school for their children because the Native-American subgroup did OK, without asking "what's OK or what does that matter to me?" Saying "meeting proficiency in state standards" truly begs many questions. People want a safe school with solid academics to maximize the chances of their children becoming successful. Everything else, outside of athletic considerations, is silly fluff for irrelevant-to-learning, but not to concerned bureaucrats in the education business. This can be nasty sounding. For example, a school with a high dropout rate isn't really an issue to successful students. It may actually be a plus: get rid of low-performing riffraff. This is what sport teams on campuses know also.

The Challenge Index simply and effectively helps parents and students pick schools from their perspective! Other measures may have some utility for education bureaucrats, but not for families. Bureaucratic measures shouldn't be mentioned in public because they lead to confusion like those from advocates of social group selection in the early 1960's.

Learning Singapore Math Through Great Teachers

2010-01-16T22:53:00.000-08:00

Games Played by Len Fisher

2010-01-01T13:22:00.000-08:00

The subtitle of the book is a variation on its "real" title: Game Theory in the Everyday Life of Len Fisher. While pleasant, and somewhat helpful as an introduction, a better book is struggling to get out.

Rock, Paper, Scissors is best read by reading the chapters in reverse order. Fisher really wants to write about trust and how to gain it, by realizing that game theory not only describes situations (the seven dilemmas identified by Nash equilibriums), but also identifies methods for breakthroughs. Various problems in everyday life (mainly Fisher's!) and some business/political ones can be identified, then addressed. This is good stuff. Knowing the Ultimatum and Centipede games provide value.

A reader upon completion will most likely believe that while the book was worth the time and effort, a better book should be available with more interesting examples, that would have been MORE worth the time and effort. It's as if Fisher "mailed" it in. He couldn't have spent more than a few weeks (if that long) writing it. It's merely a money-maker that doesn't show great depth of knowledge or effort by the writer, but it is understandable.

Book Review - A Certain Ambiguity

2009-12-22T12:38:00.000-08:00

A Certain Ambiguity was disappointing and bordering on the trivial, sadly. In 1919, a fictional, yet exceptional Indian mathematician, worthy of being invited to a US university after living in Great Britain, believes like a child, that Euclid wrote about truth, and of course, rigid Christians jailed him. The only thing missing from the test is an angry mob at night with pitchforks ready for a lynching. However, good leadership by the New Jersey governor saved the day. Thank God for educated elites!

In 1919, Riemann, Poincare, were evidently not known to all expert mathematicians as the conceit of this book. OK. A few physicists still believed in the ether also. To be fair, Riemann's 1854 lecture may not have been well known, but Poincare was pretty famous at the turn of the century. By the time of the setting of this story, topology, not geometry, was the focus of study, because formalism was well understood as the refuge for mathematics. See the fifth paragraph below.

Still, the first person narration by an intelligent Stanford grad student, who evidently didn't know anything about series from high school math, but is worthy of a full scholarship to graduate school in mathematics, was far more improbable. Maybe he took Calculus in summer school after being accepted.

The conclusion that happiness and contentment are found by knowing that absolute certainty cannot be proven may be a mantra for some, maybe a majority, of intelligent people, but patting oneself on the back, which seems to be the point of the book, is fairly self-serving at the very least. Cool people don't believe in truth, just games, evidently.

A more honest and useful book would have stressed that before Riemann, Western thought, buttressed by Kant, believed that "a priori synthetic" systems existed: that our mind by itself (a priori) could obtain real knowledge (synthetic) of the world. Euclidean geometry was the prime example of this. As a result, a proof of God, while not rigorously found, could reasonably exist. The main counter to this belief was found in "personal idealism," which Bishop Berkeley, along with many, many others lectured. At it's extreme, everything is in one's mind and it is difficult, if not impossible to truly know anything about the real world (if it even exists!). This is very unsatisfying. "A priori synthetic" was important psychologically to many people. Other philosophies, such as positivism in 1919 in Great Britain, arose to try to bridge the gap with dubious success.

However, the authors, Suri and Bal, could have taken another, less well known, but perhaps, more valuable interpretation of Godel's work and resolved the issue better; although not as correct politically. Godel proved that every logical system would have at least one truthful statement that could not be proved by the axioms of the system. In short, any system is not complete by axioms alone. This is supposed to destroy full certainty of knowledge. Maybe, but it provides one GREAT and AWESOME question: from where do the unprovable truthful statements arise? They have to come from something outside of the system! In other words, the real world isn't found in "a priori synthetic," but in "synthetic a priori!" There is something out there so to speak. What it is - is the unanswerable question! God may exist, or at least a reality, for that is now certain!

The greatest problems with the book are the two horrible math errors made by the authors that invalidate so much of what they wrote. Most critically, curved space doesn’t invalidate Euclid at all. Maybe Gauss initially thought so; but Riemann in 1854 showed that planar geometry was merely a special case of when a triangle had 180 degrees in space. Other spaces had either less or more than 180 degree triangles (like those on a sphere). There is NO CONTRADICTION of Geometry by validating Einstein, if anything, it increases Geometry’s validity. Duh! Second, and not critically, the fifth postulate is not evidence of a statement that’s true but unprovable after Godel as the authors claim. This is obvious since more than one fifth postulate is possible, not just one. Duh!

A Certain Ambiguity is novel on math written by poseurs without ambiguity - an embarrassment on many levels.

The Outliers - William Gladwell - Review

2009-08-04T22:14:00.000-07:00

The Outliers was presented to teachers at Estancia High School. It has lessons that apply to education from both student success and organizational perspectives. While motivational and entertaining, it's problems are many. It's reviews are spotty. The New Republic spent several pages on it.

_____________________

The Outliers delivers one incredibly strong lesson in its first chapter: beware of the effect of arbitrary decisions on people's lives. Beware cut-off dates on ages for example. This is admirably shown in William Gladwell's first chapter. Hockey players in Canada are chosen on teams based on their talent, but also based on their age on January first. Those born on December 31 are effectively one year younger than those born on January second. Obviously many younger players won't be as adept as older ones, but so it goes. This means it may be advantageous to have two start dates for Kindergarten in schools.

A second strong lesson of the book is that timing, out of one's control, matters. People born in the middle 1830's in history were the most successful people in history. Cute stuff, but not too usable.

The third lesson is somewhat unremarkable; although vital: social background and elite status matter in success. Children of dedicated, usually wealthy, parents who are flexible in their own accomplishments do better than those from rigid, poor families. Duh.

The point of the three lessons is that people don't succeed by themselves, but their location in time and place determines the limits on their success. This point is told in very engaging ways by Gladwell. It is worth the time to read his text, but there are some caveats.
____________________

Isaac Chotiner's valid question (The New Republic, February 04, 2009) on why the chapter on airlines and culture was included in The Outliers can be answered with these three related points.

First, Mr. Gladwell did not want his book to justify racism. If wonderful family and social support is necessary for success, then a variation of William Shockley's argument that affirmative action is of no practical value to people doomed to failure would be true: why help a poor black student with a single parent, when he or she could never be a great success like Bill Gates or Bill Joy.

Second, the Korean chapter suggests that a few tweaks to culture can fix a problem and allow reasonable success. Similarly, affirmative action for law students seems to work out OK, as long as IQ is above 120. Please note that this is questionable research.

Third, Gladwell above can be seen as differentiating great success, ability combined with wonderful circumstances and timing, from "good enough" success, which society can support at certain intervals such as during schooling.

Unfortunately, Gladwell made three choices that undermine his likability and discernment. He's simply not self-reflective in his editing. Gladwell seems so full of himself and has simple politics.

First, his excessive demeaning of Langan was coarse, bordering on mean. Langan is such a buffoon that he doesn't know there is no "thumb right on you (p. 96)" at Harvard. However, readers of TNR's article on Zeke, Rahm's brother, may have noticed his words "But it was Harvard that was most oppressive (The New Republic, July 1, 2009, p. 27)." Maybe Langan, wasn't all that wrong. Furthermore, Reed College and Montana State should have been slapped by Gladwell. They failed disgustingly; almost inexcusably. Instead, Gladwell blesses their bureaucratic ineptness and laziness in dealing with Langan, because liberal Reed doesn't have a rigid (i.e. bad) bureaucracy. Reed, a small liberal college, simply let go one of its most promising students. As a student at Stanford, with parents having limitations, at the same time as Langan, I struggled to get my financial paperwork delivered months after it was due each year. I was never shown the exit - I was given emergency loans to pull me through. One of the 'red state' arguments against affirmative action is that it's affirmative only for preferred (i.e. liberal) people. Langan's situation makes ones wonder: is social support reliable as policy to help all people succeed?

Second, the most beautiful chapter in the book concerned how Gladwell's mother didn't claim racist discrimination in England after realizing that she and her ancestors had enjoyed generations of success because of the light tone of their skin. Sweet. Her blessed son disparages an abused man Langan (who has overcome a great deal) in print and left a pointless sentence in his book "Kiddo, when you leave New York, every place is Bridgeport. (p. 138)" Yes, Mr. Gladwell may be on the A-list of the chattering class and power clique at Harvard, but his framework is immature.

Third, Gladwell acts like a 'fellow traveller.' The chapter on KIPP read like a propaganda piece by Shaw when visiting Stalin in the 1930's, where his railroad car attendants had read his work! Yeah, sure. My high school junior read the chapter and asked "Is KIPP for stupid people? They work so hard, but only 83% are proficient." Gladwell may be smart, but you could sell him some swampland near Forrest Gump.

Ten Commandments for Teachers - George Polya

2009-08-04T08:24:00.000-07:00

I.    Be interested in your subject.

II.   Know your subject.

III.  Know about the ways of learning: 
      the best way to learn anything is to discover it by yourself.

IV.   Try to read the faces of your students, 
      try to see their expectations and difficulties, 
      put yourself in their place.

V.    Give them not only information, but "know-how," attitudes of mind, 
      the habit of methodical work.

VI.   Let them learn guessing.

VII.  Let them learn proving.

VIII. Look out for such features of the problem at hand as may be useful
      in solving the problems to come -- try to disclose the general 
      pattern that lies behind the present concrete situation.

IX.   Do not give away your whole secret at once -- 
      let the students guess before you tell it --
      let them find out for themselves as much as feasible.

X.    Suggest it; do not force it down their throats.

PLC - Extensions to Education Central Office - Comparison to JiT Quality Circles

2009-04-27T21:11:00.000-07:00

Prior Background

Starting in the early 1980's, US manufacturers implemented Just-in-Time (JiT) and Six Sigma data-driven strategies. One of methods employed was named Quality Circles. Professional Learning Communities, PLC's, can be considered variations of Quality Circles. Analogously to a Quality Circle, a PLC focuses a school on identifying problems and responding to (student) needs quickly by using data and teams. Furthermore, the twin overarching goals of JiT are reducing cost and increasing responsiveness by eliminating waste - waste of time, waste of effort, and the waste of resources and materials. In short, distractions and disruptions kill profit and responsiveness. The overarching goal for schools is student learning. All activities that detract from this goal are waste.

It should be realized that Quality Circles have a exceptionally high failure rate in business. They need a sustained level of support and guidance. PLC's are no different.

Lack of Real Support is a Reason for Failure

While most Quality Circles fail because the teams don't function well; others fail because they need real support, in the change of administrative functions, from superiors. Real Support can be unpleasant. Consider a manager getting a request from a Quality Circle: "Your policy is stupid... Do it this way... Now!" Consider pilots, graduates of military academies, listening to poorly educated soldiers: "you missed again" or "you just targeted us, you @#$@##@$@." Support means many things, including a change in methods by the boss. Letting Quality Circles die can be pleasant!

As long as PLC's don't ask the central or district office for bureaucratic change, PLC's can be very popular with central offices. This can be seen by the paucity of research and boilerplate statements on what district offices do in increasing student learning. District offices can easily forget that their role in increasing student learning must include eliminating their waste: waste of time, waste of money, and waste of focus on bureaucratic impulses.

Typical PLC-Generated Concerns for a District Office

Instead of tracking cuts in attendance; track and act on absences; since an absence is an absence (lost time) to student learning.
The same course number used for two different classes violates the most basic data organization rules. A year long class with the same course number where each semsester is graded independently confuses everyone in remedial course assignments, credit issuance, and transcript analysis.
Combining district data-analysis software with mandatory test-design software may actually inhibit collecting local data. Integrated databases are a priority, but its the responses to the questions, that require analysis and tight integration. Flexibility in question design (not just multiple-choice) and the student front-end are separate concerns that are about ease-of-use. Neglecting these limits data collection.
Separating a district SIS from an external grade book, when both are frequently integrated, is the denial of necessary database integration. The structure of PLC's and the routines of RTI coexist poorly with a whimsical district-centered approach to student data.
Keeping outdated student software, such as six-year-old web browsers, as standard inhibits technology implementations. Stating that this is for security, when the district office uses newer software, creates distrust and signifies that PLC is merely a sideshow at the district level.
Standardizing textbooks across the district for all skill levels and expecting differentiated instruction to compensate is actually a non-PLC focus. Standardization within a school or school zone takes priority. District driven standardization is a distraction from the main goal of student learning. Student learning for all does not mean the same modified teaching for all. The stereotypical assembly line became obsolete 50 years ago. It serves poorly as a metaphor for education today. Claiming that a court settlement forces this is not true and lessons respect for the district.

Literature

2008's Revisiting Professional Learning Communities at Work dedicates 40 of its 519 pages to the role of a district. Key points include:

Remove competing programs and requirements.
Do not leave school improvement to the schools alone.
Install systems to ensure priorities are addressed in schools.
Focus on improvement, not on rankings.

However, there is no mention of how the district should be manage itself. This lack of requiring self-reflection in organizations contradicts the need for continuous self-reflection in the schools and the teaching staff.

Conclusions

It's important for district personnel to be seen as working intelligently toward the goal of student learning, not going through bureaucratic motions. This isn't just for PLC morale, but for enhanced student learning.
From a PLC perspective, the units of interest are the individual child, the school, and for vertical articulation, the school zone. Surprisingly, other school zones in a district really are no different than school zones in other districts. Districts are legacy agencies, LEA's-only, in a world of state standards and state money.
Districts need to be lean and mean. Delays in providing services, due to only internal district issues, are truly unacceptable. Any district usage of funds denies funds needed for student learning; unless spent carefully. Expending money on schools is the default.

Living By Chemistry - Key Curriculum Press - Ninth or Tenth Grade Chemistry for Everyone

2009-04-20T17:29:00.000-07:00

Background

The University of California/Lawrence Hall of Science/NSF ESI-9730634 generated curriculum Living by Chemistry, with Dr. Angelica M. Stacey as the lead writer raises inquiry-based, high school Chemistry to an incredibly accessible level. It simply allows more students with different backgrounds time to practice being a scientist while learning standards. Obviously, it can be adopted as an alternative text at many schools, but its greatest impact could be felt by convincing many students to take Chemistry in ninth or tenth grade, and, possibly, reducing the number of dropouts.

ACT research clearly shows that taking Physics, Chemistry, and Biology in high school correlates well with graduating college. Leon Lederman has convincingly argued that a sequence beginning with Physics First works best. However, with Biology being the 10th grade NCLB test in California, a sequence of Chemistry - Biology could serve students and that state adequately. From an opportunity-cost standpoint, the current practice of ordinary students taking ninth grade Earth Science or Integrated Science does not correlate with college graduation. In effect, ninth grade non-core science requires that students complete four years of science. Yeah, that happens. Bluntly, students in non-core ninth or tenth grade courses do not graduate college from a statistical basis. However, the core science alternative is beset with problems; since many students have weak backgrounds that preclude success using conventional Chemistry texts. Living by Chemistry offers light, engaging paperbacks with numerous experiments to drive students into classes. It helps solves the rigor/engagement problem.

Goal

Keeping students in school with interesting academics and supporting teachers with easy-to-use materials are the purposes behind the Living in Chemistry curriculum. Typical students and science teachers can thrive on the small texts, detailed teacher guides, and exercise kits. More interestingly, practicing Chemistry is real and different from other courses. It gives students a flavor of real academic work. It's risk entices. More students in Chemistry may correlate with the holy grail of increased rigor concommitant with a higher graduation rate.

Implementation

Designate one teacher to offer one to two sections of Chemistry with ninth graders having priority. Make sure texts are approved for full year piloting or satisfy whatever rules are necessary. Try not to issue a new course number - Chemistry standards are Chemistry standards. The next Chemistry class to students would be AP Chemistry anyway.

Debug the course over the year. If successful, add additional sections as more teachers and classrooms become capable of teaching the course. In California, an Earth Science teacher has to pass on Chemistry CSET, but this isn't about eliminating Earth Science, but increasing the number of students taking the core science courses. Remember, ninth grade Biology was rendered obsolete with the advent of molecular Biology 50 years ago. It's time to change. The world has. Taking Chemistry before Biology enriches the curriculum for all.

Why Singapore Math

2009-03-29T17:52:00.000-07:00

In 1983, Singapore ranked 17/26 in TIMSS. Singapore then adopted a new national curriculum for all schools. In 1995, Singapore ranked 1/41. Singapore has remained in the top 1 or 2 since. Hong Kong SAR is the main challenger with Finland close.

Singapore has recently adopted a heavily revised curriculum that is more focused on problem-solving. The impact of the revision, particularly on calculation/number sense, isn't clear at this time. "Singapore Math" refers to the 1994 revision, with modifications for California.

Singapore Math can be seen as having these distinguishing features:

1. Going in depth on a few topics for mastery learning
2. Extreme emphasis on building Number Sense
3. A coherent, longitudinal approach in the use of modeling to solve word problems

Instruction follows a basic sequence of Concrete - Pictorial - Abstract - Mental Math. One hour per day with little homework is employed.

Mental Math means that students learn to add, subtract, multiply, and divide internally. Flash cards are barely known as existing! Calculators are unnecessary. For example, 15 is seen as 10+5, which means that students may determine internally that 9+6 = 9+(1+5) = (9+1)+5 = 10+5 = 15 or 28-13 = (28+2)-(13+2) = (20+10)-(10+5) = (20-10)+(10-5) = 15. One way isn't mandated, but students must explain their process. In short, place value and the use of tens are paramount to an extent that is unknown in the United States. Abstract algorithms such as multiply and carry or long division are delayed for as long as feasible.

Developing models, as precursor for algebra, follow an orderly progression, by doing 1-3 daily word problems.

     K-1 Manipulatives
        2 Base 10 blocks
     3-4 dots/disks
     5-6 Rectangles

Each word problem is solved following the same form: Model - Equation(s) - Sentence answer - (scratch area). Neatness and completeness matter in this MES system.

One implication of Singapore Math is to ask parents not to help! Americans teach the wrong methods too early.
_________________________

The above words are edited notes of a presentation by Corrine Khoo-Lieu (Palo Alto) of the Pi Project on March 28 in Los Angeles. Extensive demonstrations of activities were performed. One of several small training consultancies on Singapore Math. Richard Bisk (Massachusetts) is another highly sought after consultant.
_________________________

The SmartMath software, written in Hong Kong, used in the CRO, mimics much of Singapore Math. If a district wanted to implement Singapore Math, a rollout works best, but K2 can be done easily at one time. 3-4-5 could follow year by year or one year after K2.

Alternative Attendance Measure in Instruction

2009-03-17T09:43:00.000-07:00

Reducing cuts is important. However, contacting parents or student for excuses after a student's return makes less sense now than in the past.

Before a PLC (Professional Learning Community) emphasis, teachers would issue zeros for missing work if students cut. The reward for bad behavior was no work, followed by more poor behavior because students quickly realize that zero's force them to fail in a standard 0-100 point system, which creates more hassle and costs for the school system as a whole and dropouts. Now, students must complete their work: attendance is irrelevant for grading, but vital for learning. More subtlely, the joy of being sick goes away to the student. This approach has been used successfully in summer school for years: excuses are irrelevant. The metric that matters is attendance, not the reason. The three-days-to-change-a-cut rule remains somewhat useful for awards, but no reminders to students and parents to clear a cut need or should be made. Getting students to school is the issue, not asking them or parents for an excuse when they arrive or afterwards.

Furthermore, sadly, there is a correlation between poor attendance and disruptive behavior. Since students can be transferred at no, or little charge, to a County ACCESS High School after four full days of cuts, it actually behooves schools and the majority of students within them to have absences marked as cuts. It gives schools more flexibility in dealing with, frankly, dangerous students. Reminding returned students or requiring excuses before students return to school is self-defeating and wasteful of everyone's time. It's merely going through the motions of improving attendance.

In short, attendance is the only issue. Excuses are irrelevant. Higher attendance does not result by administratively pressuring ourselves to reduce the number of marked cuts. The enemy to learning isn't cuts, but excused absences! Working this number down would have positive effects.

Possible Metric

a. ID the number of First Period Absences in last semester as a baseline.
b. ID the number of Full Day Absences in last semester as a baseline.
c. Record the number of First Period Absences and Full Day Absences this semester.
d. An increase in First Period, but a decrease in Full Day means a real system improvement has occurred.
e. Decrease/Increase in all absences is the obvious main statistic.
f. Trend the two numbers above and single period skips.

When Multiple Choice Becomes Continuous Assessment with Positive Reinforcement

2009-02-16T21:40:00.000-08:00

Multiple-Choice, MC, assessments inhibit long term learning. As a rule, they may work for summative assessment, but not formative. Furthermore, in mathematics, since guessing can yield correct answers, false positives usually cloud software responses. As a result, more MC problems are needed for students to solve in online classes, which usually decelerates learning. One of the secrets of better adaptive math software, such as ALEKS and Carnegie Tutor, is that they employ only a few constructed response questions. They allow a student to show mastery faster than most multiple-choice programs which struggle to compensate for false positives; especially since quick guessing is a common strategy with low achieving students. MC programs generate unexpected student responses because they are too ready to help. XLPrep and possibly Study Island, are examples of MC software that may frustrate student learning because their response to errors or successes don't demand that each student needs to want instruction at that moment and struggle through it! While at first counterintuitive, pretty instruction is merely a time-killer for many low-achieving students. ALEKS and SmartMath offer simple explanations only after a student, somewhat reluctantly, asks for it, knowing that he or she, will have to read to understand. This may also be a problem with the constructed-response software iPass. It's detailed instruction is beautiful, but students eyes wander during the videos, because they are forced to watched.

However, multiple-choice software doesn't have to suffer from the conventional maladies. In particular, SmartMath from Encyclopedia Brittanica (USA) and Planetii (Hong Kong) demands students answer 30 MC questions in a row without error! Random guessing is automatic test failure, not just a missed question. Students can earn stars, actually limited insurance, to save themselves from immediate failure by doing many problems correctly during earlier practice sessions. Adapting to a rapid train of MC questions seems to turn the problem of inhibited long term learning on its head. Instead of letting distractors interfere with their learning, students quickly seek them out to discard them in the search for a correct answer. Distractors seemingly concentrate thinking, not dissipate it. Finally, the active decision-making on choosing to earn zero to six stars, which allow 30 out of 30 to 30 out of 36 (a missed question generates an equally difficult question) involves the students responsibly in their own learning. They have to decide when to take the test because earning six stars takes a long time. This engagement and active self-assessment is the secret behind SmartMath, which allows issues with multiple-choice to evaporate.

After using many different brands of software in classrooms using during semester trials over the last four years, two programs have worked well together for full class coverage: SmartMath and ALEKS. The results of a quick assessment place students into SmartMath or ALEKS. While SmartMath has a rapid mastery option, students can take a Billy Madison approach: they try to spend only 1-2 weeks per level (six levels total) and start at Level One, which is a tough first grade! With cute, spinning avatars jumping for joy with correct answers, students march through the curriculum feeling their way through the inherent difficulties. As a subtle extra motivator, stressing that SmartMath was originally developed in Hong Kong also raises the importance of each individual's success. Students realize that they are being evaluated from an international perspective. Success matters more.

The Key Results of the NMAP Report.

2008-12-29T15:40:00.001-08:00

The tables and what readers infer from them in the National Math Advisory Panel Report are what truly matters.

A streamlined curriculum means that mandated topics need not be 100% of a math course. This is the great unwritten benefit of the report. Without stating it, NMAP agrees with the Core Knowledge, CK, method of using a core curriculum: the core hovers around 50% of a course in a CK classroom. The actual percent of time spent on streamlined curriculum will depend on students and their groups, which is a difficult issue to address in print. This allows enrichment and remediation to occur in real-time, while staying on an acknowledged, understood national path.

The Benchmark Table is what regulates math instruction. The table implies that mastery learning be implemented within a streamlined curriculum and its assessment. It's about learning, not teaching!

The School Algebra Table, California Algebra 2 without conics, adjusts the pathways of the high school math curriculum, striking a balance between rigor and realism. Algebra 2 is absolutely necessary, but High School Geometry, isn't! Knowing how to determine the measures of inscribed angles isn't really vital. Yes, A1-G-A2 may be the standard and wonderful, but A1-A2 works.

All of the comments and responses on research methods, etc. are embarrassing. They really are beside the point. Words on research-based are merely buzz or rants of the chattering class, but a reasonable, streamlined curriculum that demands mastery learning - now that's something special. Are there any comments that the tables of the NMAP Report are unreasonable or a poor starting point? No. In short, opponents of the report, need to ask themselves: are we bricks in the wall? (with thanks to Pink Floyd)

Donation from Costa Mesa Community Foundation

2008-12-06T08:27:00.000-08:00

Times are tough, but the people of the Costa Mesa Community Foundation believe in helping students stay in school by completing their math requirements - math failures equals dropouts. Please thank them for helping sustain ALEKS use in Newport-Mesa. ALEKS is the fastest way to mastering math.

Embracing CHSPE Allows a Pathway to School Reform

2008-11-25T19:34:00.000-08:00

The California High School Proficiency Exam, CHSPE, which is lawfully equivalent to a high school diploma for any purpose in California, serves as the linchpin for comprehensive, yet low-cost, school reform in California. It accomplishes this through three critical benefits:

The CHSPE serves as graduation insurance for students as schools increase rigor.
The CHSPE helps implement an Early College, which improves college success.
The CHSPE allows students to take courses they want to take, which reduces dropouts.

Schools want to increase rigor. For example, Algebra 2 or three years of science could be graduation requirements. However, the very real risk of increasing dropouts makes this effort very risky. For a principal or superintendent to bet the future on the words of pundits or a few researchers claiming that more rigor also will magically reduce dropouts is foolhardy, but if a safety net presented itself that also enhances the transition of students to community colleges or vocations, then the vigorous deployment of not only rigorous courses, but also career-oriented courses with extra support for students starting community colleges could proceed reversibly. Reform need not mimic Cortez's burning of his ships. The California High School Proficiency Exam, CHSPE, offers each student graduation insurance, and therefore supplies an often ignored mechanism in gaining community support in reforming schools.

In brief, CHSPE-based reform helps solve the problems of many courses being too easy, students needing remedial courses in college, students not completing college, and high drop-out rates, with the possibility of improved API scores.

Increasing Rigor Flexibly

a. The high school must request a waiver from its district for added graduation requirements for incoming ninth graders. For example, while different pathways to rigor exist, many graduation requirement sets would include either three years of both science and math or statements like Chemistry, Biology, Physics or Geometry, Algebra 2, Pre-Calculus or Algebra 1, Algebra 2, Statistics. The requirement set could be modified each year, and hold for the entering class.

b. Similar to colleges stating graduation requirements for entering students, a high school would notify eighth graders that its requirements will be different than the standard in the district. Eighth graders would have the option of starting at another high school, if space is available. They also would be told that they could take the CHSPE in tenth grade and graduate early or stay in school with a special schedule, if they so chose after passing the CHSPE.

c. Graduation requirements could be modified for each entering class as feedback on student success and difficulties and results on increased rigor became available. In particular, the choices that students make after taking the CHSPE and later, the actual results of those decisions would determine the effectiveness of this approach to high school reform.

CHSPE and Student Decision-Making

d. Eight and ninth grade students would be informed that those who complete Algebra and two years of high school math strongly perform well on CHSPE and graduate early. Those who neglect studying flounder and struggle through four years of high school.

e. The CHSPE would voluntarily be taken in February and June during tenth grade. With a cost of nearly $100, students would be careful in taking it. There is no legal reason for a school to pay for the CHSPE. However, organizations such as a PTA could partially subsidize the fee.

f. Students who pass the CHSPE would enjoy these options:

Simply stay in high school and graduate at the end of 12th grade.
Graduate immediately with family permission. This would allow a full community college course load with fees. However, student failure is likely. Early high school withdrawal could be effectively discouraged by the obvious benefits of the other choices. However, early withdrawal would serve students who want to start a non- or low-technical trade program or possibly those who seek a certificate program from a community college.
Complete, but do not file, school withdrawal papers. Students would gain these benefits:

1. Able to take two community college classes without fees

2. Attend high school on a reduced schedule with study halls for college classes

3. Reduced schedule could include focused courses such as robotics or drama

4. Reduced schedule could simply be independent study courses supporting college classes

5. Enjoy food and activities such as sports, which would be inappropriate for those NCAA-bound

Students, who graduate early, would be welcome to reapply for admittance. There is no need to penalize students for making unfortunate choices that could be mitigated.
Instruction in 11th and 12th grade would operate at higher levels than currently employed. Students who couldn't or wouldn't meet the standards could always opt-out by passing the CHSPE or transferring to another high school, if remediation proved ineffective.
Students who cannot pass the CHSPE would be served as current students are. However, with, hopefully, fewer numbers they could be identified and focused on better than today.

The Opposite of Cynicism

In could be said that encouraging CHSPE is an improper way of increasing a school's graduation rate or decreasing it's dropout rate, but the opposite has been far worse for decades. Although aware, very few California school officials tell parents and young adults of the CHSPE's availability because bodies are dollars in ADA districts. Arguments against the CHSPE are self-serving, while arguments for the CHSPE are informational and grant options to students and parents. It young adults another way, perhaps their only way, to succeed. Explaining the benefits and disadvantages of the CHSPE is professional and proper.

In Basic Aid districts, not ADA districts, a student leaving school is close to revenue-neutral.

Note: CAHSEE vis a vis CHSPE

The CAHSEE is a necessary condition for awarding a high school diploma, as set by state law. The CHSPE is sufficient to be recognized as a diploma for ANY PURPOSE under state law. The CAHSEE is easier than CHSPE because its tests lower level math standards. In addition, the CHSPE includes an essay examination in its English componenent.

Let Successful CHSPE Students Walk in Graduation

2008-11-25T19:33:00.000-08:00

Yes, the CHSPE is easier to earn than a district high school diploma, and from an initial, gut reaction, letting CHSPE students walk in graduation doesn't seem fair because they have accomplished less than most of the other students, but consider the advantages to all parties, and a 180 may be warranted!

Positive Reasons to Encourage Students to Walk

Don't let the best be the enemy of the better. With 25% of students dropping out of school, it may be that most students taking and passing the CHSPE have a close to 50% chance of not graduating otherwise. Walking through graduation may be their only motivation to even continue with their education. The CHSPE is an educational compromise. Passing it can be joyous; not a moment of regret. Save criticism for dropouts; especially since CHSPE students frequently plan to continue their studies at a community college. Students and their families should be legitimately proud of earning the CHSPE, and remember they are the foundation of education - they're called taxpayers and voters.

Early graduation is not rejection. A school administration need not think that a student taking the CHSPE is rejecting them, the students are simply rejecting two more years of conventional school after completing eleven or twelve years. In short, school leaders shouldn't take CHSPE results as reflecting poorly on them. Passing CHSPE can be considered a vindication - students have succeeded early and are ready to move on; albeit not perfectly. They shouldn't be punished for leaving the nest; nor should administers think they failed.

Motivate ninth and tenth graders. The prospect of graduating school after 10th grade may help ninth and tenth graders try harder in math and language classes. Seeing happy people move on in a graduation ceremony, not a second class disappearance, serves as a powerful image. Hearing other students moan about not knowing enough math to pass the CHSPE will also have effects. In Alt Ed, juniors perform better than sophomores because they see the end of school and the pleasures of walking in graduation. The resulting success may even encourage them to stay!

Discourage pettiness. Do many hard-working honor/AP students and their parents seriously claim that "the normal students" don't deserve to be in graduation? Surely some do, but the complaints are ignored. Similarly, would normal graduates strongly state that those CHSPE students have no right to walk in our procession? It's absurd to believe they would. Should administrators be petty for them? Letting holders of CHSPE certificates walk brings joy with little cost to students who have been in the system for eleven years. In their mind, they have paid their dues to ed code. Advising that they stay in school is one thing. Denying them a small benefit of completing state requirements truly seems inappropriate.

Acknowledge the academic truth. How many at-risk graduates could pass the CHSPE anyway? Many retake the CAHSEE several times and CHSPE is far more difficult. Are conventional at-risk graduates actually more academically qualified? Where's the evidence of this? To err towards hurting people in this situation seems cruelly unwise.

Increase morale of instructors and staff. Teaching young adults who don't want to be in school yields poor learning results. Below Basic on CST's after a year of work is neither an honor for teachers nor students. Teachers may complain, but they also want to keep challenging students in Alt Ed. CHSPE students are in the highest quartile in Alt Ed. Yes, they should be encouraged to stay in school, but denied walking in graduation because they are more talented than other Alt Ed students? Upon reflection, most teachers would praise walking and the benefits it indirectly grants to their classrooms.

Embrace the CHSPE. There are many incredible and surprising advantages of students passing the CHSPE. Setting the stage for increasing it's deployment is enhanced by letting students walk in graduation.

Legal Considerations to Let Students Walk

California law states that the CHSPE certificate is equivalent to a high school diploma FOR ANY PURPOSE to agencies operating under California law. On the other hand, LEA's (e.g. school districts) have large sway in making policy under many precedents. In short, parents could sue to allow their child to walk with reasonable grounds for success. However, the proceedings will be messy and expensive and unproductive. The issue really is just being able to walk in graduation. It is simply too small an issue for an administration to fight considering the text of the state law. Where is the compelling school need to circumvent state law?

To count requirements twice can be construed as an effort to violate state law deliberately. A school may state that a diploma and other requirements such as community service and senior projects are required to walk in graduation ceremonies. This may seem reasonable, but a diploma is not issued until community service and a senior project are accepted. They are requirements for a diploma, not graduation! Where is the compelling school need to circumvent state law? In short, applying non-diploma requirements suggests that parents who sue should seek monetary damages from individuals, not just the right to walk from a school or district.

Precedent has been set for letting students not complete requirements in courses, but receive credits and grades of A with a boost in GPA. It is said that this practice is unofficial, but it is publicly recognized and accepted by administrators, with the caveat that by law teachers have this right in grading. However, these grades are used by the administration in boosting GPA scores that are used in school awards. This makes them official, not just tolerated. This is NOT a gray area as a result, but subjects schools to charges of hypocrisy, which undermines any LEA's arguments on consistency or integrity. Currently, many teachers award grades in AP courses based solely on AP test results. Classwork and participation are irrelevant. In short, the AP test is to AP course requirements as the CHSPE test is to high school requirements. If a school wants to argue that top students deserve special treatment while at-risk students should be treated brusquely . . . lots-of-luck! It is this argument that two lawyers who have reviewed this blog state would force a judge to rule in favor students. Almost without question, the official GPA boost from faulty AP grades is far more damaging to a school's environment than letting CHSPE students walk. To argue otherwise is obtuse.

Walking in graduation has been denied on behavioral grounds. For example, getting drunk at grad night disqualifies a student. Passing CHSPE is a positive event. In the past, pregnant woman and convicts who have served time, were not allowed to walk. Now they do, often with strong school and community praise. Is passing CHSPE sui generis? No. On its face, it is simply absurd to deny CHSPE students the opportunity to walk.

Algebra I Success Initiative

2008-09-06T13:53:00.000-07:00

Items 3, 4, 6 and 7 can be initiated. Simple after-school classes focused on the skill benchmarks suggested by the NMAP report will prove highly beneficial. Sixth grade must be worked with extensively this school year - now. Items 5, 8 and 9 can be combined. They will take time. The www.usfirst.org is just one way to make this happen.

from http://www.cde.ca.gov/nr/re/ht/algebrainitiative.asp

Increase instructional time for middle grades so all sixth-, seventh-, and eighth-grade students receive sufficient mathematics, pre-algebra, and algebra instruction and support. Cost: $1.5 billion in General Fund for local support.
Expand the Morgan-Hart Class Size Reduction Program to include pre-algebra and Algebra I in seventh and eighth grades. Cost: $492 million in General Fund for local support, $369 million in General Fund for school facilities and $305,000 in General Fund for state operations.
Provide funding for districts to establish and operate "Boost Classes" in elementary, middle, and junior high schools, for no more than 15 students per class identified by a student success team as needing specialized curriculum, instruction, and counseling to address the new algebra requirement. Cost: $175 million in General Fund local support and $185,000 in General Fund for state operations.
Expand school counseling services in grades four through eight to identify and provide services for students not adequately prepared to take Algebra I in eighth grade. Cost: $40 million in General Fund for local support and $185,000 in General Fund for state operations.
Expand Science, Technology, Engineering, and Mathematics (STEM) programs in grades four through eight. STEM programs increase student engagement and motivation by providing relevant and rigorous instruction that gives students a clear understanding of how academic subjects can be applied to real-world situations. Cost: $25 million in General Fund for local support and $320,000 in General Fund for state operations.
Expand the after school programs funded by Proposition 49, including weekend algebra tutorial support programs with an option for online and toll-free services. The expansion would include stipends for highly qualified teachers for supplemental mathematics activities for seventh- and eighth-grade students. Cost: $36.3 million in General Fund for local support.
Expand effective Algebra Summer Bridge programs that provide instruction for students in grades four through eight and professional development for elementary and middle school math teachers. This program targets student needs and builds teacher capacity. Cost: $10 million in General Fund for local support.
Expand Advancement Via Individual Determination (AVID), a college preparatory program targeted primarily at disadvantaged students, to improve student success in Algebra I. Cost: $5.8 million in General Fund for local support.
Expand the Mathematics Engineering Science Achievement (MESA) Program at the University of California (UC). Cost: $5 million in General Fund for local support.
Provide increased support for migrant students assessed in Algebra I. Cost: $135,000 in General Fund for state operations.
Require the California State University (CSU) and UC systems to expand through the federal work-study program the availability of trained classroom tutors for both elementary and middle schools. Cost: unknown.

Other Considerations for the Math Committee

A focus on pacing plans and California standards benchmark testing may not be the most fruitful activities to undertake at this time. However, getting courses that use HOLT texts to use standard tests in DataDirector may be best for our long term learning on obtaining and using more rapid feedback. Expanding to other courses can be done afterwards. Holt is the Pre-Algebra text. Getting this going this year would be smart.

Online, Adaptive, Database-Driven Software for Math

2008-08-30T08:18:00.000-07:00

Introduction

The best metric for an instructional program is (time to proficiency)/(cost) for each student. The instructional method must be matched to the student and situation for the fastest time. Any particular method will not be a match for all students. A set of instructional delivery systems must be available to allow student choice and/or matching.

Subtleties

Without question, the product with the best time/cost ratio for reluctant learners is ALEKS. Its secret strength is its fairly terse, text-only help. It forces students to bring themselves to the problem first in order to solve it. This is also its weakness. An educator may believe that more instructional depth and variety is needed for students. Please note that this may be more of a cultural bias than a research-driven result. For example, video instruction may be more engaging, but does it bring the student to a specific problem. In other words, are bells and whistles truly helpful or merely sales features?

Apangea's structure offers the most robust math learning system for an independent learner. It's design has online instruction, supplemented by an automatic avatar (similar to the animations that arise in Microsoft Office) that offers help when the software system senses student difficulties. When difficulties persist, a real human, currently based in Pittsburg, comes online to help the student. This is unique, because it allows students to work without teacher support and it does allow students to obtain a more robust proficiency than ALEKS. The actual quality of its instruction has not been determined by me.

It is useful to see that ALEKS at $40 and Apangea at $130 are the two quality extremes of the same spectrum. Other products try sell similar features at lower costs and need to be offered when students reject ALEKS/Apangea or when budgets are unavailable.

Specific Choices

Carnegie Tutor offers much of Apangea's design sans the avatar and remote human intervention at a much lower cost. Carnegie joins ALEKS and Apangea in having the best artificial intelligence systems for adaptive, data-driven learning. iPass offers a limited course offering, basically just Algebra Readiness, but it is the product that exists in the middle of spectrum, because it uses constructed responses as does ALEKS.

The I Can Learn system is primarily purchased when a large grant is available and annual costs must be minimized. It is a school-based system only and not for at-home use. APEX Learning, which our district enjoys and I support, isn't a great method of delivering math instruction, because it doesn't adapt to student struggles. Its feedback design isn't appropriate for math considering its cost. Apex is better for high content courses, such as World History or Biology. It offers a consistent interface to all courses, which simplifies both student and teacher management chores.

SmartMathPractice (Planetii) and XLPrep can be thought of as competitors to ALEKS, both are adaptive at $20 each. Their weakness is that they use multiple choice. Please note that multiple choice inherently slows the time-to-proficiency in an adaptive system because guessing must be dealt with by having students complete more questions. Guessing gives false positives. This cannot be mitigated, CAHSEE's sub-categories being classic examples; although SmarthMathPractice and BrainX try by including a student's belief in his or her own knowledge into the software's decision-making.

Almost all of the other products, such as StudyIsland, are variations of XLPrep, or vice-versa. They offer more immediate help than ALEKS on the displayed page of the problem, but their multiple-choice nature hinders learning.

Conclusion

Apangea should be tried with an independent school's higher achievers and, possibly, as a strong prep course for a student attempting to enter seventh grade Algebra or eighth grade Geometry. As a learning community, we need to try it and determine its fit and appropriateness. The software provider claims that it's best market is actually in alternative ed.

Supplemental Opinion

In my experience with reluctant learners, they must be allowed to skip instruction and do problems until they exhaust themselves and are emotionally ready to accept instruction. ALEKS and SmartMathPractice are superb under this scenario and iPass horrible. XLPrep and RevolutionPrep (CAHSEE) immediately provide short instructional help after a failed problem. Some students prefer this. More stable students will read/watch delivery without having to fail first; in other words, their maturity allows them to use the types of software that appeal to educational buyers. Please re-read the second paragraph above.

Credit Recovery at a Distance

2008-07-31T18:07:00.000-07:00

Please comment on this post. It is only meant as a start for brainstorming or refinement and it has errors in fact and judgement.

An online program, LearningStation, that the Alt Ed principal found at CUE has been approved for use by the district at the CRC. It should be noted that the district goal is not to conflict with DataDirector. While DataDirector can generate tests, LS allows online student testing in addition to scantrons. It is also easier to use. When DataDirector improves a bit more LS will go away.

For $2 per student per year, a student can take tests, generated by teachers from a standards-based test bank or personally. It is reasonable to make several tests (hopefully randomized questions), so that students can take them in a 'light, proctored' setting. For example, in the PC lab after school with a monitor such as a parent volunteer (no cell phones, etc.). Please note that a cell phone means cheating automatically: take a picture, send it, text received "b." Welcome to Trabuco Hills.

In short, this would allow credit recovery at a distance in a variety of courses. I will try to coordinate it with a non-CRC high school, but I only have a few non-CRC licenses available. An independent study teacher would have to approve of the test and sign off on results in this situation. However, math is the toughest to test-out subject. Failures can be enrolled in a standard online class (Geometry, Algebra 1, Algebra 2). A certain number of hours or attainment of a completion level can be demanded before either retaking an LS test or a 'light, proctored' test (e.g. ALEKS).

The weakness with this base level is no personal instruction. An alternative could be modelled as an afterschool summer school CRC however. A teacher for math or science could be present to assist students. It may not be necessary to staff it every day. It would depend on the number of students.

AfterSchool Credit Recovery

2008-07-31T11:57:00.000-07:00

Student Characteristics

50 ninth and tenth grade students, who had failed either Algebra 1A or Geometry A undertook an afterschool program to earn a C in those classes while concurrently enrolled in Algebra 1B or Geometry B. Three students did not complete enough coursework; although they did attend, off and on, through the end of the course.

Less than 10% actually struggled to comprehend the material. The rest fit two profiles:

active in activities that had taken priority over math for several years
disliked teacher and/or had missing homework count for too high of a percentage to pass

On the other hand, the students from this school, could work for extended periods without supervision; unlike the other three high schools in the district. This is what really sets the school apart. However, the students just could not juggle time to learn math taught in a particular style while satisfying their personal priorities. Texting was their most common addiction and/or sports ate their time.

Design of Instruction

For credit, students were told that they needed to attend for 60 class hours.

While not strictly needed from a credit recovery basis, the fact that no student passed an initial test-out meant that math schoolwork needed to be accomplished.
The school is paid on a per student hour basis. Too few students makes the afterschool program unable to sustain itself. All students needed to be enrolled for the entire time.
Main Problem: Given that these students are actually far behind in mathematics, 60 hours, far less than what is normally found in a semester, really cannot help them achieve proficiency unless accelerated methods are used:

Adaptive math instruction with continuous formative assessment
Calculators for adding fractions to speed students through material (a necessary evil)

Instructional Solutions

ALEKS online, data-driven, math software
Casio fx-300ES two-line calculator with natural display inputs and outputs.
Teacher provides one-on-one tutorials on an as-needed basis.
Students start where they are mathematically comfortable before they undertake specific class coursework. This builds confidence and addresses underlying issues. The mutual burden is for the teacher to press each student to work as fast as possible and students to understand why. This remains problematic at other high schools, but was well-accepted at this school.
With continuous formative assessment, no summative assessment is given. Doing math becomes the point of the class, not how many wrong answers still constitute a pass.
As long as time requirements were met and progress was demonstrated, a C was rewarded, a B could be earned for exceptional work or if a B was earned in a student's concurrent math class. Students accepted this, but still complained during the last week of the course. Students considered their work of higher quality than it was.
Because of start-up problems, the 60 hours of class time was not matched with 60 hours of computer time. For this first class, 40 hours of computer time was mandated as a minimum. In the future 50 hours will be expected.
Unlike traditional summer school, mandatory attendance at a set time did not work with the majority of the students. Changing the course from Algebra for 2 hours on Monday and Wednesday and Geometry from 2 hours on Tuesday and Thursday to simply 4 hours per week helped the students succeed and gave them a chance to stay on track. Athletic activities frequently kept them from class at the originally scheduled time. In short, the two courses met simultaneously in a math lab.

Issues

The above approach keeps students on problems on which everyday students also work. The more conventional approach to remedial or intervention classes is to offer simplified instruction. This common cursory review of all standards is not considered fruitful by me, but of course, this is a value judgement. A principal can direct that an AGS or worksheet approach be used instead.
Many brands of math software exist, ALEKS offers the fastest path to proficiency, bar none. Also, from a practical standpoint, it also allows license reassignment, which is important in environments where students drop easily. For example, one $40 annual license is normally used four times: Two semesters, one summer school, and one reassignment. Other programs don't offer this reset capability.
Having one standard computer login greatly helped. The student ID/password scheme, while it has been improved greatly (Thanks Mr. O), doesn't fit the approaches of many of these students. They login under various names unless simply given a default one.
Individual student progress was recorded weekly in a spreadsheet.

Math Lean Curriculum Strategy

2008-06-10T13:59:00.000-07:00

Strategic Constraints
1. Implement National Math Panel Report inferences in compliance with California Standards.
2. Press forward with rigor in accordance with the American Diploma Project & Algebra 2 test.
3. Cope with bifurcation of student math achievement by minimizing dropouts.

Implementation
A. Use Singapore Math for K during 2008-9 school year (training must occur during summer).
If this is not achievable, then at least one school must step up to implement.
B. Do not choose any other K-5 texts during the new textbook cycle - unless failure occurs.
C. Use Singapore Math for K-1 during 2009-10, K-2 during 2010-11, . . . .
D. During 2008-9, form a team to refine the Algebra 1/2 curriculum to align with Panel.
E. Start Algebra 1/2 sequence in 2009-10.
F. During 2008-9, form a team to refine Algebra ABCD and Intermediate Algebra to align with the panel and to decrease drop-outs. This may entail technology such as ALEKS and a end-focus on CHSPE prep.
G. Grants may have to be sought to encourage/demand CHSPE participation for IA students.
H. Insure that the CRC obtains a state school code and conducts summer school around the district. Year-round summer school credits must not be issued by EHS, CdM, H, or CM.
I. Summer School needs to be loosely scheduled for dropout prevention. Classes need to be open for over 60 hours, but only require 60 hours for attendance. More than one teacher can be assigned to a class so that the lead teacher's attendance burden is also minimized.

Textbook Pilot Voting

2008-01-24T20:52:00.000-08:00

As I understand it, currently the pilot participants will vote with these choices:

a. Textbook A definitely, B not
b. Textbook B definitely, A not
c. A, B is ok
d. B, A is ok
d. No pick - use current materials

It would be advantageous from a professional development standpoint to augment the following choices.

a. Textbook A definitely
b. A, B is ok
c. Textbook A or another text that eases teacher professional development
d. Textbook B definitely
e. B, A is ok
f. Textbook B or another text that eases teacher professional development
g. No pick - current materials are adequate or another text that eases teacher professional development

This option set applies to Pre-Algebra (Grade 7 math) in particular. If the other groups (AR-A1-G-A2) pick the same vendor, then it would ease teacher training and workloads by using one supplier for all. It might help the students be more comfortable. Remember that they have different online suppliers for their other textbooks. They have learning curves.

Technology Implications of New Math Textbooks

2008-01-24T13:08:00.000-08:00

After viewing McGraw-Hill's, Prentice-Hall's, McDougal-Littell's, and Holt's short presentations, please accept these thoughts:

1. An LCD projector is mandatory for each math teacher with a new curriculum. A Smartboard may be nice, but only after ALL math teachers have Epson 83c LCD's (about $725 each). Budgets are/will be tight! Room layouts need to be tweaked this year in anticipation.

2. The answer to how all of the wonderful online math software solutions will survive or morph has been partially resolved: they will be rolled-up into major publisher technology components. Prentice-Hall has done a far better job than McGraw-Hill in integrating outside vendors. In particular, the lessons of NutShell Math, the interactive animations of Gizmos, and the supplements of MathXL to its Algebra Readiness program stand out. Also, the integration of MindQuiz into its Algebra Readiness allows teachers to write grants for "clickers" to enhance instruction with no extra software purchase needed. McGraw-Hill/Glencoe's animations are rudimentary. It may have been wise of McGraw-Hill to acquire some of Heymath's technology to be compete with Gizmos.

McDougal-Littell took an independent approach. It wrote lesson tutors, dynamic graphing software, and online animations on its own. The results are quite impressive. Prentice-Hall may have more to offer, but McDougal-Littell's is integrated best for the easiest teacher usage of a large amount of tech with complete teacher support by the integration of graphic organizers, etc. Holt provides a DVD with online duplication. It would be easiest for teachers and students to start with Holt, but over seven years ....

3. Of future importance is the integration of ExamView into all of the textbooks. Besides ExamView becoming the district benchmark test source, it can be used for formative assessment in Jeopardy style games as some point for some teachers. See MindQuiz. It should be noted that ExamView just purchased Interwrite, which makes clickers. In short, teachers writing grants for clickers should be encouraged to buy eInstruction/Interwrite brands, such as Cricket or eInstruction's. There will be a future synergy. Of additional note is that the "front-end" to ExamView is slightly different in each program. McDougal-Littell has the easiest selection of problems, followed by Prentice-Hall. Both McGraw-Hill and Holt's test generation would take a bit more work than the first two. Finally, McDougal-Littell has added many additional problems (classics) into its ExamView library.

4. Both ExamView and Data Director offer test bank libraries. How they compare or are used should be a priority of the math committee. Holt claims that only its test results from ExamView flow into Data Director (which would be very advanced for our district), because Holt owns Data Director. This sounds like a great feature, but it raises a bad question: Isn't Data Director meant to be open? If we purchased a system that is trying to lock out competitors data, it's worth is diminished. This is a serious breach of contract. Holt may be doing a Microsoft. API's to Data Director should be available to everyone (They may not want to offer a connection, but that's another issue.). The managers of Data Director should be spoken with in a direct, straight talk manner. This is not a trivial issue. Interoperability is vital to all.

5. Academic vocabulary is weak in all systems; yet Prentice-Hall is trying the best. It's Algebra Readiness is particularly strong in this area, where real academic words like "isolate" are defined (not just "get x by itself to solve"). By skipping the teaching of words like "consequently" and only focusing on Math jargon, teachers make a major error. Teaching academic vocabulary isn't asking students to write about how they feel about math, it is a valuable component in passing CST and CAHSEE Math, which rival vocabulary tests. This is an important area for professional development.

6. The use of multiple choice during learning, which all of us are guilty of to some extent, is poor from a brain research perspective. Momentum Math is extremely guilty on this topic. Error analysis too soon confuses students long term. The MI pilots have the most extreme difference between the two curriculums.

7. It would appear that due to the disposable nature of MI, that we don't have to make a 7 year committment to it. In my experience, the iPass software product should be sought by teachers who want to use it for MI and can raise the funds for it. It should be considered.

8. Of subtle importance is that the use of math technology will allow the district to pursue more of a "Singapore Math" approach in the next adoption, if the district is willing. The real difference is that "Singapore Math" pushes mastery, then promotion, and tries to keep students in a math register. It doesn't spiral like the US curriculum. Technology should allow highly efficient intervention. We can start planning the future now. The math curriculum of the primary/elementary grades should interest us.

Classroom Computing Hardware & Software

2007-12-31T15:24:00.000-08:00

2:1 Classroom Computing with leveraged, network computers demands easy-to-maintain, easy-to-manage systems. Furthermore, since many software programs run only under Windows; systems that run Windows should be sought. Note that this may make the systems harder to maintain and more costly. However, if only Internet access is desired with the addition of a Microsoft Office (tm) type program (eg OpenOffice), then Linux operating systems, such as Ubuntu, should be used. Nonetheless, if Windows is selected, then free StarOffice (tm) or OpenOffice (tm) could and should be installed as a cost savings.

Leveraged network computers include thin clients and multi-user systems. If network congestion is a major issue, then classroom multi-user systems may be the wisest choice: X300 from NComputing leads the market. Hardware for computer labs is another issue.

It is best to have 7 workstations per PC, not 4 which would require more PC's, more money, with more chances for failure. Yes, each PC failure would be less disruptive, but there would be more disruptions overall and the reliability of the classroom would be less. For example, with 7 workstations per PC, a classroom with 21 workstations would require 3 Ethernet ports plus 1 for a network printer and maybe one more for a laptop connected to a SmartBoard. No switches would be needed, which are actually the main cause of network failure (students kick them!).

Future teacher computers should be capable of handling two x300 cards. It may be appropriate to place one x300 and appropriate memory in the teacher computer initially. Let teachers adjust their rooms and add workstations when they are comfortable with them and their locations. It is surmised that seven is the maximum number that supports standard classroom supplemental uses, adding additional workstations means that the class has a computerized instructional focus. In short, the x300 supports pedagogical evolution of each teacher at low cost with high ease.

Getting to this doesn't require tossing older computers. Some classrooms will have seven computers, some seven workstations. Moving computers should be expected.

Finally, the x300 forces issues with network speed to move from the classroom to either network hardware (e.g. "da pipes") or network software (i.e. pipe clogging). IT would have a network focus, not a computer failure focus.

Classroom Computing Approach

2007-12-31T15:09:00.000-08:00

Each classroom is different both in layout and wiring senses and also in teacher comfort and purpose when it comes to using computers. One size does not fit all. Policy should allow teachers to incorporate computing as they become not only more comfortable with computer-based instruction but also more understanding of the appropriate trade-offs between facilitated online learning and direct instruction. These are different roles. Some teachers are better at one that the other. Also, students vary in their aptitude and maturity in using computers. As a result, it is best for a district or school to provide computers as requested into a classroom, not install the same number in each or blindly pursue some policy like 1:1 or 5:1.

2:1 Classroom Computing with leveraged, network computers provides a framework for school support of classrooms that flexibly and rapidly adapts to teacher and student needs. This design should be modeled for teachers. It permits both small group instruction and computerized instruction: one day half of a class works on the computers individually and the other half work directly with the teacher. The next day the students switch. There are several ways to model this.

Donors Choose

2007-12-02T14:59:00.000-08:00

Donors Choose works. Ten special Casio fx-300ES calculators are arriving soon, and I've started a challenge to fund headphones for iPass software and extensions which will allow good district computers to be used by more students.

This effort and the seeding of computers in the other two CRC classrooms has created a demand from teachers for computers! Our students can deliver work, not just dawdle in our classes now. This is big in an environment of individualized instruction.

Ongoing Projects

2007-11-25T11:27:00.000-08:00

2:1 Classroom Computing with donated computers
2:1 Classroom Computing with leveraged, network computers
CAHSEE for Sophomores - Prep & Enhancement for API
Multiple Measures: ALEKS, Planetii, FasttMath, iPass, and MDTP
Minimal Angel - Use Web Lockers for Simplified Student Essay Handling
Textbook Adoption - one unusual approach vs one conventional approach
Smarter Purchasing - Identify a company like Dell to buy computers from
Expand the Math Tech Club membership
Determine true Network requirements
District-wide after school network for all students

Math Textbook Selections

2007-11-14T12:03:00.001-08:00

First, for Algebra Readiness, the Mind Reseach Institute's Blueprint text & software must be thoroughly examined. Also, it should be examined as one of the two Math Intervention texts. If it works well, a seventh grade Algebra Readiness class can be offered instead of Math Intervention. This is semantics only. It should allow state funds to be used for the Blueprint text.

Second, for the normal math sequence, CGP's Algebra text should be one of the two evaluated. It is straightforward, lightweight and relatively inexpensive. If it is evaluated, then its seventh grade and sixth grade editions should also be tested in classes. Bridging k-12 is something we must do. We have plenty of our own tech resources to complement the CGP text.

Third, in my humble opinion, if CGP is selected for Algebra, then the Dolciani-inspired Geometry and Algebra Book 2 (McDougall-Littell) should be evaluated. Sacramento has specifically demanded that these texts remain current and complete. Again, this is merely an opinion, but I think there is a good flow between the two series. Again, we have plenty of our own tech resources to complement the Dolciani-inspired text.

Fourth, the other texts to evaluate should be one of the mainstream publishers for Grade 7 - Algebra 2. For example, the Glencoe texts or Holt or Prentice-Hall. Consistency of approach does matter. Learning curves for students and teachers are easier. Also, it seems strange to say "I like the vocabulary treatment in this series in 7th grade, but it doesn't matter in 8th grade." Picking different publishers is really saying, the publisher doesn't matter, which, if true, lets just flip a coin and save the trouble.

Our decision at the end of November is to select a mainstream publisher to compare CGP and Dolciani against. Comparing mainstreams to each other will yield minor differences.

ALEKS Tip - Making a Useful Report

2007-11-14T11:16:00.000-08:00

The two most useful reports on ALEKS to me are

1. Individual detailed progress history - Full progress over last 6 months
2. Report for a single student in this class

The first report I save weekly as a history, and the second report I save when a student completes or leaves a class. I make a folder called ALEKS and keep them all in it.

However, this isn't quite useful for decision-making and seeing weekly progress. I make a spreadsheet that records the number of hours completed by the student and the percentage of the course completed once a week. A chart of hours and a chart of percentages tells more than any other. An example (template) can be found, by going to www.editgrid.com. Register, then search using the FINDER and entering ALEKS. Several spreadsheets and templates will display. Click USE on the obvious one, save it, and then use it. You may want to save it as an EXCEL file on your hard drive.

2:1 Computing - High Classroom Productivity

2007-11-13T21:34:00.000-08:00

Math teachers using computer labs on a scheduled basis, can increase school productivity, by installing computers in their classrooms that can be used by half of the class at one time.

2:1 is useful when using software such as ALEKS, iPass, or Carnegie Tutor on an alternate day basis. If 36 students are in a class, then 18 can be on the computers, while the other 18 receive Direct Instruction.

This can be done very economically. This layout is intentionally messy. No IT involvement was necessary. Just a teacher's willingness to make it happen, and few ethernet switches and power strips.

Please note that no computer lab is needed for the same amount of computer time and small group instruction is facilitated by this approach. It's almost a no-brainer.

ALEKS - Middle School Usage

2007-11-13T21:22:00.000-08:00

The three hour free trial over a 48 hour period allows all students to be tested and progress in Math recorded. It is useful to follow these directions:

1. Sign up the students before class. It takes about one to two minutes per student to do this. During sign-up, record the user name, eg Guest465232, and rewrite the password to a standard one (this will save time), such as newport. Write a teacher's email address in the sign-up. The "marketing" box should be K-12, and it is strongly suggested that "Essential Math" be chosen as the evaluation.

2. Usually a student will complete an assessment within an hour, but two class periods should be scheduled.

3. Essential Math is a strong pre-Algebra program (for the good old days of 8th grade pre-Algebra). By starting in seventh grade, real progress can be recorded. The only decision is whether to take the initial score or allow three hours. Both approaches work well, but give different results. Three hour results show dedication and responsiveness under stress. This is a math skill.

4. Obviously, scores and possibly category scores, need to be recorded in a spreadsheet or database. It is important to record the score before the three hour period is completed; otherwise the data isn't available.

5. This isn't a rip-off of ALEKS Corporation. Students frequently ask to stay on ALEK afterwards. Many feel (correctly), they are accomplishing something.

ALEKS - Streaming Mode on Macs & PC's

2007-11-13T21:15:00.000-08:00

Aleks streaming mode installs additional java code in the browser's cache, not in the Java directory. The first time aleks.com/plugin is run (the address will read www.aleks.com afterwards - don't panic), it takes several minutes for the software to download. After that, when aleks.com/plugin is run, which is a must, then only one or two seconds is used.

Streaming is used when old Macs or PC's that have non-current software or are locked by administrators to prevent installation of software, such as ALEKS, are used.

For example, on an iMac that had no administrator access and two years since the last update, the ALEKS stream worked with the old Java and old Safari browser. This is a big win.

This feature has a secret benefit, if the three hour trial mode of ALEKS is used on non-ALEKS computers, then many students can be tested without IT support. This saves money.

ALEKS - Streaming Mode on Ubuntu (Linux)

2007-11-13T21:09:00.000-08:00

For users of PC's running the 7.10 version of Ubuntu with Firefox, a very popular free Debian-based Linux distribution, which runs quickly with easy maintenance on Pentium 3's having 256 MBytes of memory, ALEKS runs easily without difficult Linux commands or installations.

Ubuntu (or Fedora or Freespire) are used, if PC's are available or donated with corrupted or illegal Windows installs.

1. Install Ubuntu and update. (Skip Edubuntu, etc.). This requires one long download and a CD burn of an Install CD. Updating takes longer than an install. Ubuntu has the simplest graphics; therefore it runs quickly on old PC's. Freespire has a more beautiful interface, but that slows computers down.

2. Run Firefox, go to ALEKS, then Downloads, then click Install 3.6.

3. Firefox will say a Plugin is needed to run the ALEKS download. Four choices are offered, select Java 6.3 or higher.

4. After this flavor of Java is installed, run www.aleks.com/plugin. ALEKS works!

5. It would be best to make ALEKS the homepage. Edit Firefox Preferences for startup as aleks.com/plugin, and click CLOSE.

6. It would be wise to place ALEKS on the Firefox Bookmark Toolbar also. Edit the bookmark's properties to aleks.com/plugin.

I'm running Ubuntu on five old PC's currently. The only problem is that sometimes the ALEKS page doesn't allow keyboard typing. Clicking refresh fixes this issue - a small price to pay for a free, legal, updated computer and software.