Wednesday, May 26, 2010

Math Software @ NCTM

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.

  • 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
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.
  • 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.
  • 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.

    Sunday, May 23, 2010

    Book Review - Mathematicians by Mariana Cook

    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.

    Thursday, May 13, 2010

    Two Year Algebra - Reboot

    Struggling students can succeed in Algebra and complete high school.

    • 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
     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:
    1. If the Computer Lab License only, the students can use the text, but you don’t get any scoring information for them. 
    2. Use the Computer Lab License with online homework. With this you can track what the students do for homework that you assign. 
    3. 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. 
    4. 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.

        Friday, May 7, 2010

        Why ALEKS Provides "the Best" Math Software

        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 ( 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.


        Dennis Ashendorf has extensively used the following:
        • ALEKS
        • APEX
        • iPass
        • IXL
        • RevolutionPrep
        • SmartMath
        • XLPrep
        Dennis Ashendorf has lightly used
        • Carnegie Tutor
        • STMath

        Sunday, May 2, 2010

        Threats to Public Education

        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

        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 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