Secondary Curriculum Advances @ NCTM

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

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

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

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

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

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)

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.