Thursday, April 29, 2010

Calculators @ NCTM

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.

Tuesday, April 27, 2010

Primary Curriculum Advances @ NCTM

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:,,, and  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

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.


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.

Monday, April 26, 2010

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)

Sunday, April 25, 2010

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!

Monday, April 19, 2010

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.