Tuesday, March 31, 2009

Approximation & Estimation: Vital Skills

Today's New York Times has an interesting article on the importance of estimation in society (and thus the importance of it in our classroom and mathematics standards). In The Biggest of Puzzles Brought Down to Size, Natalie Angier writes:
Importantly, you are not looking for an exact figure but rather a ballpark approximation, something that would be within an order of magnitude, or a factor of 10, of the correct answer. If you got the answer 900, for example, and the real answer is 200, you’re good; if you got 9,000, or 20, you go back and try to find where you went astray.

Saturday, March 28, 2009


Many anti-reformists point to Singapore (due to its TIMSS scores) as the place to emulate. What the anti-reformists fail to realize is that the Singapore mathematics syllabus is very similar to standards based mathematics. Below appears statements directly from the 2007 primary math syllabus which reflects an emphasis on conceptual understanding, the use of calculators, and discovery (yes, constructivism in Singapore) - don't tell the anti-reformists!

The 2007 Primary Mathematics syllabus reflects the recent developments and trends in mathematics education. The revised syllabus continues to emphasize conceptual understanding, skill proficiencies and thinking skills in the teaching and learning of mathematics. These components are integral to the development of mathematical problem solving ability.

Advances in technology have changed the way we teach and learn mathematics. The computer and hand-held calculator, for example, offer great potential to enhance the teaching and learning of mathematics.

Students will have opportunities to discover, reason and communicate mathematics. They will engage in stimulating discussions and activities where they can explore possibilities and make connections. These qualitative changes require a change in the teaching and learning approaches; incorporating activity-based and learner-centered methodologies.

The rationale for introducing calculators to Singapore's students is to:
(1) Achieve a better balance between the emphasis on computational skills and problem solving skills in teaching and learning and in assessment
(2) Widen the repertoire of teaching and learning approaches to include investigations and problems in authentic situations
(3) Help students, particularly those with difficulty learning mathematics, develop greater confidence in doing mathematics

Thursday, March 26, 2009

High School Update

Some interesting updates from the state about high school assessments follow:
(1) The pilot algebra I EOC assessment will be given to 35,000 students nationwide of which 33,000 are from NJ. It seems NJ is the only state to retain interest in this exam. It costs NJ approximately $20/student to give this exam, thus over $600,000 is being spent on this exam.
(2) The state wishes to develop a Geometry EOC exam but, to date, has not begun this process.
(3) While an algebra II course nor an algebra II EOC exam will be required For graduation of students, a third year of mathematics that builds on algebra I and geometry will be. This implies that an alternative to Algebra II will need development and hopefully will include data analysis, probability, and additional algebraic skills and applications.
(4) The current DOE thinking is to require 2 EOC mathematics exams to be passed for graduation. This raises many questions since Algebra II will not be a requirement and Geometry has not begun development.
(5) Next year's entering freshman will NOT have to pass any new EOC exam to graduation. The HSPA will remain the graduation test of record for next year's freshman.

Wednesday, March 25, 2009


Another document was distributed at the conclusion of the task force meeting.  It is a Progress Report from the Mathematics Curriculum Framework Revision Panel (dated March 24, 2009). Massachusetts is the only state in the Union that out performs NJ students on the 4th grade NAEP in mathematics.

PM Session

The PM session of the first meeting has concluded.
Discussion of calculators and algorithms took place.
Debate was on both sides.
Two members wanted to ban calculators until 7th grade.
Singapore does not use calculators till 5th grade, while Massachusetts limits use until 4th grade.
I was charged with drafting a white paper delineating appropriate use and non-appropriate use of calculators.

The standard algorithm discussion centered around the word "the" as in the standard algorithm.
No common ground was found, but there was strong sentiment that students must be able to use efficient and accurate algorithms - with the emphasis on the 's' - algorithms. Lattice multiplication was portrayed in a negative light by a few because it takes up so much space on the paper. Partial products multiplication was portrayed in a positive light by several. Cultural diversity with respect to algorithms was also mentioned.

First Task Force Meeting AM

The AM part of the first math task force meeting is completed.
News: The math standards will NOT go to the state board until Dec 2009.

One task force member spoke eloquently about Asian students including best practices such as:
• lower class sizes
• interventions that add more time for students to learn math
• best teachers work with the worse (bad word choice) kids
• engineering view of standards (they have a speed standard)
• the answer is only the beginning of the process
• STEM vs Humanities tracks in high schools

The task force also debated the article: Reaching for Common Ground in K-12 Mathematics Education

One quote in the article below:
By the time they leave high school, a majority of students should have studied calculus
Many disagreed with the above statement

Tuesday, March 24, 2009

Comparisons of Drafts

During the past few weeks, a four-column chart was created so that the two versions of Standard One (Numerical Operations) – the December 2008 version created by the Department of Education’s writing team and the February 2009 version created by DOE staff – could be compared and evaluated, and so that a new version of the standards could be developed. The left two columns of the chart contain the text of the two versions, the third column includes comments on the two versions, and the fourth column contains recommended language for the next version of the math standards.   This document has been distributed to the ALL of the NJDOE math task force members, which will meet for the first time tomorrow (Wednesday March 25th).  I also recommend for anyone following this debate to read Alan Schoenfeld's (pictured on left) The Math Wars.

Monday, March 23, 2009

Feb NJ Math Standards copied from Indiana

An article appears today (Monday April 23rd) in the Daily Record about the math standards controversy. The author shows both sides of the debate. Commissioner Davy (on left) says she is not taking sides but then she states that the Dec standards rely too much on conceptual understanding. She continues by trashing the performance of NJ students on the NJASK. The full article.

Friday, March 20, 2009

NJDOE Math Task Force Formed

NJDOE has formed a math task force to review the two drafts of the NJ math standards.
The December draft written by the writing team and the February draft written by NJDOE personnel.
There will be three meetings over the next two months on March 25, April 14, and April 20th.
This blog will hold the members accountable for their rhetoric at the meetings.
The members of the task force can be found below.

1. Willa Spicer
2. Amy Flax
3. Carol deRuyter
4. Cindy Cittadino
5. Darren Mischel
6. Deb Ives
7. Eric Milou
8. Gwen Seneschal
9. Heather Henderson
10. Helen M. Roberts
11. Jane Hannon
12. Jay Doolan
13. John K. Bechtold
14. Kathleen Serafino
15. Kimberly Mueller
16. Lisa Solmose
17. Marian Palumbo
18. Patti Hulsen
19. Phil Daro
20. Robert A. O'Donnell
21. Roberta Schorr
22. Sandra Alberti
23. Shirley Cooper
24. Tim Giordano
25. Timothy Brennan
26. Tom Corcoran
27. Robert Riehs