kitchen table math, the sequel: United States for World Class Math

Wednesday, June 17, 2009

United States for World Class Math

Just in: a website for people like us who want a seat at the table when it comes to national math standards:

United States Coalition for World Class Math

Check out their Design Principles for K-12 Mathematics Standards:

1. All students should be expected to master foundational concepts and skills – especially in arithmetic – that are prerequisite to an authentic Algebra I course in a logical progression from grade to grade in the elementary and middle school years. The Final Report of the National Mathematics Advisory Panel (NMAP) should be the guiding document describing appropriate mathematical content.

2. The K-7 standards should be designed to prepare as many students as possible for an authentic Algebra I course in Grade 8. K-7 standards should be based on the "Critical Foundations of Algebra" described on pages 17-19 of the NMAP’s Final Report. Standards for authentic Algebra I and Algebra II courses should be based on "The Major Topics of School Algebra" described on pages 15-16 of the NMAP’s Final Report.

3. Standards-based alternatives could be written for less prepared students and alternate paths after algebra and geometry for high school students, depending on student achievement, interests, and career goals. For example:

a. The standards document could outline the possibility of a two-year course spanning Grade 7 and Grade 8 based on Grade 7 standards for students who, at the end of Grade 6, are judged to need more time to master foundational concepts and skills for Algebra I.

b. The standards document could outline a two-year course spanning Grade 8 and Grade 9 based on authentic Algebra I standards for students completing Grade 7 who are judged to need two full years to master Algebra I standards.

4. As emphasized by the National Mathematics Advisory Panel, "a focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided." Placement of the standards should reflect the grade level at which mastery is expected, and standards should not be repeated from year to year.

a. The sequence of the standards should be logical and hierarchical, following the structure of mathematics itself and should be modeled after the strong standards in California, Indiana, and Massachusetts.

b. "Benchmarks for the Critical Foundations" (pages 19-20 in the National Mathematics Advisory Panel’s Final Report) and recommendations from the National Council of Teachers of Mathematics’ Curriculum Focal Points should be used for grade level placement.

c. Concepts and skills, once mastered, should be used in subsequent years with a minimum of review.

5. In order to focus on building solid foundations for the more advanced mathematics – including algebra – that occurs in Grades 8-12, extraneous topics including aspects of geometry such as tessellations, nets, statistical approaches to geometric properties, much of data analysis, probability and statistics, and non-algebraic concepts such as pattern recognition should not be present in the K-7 standards.

6. In Grades K-7, the distribution of content by strand should be stated explicitly as percentages at each grade level and should change as students move up through the grades.

a. Early grades should concentrate on the arithmetic of whole numbers and measurement, with a limited amount of geometry and graphing. Certain aspects of algebra, as well as preparation for algebra, should be present from the earliest grades, as is the case with the California and Massachusetts standards.

b. Students should be expected to acquire automatic recall of basic number facts at least to 10 x 10 and 10 + 10.

c. Students should be expected to understand and use the standard algorithms of whole-number arithmetic in the early elementary grades (i.e., addition, subtraction, multiplication, and long division).

d. Students should be expected to understand and use the standard definitions for operations with fractions in conjunction with the standard algorithms of whole number arithmetic to compute sums, differences, products and quotients of fractions, including fractions expressed as decimals and percents.

e. The algebra strand gains emphasis in the middle grades, focusing on the content specified by the National Mathematics Advisory Panel.

7. The organization of the standards should change at Grade 8.

a. In grades K-7, standards should include multiple strands of mathematics, with their relative weight appropriately adjusted through the grades.

b. For algebra and beyond, standards should be given for a single-subject course sequence (Algebra I, Geometry, Algebra II, Pre-calculus, etc.) and their components re-ordered for alternative integrated mathematics courses. The standards for the Geometry course should require students to do proofs and to understand postulates, theorems and corollaries.

8. Mathematical problems should have mathematical answers.

a. In general, students should learn techniques for problem solving that can be applied to many contexts. Problems should be contextualized in the "real world" only when the context is sensible and relevant and contributes to an understanding of the mathematics in the problem.

b. Standards documents should include example problems. The level of difficulty of these problems should reflect mathematical complexity rather than non-mathematical issues.

9. K-12 math standards should meet the criteria specified by the American Federation of Teachers. They should be:

a. Clear and specific enough to provide the basis for a common core curriculum.
b. Rooted in the content of mathematics.
c. Clear and explicit about the content and the complexity students are to learn.
d. Measurable and objective.
e. Comparable in rigor to the standards of A+ countries, with grade-level specificity.

10. Standards documents should appropriately emphasize the attainment of procedural fluency. Students must be competent in performing all K-7 tasks without using a calculator.

11. Standards documents should only address mathematical content; language pertaining to pedagogy should be excluded.

12. As emphasized by the National Mathematics Advisory Panel, mathematicians should be included in greater numbers, along with mathematics educators, mathematics education researchers, curriculum specialists, classroom teachers, and the general public, in the standard-setting process and in the review and design of mathematical test items for state, NAEP, and commercial tests.

CO Coalition for World Class Math
CT Coalition for World Class Math
NJ Coalition for World Class Math
PA coalition for World Class Math
United States Coalition for World Class Math
Parents' Group Wants to Shape Math Standards

Common Core Standards: Who Made the List?


SteveH said...

Thanks for putting in the link Vicky. You beat me to it.

This is my favorite:

"Mathematical problems should have mathematical answers."

I would add that they all should be mathematical problems.

VickyS said...

Steve, were we separated at birth?

Had I had the time when I quickly made this post, I would have called that out as my personal favorite as well!

VickyS said...

And by the way, this grassroots initiative is looking for state chapters. So ya'll with extra time, check it out! They hope to be a credible voice for real math at both the state level and in connection with the push for national standards.

VickyS said...

NCTM is worried about being left out of the standards discussion so has produced a set of Guiding Principles for Mathematics Curriculum and Assessment. Like the Focal Points, some bones are thrown toward sequential, mastery-based math ("A curriculum is more than a collection of activities: It must be coherent, focused on important mathematics, and well articulated across the grades.") but the overall tone is fuzzy:

"If a voluntary national mathematics curriculum is developed, the topics studied in that curriculum must be taught and learned in an equitable manner in a setting that ensures that problem solving, reasoning, connections, communication, and conceptual understanding are all developed simultaneously along with procedural fluency."

Res ipsa loquitur.

In a recent Edweek article, the National Conference of Governors has said that subject matter groups like NCTM have been left out so far because the NGA has been focusing on the transition from high school to college. I hope that's a good sign--Steve has made the good point that you should start with what's necessary for college and work backwards when designing the curriculum.

Of course if you pan back it just isn't that complicated. Call me lost in the past but if you took the scope and sequence used when baby boomers like us were in school as a framework and tinkered with it to fix a few problems, you could probably arrive at a national curriculum pretty quickly.

By the way NCTM will soon come out with another pronouncment, stating that the forthcoming Focus in High School Mathematics: Reasoning and Sense Making (2009) will address mathematics education in high school.

Reasoning and Sense Making...gosh I can hardly wait!

Barry Garelick said...

Call me lost in the past but if you took the scope and sequence used when baby boomers like us were in school as a framework and tinkered with it to fix a few problems, you could probably arrive at a national curriculum pretty quickly.

I agree, Vicky. Unfortunately that scope and sequence is often derided and mischaracterized as having "failed many students" in math education, and was based on rote memorization, problems presented in isolation, etc etc.

SteveH said...

"... you could probably arrive at a national curriculum pretty quickly."

I agree too. I was able to get to calculus in high school with no help from my parents.

"failed many students"

It failed their pedagogical litmus test.

This is not to say that there weren't problems. It's just that modern educational pedagogues want to spin them to their own advantage.

When I was growing up, there was a certain amount of sink or swim. They could have done a better job of ensuring mastery. However, you had to pass or you were held back. Teachers couldn't just slack off and pass the mastery problems to the next grade. It wouldn't look good for a teacher to have a lot more kids flunk than the teacher in the next classroom.

Nowadays, there are no checks at all. If kids do poorly, teachers point to the spiral and say that everything will be fine. They are just not ready yet for the material. They make no attempt to set higher expectations and push a little bit. There is nothing to compare how one teacher is doing compared to another. All kids get passed along and nobody knows that there is a problem until it's too late.

It would be one thing if they said that it failed many students, so they are going to slow down coverage of the material to emphasize topics and skills that are needed by the average adult. Then they could say that if you want your child to be ready for a math, science, or engineering degree in college, you have to do something else.

Wu has a great paper (I forget which one) that shows the nonlinear learning requirement to go from K-6 math to a high school's AP track.

There is still the issue of sink or swim today, but parents won't know that their kids are sinking until they hit the math track split in 7th grade.

Catherine Johnson said...


I've finally read this.


Folks: Vicky's right; they need chapters in all the states.

I've agreed to set up shop for the NY site & Tex is going to help --

Catherine Johnson said...

If you figure out which Wu paper it is, let me know.