We are at a tipping point and our economic survival is at stake Already, our major high tech industries including IBM, Intel, and TI have moved or are moving both their research and their manufacturing offshore Major industries including GM and Ford are cutting large percentages of their workforces in North America and closing manufacturing plants

We cannot produce sufficient engineers and other high tech workers – NASA and the National Labs are not able to replace their aging top scientists and engineers, to say nothing of high tech industry’s hiring problems

The root cause is the failure of mathematics education in K-12, particularly K-8 And ultimately, this failure is tied to the way we train our teachers in mathematics.

Here is the Result

Problem From WA Practice Exit Exam 5 of first 8 were mathematically incorrect.

NAEP – The Nation’s Report Card Last year, The Brookings Institute asked me to review the algebra questions on the NAEP Of the 41 eighth grade NAEP algebra problems provided, 8 were incorrect and one was meaningless Moreover about 10 of the correct problems were just questions about vocabulary, not mathematics

Of the 22 grade 4 questions provided, four were incorrect, four others were essentially vocabulary, only one could be judged mildly challenging at fourth grade level

From NAEP

What’s wrong with patterns?

Over the past 3 years two communities - math education, mathematics - have begun to cooperate at the national level to bring the strengths of international curricula to the United States The amount of common agreement between us is vast

Common Ground With support from the business community, the NSF and the major mathematics associations a group of leading math educators and mathematicians met and carefully analyzed their perceptions and beliefs. The resulting article indicated both that our differences are not as great as they are pictured, and our areas of agreement are very wide. For example, among the things we agree about is that the majority of high school graduates should have some calculus in high school as is the case in the high achieving countries.

Notices of American Mathematics Society, Oct. 2005

There are Three Dimensions to the Problem Standards Curricula Teacher Training

Our State Math Standards can be Characterized as An Inch Deep and a Mile Wide At each grade level there are a huge number of topics

The California Standards come in two flavors General Standards – Better than most, maybe a block wide Green dot standards

The key topics Place value and basic number skills Fractions and decimals Ratios, rates, percents and proportions The core processes of mathematics Functions and equations Measurement and basic geometry

And now we have the NCTM Focus Topics

NCTM has just approved a sequence of focus topics, three per grade in grades Pre-K - 8, with the advice that at least 60% and preferably 80% of instruction be devoted to these topics

The Role of the Focus Topics NCTM regards the Focus Topics as a description of the keys to an effective curriculum in mathematics. The California Green Dot standards closely align with the Focus Topics.

Focus Topics – Numbers

Focus Topics Fractions

Focus Topics Fractions, Ratios

Focus Topics, Algebra, Data

It is Clear that we are Achieving Common Ground on Standards There are Differences in Grade Level but not in the view of what matters

There are Three Dimensions to the Problem Standards Curricula Teacher Training

Curricula that Match the Focus Topics This is an area where there are severe problems. None of the NSF funded curricula, including IMP, CorePlus, TERC, Everyday Math and CMP match up well with either the Focus Topics or the Green Dot standards.

There are Three Dimensions to the Problem Standards Curricula Teacher Training

At the Same Time our Content Expectations for Pre-service Teachers are Minimal Contrast this with the expectations in high achieving countries

Typical Requirements in High Achieving Countries: K Sets and logic; relations, functions, sequences 1.2 Elementary Number Theory 1.3 Mathematics Education I. 1.4 Mathematics Education II. 1.5 Teaching Geometry and Measurement 1.6 Combinatorics, Probability, Statistics and its instruction

Typical Requirements in High Achieving Countries: 5-8 Algebra Semester I (number theory) Semester II (classical and linear algebra) Semester III (abstract algebra) Four Semesters of Analysis Three Semesters of Geometry Three courses on math methodology and teaching Three field work courses

We clearly have a long way to go But there is a growing consensus about what matters and how to organize the topics There remain very contentious issues with pedagogy that will be harder to work out And there is strong resistance to the idea that our pre-service teachers must have a much more solid background in mathematics, especially in K – 8. But the communities are communicating now, so there is a basis for optimism.