Our major high tech industries including IBM, Intel, and TI have moved or are moving both their research and their manufacturing offshoreGM is in the process of cutting 30% of their workforce in North America and closing 12 plantsFord Motor Co. is closing at least 10 plants and cutting more than 35,000 hourly jobs in North America – over 30% of their workforce

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

What’s the problem?

Two thirds of the new jobs in this country require at least some college background, and one third require a college degree.The greatest single predictor of success in college is highest level math course in high school

The root cause of our problem is the failure of mathematics education in K-12, particularly K-8

In Most High Achieving Foreign Countries Calculus is a High School Graduation Requirement

And better than 90% of their populations graduate from high

school

Ultimately, this failure is tied to the way we train our teachers in mathematics. Different states have different requirements but most states only require one very weak course for elementary school certificationIn CA they also have to pass an exam, the CBEST, where the average level of difficulty is between 4th and fifth grade, and the hardest problems are at seventh grade level.

Here is the Result

Aconcagua is 6962 meters high. Mount McKinley is 6194 meters high. Which will take longer to climb?

Problem from Current U.S. Text

Problem From WA Practice Exit Exam5 of first 8 were mathematically incorrect.

What’s wrong with patterns?

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 the NAEP

From NAEP

Now Let’s Look at the Mathematics that’s Taught in

High Achieving Countries

First GradeRussia

First Grade:Russia: Restof Lesson

A Third Grade Lesson from Singapore

A lone goose was flying in the opposite direction from a gaggle of geese. He cried: “Hello, 100 geese!”The leader of the flock answered: “We aren’t 100! If you take twice ournumber and add half our number, and half of half of our number, andfinally add you, the result is 100, but … well, you figure it out.”How many geese in the gaggle?

A Problem From Russia: Grade 4

99/(11/4) = 36

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 CurriculaTeacher Training

Our Various State Math Standards can be Characterized as

An Inch Deep and a Mile WideAt each grade level there are a huge number of topics

The Count of Utah Math Standards

Of course, besides the depressing number of topics, there are also serious mathematical errors in the Utah Standards

The California Standards come in two flavors

General Standards – Better than most, maybe a block wide

Green dot standards

And now we have the NCTM Focus Topics

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 CurriculaTeacher Training

Here’s a 10th Grade Lesson from an NSF Funded High School Program Popular in Some States

IMP 2Page 199

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 CurriculaTeacher Training

Carnegie Foundation

Carnegie Foundation is running a study of courses taught in tandem by mathematicians and mathematics educators at five sites throughout the country.Liping Ma and I are working together at Stanford.

Carnegie Foundation

Coordinating such a project is difficult. And the proper balance between learning aspects of mathematics pedagogy and mathematics is not easy to achieve.However, Liping and I both agree that the first priority for these students is learning the mathematics.

The Original Course Plan

Note that we see the same structure as was evident in the Focus Topics and

the Green Dot Standards

Liping Ma Explaining Place Value

This snippet is rich with issues

Originally, I thought what was important was the shakiness of the students understanding of place-value.However, on further thought, I realized they do understand. They were, however, sensing the lack of a definitionLiping’s failure to initiate the discussion with a precise definition is critical

This snippet is rich with issues

Definitions are a key part of the signature pedagogy of mathematics, and this pedagogy is there for a reason.

Real Thought Must be Given to Mathematics Pedagogy in Pre-service Teacher Training

This is a Case where One Size Does not Fit All

Among the issues are that for pedagogical reasons definitions play virtually no role in elementary math instruction in this countryAs an example: It is not unusual for a teacher to let students define fraction addition and multiplication for themselves via class discussion. So we often see

Fraction Addition

Which is closely related to

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-41.1 Sets and logic; relations, functions, sequences1.2 Elementary Number Theory1.3 Mathematics Education I.1.4 Mathematics Education II.1.5 Teaching Geometry and Measurement1.6 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 AnalysisThree Semesters of GeometryThree courses on math methodology and teachingThree 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 topicsThere remain very contentious issues with pedagogy that will be harder to work outAnd 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 real basis for optimism.