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We are at a tipping point and our economic survival is at stake

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

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We are at a tipping point and our economic survival is at stake

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  1. 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

  2. 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

  3. 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.

  4. Here is the Result

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

  6. 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

  7. 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

  8. From NAEP

  9. What’s wrong with patterns?

  10. 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

  11. There are Three Dimensions to the Problem • Standards • Curricula • Teacher Training

  12. 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

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

  14. 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

  15. And now we have the NCTM Focus Topics

  16. 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

  17. 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.

  18. Focus Topics – Numbers

  19. Focus Topics Fractions

  20. Focus Topics Fractions, Ratios

  21. Focus Topics, Algebra, Data

  22. 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

  23. There are Three Dimensions to the Problem • Standards • Curricula • Teacher Training

  24. 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.

  25. There are Three Dimensions to the Problem • Standards • Curricula • Teacher Training

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

  27. Typical Requirements in High Achieving Countries: K-4 • 1.1 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

  28. 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

  29. 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.

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