Dec 20, 2015
We are at a tipping point and our economic survival is at stakeAlready, our major high tech industries including IBM, Intel, and TI have moved or are moving both their research and their manufacturing offshoreMajor 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-8And ultimately, this failure is tied to the way we train our teachers in mathematics.
Here is the Result
Problem From WA Practice Exit Exam5 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
There are Three Dimensions to the Problem
Standards CurriculaTeacher Training
Our 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 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 skillsFractions and decimalsRatios, rates, percents and proportionsThe core processes of mathematicsFunctions and equationsMeasurement and basic geometry
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
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
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 basis for optimism.