From the late 1980’s to the mid ’90’s the hi-tech hiring problem grew to crisis proportions in California Most of the huge increase in H1b visas were going to people needed in California

The K-12 system in California was not producing graduates capable of hi-tech work or obtaining a university degree in a hi-tech area

Percentages of Entering CSU Students Requiring Remedial Mathematics Courses Year **9493* % remediated

The * indicates that from 1993 three years of high school mathematics were required for admission to the CSU system. The ** indicates that in this year the special admission students are not counted. In 1998 approximately 80% of entering students in the CSU system failed the Entry Level Mathematics Examination, ELM The average question on this examination is set at mid-sixth grade as measured against the current California Mathematics Standards

It should be no surprise that by high school our students, nationwide, ranked at the bottom internationally in the ’90’s The only industrialized nations that did worse were Italy and New Zealand

The CA State Board of Education in 1997 Yvonne W Larson, President Robert Trigg, Vice President Marion Bergeson Timothy Draper Kathyrn Dronenberg Marion Joseph Marion McDowell Janet Nicholas Gerti B. Thomas Marina Tse Richard Weston

Yvonne Larson and Marion Joseph are nationally known educators Marion Bergeson was the previous CA secretary of education Janet Nicholas was the governor’s chief trouble-shooter

The California Board decided to apply the best available knowledge to fix the system in California Not just from the US Education Establishment but From All Over the World.

The actual Genesis of the Current California Mathematics Standards were Foreign Models Only the highest achieving countries were used We did not use New Zealand We did use Singapore, Japan, and Poland as guides to what works for all students.

In these countries virtually every citizen graduates high school and upwards of 90% of graduates have had calculus in high school

Next we Put Together a Framework Throughout the Framework we reiterated that we would not recommend teaching methods. This was the proper domain of teachers But we carefully delineated the mathematical issues and likely problems in teaching each standard The Framework also served as the legal specification of the material that publishers had to provide to sell their programs in California.

The new standards balanced problem solving and skills development They back-mapped against the objective of algebra for all students by eighth grade The problem solving component was a big improvement on the previous California (and current NCTM) model

Making algebra in grade 8 possible for all students was a critical part of the development of these standards.

Math in high school determines success in college

For a program to be purchased in California, it has to meet the criteria of the Framework In the successful programs for K – 6, typically every third lesson involves problem solving These lessons use the California problem solving model

AND NOW WE BEGIN TO SEE THE RESULTS

Note the troubling lack of improvement in scores for students who were in grade 6 or above in At the same time students in lower grades rapidly reached the limits of validity for the test.

Every 7 years California is required to revise the standards For the first time the Board decided not to change the Framework in any way.

With this Data Set We Can Look at Individual Districts

Outcomes for Selected Districts in California Grade 5 SAT 9 Scores, California Los Angles San Fran Oakland San Diego San Jose Inglewood

San Diego Unified Decided to use Foundation Money to buy programs like Connected Mathematics, TERC, Everyday Math and IMP, not California aligned programs.

Scores for San Diego Elementary Schools

Scores for San Diego High Schools

IT SHOULD NOT BE THOUGHT THAT THE CALIFORNIA PROGRAM HAS SOLVED ALL OUR PROBLEMS WITH MATH ED AT BEST IT HAS ONLY PICKED THE LOW-LYING FRUIT

TO GET FURTHER WE MUST IMPROVE TEACHER CONTENT KNOWLEDGE IN MATHEMATICS

But this is not simple. The way in which teachers need to know school mathematics is different from the way in which engineers need to know it.

Also, the prevailing culture in mathematics departments makes them unwilling to expend the effort and value the results when mathematicians try to construct courses for prospective elementary school teachers.

Likewise, most Education Schools seem equally unhappy when actual mathematics content is required for prospective elementary school teachers

But having mathematics faculties teach well designed content rich courses to this audience provides the only hope for a long term fix.

Secretary Paige’s Office is Supporting this Development We are creating new courses for pre- service teachers to be taught by mathematicians Among the most difficult of the issues we’ve had to work through is how to present a more robust model for problem solving in these classes

We’ve also had to rethink the role (or more properly the absolute lack) of definitions in K–6 mathematics We’ve had to revise the teaching of fractions and we’re still discussing How to even define ratio, rate, percent and proportion

A test case is standard algorithms We don’t care if students become highly skilled at long division, but Long division contains within it the core of understanding approximation and convergence. Understanding WHY long division works opens the doors for more advanced mathematics to students. Not teaching it (or teaching it as a rote skill) helps close those doors for many students.

What are the key topics in algebra that teachers need to know? Currently symbolic manipulation has been almost entirely removed from the K – 8 curriculum What is the best way to explain to prospective teachers why it has to be part of the curriculum? What is the best way to present this material to prospective teachers?