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 98 97 96 95** 94 93* 92 91 90 89

% remediated 54 54 53 52 48 45 39 26 24 23

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, ELMThe 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 teachersBut we carefully delineated the mathematical issues and likely problems in teaching each standardThe 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 1998.

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

0

10

20

30

40

50

60

70

1998 1999 2000 2001 2002

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

San Diego City Unified API

0

1

2

3

4

5

6

7

8

9

API

SIM SCH

API 5.95833 5.95081967 5.6 5.6667

SIM SCH 8 7.81967213 6.7419 6.6538

1999 2000 2001 2002

Scores for San Diego High Schools

San Diego Unified School District High School API

0

2

4

6

8

API

SIM SCH

API

SIM SCH

API 5.421053 5.7368421 5.47368921 5.21052632

SIM SCH 6.947368 7.15789464 6.10526316 6

API 5.421053 5.7368421 5.47368921 5.21052632

SIM SCH 6.947368 7.15789464 6.10526316 6

1999 2000 2001 2002

San Diego Unified School District High School API

0

1

2

3

4

5

6

7

8

API

SIM SCH

API 5.421053 5.7368421 5.47368921 5.21052632

SIM SCH 6.947368 7.15789464 6.10526316 6

1999 2000 2001 2002

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 mathematicsWe’ve had to revise the teaching of fractions and we’re still discussingHow 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, butLong 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?