High School Mathematics: Where Are We Headed? W. Gary Martin Auburn University

High School Mathematics: Where Are We Headed?

W. Gary Martin

Auburn University

Agenda

We will address the following questions related to high school mathematics:

1. How are we doing?

2. What do students need?

3. Where should we be heading?

How Are We Doing?

National Assessment of Educational Progress (NAEP)

“The Nation’s Report Card” Given in all subject areas, including

mathematics. Most recently given to grade 12 students

in 2005.

Sample Questions

Answer the three questions. Predict what percent of grade 12 students

answered it correctly.

Sample Question #3

Responses to #3

Sample Question #17

Responses to Question #17

Question #16

16. If f(x) = x2 + x and g(x) = 2x + 7, what is an expression for f(g(x)) ?

Responses to #16

NAEP Achievement Levels Advanced (≥216)

Proficient or above (≥176)

Basic level or above (≥141)

Below basic (<141)

(see p. 21)

2%

23%

61%

39%

Briefly review the report…

Subgroups on NAEP

70% of African-American students are below basic

6% proficient or above Also, big gaps for Hispanic students,

students with disabilities and ELL No major differences by gender

Impact of Course-Taking

COURSE AVERAGE SCORE

AVERAGE LEVEL

Algebra I or less 117 Below basic

Geometry 126 Below basic

Algebra II 141 Basic

Pre-calculus 165 Basic

Calculus 182 Proficient

Trends The NAEP math assessment hadn’t been given

to grade 12 students since 2000. This is a new framework and new scale, which

makes comparisons to previous years difficult. An analysis of common items to the two

assessments suggests that there is a “probable” increase, from 42% to 44% correct.

Programme for International Student Assessment (PISA)

Measures 15-year-olds’ capabilities in reading literacy, mathematics literacy, and science literacy every 3 years. One area is focused on each cycle. Math was the focus in 2003. 41 countries were included.

Mathematics Literacy “...an individual’s capacity to identify and

understand the role that mathematics plays in the world, to make well-founded judgements and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned, and reflective citizen.”

Thus, PISA’s emphasis is on the ability to apply a range of knowledge and skills to a variety of problems with real-life contexts.

Sample Problems

See pp. 8 and 9.

Results

International average: 501U.S. average: 476

U.S. students averaged: Better than students in 9 countries The same as students in 4 countries Worse than students in 26 countries

More Results

U.S. students did best in “Uncertainty” and worst in “Space and shape”

Trends in Mathematics and Science Study (TIMSS) Grade 12 was last tested in 1995 (released in

1998). General performance.

U.S. was significantly below international average.• Outperformed by 14 countries• Similar to 4 countries• Outperformed 2 countries

Advanced students. U.S. was significantly below international average.

• Outperformed by 11 countries• Similar to four countries• Did not outperform any country

What Can We Conclude?

What Do Students Need?

An Agenda for Action (NCTM, 1980)

Problem-solving should be the central focus Include estimation, geometry, measurement, data analysis,

modeling, computer literacy -- not just computation Take full advantage of the power of technology Require more mathematics study and a curriculum that meets

the needs of all students. 3 years of math in high school; those going on to further study should

have 4 years Meet the needs of different groups of students

• Further study --vs.-- “Consumer math” (which should include a broader focus on quantitative literacy)

However -- Problem solving for all AND Algebra for all Move away from focus on calculus

NCTM’s Standards

Curriculum and Evaluation Standards for School Mathematics (1989)

Principles and Standards for School Mathematics (2000)

Compare and contrast recommendations for 9-12 to An Agenda for Action

Ready or Not: Creating a HS Diploma that Counts

DISCUSS: Why might they consider the high school

diploma an issue? Read pp. 1-2

Two Audiences

The project looked at both: Requirements for the workplace Requirements for postsecondary education

DISCUSS: How do you think the requirements for these

populations are the same or different?

Read p. 3.

What Is the Solution?

The American Diploma Project set out to define the content needed by students in order to: Succeed in postsecondary education Succeed in the workplace

They concluded that this is more alike than different through Algebra II!

Summary The traditional middle class based on

manufacturing is disappearing. “Good jobs” ($25,000+/year, plus benefits)

increasingly require advanced preparation in mathematics. Preparation in algebra, geometry, data analysis Think creatively, solve problems

Algebra II is increasingly seen as the gateway course to future success For higher education For the workforce

Competitiveness The U.S. is losing its leadership position in science,

technology, engineering, and mathematics. (Rising Above the Gathering Storm)

By 2010, more than 90% of all scientists and engineers will be living in Asia. (Tapping America’s Potential, Business Roundtable)

Decreasing numbers of students are majoring in mathematical sciences. (CUPM Report, MAA, 2004)

Mathematics is a key to improving performance in science

New Demands for Mathematics The challenge of globalization and the rise of

technology (The World is Flat) The need to extend beyond the traditional

curriculum leading to calculus (MAA Curriculum Foundations)

Statistics is increasingly important (GAISE) The business community is calling for ability to

solve problems, communicate, and learn in teams (Ready or Not)

Where Should We Be Heading?

NCTM’s Next Effort “Focus on the High School Curriculum” Issues:

Increasing options for success Ensuring equity Promoting reasoning Important mathematics Technology A coherent program

Project Model

A core document: 40-60 pages Shorter versions for particular audiences

Policymakers Administrators Parents and community

Additional products for teachers

Thoughts

How can this effort be more effective?

State Level

What are the ramifications for state high school standards?

What are other implications for state policy?

Personal Connections

Teacher Educators What can do differently to prepare students

to teach high school? Teachers

What can we do differently in classrooms?