High School Mathematics: Where Are We Headed?

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High School Mathematics Where Are We Headed?

• W. Gary Martin
• Auburn University

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Agenda

• We will address the following questions related
  to high school mathematics
• How are we doing?
• What do students need?
• Where should we be heading?

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How Are We Doing?
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National Assessment of Educational Progress (NAEP)

• The Nations Report Card
• Given in all subject areas, including
  mathematics.
• Most recently given to grade 12 students in 2005.

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Sample Questions

• Answer the three questions.
• Predict what percent of grade 12 students
  answered it correctly.

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Sample Question 3
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Responses to 3
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Sample Question 17
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Responses to Question 17
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Question 16

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

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Responses to 16
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NAEP Achievement Levels

• Advanced (216)
• Proficient or above (176)
• Basic level or above (141)
• Below basic (lt141)
• (see p. 21)

• 2
• 23
• 61
• 39

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Briefly review the report
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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

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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
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Trends

• The NAEP math assessment hadnt 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.

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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.

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Mathematics Literacy

• ...an individuals 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 individuals life as a
  constructive, concerned, and reflective citizen.
• Thus, PISAs emphasis is on the ability to apply
  a range of knowledge and skills to a variety of
  problems with real-life contexts.

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Sample Problems

• See pp. 8 and 9.

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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

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More Results

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

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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

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What Can We Conclude?
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What Do Students Need?
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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

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NCTMs 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

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Ready or Not Creating a HS Diploma that Counts

• DISCUSS
• Why might they consider the high school diploma
  an issue?
• Read pp. 1-2

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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.

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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!

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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

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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
  Americas 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

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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)

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Where Should We Be Heading?
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NCTMs Next Effort

• Focus on the High School Curriculum
• Issues
• Increasing options for success
• Ensuring equity
• Promoting reasoning
• Important mathematics
• Technology
• A coherent program

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Project Model

• A core document 40-60 pages
• Shorter versions for particular audiences
• Policymakers
• Administrators
• Parents and community
• Additional products for teachers

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Thoughts

• How can this effort be more effective?

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State Level

• What are the ramifications for state high school
  standards?
• What are other implications for state policy?

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Personal Connections

• Teacher Educators
• What can do differently to prepare students to
  teach high school?
• Teachers
• What can we do differently in classrooms?