CPMP-Tools:
Innovation in Design, Access to,
and Use of Software Tools for
High School Mathematics
Christian Hirsch
Western Michigan University
Kalamazoo, Michigan
USA
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Session Overview
 Overview of the Core-Plus Mathematics Project
 Genesis and design of CPMP-Tools
 Examples
 Participant comments and questions
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The Core-Plus Mathematics Project is a
curriculum research and development project
funded by the National Science Foundation.
www.wmich.edu/cpmp/
3
Core-Plus Mathematics
4th-year
Course
Options
3rd-year
Course
2nd-year
Course
1st-year
Course
A Three-Year Core Program
Plus
A Flexible Fourth-Year Course
4
Core-Plus Mathematics Units
Course 1
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Course 2
Patterns of Change
Patterns in Data
Linear Functions
Vertex-Edge Graphs
Exponential Functions
Patterns in Shape
Quadratic Functions
Patterns in Chance
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Functions, Equations, and Systems
Matrix Methods
Coordinate Methods
Regression and Correlation
Nonlinear Functions and Equations
Network Optimization
Trigonometric Methods
Probability Distributions
Course 3
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Reasoning and Proof
Inequalities and Linear Programming
Similarity and Congruence
Samples and Variation
Polynomial and Rational Functions
Circles and Circular Functions
Recursion and Iteration
Inverse Functions
5
Core-Plus Mathematics Units
Course 4
Preparation for Calculus
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Families of Functions
Vectors and Motion
Algebraic Functions and Equations
Trigonometric Functions and Equations
Exponential Functions, Logarithms, and Data Modeling
Surfaces and Cross Sections
Concepts of Calculus
Counting Methods and Induction
6
Technology Support
In spite of the considerable promise that
computer technology provides for the
improvement of school mathematics and student
learning, the fulfillment of that promise has been
stymied by issues of finance, access, and equity,
among others (Heid 1997, 2005).
7
What would it take for computer tools like
spreadsheets, computer algebra systems (CAS),
and interactive geometry, discrete mathematics,
and statistics tools to become a more integral part
of student learning and work?
• universal availability
• potential to be tailored for
particular purposes
• curricula that incorporate
these tools as an integral
part of the development of
mathematics (Heid 2005)
8
Some Background
87% of U.S. teens aged 12–17 use the internet.
Of those, 87% have internet access at home.
Among the survey respondents—
89% of Hispanic youth indicated going online
87% of white youth indicated going online
77% of African-American youth indicated going online
Teens and Technology, July 27, 2005
Pew Internet & American Life Project
9
93% of youth aged 12–17 are online
91% of youth or parents own a computer
76% of online teens report using the internet
mostly at home
75% of online teens report having broadband
internet use at home, and less than 1% say
school is their only access
Parent and Teenager Internet Use, Oct. 24, 2007
Pew Internet & American Life Project
10
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Design Features
• The software toolkit was developed from the
ground up with specific curriculum applications in
mind.
• Tools were developed for each strand of the
curriculum.
12
Algebra tools include an
electronic spreadsheet and
a computer algebra system
(CAS) that produces tables
and graphs of functions,
manipulates algebraic
expressions, and solves
equations and inequalities.
The functionality of the
CAS and other tools
increases with each
course level.
13
Geometry tools include an
interactive drawing tool for
constructing, measuring,
manipulating, and
transforming geometric
figures, a simple objectoriented programming
language for creating
animation effects,
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and a set of custom tools for
studying geometric models
of physical mechanisms,
tessellations, and special
shapes.
15
Statistics tools include
tools for graphic display
and analysis of univariate
and bivariate data,
simulation of probabilistic
situations
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and mathematical
modeling of quantitative
relationships.
Software includes
pre-loaded data sets
appearing in the student
texts.
17
Discrete Math tools
include tools for
constructing,
manipulating, and
analyzing vertex-edge
graphs and their
representations as
adjacency matrices.
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Design Features
• The software toolkit was developed from the
ground up with specific curriculum applications in
mind.
• Tools were developed for each strand of the
curriculum.
• Tools and their functionality are organized by
course to focus on the intended mathematics and
to reduce the steepness of the learning curve.
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• Tools share similar menu screens and interface
promoting learning transfer from one tool to
another.
• Tools are built using Java WebStart, which
permits safe, easy, and reliable distribution of
software and software updates across different
types of computers.
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• CPMP-Tools is available under a Gnu-public
license at
www.wmich.edu/cpmp/CPMP-Tools
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Now to some examples of
CPMP-Tools use . . .
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