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CPMP-Tools:

Innovation in Design, Access to,

and Use of Software Tools forHigh School Mathematics

Christian HirschWestern 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/

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Core-Plus MathematicsCore-Plus Mathematics

A Three-Year Core ProgramA Three-Year Core ProgramPlusPlus

A Flexible Fourth-Year CourseA Flexible Fourth-Year Course

a

2nd-yearCourse

3rd-yearCourse

1st-yearCourse

4th-yearCourseOptions

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Core-Plus Mathematics UnitsCore-Plus Mathematics UnitsCourse 1Course 1

Unit 1Unit 1 Patterns of ChangePatterns of ChangeUnit 2Unit 2 Patterns in DataPatterns in DataUnit 3Unit 3 Linear FunctionsLinear FunctionsUnit 4Unit 4 Vertex-Edge GraphsVertex-Edge GraphsUnit 5Unit 5 Exponential Exponential FunctionsFunctionsUnit 6Unit 6 Patterns in ShapePatterns in ShapeUnit 7Unit 7 Quadratic FunctionsQuadratic FunctionsUnit 8Unit 8 Patterns in ChancePatterns in Chance

Course 2Course 2Unit 1Unit 1 Functions, Equations, and Functions, Equations, and SystemsSystemsUnit 2Unit 2 Matrix MethodsMatrix MethodsUnit 3Unit 3 Coordinate MethodsCoordinate MethodsUnit 4Unit 4 Regression and CorrelationRegression and CorrelationUnit 5Unit 5 Nonlinear Functions and Nonlinear Functions and EquationsEquationsUnit 6Unit 6 Network OptimizationNetwork OptimizationUnit 7Unit 7 Trigonometric MethodsTrigonometric MethodsUnit 8Unit 8 Probability DistributionsProbability DistributionsCourse 3Course 3

Unit 1Unit 1 Reasoning and ProofReasoning and ProofUnit 2Unit 2 Inequalities and Linear Inequalities and Linear ProgrammingProgrammingUnit 3Unit 3 Similarity and CongruenceSimilarity and CongruenceUnit 4Unit 4 Samples and VariationSamples and VariationUnit 5Unit 5 Polynomial and Rational Polynomial and Rational FunctionsFunctionsUnit 6Unit 6 Circles and Circular FunctionsCircles and Circular FunctionsUnit 7Unit 7 Recursion and IterationRecursion and IterationUnit 8Unit 8 Inverse FunctionsInverse Functions

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Unit 1Unit 1 Families of FunctionsFamilies of FunctionsUnit 2Unit 2 Vectors and MotionVectors and MotionUnit 3Unit 3 Algebraic Functions and EquationsAlgebraic Functions and EquationsUnit 4Unit 4 Trigonometric Functions and EquationsTrigonometric Functions and EquationsUnit 5Unit 5 Exponential Functions, Logarithms, and Data ModelingExponential Functions, Logarithms, and Data ModelingUnit 6Unit 6 Surfaces and Cross SectionsSurfaces and Cross SectionsUnit 7Unit 7 Concepts of CalculusConcepts of CalculusUnit 8Unit 8 Counting Methods and InductionCounting Methods and Induction

Core-Plus Mathematics UnitsCore-Plus Mathematics Units

Course 4Course 4Preparation for Calculus

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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).

Technology SupportTechnology Support

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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)

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87% of U.S. teens aged 12–17 use the internet.

Of those, 87% have internet access at home.

Teens and Technology, July 27, 2005Pew Internet & American Life Project

Among the survey respondents—Among the survey respondents—

89% of Hispanic youth indicated going online89% of Hispanic youth indicated going online

87% of white youth indicated going online87% of white youth indicated going online

77% of African-American youth indicated going online77% of African-American youth indicated going online

Some Background

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Parent and Teenager Internet Use, Oct. 24, 2007Pew Internet & American Life Project

93% of youth aged 12–17 are online

91% of youth or parents own a computer91% of youth or parents own a computer

76% of online teens report using the 76% of online teens report using the internet internet mostlymostly at home at home

75% of online teens report having 75% of online teens report having broadband broadband internet use at home, and less internet use at home, and less than 1% say school is their only accessthan 1% say school is their only access

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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.

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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.

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Geometry tools include an interactive drawing tool for constructing, measuring, manipulating, and transforming geometric figures, a simple object-oriented 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.

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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.

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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 . . .