1 CPMP-Tools: Innovation in Design, Access to, and Use of Software Tools for High School Mathematics Christian Hirsch Western Michigan University Kalamazoo, Michigan USA

2 Session Overview  Overview of the Core-Plus Mathematics Project  Genesis and design of CPMP-Tools  Examples  Participant comments and questions

3 The Core-Plus Mathematics Project is a curriculum research and development project funded by the National Science Foundation.

4 Core-Plus Mathematics A Three-Year Core Program Plus A Flexible Fourth-Year Course

5 Core-Plus Mathematics Units Course 1 Unit 1Patterns of Change Unit 2Patterns in Data Unit 3Linear Functions Unit 4Vertex-Edge Graphs Unit 5Exponential Functions Unit 6Patterns in Shape Unit 7Quadratic Functions Unit 8Patterns in Chance Course 2 Unit 1Functions, Equations, and Systems Unit 2Matrix Methods Unit 3Coordinate Methods Unit 4Regression and Correlation Unit 5Nonlinear Functions and Equations Unit 6Network Optimization Unit 7Trigonometric Methods Unit 8Probability Distributions Course 3 Unit 1Reasoning and Proof Unit 2Inequalities and Linear Programming Unit 3Similarity and Congruence Unit 4Samples and Variation Unit 5Polynomial and Rational Functions Unit 6Circles and Circular Functions Unit 7Recursion and Iteration Unit 8Inverse Functions

6 Unit 1Families of Functions Unit 2Vectors and Motion Unit 3Algebraic Functions and Equations Unit 4Trigonometric Functions and Equations Unit 5Exponential Functions, Logarithms, and Data Modeling Unit 6Surfaces and Cross Sections Unit 7Concepts of Calculus Unit 8Counting Methods and Induction Core-Plus Mathematics Units Course 4 Preparation for Calculus

7 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 Support

8 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)

9 87% of U.S. teens aged 12–17 use the internet. Of those, 87% have internet access at home. Teens and Technology, July 27, 2005 Pew Internet & American Life Project 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 Some Background

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

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12 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.

13 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.

14 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,

15 and a set of custom tools for studying geometric models of physical mechanisms, tessellations, and special shapes.

16 Statistics tools include tools for graphic display and analysis of univariate and bivariate data, simulation of probabilistic situations

17 and mathematical modeling of quantitative relationships. Software includes pre-loaded data sets appearing in the student texts.

18 Discrete Math tools include tools for constructing, manipulating, and analyzing vertex-edge graphs and their representations as adjacency matrices.

19 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.

20 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.

21 CPMP-Tools is available under a Gnu-public license at

22 Now to some examples of CPMP-Tools use...