Modeling and Data Analysis (MODEL)
The T3 MODEL Institute is a week-long professional development program for secondary mathematics teachers who have recently taught Algebra 2 or Precalculus. The institute will focus on data analysis and mathematical modeling. Institute participants will explore ways to incorporate data analysis and mathematical modeling into secondary mathematics classes and to use these themes to motivate the study of functions, trigonometry, and matrices. Participants will take part in hands-on activities that reinforce effective classroom use of technology. The goal of the program is to instruct teachers in new and innovative ways to effectively teach contemporary mathematics using technology in the spirit of NCTM's Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and Professional Teaching Standards (NCTM 1991).
The objectives of the T3 MODEL Institute are:
- To provide opportunities for teachers to experience an exploration/investigation mode of learning secondary mathematics so that they can be better prepared to incorporate these methods into their own teaching.
- To study techniques of data analysis and the use of data analysis as motivation for the study of other topics.
- To use techniques of mathematical modeling to solve real world problems, particularly those that are extended and might incorporate many mathematical ideas in their solution.
- To develop teachers' familiarity and facility with the graphing calculator.
- To help teachers find effective ways to use the graphing calculator to improve the teaching and learning of mathematics.
- To share ideas regarding assessment techniques.
Participants in the T3 MODEL Institute should be inservice secondary mathematics teachers in grades 9 through 12 who have recent experience teaching Algebra 2 or Precalculus. Participants should be interested in using data analysis and mathematics modeling to motivate the study of secondary mathematics.
Day 1: Introduction to Data Analysis and Modeling
Overview of the modeling process; median-median line and least squares line; data gathering and curve fitting; assessment ideas.
Day 2: Using Functions to Model Data
Introduction to toolkit functions; transformations of functions; calculator graphs; extended problems that incorporate modeling and data analysis; re-expression to linearize data; introduction to the CBL.
Day 3: Using Functions as Models
Modeling exponential data calculator techniques' underlying mathematics, related CBL activities; modeling sound data; parametric equations and predator/prey models to motivate the unit circle in trigonometry.
Day 4: Iteration and Modeling
Data modeled by power functions; using recursion and the calculator sequence mode to solve problems; an extended modeling problem; assessment issues.
Day 5: Matrices as Mathematical Models
Applications of matrix multiplication; Markov chains; Leslie Model of Age - Specific population growth.