A.  Mathematica Sequence (MMC) ( 2 sem. hrs.):

Module 3.   Using Mathematica in Mathematics Instruction.
Brief Description: This module is designed for mathematics teachers at the 9 - 14 grade levels who are beginners with Mathematica and who want to learn to use this software package to create classroom resources, computer demonstrations, and interactive student lessons for their mathematics classes. This module is available for both Version 4.0 and Version 5.0 of Mathematica. Credit: 2 grad. sem. hrs.

B.  Calculus Mathematica and Computers Sequence (CMC) (1 sem. hr. total):

Module 1.  Calculus&Mathematica for Mathematics Teachers.
Brief Description:  Calculus&Mathematica is a university credit, modern calculus course based on an interactive, electronic text. This module introduces teachers to the content and pedagogy of the Calculus&Mathematica course. This module is suitable for any mathematics teacher interested in teaching, or simply learning more about, the Calculus&Mathematica course. Credit: 1 grad. sem. hr.

C.  Dynamic Geometry Sequence (DGS) (2 sem. hrs. total):

Module 4. Using the Geometer's SketchPad
Brief Description: The Geometer's SketchPad is an electronic ruler and compass for today's technological geometry classroom. This module is designed to familiarize teachers with this new tool through interactive tutorials and then to demonstrate how it can be used effectively in the teaching of geometry. A final classroom project based on Geometer's SketchPad is required. Credit: 1 grad. sem. hr.

Module 10: Dynamic Geometry with Geometer's SketchPad
Brief Description: The purpose of this module is to show teachers how the dynamic features of geometry software such as the Geometer's SketchPad can be used in geometry courses to illustrate theorems, to foster experimentation, to support problem solving, and to encourage conjecture. Teachers will also learn new geometry content closely related to the geometry that is taught in high school. Prerequisite: Module 4 or facility with a geometry sketchware package such as Geometer's SketchPad. Credit: 1 grad. sem. hr.

D.  Calculator-based instruction sequence (CIS) (2 sem. hrs. total):

Module 5. Algebra Through Modeling with  the TI-82 Graphing Calculator.
Brief Description: This module is designed to familiarize teachers with an innovative advanced algebra course.  This course presents algebra from the perspective of modeling and data analysis using the basic algebraic functions and a graphing calculator with data analysis capabilities such as those of any of the TI-83 family of graphing calculators including the TI-82, 83, 83+ and 83+ Silver Edition . This new approach will be useful in high school and college for students who have completed two years of algebra but are not ready for pre-calculus. It reviews algebra without repeating earlier course work, and it clearly demonstrates the importance of algebra to the solution of real world problems. Credit: 1 grad. sem. hr.

Module 11: Discrete Dynamical Systems for Mathematics Teachers.
Brief Description: Discrete dynamical systems can be used to model and analyze many real-world problems including population growth, compound interest and annuities, radioactive decay, pollution, and drug dosages. Such problems are usually delayed until calculus; however, the discrete dynamical systems approach uses only advanced algebra.   Teachers who complete this module will be able analyze a variety discrete dynamical systems using the TI-82 or TI-83 calculators (or any other calculator with similar graphing and sequence capabilities). They will also learn how to integrate this material into advanced algebra, precalculus, and calculus courses. Credit: 1 grad. sem. hr.

E.  Teaching Statistics in High School (TS) ( 4 sem. hrs.):

Module 6.  Teaching Statistics in High School
Brief Description: This is a Web-based, technology-intensive short course developed jointly by the U of I Departments of Statistics and Curriculum & Instruction. The topics to be covered will include: descriptive statistics (central tendency and variation); expectation; probability; regression and data collection . Both the content of statistics and effective instructional strategies will be dealt with--reflecting the NCTM Standards for curriculum and for teaching. This module is composed of the following five units:

• Unit 1: Exploring Data: Tables and Graphs
• Unit 2: Summarizing Data: Centers and Spreads
• Unit 3: Linear Relationships: Regression and Correlation
• Unit 4: Probability and Expected Value
• Unit 5: Probability Distributions and Random Sampling

Participants will complete one unit at a time, but must complete all five units to earn credit for the module. Credit: 4 grad. sem. hrs.

F.  Teaching AP Statistics Part II: Inferential Statistics (TS2) ( 4 sem. hrs.):

Module 6B.  Teaching AP Statistics Part II: Inferential Statisticsl
Brief Description: This is a web-based, technology-intensive course for in-service teachers wishing to update and/or review topics in descriptive statistics for AP Statistics courses at the high school level. The objective of this course module is to aid high school educators in teaching the second semester of a full year course of AP Statistics. Together with the companion course Module 6 Part I, these two courses provide the necessary background in statistics to teach a full-year high school course in AP Statistics.

The primary focus is teaching statistics and improving the quality of instruction by using assistive technology. Both the content of statistics and effective instructional strategies reflect the NCTM Standards for curriculum and for teaching and the College Board AP Statistics course description.

This module is composed of the following eight units

• Unit 1: Introduction and Teacher's Perspective
• Unit 2: Central Limit Theorem
• Unit 3: Estimates (Confidence Intervals)
• Unit 4: Hypothesis Testing with One Sample
• Unit 5: Hypothesis Testing with Two Samples
• Unit 6: Tests of Correlation and Regression
• Unit 7: Multinomial Experiments; Contingency Tables
• Unit 8: ANOVA

Enrollees will complete one unit at a time, but must complete all eight units to earn credit for this module. Credit: 4 grad. sem. hrs.

Module 16.  Using Fathom in the Classroom
Brief Description: Fathom is a software package designed to enrich your mathematics curriculum, allowing you to use technology to more efficiently examine data and the statistical process that are commonly taught in middle grade and high school mathematics classes. The software provides ways of dealing with meaningful data sets, allowing the user to easily examine the data as a collection, explore it graphically, look at it tabular form, and to search for correlations within the data set. The data examined can be data that was generated in the classroom, data from data sets that are supplied with Fathom, and by the use of drag-and-drop techniques even work with data taken directly off of the Internet. Fathom also is well designed to handle sampling and simulation activates that are commonly used in the middle school through high school mathematics curriculum.

This module is designed to familiarize teachers with this new tool through interactive tutorials and then to demonstrate how it can be used effectively in middle grade math classes through advanced level high school statistic classes. Credit:1 grad. sem. hr.

H.  Calculus Refresher for Teachers (CRT) ( 3 sem. hrs.):

Module 9.  Calculus Refresher for Teachers
Brief Description: This module is a calculus refresher course designed for math teachers. It covers a review of the topics covered in differential and integral calculus with an emphasis on reform . The course covers the material using the content and pedagogy of Calculus&Mathematica.

Calculus&Mathematica is a modern calculus course based on an interactive, electronic text. It is currently offered on campus at a number of universities, and by distance education at many high schools. Students in this course will review first semester calculus and submit a final project based on teaching calculus and the NCTM standards. Credit: 3 grad. sem. hrs.

I.  Measurements in Geometry (MG) ( 1 sem. hrs.):

Module 15.  Geometric Measurement Formulas - A Teacher's Perspective
Brief Description: This module provides a systematic and coherent development of the measurement formulas for computing distances, area and volume of geometric figures in the plane and in space including all of the formulas discussed in high school geometry. It also discusses a variety of problems and results in plane and solid geometry that relate to distance, area and volume as well as the rich history of geometric measurements.

The required textbook for this module is Mathematics For High School Teachers by Usiskin, Peressini, Marchisotto and Stanley. The corresponding content for this module is drawn from Chapters 8 and 10 of the text and the module is written so that it can be completed without reference to other chapters of the book.

This module is divided into the following units:

• Unit 1: Measuring distance in ordinary and unusual ways.
• Unit 2: Understanding the area formulas of plane geometry.
• Unit 3: Understanding the volume and surface area formulas of solid geometry.

These units deal with topics that are either in the typical high school geometry curriculum or are closely related to topics taught high school geometry. However, these topics are treated from a more advanced standpoint that assumes some of the collegiate background that prospective high school mathematics teachers take as undergraduates. This module complements the textbook treatment of this content with web-based resources and dynamic geometric sketches that are not available in any print textbook. Credit: 1 grad. sem. hr.

J.  The Algebra of Geometric Constructions (AGC) ( 2 sem. hrs.):

Module 13.  Compass and Straightedge Constructions in Geometry
Brief Description: This module is designed to familiarize teachers with the close connection that exists between compass and straightedge constructions and the real number system. Most geometry teachers are aware that certain geometric constructions such as trisecting certain angles or squaring a circle (ie. constructing a square whose area is equal to that of a given circle) are known to be impossible, but they may not know why. This module explains the relationship between geometric constructions and a set of real numbers called the constructible real numbers, and uses this relationship to decide the possibility or impossibility of certain geometric constructions. The methods used in this module avoid the intricate machinery that is sometimes used in discuusing these problems in college level courses in abstract algebra.

This module is divided into the following units:

• Unit 1: Discovering geometry through geometric constructions.
• Unit 2: Geometric constructions and the real number system.

Although these units deal with topics directly taught high school mathematics, their content is not intended for use directly in the high school classroom. However, teachers will find that the content of these units directly informs and influences their teaching of geometry in the high school classroom.

Credit: 2 grad. sem. hrs.