# Mathematical Sciences

## 2012

**Active Classroom Lesson Modules – Math**

Lisa Green, Scott McDaniel, Ginger Rowell

## 2011

**Dynamic Statistics Technology Project**

Jeremy Stayer

## 2007

**Demonstrating the ACSI 4240, 4360, STAT 4200, Stat 4230**

Rajesh Barnwel

## 2006

**Applets for Aiding the Instruction of Advanced Statistics**

Basic and Applied Sciences

Lisa Bloomer-Green

lbgreen@mtsu.edu

A JAVA applet to demonstrate the concept of maximum likelihood estimation was designed. After a compiler was downloaded and installed, the components of the applet were written. Some of the components work, others are still in the debugging stage. A similar demonstration was implemented in Microsoft EXCEL, and a worksheet for students was written.

Applets for Aiding the Instruction of Advanced Statistics: ITD Grant Final Report

I was the recipient of a Spring 2006 Instructional Technologies Development Grant that gave me release time to work on creating applets for the teaching of advanced statistical concepts. An applet is a short computer program usually embedded in a web page that performs a simple task. In this case, the applet will demonstrate the concepts behind maximum likelihood estimation by generating random variables and displaying the corresponding likelihood function. Buttons and pull-down menus would allow for important numbers to be changed and actions to be initiated or repeated.

Maximum likelihood estimation is a central concept in a mathematical statistics class. It is the most common method of selecting a statistic to address a given problem. A typical mathematical statistics course will show that the sample mean is the maximum likelihood estimator for the problem of estimating the mean of a set of normally distributed random variables. Similarly, this method is used to find estimators for other parameters under other assumptions. However, students typically learn to perform the calculations involved but do not understand the theory behind them. An applet can demonstrate how the maximum likelihood function is related to the data and to the assumptions made in each problem. Students tend not to understand that the function itself is random and therefore the maximum of the function is random. The applet can demonstrate this because with every click of the "repeat" button, a new function appears. An applet that allows the sample size to change will allow students to observe how the estimator gets more accurate as more data are collected.

I have not finished writing and debugging the applet. Because the programming was more difficult than I had anticipated, I implemented a similar idea in Microsoft Excel. This spreadsheet, along with a worksheet I also wrote, can demonstrate the same ideas that the applet could. However, one downside of the spreadsheet is that the student can too easily change the values in it, making it no longer accurate. Another is that it can only be run on a computer with the correct software, but since a large proportion of computers do have Excel, this is a minor problem.

Progress on Creating Applet

I installed a compiler for JAVA on my computers and figured out how to get programs to compile. This was surprisingly difficult. It was easy to get small programs ("Hello World") to compile, but larger programs that consisted of many files would not compile. After asking a student who happened to be a JAVA programmer at his work, I found out that the files that contain JAVA code must be in a particular file structure and be named in specific ways for the compiler to recognize them.

I modified a program that I found on the Sun web site, which has a JAVA tutorial, to create a program that opens a window and graphs a function. Then I modified another program, found on a web site containing several statistical applets, to be able to embed an applet in a web page, open a window, and include buttons and menus in this window. <p>I wrote a modification of the same program to create a histogram and graph it in the window. Unfortunately this compiles and runs, showing the axes for the graph, but does not populate the graph with bars. I am still debugging this.

I wrote a component that chooses data randomly with a normal distribution. However, while this component compiles, I have not been able to display the data to ensure that the component is working correctly. I also have written a component that will graph the likelihood function for this data. It compiles, but I have not been able to verify that it works correctly.

## 2005

Basic and Applied Sciences

Curtis Church

cchurch@mtsu.edu

Basic and Applied Sciences

Ginger Holmes-Rowell

rowell@mtsu.edu

Basic and Applied Sciences

Ping Zhang

pzhang@mtsu.edu

## 2003

**Implementing The Geometer's Sketchpad in the Geometry Curriculum**

Basic and Applied Science

Rebecca Zijlstra

zijlstra@mtsu.edu

Every mathematics major at MTSU who is seeking licensure to teach mathematics at the secondary school level is required by the Tennessee State Department of Education to take a geometry course (MATH 3070 - College Geometry) as part of their major course work. A recommendation of the Southern Association of Colleges and Schools as well as the National Council of Teachers of Mathematics is that appropriate technology be a component of this course. The Geometer's Sketchpad would be such a technology that would allow the student to become more actively engaged in the learning process through individual and cooperative group learning activities centered around the computer as a problem solving tool. The Geometer's Sketchpad is an interactive geometry software that enhances the learning of geometry for the middle grades through college level learner. As students learn geometry through their active involvement with The Geometer's Sketchpad, they are provided opportunities for discovery-based learning through the creation and manipulation of geometric shapes on the computer. Students experiment with geometrical ideas in an intuitive and dynamic way leading to more widespread understanding of geometry than is possible with traditional tools such as pencil-and-paper or compass and straightedge. The Sketchpad software stimulates these future teachers to explore problem posing and problem solving in geometry. As a dynamic software, Sketchpad allows the student the opportunity to investigate relationships, discover new connections, and reason inductively by drawing generalizations from particular examples. It encourages a process of discovery in which students first visualize and analyze a problem, and then make conjectures before attempting a proof. Without technology, this powerful visualization of mathematical theory would not be possible.

The purpose of the project was to implement and adapt existing technology in the geometry curriculum, specifically the course MATH 3070 College Geometry. Students in this course used The Geometer's Sketchpad to engage in discovery-based learning through the creation and manipulation of geometric shapes on the computer. As a result, they become more actively engaged in the learning process through individual and cooperative group learning activities centered around the computer as a problem solving tool. The project would not have been possible without the support of the Instructional Technologies Development committee and I wish to thank them for funding this proposal. The funded work has greatly helped to enhance and improve the learning of geometry by the mathematics major in the Department of Mathematical Sciences. The goals proposed and the outcomes are addressed below. Support procedures that could significantly affect existing courses MATH 3070 -College Geometry has a direct tie-in with MATH 3330 -Teaching Mathematics in Grades 9-12, as all students who take MATH 3070 also take MATH 3330, often times concurrently. Mathematics educators teaching MATH 3330 require students to teach a geometry lesson to high school students in surrounding counties that incorporate The Geometer's Sketchpad through the Satellite Video-Conference Center on the MTSU campus. The solid foundation in geometry in combination with familiarity with Sketchpad formed a basis for success in the corresponding MATH 3330 course. Students who had in-depth exposure to Sketchpad through MATH 3070 were able to concentrate on the mathematical pedagogy aspect of MATH 3330. More discussion needs to be held concerning MATH 3070 as either a pre- or co-requisite of the MATH 3330 course. Offer a more flexible approach to instruction that is better adapted to individual capacities and needs of students. Since the Sketchpad software was part of the required materials for the course, students worked on laboratory activities outside of the classroom, usually off campus and emailed results directly to the instructor. As a result of being able to review student's work and offer immediate feedback, the time spent by the student on the course and active involvement in the learning of geometry was increased. One-third of the way into the course, every student was asked to evaluate the use of Sketchpad and to indicate if they preferred a reduction in attention to the utilization of the software. Every student indicated that they wished to continue with the Sketchpad component of the course and asked for more assignments that used it. Some students started using the software for assignments even when it was not a requirement.

## 2002

**Web-based Regression Tutorial Assessment**

Basic and Applied Science

Ginger H. Rowell

rowell@mtsu.edu

The purpose of this project is to use the content of the Web-based Regression Tutorials Project during the fall 2002 semester in a Regressional Analysis class and to assess their effectiveness for student learning and their potential for being used in future on-line versions of this course. Some tutorials will also be used as a component of an introductory statistics course.

During the Fall 2002 semester, my ITD grant focused on the assessment phase of the development of a comprehensive web called "Web-based Regression Tutorials." This web has tutorials for learning and/or reviewing the statistical methods associated with Regression Analysis and is located at www.mtsu.edu/~stats (select "Regression Analysis"). This web provides instruction for the very beginner and goes through material that is used in graduate level statistics courses. The tutorials also provide detailed instructions for completing the procedures or the analysis using MS Excel and the statistical software Minitab as well as complete information for understanding the concepts and interpreting the results. During the Fall 2002 semester, I was able to meet the assessment objectives described in the original proposal.

Conclusion: I am pleased with the Web-based Regression Tutorial website as a very strong teaching supplement to the STAT 4360/5360, Regression Analysis class. Though I thought it would be good for a distance learning course, based on my students' comments and testing resutls during the Fall 2002 semester, I think the complexity of the material is such that a complete on-line course is not a good idea for our students at MTSU. However, I can envision these tutorials being used with a partial on-line course. There are students who would like to take a course like this but cannot because of their work schedule. Perhaps a mix of web-based and Saturday intensive-study classes would be a good combination for an alternative approach for this course. I will continue to use these tutorials for workshops for high school and middle school teachers and in many of the probability and statistics courses at MTSU. I will also continue to explore new venues for using these tutorials at least as a partial distance education course.

## 2001

**Web-based Regression Tutorials**

Basic and Applied Science

Ginger Holmes Rowell

rowell@mtsu.edu

During the Spring 2001 semester, I received an "Instructional Technologies Development Grant" for one course release to work on the Web-based Regression Tutorials project. This project is a continuation of work started during the summer of 2001 when I was a NASA/ASEE Summer Faculty Fellow at Marshall Space Flight Center's (MSFC) Engineering Cost Office (ECO). One of my tasks at MSFC was to provide training for the ECO employees to learn more about regression analysis and the new software application, Minitab, that they had recently purchased. Regression Analysis is a statistical method used by the ECO to predict cost of space flight vehicles. Since it was difficult to coordinate people's schedules and many people were frequently out of town on travel, we decided to make the tutorials web-based.

I was pleased to receive an "Instructional technologies Development Grant" during the spring semester to continue work on this project. Though I have not received any extra release time or compensation, I have continued work on the project this summer and will continue the work this fall. The expected completion date of the existing outline of tutorials is the end of December 2001.

The highlights of the project work are listed below:

- Set up the MTSU website where the Regression Tutorials would be located.
- Transferred the existing files from the format used for the MSFC Macintosh web server to MTSU's server.
- Added and corrected website content.
- Presented "Web-based Regression Tutorials: A Project Overview" at the Department of Mathematical Sciences Presentation which was open to the MTSU community.
- Wrote and received a grant for approximately $15,000 from NASA's MSFC ECO to support one graduate and three undergraduate students to work on this project in the Fall 2001 (and some summer work).
- Wrote and won a MTSU grant for 25 Student Versions of Minitab for the Mathematics Department Computer Laboratory. This is the statistical analysis software for which the tutorials provide explicit instructions.
- Tested some "Introduction to MS Excel Lesson" in my courses during Spring 2001.
- Introduction to Regression for High School Algebra teachers at two workshops for Dr. Mary Martin (one in Rutherford County and another in Warren County). I will use a modification of this for a video conference for teachers in October.

**Web-based Supplementary Instruction for the Use of the T1-83 Graphing Calculator**

Basic and Applied Science

Joan Raines

jraines@mtsu.edu

The Instructional Technologies Development Grant has allowed me to create a web site that gives students an additional tool to enhance their understanding of the use of the TI?83 graphing calculator. This project was started as a way to assist students who needed additional help, who missed class, or who took a class by correspondence. My objective was to create a site that would give step?by?step keystroke instructions for using the graphing calculator. This objective was accomplished and the site was put into use during the Spring 2001 semester. The site provides off-campus and after-hours access to instruction.

I have received very positive feedback from students and teachers. Students feel the site makes using the calculator less frustrating, is a helpful supplement to the textbook, and is a useful reference outside of class. They thought the instructions were clear, concise, easy to follow, and that the site should be maintained from semester to semester. Instructors teaching in a classroom equipped with the appropriate technology access the site during class instruction and refer students to it for further assistance. <p>From the feedback I received from students, I am now in the process of updating/revising some of the pages on the site. These pages will include calculator window screens and more example problems. The site can be accessed at http://www.mtsu.edu/~math141 I would like to thank the committee for the opportunity to create this web site.

## 1999

**Enriching Instruction Through Technology: Implementing the Geometer's Sketchpad into
the Math 201 Curriculum**

Basic and Applied Sciences

Leslie N. Aspirwall

Leslie used technology to revise, update, and implement new materials for use with the MATH 201 course using Geometer's Sketchpad. He continued work started in the Fall of 1998.

People tend to see new technology in terms of the past--originally, the automobile was a horseless carriage and the radio a talking box. When replacing hand methods by machine methods, you do not do the same job. Hand computing is not the same as machine computing. When the computer revolution is finally over, education will not look like it does now. (Selden, A., & Selden, J, 1993, p. 12)

Introduction

Calls for reform in school mathematics have suggested that new methodologies are needed in teacher education programs. All industrialized countries have experienced shifts from industrial to information societies, shifts that have transformed both the nature of mathematics that students must encounter in their learning environments and the concepts they must learn if they are to be self-fulfilled, productive citizens in the twenty-first century. These social and economic shifts can be largely attributed to the availability of low-cost calculators, computers, and other technology. This project started as a desire to change the learning environment in MATH 201 - Geometry for Elementary School Teachers to more actively engage students in the learning process through individual and cooperative group learning activities centered around the computer as a problem solving tool.

An Instructional Technologies Development Grant from the Office of Instructional Technologies has supported the development of curricular materials that introduce a new computer technology into the MATH 201 curriculum. As part of the project, a series of lesson plans have been developed, piloted, and evaluated that enable the use of The Geometer's Sketchpad in MATH 201 - Geometry for Elementary School Teachers. This dramatically alters the course as students learn through active involvement with The Geometer's Sketchpad. Such engagement by students provides opportunities for discovery-based learning through the creation and manipulation of geometric shapes on the computer. Students experiment with geometrical ideas in an intuitive and dynamic way leading to more widespread understanding of geometry than is possible with pencil-and-paper alone. The Geometer's Sketchpad stimulates these future teachers to explore problem posing and solving in geometry and offers students a new window into geometry. Moreover, The Geometer's Sketchpad has unique advantages: it offers each student a starting point in geometry by connecting with something the student already knows. A central idea of The Geometer's Sketchpad is the idea of. After relationships have been determined, say among points, lines, and shapes, The Geometer's Sketchpad preserves all these relationships even when one of the basic components is dragged, or moved about on the screen by a mouse. For example, a rectangle with diagonals drawn can dragged so that its length is increased. The student can conjecture and then experiment to determine what happens to the diagonals of a rectangle when its length is distorted. Students can investigate relationships, discover new connections, and reason inductively by generalizing from particular examples. Thus, students can generate hypotheses about geometric correlations instead of developing into passive receivers of geometric facts.

Mathematics teacher educators have an incumbent responsibility to utilize computers in their teaching, since prospective elementary school mathematics teachers, as they begin their own teaching practices, model the instruction they receive as undergraduates in mathematics education courses.

## 1998

**Enriching Instruction Through Technology: Implementing the Geometer's Sketchpad into
the Math 201 Curriculum**

Basic and Applied Sciences

Leslie N. Aspirwall

laspinwa@mtsu.edu

Leslie used this grant time to use technology to revise, update, and implement new materials for use with the MATH 201 course using Geometer's Sketchpad.