The Assessment of Technology in a Multivariable Calculus Course

1. The Assessment of Technology in a Multivariable Calculus Course The Characterization and Evaluation of CAS Assisted Teaching Practices by Zsolt Lavicza University of Michigan The Characterization and Evaluation of CAS Assisted Teaching Practices

2. Outline • Give an overview of the use of technology in the multivariariate calculus course • Provide a summary of the research in the past year • Give an example from the data • Outline plans for future investigations The Characterization and Evaluation of CAS Assisted Teaching Practices

3. The goals of the project Develop instruments to evaluate teaching and learning in undergraduate mathematics courses with particular attention to technology use • Current effort: look at teaching in multivariate calculus, evaluate instruments to characterize it • Next: build on this with classroom experiments to measure effectiveness of teaching, determine how to improve it The Characterization and Evaluation of CAS Assisted Teaching Practices

4. The structure of the course Math215 3D animations prepared to help instructors to visualize math concepts in lectures GSIs introduce lab topics, students may work on labs in class (10-40 minutes) • Students biweekly submit assignments prepared with Maple in 3-4 member groups. • Topics: • Project 1: Space Curves and Parametric Surfaces • Project 2: Graphs and Level Curves • Project 3: Gradients and Rates of Change • Project 4: Double Integrals and Polar Coordinates • Project 5: Circulation and Curl Students solve 5-8 problems closely aligned with the lecture and submit their solution on the web. (weekly/bi-weekly) 3 lectures / week 1 Recitation Outside of class Maple Lab Projects Maple Demos Lab Project practice Web Homework Technology The Characterization and Evaluation of CAS Assisted Teaching Practices

5. Summary of research in the past year What did students find helpful regarding technology? CAS helps to visualize math concepts both in lectures and labs CAS is helpful to compute and check results Helps to be prepared for exams What did students find helpful regarding technology? Takes way too much time to complete lab projects Maple is slow and incompatible Students did not receive enough tutorials to use Maple Spring/Summer 2003 Fall 2003 Winter 2004 • Study students’ perception/attitudes toward technology in Math215 • Instruments • Surveys • Interviews • Findings • Students found Web homework most helpful for their learning • Students value Maple demos in lectures • Students found Maple Labs helpful, but long and tedious • Study teaching practices with Maple demos in lectures • Instruments • Video records • Instructor logs • Interviews • Expected findings • Understand different teaching methods with Maple • Characterization of these methods • Seminar of Teaching Mathematics inspired the project • Setting goals and developing evaluation instruments • Initial goal: • Understand the effects of computer visualization on students’ • understanding of math concepts • Altered goals for the Fall semester • Measure students’ perceptions and attitudes (and how they change) • toward technology in Math215 The Characterization and Evaluation of CAS Assisted Teaching Practices

6. Characterization of Teaching Practices • Data • Video records of 5 instructors • Instructor Logs • Interviews • Identify patterns in the use of Maple Demos • Understand current teaching methods with Maple Demos • Pinpoint strength and weaknesses in their use and in the demos themselves • Descriptive analysis The Characterization and Evaluation of CAS Assisted Teaching Practices

7. Example from the data • Previous material: vectors, 3-space, vector functions, derivatives of functions of many variables • Topic: Introduction to double integrals Clip • Instructor reviews double integrals from previous lecture, illustrates Riemann sums on the board, clarifies notation and defines the double integral • Instructor uses the Maple demo for approximately 30 minutes in his lecture • Lecture is compressed for presentation purposes The Characterization and Evaluation of CAS Assisted Teaching Practices

8. Furbini’s Theorem Double Integrals Maple Demos in the clip The Characterization and Evaluation of CAS Assisted Teaching Practices

9. Introduction to Double Integrals The Characterization and Evaluation of CAS Assisted Teaching Practices

10. Data Analysis • Segmentation of Clips • Codes are under development • Coding • The role of Maple demos in lectures • Instructor references to Maple demos • Technology problems that instructors encounter with and their solutions • Maple as a software tool • Students involvement in discussions of Maple demos • References of Maple use outside of lectures • Problems with the Demos The Characterization and Evaluation of CAS Assisted Teaching Practices

11. Hoping to get from this stage • Better understand the use of CAS in this course • The description of teaching will provide us assistance to develop further evaluation tools • Help to develop initial teaching experiments The Characterization and Evaluation of CAS Assisted Teaching Practices

12. Where we go from here Summer 2004 2004/2005 • Data analysis and setting directions • Instruments • Developing codes • Segmenting video records • Code and analyze data • Expected findings • Characterization of teaching practices with Maple demos • Development of new instruments • Recommendation for course improvement • Further data collection, implementation of changes, experiments • Using new instruments developed during the summer • Implementation of recommended changes in the course • Preparation for teaching experiments • Possible development of a teacher preparation workshop • Possible extension of the research to other courses • Involvement of other faculty and graduate students • Extension of the project with the assistance of the NSF The Characterization and Evaluation of CAS Assisted Teaching Practices

13. Summary Develop instruments to evaluate teaching and learning in undergraduate mathematics courses with particular attention to technology use • Descriptive analysis • Experimentation with teaching methods • Understanding students’ learning The Characterization and Evaluation of CAS Assisted Teaching Practices

14. Thank you! Questions? The Characterization and Evaluation of CAS Assisted Teaching Practices

15. Another Example The Characterization and Evaluation of CAS Assisted Teaching Practices