ED359 Research on Math Education

1. ED359 Research on Math Education Final Project A research on case studies on the use of video-based instruction for the teaching and learning of mathematics By Yeong Haur Kok Stanford University, Fall 2006 School of Education

2. Overview The purpose of the study is to provide an overview on the issues pertaining to the use of video-based instruction for the teaching and learning of mathematics. It does this by: • Reviewing existing literature • Reviewing three video-based projects Hopes to: • Highlight reasons and potential for use of videos in math • Share important design issues • Share findings of effects of such instruction on students’ learning Stanford University, Fall 2006 School of Education

3. Introduction • Potential of video as educational tool • Videos provide a highly efficient way of conveying information • Developments in computer animation,visualization and computer software are used to video material with mathematical content • Provides opportunities to design and deliver a rich learning experience Stanford University, Fall 2006 School of Education

4. Current Situation • Use of video for math is mainly focused on teachers • Several video-based learning and resources designed for teachers (e.g. PBS TeacherSource) • Not many cases where video or video-based instruction were used for students’ learning of math Stanford University, Fall 2006 School of Education

5. Case Studies • Project Mathematics! • A video-based instructional project designed for teaching and learning math • Launched by Tom Apostol and Jim Blinn from CalTech in ’87 • Goal was to attract young people to math through high quality instructional videos that show math to be understandable, exciting and applicable to daily life • By 2000, project had produced ten videotapes that were used in high school and community college classrooms; enthusiastically received by teachers and nationwide • Won a dozen prestigious awards for excellence in educational video • Distributed in Australia, Canada, Denmark, U.K.; translated into Hebrew, Portuguese, French and Spanish Stanford University, Fall 2006 School of Education

6. Case Studies • Project Mathematics! • Each module consists of a videotape (not exceeding 30 min) and a workbook/study guide • Workbook is divided into sections the same way the video is • Titles produced to date are: • The Theorem of Pythagoras • The Story of Pi • Similarity • Polynomials • Sines and Cosines • Others… Stanford University, Fall 2006 School of Education

7. Case Studies • Project Mathematics! • Uses computer animation to explain concepts • Provide interesting context (e.g. tunnel of samos) Stanford University, Fall 2006 School of Education

8. Case Studies • Touching Soap Films • Popular, computer-generated educational video on minimal surfaces • A soap film is physically similar to a piece of rubber surface which tries to contract itself under surface tension to a surface with least area • Surfaces with least area appear as optimal solutions of many problems • Video uses an animated character Kalle and his exploration to explain world of soap films • Computer-generated animations Stanford University, Fall 2006 School of Education

9. Case Studies • Touching Soap Films • Under guidance of an old professor, Kalle gets fascinating insights to properties and application of soap films • While video is good, difficult to use as educational device without supplemental explanation • Package comes with video and booklet; easy to incorporate into course on applied math Stanford University, Fall 2006 School of Education

10. Case Studies • Encore’s Vacation (Taiwan) • Full title is “Mathematics in Life Series (I): Encore’s Vacation” • Based on “The Jasper Series”, a program of anchored instruction developed by the Cognition & Technology Group at Vanderbilt (CTGV) to teach mathematics • Theory-based design principles: • Video-based format • Narrative with realistic problems (rather than a video lecture), • Embedded data design • Problem complexity • Links across the curriculum • Video materials serve as “anchors” (macro-contexts) for all subsequent learning and instruction Stanford University, Fall 2006 School of Education

11. Reasons & Potential • Why video? • Visualization • Main difficulty in communication of math concepts: abstraction • Abstraction allows generalization of ideas and results • However, it has also made Math a difficult subject to teach and study • Most students lose motivation easily when they cannot see, touch or try what they are studying • Need to make the inverse way from abstraction to concrete concepts • Hence, concretization of ideas is very important in learning mathematics • Visualization is one important way of concretization of mathematical ideas Stanford University, Fall 2006 School of Education

12. Reasons & Potential • Why video? • Self-Paced • Allows users to navigate, explore and reflect on the lessons at their own pace • Allows learning to be individualized • Interactivity • Simple visualization of a video not enough • Learners need to interact with the instructional modules after watching video • Problem-Solving • Video-based instruction a suitable medium for providing and incorporating problem-solving opportunities • Real-world context & application Stanford University, Fall 2006 School of Education

13. Design Issues • Situated Learning • Highlighted as a guiding principle in the design of instruction in the case studies • Video and multimedia technology makes it possible to provide life-like inquiry situations and the connection of knowledge with daily life • Scaffolding & Zone of Proximal Development • System designed to encourage independent solution of problems as much as possible, but at the same time, sensitive to students’ needs for support and assistance • Experiential Cognition • Stressing the role of the learner who constructs, sense-makes and organizes his/her knowledge by having an experience in that relevant domain of knowledge Stanford University, Fall 2006 School of Education

14. Design Issues • Reflective Cognition • That of comparison and contrast, of thought, of decision making • Leads to new ideas and novel responses • To internalize the message, video must afford the time for reflection Stanford University, Fall 2006 School of Education

15. Effect on Students’ Learning * - Divided into three groups of high, medium and low ability based on their math and science score Stanford University, Fall 2006 School of Education

16. Effect on Students’ Learning • Performance • Improvements in performance (pretest & post-test) • Students of video-based instruction learned at least as well as students attending traditional classrooms learning • Attitude/Motivation • Positive influence • Students recognize that it was possible for them to learn mathematics • Felt more positive about, interested in and less anxious toward mathematics Stanford University, Fall 2006 School of Education