Stanford University, Fall 2006School of Education

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ED359 Research on Math Education

Final ProjectA 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 2006School of Education

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OverviewThe 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 2006School of Education

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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 2006School of Education

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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 2006School of Education

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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 2006School of Education

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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 2006School of Education

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Case Studies• Project Mathematics!

– Uses computer animation to explain concepts

– Provide interesting context (e.g. tunnel of samos)

Stanford University, Fall 2006School of Education

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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 2006School of Education

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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 2006School of Education

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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 2006School of Education

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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 2006School of Education

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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 2006School of Education

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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 2006School of Education

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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 2006School of Education

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Effect on Students’ LearningCase Study Subjects Topic Time Frame

Interactive Videodisc System

(Henderson & Landesman)

Two precalculus/trigonometry classes in high school (36 each)

Preparing for Calculus 8 sub-topics, each took two to four class periods

Computer-Video Instruction

(Henderson, Landesman & Kachuck)

1. Selected participants from five classes in high school (58/43 – experiment/control)

2. Students from summer program for basic math skills competency (11/8 – factors & primes/all modules)

Fractions, Factors and Primes

1. Three months2.Not stated

“Encore’s Vacation” (Taiwan)

1. 74 fifth-graders from two classes at public elementary school in Taipei, Taiwan (for affective domain)

2. 37 fifth-graders from one class at elementary school in suburban Taipei, Taiwan (for cognitive domain) *

Problem-Solving(time, money)

1. 8 class periods in one week

2. 8 class periods in one week

* - Divided into three groups of high, medium and low ability based on their math and science score

Stanford University, Fall 2006School of Education

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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