Developing Computer Assisted Instruction in the Pythagorean Theorem

DEVELOPING COMPUTER ASSISTED INSTRUCTION IN THE PYTHAGOREAN THEOREM TOPIC WITHIN INVESTIGATIVE APPROACHWritten by Yosep Dwi K.

INVESTIGATIVE APPROACH

The essence of an investigative approach is the application of communication, reasoning, operational and recording processes to a study of the core topics which make up the content of a mathematics curriculum.–Frobisher (1994)

TEACHERS’ ACTION

Demonstrate how to approach various aspects of the investigative processes.

Become the socializing force in helping pupils become mathematically literate by encouraging them to question, to challenge and learn anything about the real mathematical behavior

Listen to pupils so that teachers can understand pupils' beliefs about learning, the experiences they bring to specific inquiries, and to gain insight into the meanings and connections pupils construct during inquiries.

Initially give children 'short' investigations which provide short term rewards.

PUPILS’ ACTION

Become active members of a community of practice who share the responsibility of planning, conducting and reflecting on their inquiries with other members;Listen and negotiate with others; andMust have mutual trust between peers and the teacher so that mathematical thinking is shared freely.

COMPUTER ASSISTED INSTRUCTION

WHAT IS IT?

A teaching tool that involves the use of a computer program or programs to facilitate the education of a group of students. (www.questia.com)

Instruction or remediation presented on a computer. (www.readingrockets.org)

A kind of tutorial implication in which a computer helps the learner(s) to present material and acts a tutor. Using a branching model of lessons in this process, the computer presents information, asks questions, and gives feedback. (Konukman, 2003)

TYPES OF CAI

Drill and Practice

Tutorial

Simulation

Instructional Game

Problem Solving

STRATEGIES UNDERLYING EACH OF THE CAI FUNCTIONS

Function Instructional UsesStrategy

Directed Constructivist

Drill and Practice Skill practice

Tutorial Information delivery

SimulationDemonstration

Exploration

Instructional GameSkill practice

Exploration

Problem SolvingSkill Practice

Exploration

ADVANTAGES AND DISADVANTAGES

The student can choose his own way and speed.

The program can be stopped at any time.

The program can be repeated as often as the usher wishes.

The computer is not judgmental. The student can learn from his mistakes without embarrassment.

Saves time for the teacher (in the long term).

The students are more activated.

Weak students are favored.

Starting costs are high.

The staff needs to be trained.

Students have to be familiarized with the medium.

PROTOTYPEThe Theorem of

Pythagoras

The Converse of Pythagorean

Theorem

Two Special Right Triangles

Story ProblemsDistance in Coordinate Geometry

THE THEOREM OF PYTHAGORAS

INVESTIGATION BY DISSECTION

CONCLUSION OF THEOREM

MAKING PARAGRAPH

PROOFEXAMPLE

THE CONVERSE OF PYTHAGOREAN THEOREM

Investigation: Is the Converse True?Conclusion of the ConverseDeveloping ProofAlgebra Connection: Radical Expressions

• Investigation I: Isosceles Right Triangle• Conclusion

• Investigation II: 30°-60°-90° Triangle• Conclusion

TWO SPECIAL RIGHT TRIANGLE

???

The space diagonal of cube problemThe cracked redwood problemA frame cabin problemA regular hexagonal prism problemWork and force in inclined plane (science connection)

STORY PROBLEM

Introduction with a problemInvestigation: The Distance FormulaConclusionExample: Finding the perimeter of triangle on Cartesian coordinate plane

DISTANCE IN COORDINATE GEOMETRY

(12, 23)

(20, 29)

PREVIEW