developing computer assisted instruction in the pythagorean theorem
TRANSCRIPT
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