1. ALAT PERAGA MATEMATIKA (Pengertian, Klasifikasi dan Pemanfaatannya) Sumardyono, M.Pd. (PPPPTK MATEMATIKA, Yogyakarta) smrdyn2007@gmail.com

2. PENGERTIAN & KLASIFIKASI ALAT PERAGA MATEMATIKA Special or Classical Definition: “A model for a mathematical concept refers to any objects or pictures that can help a student construct or understand that concept” (Van de Walle,1990: 13) “concrete representation of mental constructs or ideas” (Johnson, Berger, & Rising, 1973: 235) Reason for Special Definition: “Pure” mathematics consist of “abstract” & “symbolic” concepts.

3. General or Modern Definition: “various kinds of instructional materials listed below. Demonstration devices (large concrete representations, including charts), Manipulative device, Computational devices, Instruments for measuring and drawing, Kits, Games and puzzles, Science apparatus, & Realia (ordinary objects) “. (Johnson, Berger, & Rising, 1973: 235) Reason for General Definition: Various kinds of mathematical competencies PENGERTIAN & KLASIFIKASI ALAT PERAGA MATEMATIKA

4. Manipulatives: the term manipulative devices refers to those concrete objects which, when handled or operated by the pupil and the teacher, provide the pupil with an opportunity to attain specific objectives... (Jackson, 1973: 301) Benefits of manipulatives: “contructed” concepts by puils depends on his ability & his approach. PENGERTIAN & KLASIFIKASI ALAT PERAGA MATEMATIKA

5. “Because much of mathematics is concerned with abstraction, there is a special need for models in mathematics. Mathematicians recognize this when they create new mathematics”. (Johnson, Berger, & Rising, 1973: 235) PENTINGNYA ALAT PERAGA MATEMATIKA “Untuk meningkatkan keefektifan pembelajaran, sekolah diharapkan menggunakan teknologi informasi dan komunikasi seperti komputer, alat peraga, atau media lainnya.” (SI Mata Pelajaran Matematika, Latar Belakang, lampiran Permendiknas no. 22 tahun 2006). “Instruction needs to be fundamentally based on the stimulation provided by objects and events. … Objects and events are the stimuli from which concepts are derived.” (Gagne dalam Jackson, 1973: 302)

6. Models provide a setting for discovery of concepts Models can be used to focus attention on ideas that are under discussion Models provide a means for making independent investigations Models can be used to provide for individual differences Models can be used to generate interest in a new topic Models can be used to promote enjoyment of mathematics Models can be used to build appreciation for mathematics A major function of models is their positive effect on retention Models can be used to teach application [Johnson, Berger, & Rising, 1973: 236-264] MANFAAT ALAT PERAGA MATEMATIKA

7. “A model is only effective if the student actually construct the desired relationship” (Van de Walle, 1990: 14) “Both from action psychology as well as from cognitive psychology it can be understood that the danger exists that working with manipulative material does not prepare for working without manipulative”. (Gravemeijer, 1991: 75) PETUNJUK PEMANFAATAN ALAT PERAGA MATEMATIKA

8. “To use models effectively, a teacher needs to be aware of what models are available” (Johnson, Berger, & Rising, 1973: 279) “the crucial question is which devices should be used with particular pupils in teaching certain concepts” (Jackson, 1973: 332) “The first danger is that of a teacher`s wholesale acceptance of one all-purpose device. …. The second danger arise from the belief that devices teach mathematics” (Jackson, 1973: 332) PETUNJUK PEMANFAATAN ALAT PERAGA MATEMATIKA “mathematics is made up of ideas-not material; it can be illustrated with devices and has application to many concrete situation, but it must be understood as a system of ideas” (Sole dalam Jackson, 1973: 302)

9. 1.Select the proper aid to use in order to attain the desired objective 2.Prepare yourself to use the teaching aid that has been selected 3.Prepare the classroom 4.Prepare the class 5.Use the teaching aid selected in the most effective manner possible 6.Provide follow-up activities 7.Evaluate the effectivenees of the aid (Berger & Johnson dalam A Guide to the Use and Procurement of Teaching Aids for Mathematics) PETUNJUK PEMANFAATAN ALAT PERAGA MATEMATIKA

10. Thanks a lot