Using manipulatives to Using manipulatives to connect theory to practice.connect theory to practice.

ByBy

Aileen Machado, M. EdAileen Machado, M. Ed

&&

Daniela Fenu Foerch, M. EdDaniela Fenu Foerch, M. Ed

Introduction to the Introduction to the TheoryTheory

Accountability era: classrooms Accountability era: classrooms have lost the fun and exploration have lost the fun and exploration

Jerome BrunerJerome Bruner Jean PiagetJean Piaget Lev VygotskyLev Vygotsky Zoltan P. DienesZoltan P. Dienes Constance KamiiConstance Kamii

Jerome Bruner Jerome Bruner

According to Bruner, According to Bruner, manipulatives are manipulatives are necessary when learning necessary when learning math in order to jump from math in order to jump from one stage of learning to one stage of learning to another. another. His theory aims at His theory aims at three stages of learning: three stages of learning: enactive (action), pictorial enactive (action), pictorial (visual), and symbolic (visual), and symbolic (abstract). (abstract).

Jean PiagetJean Piaget

Logico-mathematicalLogico-mathematical

Knowledge is constructed by the Knowledge is constructed by the child from within through child from within through reasoning and the interaction with reasoning and the interaction with the environment, rather than the environment, rather than internalized from the environment internalized from the environment (1951; 1971).(1951; 1971).

Children create logico-Children create logico-mathematical knowledge by mathematical knowledge by connecting previously established connecting previously established relationships with new relationships with new relationships (Kamii, 2000). relationships (Kamii, 2000).

Lev VygotskyLev Vygotsky

Children could be guided to Children could be guided to stronger mathematical stronger mathematical understandings as they understandings as they progressively analyze complex progressively analyze complex skills on their own with the skills on their own with the teacher’s guidance to scaffold or teacher’s guidance to scaffold or facilitate as needed (Baroody, Lai facilitate as needed (Baroody, Lai & Mix,2006).& Mix,2006).

Zoltan P. DienesZoltan P. Dienes

He believes that learning He believes that learning mathematics does not have mathematics does not have to be perceived as a difficult to be perceived as a difficult task. Rather, it should be task. Rather, it should be introduced to students, introduced to students, especially to young children, especially to young children, through fun and exciting through fun and exciting games (Holt & Dienes, games (Holt & Dienes, 1973).1973).

Constance KamiiConstance Kamii

Math concepts can be acquired Math concepts can be acquired and internalized by young children and internalized by young children by using “two kinds of activities: by using “two kinds of activities: situations in daily living… and situations in daily living… and group games”(1984).group games”(1984).

ReferencesReferences

Baroody, A.J., Lai, M., Mix, K.S. “The Baroody, A.J., Lai, M., Mix, K.S. “The development of development of young children’s early number young children’s early number and operation and operation sense and its implications tor sense and its implications tor early childhood early childhood education,” pp.187-211. In education,” pp.187-211. In Spodek, B. and Spodek, B. and Saracho, O.N.(2006). Saracho, O.N.(2006). Handbook Handbook of research on of research on

the education of young childrenthe education of young children, Second ed. , Second ed. Mahwah, NY: LEA.Mahwah, NY: LEA.

Bruner, J. (2003). Bruner, J. (2003). The Process of Education: A The Process of Education: A Landmark in Educational Theory. Landmark in Educational Theory.

Cambridge, Cambridge, MA: Harvard University PressMA: Harvard University Press Holt, M. and Dienes, P. Z. (1984). Holt, M. and Dienes, P. Z. (1984). Let’s Play Math. Let’s Play Math.

New York: Walker and Company. New York: Walker and Company.

ReferencesReferences

Kamii, C. (1984). Kamii, C. (1984). Young children reinvent Young children reinvent arithmetic.arithmetic. New York: Teachers College New York: Teachers College Press. Press.

Kamii, C. (2000). Kamii, C. (2000). Young Children Continue to Young Children Continue to Reinvent Arithmetic,Reinvent Arithmetic, 2nd Grade. New 2nd Grade. New

York: York: Teachers College Teachers College Press.Press. Piaget, J. (1951). Piaget, J. (1951). Play, dreams, and imitation in Play, dreams, and imitation in

childhoodchildhood. New York: Norton.. New York: Norton. Piaget, J. (1971). Piaget, J. (1971). Biology and knowledgeBiology and knowledge. .

Chicago: University of Chicago Press.Chicago: University of Chicago Press.