Moving beyond the Moving beyond the standards: Enhancing math standards: Enhancing math

instruction through instruction through interactive learninginteractive learning

ByBy

Aileen Machado, M. EdAileen Machado, M. Ed

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Daniela Foerch, M. EdDaniela Foerch, M. Ed

Introduction to the Introduction to the TheoryTheory

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

Jean PiagetJean Piaget

Logico-mathematicalLogico-mathematical

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

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

Lev VygotskyLev Vygotsky

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

Zoltan P. DienesZoltan P. Dienes

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

Constance KamiiConstance Kamii

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

sense and its implications tor early childhood sense and its implications tor early childhood education,” pp.187-211. In Spodek, B. and education,” pp.187-211. In Spodek, B. and Saracho, Saracho, O.N.(2006). O.N.(2006). Handbook of research on Handbook of research on

the education of young childrenthe education of young children, Second ed. , Second ed. Mahwah, Mahwah, NY: LEA.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: MA: Harvard University PressHarvard 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 York: 2nd Grade. New 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: Chicago: University of Chicago Press.University of Chicago Press.