Math Manipulatives

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Math Manipulatives

  1. 1. Using manipulatives to connect theory to practice. By Aileen Machado, M. Ed & Daniela Fenu Foerch, M. Ed
  2. 2. Introduction to the Theory <ul><li>Accountability era: classrooms have lost the fun and exploration </li></ul><ul><li>Jerome Bruner </li></ul><ul><li>Jean Piaget </li></ul><ul><li>Lev Vygotsky </li></ul><ul><li>Zoltan P. Dienes </li></ul><ul><li>Constance Kamii </li></ul>
  3. 3. Jerome Bruner <ul><li>According to Bruner, manipulatives are necessary when learning math in order to jump from one stage of learning to another. His theory aims at three stages of learning: enactive (action), pictorial (visual), and symbolic (abstract). </li></ul>
  4. 4. Jean Piaget <ul><li>Logico-mathematical </li></ul><ul><li>Knowledge is constructed by the child from within through reasoning and the interaction with the environment, rather than internalized from the environment (1951; 1971). </li></ul><ul><li>Children create logico-mathematical knowledge by connecting previously established relationships with new relationships (Kamii, 2000). </li></ul>
  5. 5. Lev Vygotsky <ul><li>Children could be guided to stronger mathematical understandings as they progressively analyze complex skills on their own with the teacher’s guidance to scaffold or facilitate as needed (Baroody, Lai & Mix,2006). </li></ul>
  6. 6. Zoltan P. Dienes <ul><li>He believes that learning mathematics does not have to be perceived as a difficult task. Rather, it should be introduced to students, especially to young children, through fun and exciting games (Holt & Dienes, 1973). </li></ul>
  7. 7. Constance Kamii <ul><li>Math concepts can be acquired and internalized by young children by using “two kinds of activities: situations in daily living… and group games”(1984). </li></ul>
  8. 8. References <ul><li>Baroody, A.J., Lai, M., Mix, K.S. “The development of young children’s early number and operation sense and its implications tor early childhood education,” pp.187-211. In Spodek, B. and Saracho, O.N.(2006). Handbook of research on </li></ul><ul><li>the education of young children , Second ed. Mahwah, NY: LEA. </li></ul><ul><li>Bruner, J. (2003). The Process of Education: A Landmark in Educational Theory. Cambridge, MA: Harvard University Press </li></ul><ul><li>Holt, M. and Dienes, P. Z. (1984). Let’s Play Math. New York: Walker and Company. </li></ul>
  9. 9. References <ul><li>Kamii, C. (1984). Young children reinvent arithmetic. New York: Teachers College Press. </li></ul><ul><li>Kamii, C. (2000). Young Children Continue to Reinvent Arithmetic, 2nd Grade. New York: Teachers College Press. </li></ul><ul><li>Piaget, J. (1951). Play, dreams, and imitation in childhood . New York: Norton. </li></ul><ul><li>Piaget, J. (1971). Biology and knowledge . Chicago: University of Chicago Press. </li></ul>

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