Models And Manipulatives

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The different models and manipulatives to help elementary students in understand the concept and backbone of mathematics has been in place for some quite time. The most recent pioneers in this field are Jean Paiget (1896-1980) and Zoltan Dienes (1916-). In 1952 Piaget suggested that children begin to understand symbols and abstract concepts only after experiencing the ideas on a concrete level. Piaget emphasized that children learn best when they are active and seek solutions for themselves by making discoveries reflecting on them, and discussing them, rather than by blindly imitating the teacher (Santrock, Page 386). This also applied to Vygotsky’s theory which states that the teacher should encourage the student to focus on real life experience …show more content…

Models and Manipulatives not only allow students to construct their own cognitive models for abstract mathematical, they also provide a common language with which to communicate these models to the teacher and other students. In addition manipulatives have the advantage of engaging students and increasing both interest in and enjoyment of mathematics. Students who are presented with the opportunity to use manipulatives report that they are more interested in mathematics. Long-term interest in mathematics translates to increased mathematical ability (Sutton & Krueger, 2002). In fact one teacher that worked hand in hand with Constance Kamii another theorist commented that after introducing the nontraditional way, her class displayed a love for math. During her experiment Constance Kamii results where astonishing. When two classes undertook the same exam, there was not that much difference between the class that was thought math in the constructivist way than the class that was though the conventional way. Another group of researcher from Purdue University presented problems to student to …show more content…

It uses Dienes ten block system, so that the student can visualize the multiplication. Billstein, gives us a perfect example on how to find the product 4 x 12. (Page 152). This can be computed by using block models. The student will prepare 4 rows under each other of twelve blocks. The student will group ten blocks to create a 10 and two individual units of one. By regrouping each individual line, the student can count the blocks easier and faster. Another alternative multiplication algorithm is the Lattice Multiplication. This low-stress algorithm has the advantage of delaying all additions until the single-digit multiplication are complete. (Billstein Page

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