Thus, the goal of math education is to assist learners or children invent procedures for solving mathematical problems as well as in constructing "a network of numerical relationships" (Kamii 1996, 101). As pointed out by Piaget, mathematical knowledge is different from physical knowledge because the former is not observable while the latter is (Kamii 1996: 102). Following Piaget, Kamii said that "there is no such thing as addition fact" because sums are internalized or constructed from within (1996: 102). In illustrating Piaget thinking, Kamii said that one example of a network of relationship is in the situation when a child learns that 5 + 6 = 11 because 5 + 6 = 10 +1 (1996: 102). To solve a subtraction mathematical problem 53-24, there can be several options: a) treat it as 50-20=30, 3-4=1 less than zero, and 30-1=29; b) view the mathematical operation instead as 50-20=30, 30-4=26, and 26+3=29; and c) confront the problem as 50-20=30, 30+3=33, and 33-4=29. To address a mathematical problem in multiplication like 125x4, some of the options are: a) handle it as 4x100=400, 4x20=80, 4x5=20, and 400+80+20=500; or b) consider it as 4x100=400, 4x25=100, and 400+100=500.According to Kamii, the Piaget method does not use textbooks because textbooks employ "repetition and reinforcement from the outside" (Kamii 1996: 102). Instead, an educational approach that follows Piagets theory uses "numerical reasoning in daily living, group games, and problem-solving". As we will show later, the Montessori method uses experiences, group games, and problem-solving in pedagogy or teaching children. Acquiring knowledge through the rigours of living has been the fundamental way that a child has been acquiring knowledge and, for Kamii, it follows that the teacher schooled in the ways of Piaget should use the same basic procedure in the pedagogy (Kamii 1996: 102). The use of a problem-solving approach is promoted because the Piaget approach emphasizes a "constructivist program" wherein exchange of views or conversation is important (Kamii 1996: 105). Dialogues and discussions are extremely important in the Montessori method, especially as critical outlook is promoted.In the "constructivist program", the teacher does not reinforce right or correct wrong ones because that can stop all thinking (Kamii 1996: 105). Teachers schooled in the ways of Piaget encourage his or her class to express agreements or disagreements immediately (Kamii 1996: 105). If no one among the
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