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Every branch of science has its own special methods teaching within the perspective of its purposes. A teaching method which is appropriate for the structure of mathematics should be according with these stated purposes below (Van de Wella, 1989 );The students;Ø Conceptual knowledge of mathematics Ø Procedural knowledge of mathematicsØ Connections between conceptual and procedural knowledgeThese three purposes are called as connectional knowledge. Conceptual knowledge can be defined as knowledge of mathematical structures (concepts and its elements) and giving them with symbols; and benefiting from its utilities; the knowledge of procedural techniques of mathematics and giving them with symbols; formatting the connections and relations among methods, symbols and concepts. By studying students’ knowledge of mathematics in terms of learning psychology that mentions two kinds of mathematical knowledge. First one is an entirely mechanical data consist of some abilities such as recognizing the symbols, doing the operations ; second one is the ability to put symbols into some mathematical concepts, forming some relationships among them and doing operations by using them (Baki, 1998). While in procedural knowledge, it is necessary to know only how to use knowledge without needing to know the meaning of a concept or an operation; in the conceptual knowledge, the act of conception becomes important (Baki, 1997). Conceptual knowledge and procedural knowledge are two-dependent components. Both conceptual and procedural knowledge are very important in mathematics (Hiebert, and Carpenter, 1992). A permanent and functional learning in mathematics is only possible with balancing conceptual and procedural knowledge (Baki, 1998). It has been more important to have operational knowledge in mathematics, whereas the conceptual knowledge should be predominantly focused on. In other words, the conceptual and operational data are not balanced in teaching mathematics. For the conceptual and operational data are not balanced in teaching mathematics, the subjects are not learned conceptually (İşleyen, and Işık, 2003). For the lessons are not explained conceptually, the subjects are memorized instead of being learned. Most students are not aware of that there are concepts at the basis of the subjects they learn, and they do not know what mathematics means. They believe that learning mathematics is to operate on meaningless symbols, and they try to learn mathematics by memorizing it (Oaks, 1990). Generally, it is stated that abstract concepts are difficult to articulate, and this may be the reason why the students have difficulty in understanding it, however, this problem can be eliminated or at least reduced by making the concepts concrete or giving concrete means. That the more concrete but less abstract subjects can be learned more easily is a fact admitted by everybody (Ersoy, 1997 and Baki, A., 2002). The concretization of mathematics has been frequently used recently as an essential idea in literature for solving problems and constituting the mathematical concepts in the minds of students meaningfully. (di Seassa, 1994; Dubinsky, 1994; Duval, 1995; Eisenberg & Dreyfus, 1991; Glasensferd, 1991; Janvier, 1987; Kaput, 1994; Presmeg, 1986; Steinbring, 1991; Vinner, 1989; Zimmermann & Cunningham, 1990, etal) (Hitt, F., 2001). |
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