As a number of educators have obser

As a number of educators have observed, however, students' experiences of traditional mathematics teaching which emphasizes "received" mathematics are unlikely to engender attitudes and identities which enable them to take control of their own development as mathematicians (Alibert &Thomas, 19 Boaler & Greeno, 2000). Even where students are encouraged to make their reasoning explicit in an attempt to "make learning experiences more co-operative, more p. 85), lack of clarity on the conceptual and more connected" (Dreyfus, 19 part of both teachers, students and textbooks as to the relative status of different kinds of mathematical explanations militates against shared (1998, p. 237) point out ,"we, their teachers, take for granted what constitutes evidence in their eyes. Rather than gradually refining students conception of constitutes evidence and justification in mathematics, we what impose on them proof methods and implications rules that in many cases are utterly extraneous to what convinces them." That this is a subtle and partici pative process involving learning to make connections between "key ideas" the language of formal mathematical proof is demonstrated by Raman and observation of student discussion. In this study of one student's persistence in defending his insight into a problem while neglecting details of a public justification, Raman and Zandieh argue that conviction that one is right is necessary to motivate the search for a justification, but this needs to connect to argument which demands mathematical evidence. In contrast, teaching which emphasizes mathematics as already created rather than mathematics in creation will do little to contribute to this refinement, for the reasons that Schoenfeld (1994, p. 57) outlines

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As a number of educators, have observed however students' experiences, of traditional mathematics teaching which emphasizes. "Received" mathematics are unlikely to engender attitudes and identities which enable them to take control of their own. Development as mathematicians (Alibert, &Thomas 19 Boaler & Greeno 2000). Even, where students are encouraged to make their. Reasoning explicit in an attempt to "make learning experiences, more co-operative more p. 85), lack of clarity on the conceptual. And more connected "(Dreyfus 19 part, of, both teachers students and textbooks as to the relative status of different kinds. Of mathematical explanations militates against shared (1998 P. 237), point out, "we their, for, teachers take granted what. Constitutes evidence in their eyes. Rather than gradually refining students conception of constitutes evidence and justification. In mathematics we what, impose on them proof methods and implications rules that in many cases are utterly extraneous to. What convinces them. "That this is a subtle and partici pative process involving learning to make connections between key." Ideas "the language of formal mathematical proof is demonstrated by Raman and observation of student discussion. In this. Study of one student 's persistence in defending his insight into a problem while neglecting details of a, public justification. Raman and Zandieh argue that conviction that one is right is necessary to motivate the search for a justification but this,, Needs to connect to argument which demands mathematical evidence. In contrast teaching which, emphasizes mathematics as. Already created rather than mathematics in creation will do little to contribute to, this refinement for the reasons that. Schoenfeld (1994 P. 57), outlines.