Conducting Teaching Experiments in Collaboration With Teachers

• DOI: 10.4324/9781410602725.ch12
• Publication Date: 2000-04-01
• Authors: Paul Cobb

ion so that the results of activity can be anticipated and itself becomes an entity manipulated conceptually (Sfard, 1991; P. W. Thompson, 1994b; von Glasersfeld, 1991 a). One central tenets RME is starting points instructional sequences should experientially real to students in sense they engage immediately personally meaningful mathematical (Streefland, 1991). In this regard, Thompson (1992) noted from emergent perspective that: If do not become engaged imaginistically ways relate reasoning principled experience, then we have little reason believe will come see their worlds outside school as any way mathematical. (p. 10) As a point clarification, it stressed term means only experienced by students, involve realistic situations. Thus, arithmetic tasks presented using conventional notation might for whom whole numbers are objects. general, conjectures about possible nature students' experiential realities derived psychological analyses. It also even when everyday scenarios used points, necessarily differ situations experience them out (Lave, 1993; Walkerdine, 1988). To account learning, therefore, essential delineate scenario constituted interactively classroom with teacher's guidance. A second tenet addition taking current knowing, justifiable terms potential endpoints learning sequence. This implies initially informal constitute .a basis which abstract construct increasingly sophisticated conceptions participate practices. At same time, serve continue function paradigm cases rich imagery thus anchor activity. latter requirement consistent analyses emphasize important role analogies (Clement & D. E. Brown, 1989), metaphors (Pimm, 1987; Presmeg, 1992; Sfard, 1994), prototypes (Dorfler, 1995), intuitions (Fischbein, 1987), generic organizers (Tall, 1989) play 12. CONDUCTING TEACHING EXPERIMENTS 319 dealing endpoints, first two hint at tension endemic mathematics teaching. Ball (l993b) observed recent American proposals educational reform replete notions 'understanding' 'community'-about building bridges between experiences child knowledge expert 374). She inquired: How I [as teacher] create my connect what now know care but transcend present? value interests ideas arxi traditions growing centuries exploration invention? 375.) RME's attempt cope embodied third wherein argued contain activities elaborate symbolic models modeling entail making drawings, diagrams, or tables, could developing notations notations. based on conjecture that, guidance, evolve into (Gravemeijer, 1995). Dorfler (1989) made similar proposal he discussed protocols action enabling reflection analysis Similarly, Kaput (in press) suggested such records support processes entities compared possess general properties. extent occurs, would provide eventually ( 1991) tenned semantic guidance rather than syntactic social terms, shift practices symbolizing developed express take life own subsequently more formal range discussion relates design involving technology-intensive environments was provided Bowers (1995). apparent interpretation given both individual collective development. For example, speculation reorganize Further, development