The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic

@article{Noss97, abstract = {In this paper, we explore the relationship between learners' actions, visualisations and the means by which these are articulated. We describe a microworld, Mathsticks, designed to help students construct mathematical meanings by forging links between the rhythms of their actions and the visual and corresponding symbolic representations they developed. Through a case study of two students interacting with Mathsticks, we illustrate a view of mathematics learning which places at its core the medium of expression, and the building of connections between different mathematisations rather than ascending to hierarchies of decontextualisation. This revised version was published online in September 2005 with corrections to the Cover Date.}, author = {Noss, Richard and Healy, Lulu and Hoyles, Celia }, citeulike-article-id = {478873}, comment = {"While most students are able to identify a great variety of patterns (Stacey, 1989), many of these patterns do not readily lend themselves either to the expression of a functional relationship or to an algebraic representation in any straightforward way (Lee and Wheeler, 1987). Indeed, students who are able to apply a correct method to any number of specific cases often cannot articulate a general pattern or relationship in natural language (see, for example, MacGregor and Stacey, 1992), and expression in algebraic symbolism is still more problematic. There is also a question mark over the status of the algebraic expression even if it is successfully constructed by the student. Lee and Wheeler (1987) suggest that it is rare for those students who do produce algebraic representation to check these expressions - even empirically by substituting in particular examples. Stacey (1989) found that only a small proportion of students responded to requests for explanation by providing mathematical justification and, similarly, Arzarello (1991) pointed to students' difficulties in providing mathematically valid justification of their suggested algebraic rules. Taken together, the evidence suggests that algebraic formulation is often disconnected from the activity which precedes it, a meaningless extra that neither illuminates the problem nor provides a means for validating its solution. Algebra is viewed as an endpoint, a problem solution in itself rather than a tool for problem solving." p 204}, Abstract = {In this paper, we explore the relationship between learners‘ actions, visualisations and the means by which these are articulated. We describe a microworld, Mathsticks, designed to help students construct mathematical meanings by forging links between the rhythms of their actions and the visual and corresponding symbolic representations they developed. Through a case study of two students interacting with Mathsticks, we illustrate a view of mathematics learning which places at its core the medium of expression, and the building of connections between different mathematisations rather than ascending to hierarchies of decontextualisation.}, journal = {Educational Studies in Mathematics}, keywords = {abstraction, ijceell06, ijtme2006, matchsticks, situated}, number = {2}, pages = {203--233}, posted-at = {2006-01-24 17:16:42}, priority = {0}, title = {The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic}, url = {http://www.springerlink.com/link.asp?id=k565x38h21737147}, volume = {33}, year = {1997} }

TY - JOUR ID - Noss97 L3 - citeulike-article-id:478873 TI - The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic JF - Educational Studies in Mathematics VL - 33 IS - 2 SP - 203 EP - 233 N2 - In this paper, we explore the relationship between learners' actions, visualisations and the means by which these are articulated. We describe a microworld, Mathsticks, designed to help students construct mathematical meanings by forging links between the rhythms of their actions and the visual and corresponding symbolic representations they developed. Through a case study of two students interacting with Mathsticks, we illustrate a view of mathematics learning which places at its core the medium of expression, and the building of connections between different mathematisations rather than ascending to hierarchies of decontextualisation. This revised version was published online in September 2005 with corrections to the Cover Date. KW - abstraction KW - ijceell06 KW - ijtme2006 KW - matchsticks KW - situated N1 - "While most students are able to identify a great variety of patterns (Stacey, 1989), many of these patterns do not readily lend themselves either to the expression of a functional relationship or to an algebraic representation in any straightforward way (Lee and Wheeler, 1987). Indeed, students who are able to apply a correct method to any number of specific cases often cannot articulate a general pattern or relationship in natural language (see, for example, MacGregor and Stacey, 1992), and expression in algebraic symbolism is still more problematic. There is also a question mark over the status of the algebraic expression even if it is successfully constructed by the student. Lee and Wheeler (1987) suggest that it is rare for those students who do produce algebraic representation to check these expressions - even empirically by substituting in particular examples. Stacey (1989) found that only a small proportion of students responded to requests for explanation by providing mathematical justification and, similarly, Arzarello (1991) pointed to students' difficulties in providing mathematically valid justification of their suggested algebraic rules. Taken together, the evidence suggests that algebraic formulation is often disconnected from the activity which precedes it, a meaningless extra that neither illuminates the problem nor provides a means for validating its solution. Algebra is viewed as an endpoint, a problem solution in itself rather than a tool for problem solving." p 204}, Abstract = {In this paper, we explore the relationship between learners‘ actions, visualisations and the means by which these are articulated. We describe a microworld, Mathsticks, designed to help students construct mathematical meanings by forging links between the rhythms of their actions and the visual and corresponding symbolic representations they developed. Through a case study of two students interacting with Mathsticks, we illustrate a view of mathematics learning which places at its core the medium of expression, and the building of connections between different mathematisations rather than ascending to hierarchies of decontextualisation. AU - Noss, Richard AU - Healy, Lulu AU - Hoyles, Celia PY - 1997/// UR - http://www.springerlink.com/link.asp?id=k565x38h21737147 ER -