Thursday, August 5, 2010
Cognition and learning as profoundly situated
Hung, D., Looi, C.-K., & Koh, T.-S. (2004). Situated cognition and communities of practice: First-person "lived experiences" vs. third-person perspectives. Educational Technology & Society, 7(4), 193-200.
Hung, Looi and Koh set out to stress what they see as the "nondualistic epistemology and relativistic philosophy of situated cognition" and attempt to critique pervasive pedagogies where situation cognition is invoked within dualistic Cartesian frameworks whereby an positivistic objective knowledge is deemed possible (p. 193).
Within a situated cognition context, identity is seen as always implicated with knowledge construction whereby identity is constituted via local interactions. Thus, situated cognition considers a relational perspective and social process wherein the complexity of a system - context, identity, intersubjectivity, culture, discourse, embodiment - is jointly implicated in the construction of knowledge. In Heidiggerian terms being (and cognition) cannot being isolated (as some kind of entity) from one's embodied actual experience in the world. Communities of practices are seen as situations where cognition, context, identities and knowledge are co-determined .
This leads to the conclusion that descriptions of phenomena within a context cannot be overgeneralised and abstracted across contexts. For example principles of something called "academic writing skills" cannot be gleaned across contexts with different genre expectations. Thus transfer is inherently problematic. This is due they suggest to "the importance of emergence, historicity, and growth within any particular context" (p.195). A key "proverb" within situated cognition is "the map is not the territory" - an especially potent fact in mathematics.
Schools with their usually emphasis on an objectivist understanding of knowledge tend to focus on the map. These authors, however call for a rethinking of pedagogy whereby the dialectic relationship between maps and territories can be addressed.
Hung, Looi and Koh set out to stress what they see as the "nondualistic epistemology and relativistic philosophy of situated cognition" and attempt to critique pervasive pedagogies where situation cognition is invoked within dualistic Cartesian frameworks whereby an positivistic objective knowledge is deemed possible (p. 193).
Within a situated cognition context, identity is seen as always implicated with knowledge construction whereby identity is constituted via local interactions. Thus, situated cognition considers a relational perspective and social process wherein the complexity of a system - context, identity, intersubjectivity, culture, discourse, embodiment - is jointly implicated in the construction of knowledge. In Heidiggerian terms being (and cognition) cannot being isolated (as some kind of entity) from one's embodied actual experience in the world. Communities of practices are seen as situations where cognition, context, identities and knowledge are co-determined .
This leads to the conclusion that descriptions of phenomena within a context cannot be overgeneralised and abstracted across contexts. For example principles of something called "academic writing skills" cannot be gleaned across contexts with different genre expectations. Thus transfer is inherently problematic. This is due they suggest to "the importance of emergence, historicity, and growth within any particular context" (p.195). A key "proverb" within situated cognition is "the map is not the territory" - an especially potent fact in mathematics.
Schools with their usually emphasis on an objectivist understanding of knowledge tend to focus on the map. These authors, however call for a rethinking of pedagogy whereby the dialectic relationship between maps and territories can be addressed.
The problem of context when doing "maths"
Evans, J., & Tsatsaroni, A. (2000). Mathematics and its publics: texts, contexts and users. Social Epistemology, 14(1), 55-68.
Fundamentally, Evans and Tsatsaroni set out to problematise context in a number of ways and contend that mathematical knowledge is not preserved across contexts. This in turn problematises the transfer of learning and skills across contexts. They suggest that context itself needs to be read as text and that such readings are multiple, mutable, ambiguous, and open. This is an acknowledgement of the Bakhtinian view of language and discourse as subject to conservative and creative forces, polyphonic, dialogic, heteroglossic and dialogical (see Bakhtin, 1986 & 1981).
They also raise the issue of identity and how subjectivity is implicated and constituted within discursive formations. For example doing mathematics in a classroom and doing mathematics in a shop involve different social practices with differing purposes and constraints often demanding dissimilar types of answer.
Classroom mathematics texts are often independent of context and arise from educational discourses rather than everyday life discourses. Social relationships also are profoundly different in the two contexts with varying power configurations. For example in educational discourses students occupy specific spaces in hierarchical formations and through repeated subjugation come to view their identities as natural (see Graham, 2005). Thus quite contrasting subjectivities are constituted as different “performative language and intertextual reference contribute to and enhance the constitutive properties” (Graham, 2005, p.6) of the diverse discourses.
Evans and Tsatsaroni employ the term positioning when talking of subjectivities to counter an over-deterministic view of the constraints of discourse and to highlight the reality of agency. “Positioning in our view both supports and constrains the subject, in that it puts some limits on the play of signifiers, on the production of meaning, but is unable to limit all potential ambiguities in mathematical meanings and in `mathematical’ subjects” (p. 61).
They note a number of problems associated with a simplistic traditional view of the transfer of skills across contexts. These include describing the task, the neglect of the complexity of social practices and discourse in different contexts and the assumption of generalization and recontextualisation in new situations. They propose that translation across contexts require more, not less, attention to contexts and their associated signifiers, discourses, practices.
Bakhtin, one of the great Russian Linguistics is a key influence on this paper, so a few key refernces to his majors works might be in order here:
Bakhtin, M. M. (1981). The dialogic imagination (C. Emerson & M. Holquist, Trans.). Austin: University of Texas Press.
Bakhtin, M. (1986). Speech genres and other late essays (V. McGee, Trans.). Austin: University of Texas Press.
The seeds of Bakhtin’s approach to language are actually found in the following book which is seldom if ever cited by Bakhtin fans! It was written much early than the two above.
Bakhtin, M. M. (1993). Toward a philosophy of the act (V. Liapunov, Trans.). Austin, TX: University of Texas Press.
Fundamentally, Evans and Tsatsaroni set out to problematise context in a number of ways and contend that mathematical knowledge is not preserved across contexts. This in turn problematises the transfer of learning and skills across contexts. They suggest that context itself needs to be read as text and that such readings are multiple, mutable, ambiguous, and open. This is an acknowledgement of the Bakhtinian view of language and discourse as subject to conservative and creative forces, polyphonic, dialogic, heteroglossic and dialogical (see Bakhtin, 1986 & 1981).
They also raise the issue of identity and how subjectivity is implicated and constituted within discursive formations. For example doing mathematics in a classroom and doing mathematics in a shop involve different social practices with differing purposes and constraints often demanding dissimilar types of answer.
Classroom mathematics texts are often independent of context and arise from educational discourses rather than everyday life discourses. Social relationships also are profoundly different in the two contexts with varying power configurations. For example in educational discourses students occupy specific spaces in hierarchical formations and through repeated subjugation come to view their identities as natural (see Graham, 2005). Thus quite contrasting subjectivities are constituted as different “performative language and intertextual reference contribute to and enhance the constitutive properties” (Graham, 2005, p.6) of the diverse discourses.
Evans and Tsatsaroni employ the term positioning when talking of subjectivities to counter an over-deterministic view of the constraints of discourse and to highlight the reality of agency. “Positioning in our view both supports and constrains the subject, in that it puts some limits on the play of signifiers, on the production of meaning, but is unable to limit all potential ambiguities in mathematical meanings and in `mathematical’ subjects” (p. 61).
They note a number of problems associated with a simplistic traditional view of the transfer of skills across contexts. These include describing the task, the neglect of the complexity of social practices and discourse in different contexts and the assumption of generalization and recontextualisation in new situations. They propose that translation across contexts require more, not less, attention to contexts and their associated signifiers, discourses, practices.
Bakhtin, one of the great Russian Linguistics is a key influence on this paper, so a few key refernces to his majors works might be in order here:
Bakhtin, M. M. (1981). The dialogic imagination (C. Emerson & M. Holquist, Trans.). Austin: University of Texas Press.
Bakhtin, M. (1986). Speech genres and other late essays (V. McGee, Trans.). Austin: University of Texas Press.
The seeds of Bakhtin’s approach to language are actually found in the following book which is seldom if ever cited by Bakhtin fans! It was written much early than the two above.
Bakhtin, M. M. (1993). Toward a philosophy of the act (V. Liapunov, Trans.). Austin, TX: University of Texas Press.
The history of "numeracy" in the States
Cohen, P. C. (2001). The emergence of numeracy. In L. A. Steen (Ed.), Mathematics and democracy: The case for quantitative literacy (pp. 23-29). Princeton, NJ: THE WOODROW WILSON NATIONAL FELLOWSHIP FOUNDATION.
The author takes an historical look at the emergence of ‘numeracy’. However, the anachronistic use of numeracy – a term coined as late as 1959 – poses a real problem. How can we make sense of a statement like the following?
"Certainly that distinction, between numeracy as a concrete skill embedded in the context of real-world figuring and mathematics as an abstract, formal subject of study, was sharply drawn in the eighteenth and early nineteenth centuries." (p.25)
Cohen is thus importing a late definition of numeracy into a much earlier context. She also uses the term quantitative literacy anachronistically.
In the context of late 19th century education, the article rightly notes that the mathematics of those who studied at pre-college and college level in the US was highly abstract and remote from practical daily use. She however notes a more practical stream of “commercial arithmetic” being taught to boys aged between 10 and 14. This consisted of rote learning of a massive number of problems from navigation and gunnery, to discount and profit/ loss calculations.
It seems that the ‘numeracy’ problems of those years took the form of context-specific exemplars. It would be interesting to think of where such exemplars might fit on a continuum with rich meaningful contextualization at one end, and highly context-independent abstract mathematics at the other. Cohen also point to others engaged in examining “the history of numeracy” (p. 28) and calls for further efforts in “the reconstruction of the history of numeracy in America” (p. 29).
The author takes an historical look at the emergence of ‘numeracy’. However, the anachronistic use of numeracy – a term coined as late as 1959 – poses a real problem. How can we make sense of a statement like the following?
"Certainly that distinction, between numeracy as a concrete skill embedded in the context of real-world figuring and mathematics as an abstract, formal subject of study, was sharply drawn in the eighteenth and early nineteenth centuries." (p.25)
Cohen is thus importing a late definition of numeracy into a much earlier context. She also uses the term quantitative literacy anachronistically.
In the context of late 19th century education, the article rightly notes that the mathematics of those who studied at pre-college and college level in the US was highly abstract and remote from practical daily use. She however notes a more practical stream of “commercial arithmetic” being taught to boys aged between 10 and 14. This consisted of rote learning of a massive number of problems from navigation and gunnery, to discount and profit/ loss calculations.
It seems that the ‘numeracy’ problems of those years took the form of context-specific exemplars. It would be interesting to think of where such exemplars might fit on a continuum with rich meaningful contextualization at one end, and highly context-independent abstract mathematics at the other. Cohen also point to others engaged in examining “the history of numeracy” (p. 28) and calls for further efforts in “the reconstruction of the history of numeracy in America” (p. 29).
Quantitative Literacy, statistics and numeracy
Steen, L. A. (2001). The case for quantitative literacy. In L. A. Steen (Ed.), Mathematics and democracy: The case for quantitative literacy (pp. 1-22). Princeton, NJ: THE WOODROW WILSON NATIONAL FELLOWSHIP FOUNDATION.
Steen offers a brief history of quantitative literacy noting the concept belongs to the late twentieth century. However, she also falls into the trap of using numeracy anachronistically and one gets the idea that the word was actually being used in the nineteenth century:
"In colonial America, leaders such as Franklin and Jefferson promoted numeracy to support the new experiment in popular democracy, even as skeptics questioned the legitimacy of policy arguments based on empirical rather than religious grounds."
(p. 3)
While noting the contested nature of the term quantitative literacy, she uses numeracy and quantitative literacy interchangeably. Sometimes quantitative literacy was seen as related to statistics. The author rejects this and stakes a claim for quantitative literacy as a habit of mind and distinct from statistics or mathematics. However, she continues to use numeracy as a synonym for QL. One would have to say, however, that the argument that statistics is about uncertainty; whereas numeracy is about “the logic of certainty” (p. 5) is specious at best and betrays a fundamental lack of mathematical understanding.
Steen warns of the need for balance in connecting mathematics to authentic contexts as contextual details may in fact “camouflage broad patterns that are the essence of mathematics” (p.5). She also criticizes the way performance in abstract school mathematics has been traditionally use as an academic gatekeeper or measure of general academic performance and suggests that such pressures result in curricula that produces students who are unable to cope effectively with the numeracy demands of everyday life and work.
She raises a key point that numeracy should be since as a component of all subjects across the curriculum thus affording multiple contexts for making connections among mathematical ideas.
Steen offers a brief history of quantitative literacy noting the concept belongs to the late twentieth century. However, she also falls into the trap of using numeracy anachronistically and one gets the idea that the word was actually being used in the nineteenth century:
"In colonial America, leaders such as Franklin and Jefferson promoted numeracy to support the new experiment in popular democracy, even as skeptics questioned the legitimacy of policy arguments based on empirical rather than religious grounds."
(p. 3)
While noting the contested nature of the term quantitative literacy, she uses numeracy and quantitative literacy interchangeably. Sometimes quantitative literacy was seen as related to statistics. The author rejects this and stakes a claim for quantitative literacy as a habit of mind and distinct from statistics or mathematics. However, she continues to use numeracy as a synonym for QL. One would have to say, however, that the argument that statistics is about uncertainty; whereas numeracy is about “the logic of certainty” (p. 5) is specious at best and betrays a fundamental lack of mathematical understanding.
Steen warns of the need for balance in connecting mathematics to authentic contexts as contextual details may in fact “camouflage broad patterns that are the essence of mathematics” (p.5). She also criticizes the way performance in abstract school mathematics has been traditionally use as an academic gatekeeper or measure of general academic performance and suggests that such pressures result in curricula that produces students who are unable to cope effectively with the numeracy demands of everyday life and work.
She raises a key point that numeracy should be since as a component of all subjects across the curriculum thus affording multiple contexts for making connections among mathematical ideas.
Working the boundaries - social practices
Baker, D., Street, B., & Tomlin, A. (2001). Understanding home school relations in numeracy. Paper presented at the Proceedings of the British Society for Research into Learning Mathematics 21(2) July 2001. Retrieved October 25, 2007 from http://www.bsrlm.org.uk/IPs/ip21-2/BSRLM-IP-21-2-9.pdf
This article pursues the theme of mathematics and /numeracy as a social practices and the incommensurate natures of academic and everyday settings and discourses. The paper interrogates “underachievement” in numeracy from perspectives of mathematics as a social practice. Much of the discourse in explaining underachievement in numeracy has focused on institutional considerations and practices (teacher knowledge, pedagogical issues, curriculum, methodologies and so forth). This is much to the exclusion of everyday considerations and practices.
The “boundaries and barriers” (p. 42) between school and home were investigated. The authors propose that the social must not be seen in simplistic terms, but rather in explicit epistemological terms and in configurations of “ideology and discourse, power relations, values, beliefs, social relations and social institutions” (p. 42). In particular, the social relations involved in social practices involve positioning and identities afforded in differential numeracy practices which are inherently social.
The home takes on a contradictory social role – as a place of everyday numeracy practices, but also a place where academic/institutional practices are supposed to be reinforced. The home thus can become a place where knowledges are at least implicitly contested.
The authors sought in their studies to replace “deficit and hierarchical” models of numeracy practice with models in which a “social practices” account highlights multiple practices and knowledge resources (p.47). It is here where the complex interrelations between school and home practices are acknowledged.
This article pursues the theme of mathematics and /numeracy as a social practices and the incommensurate natures of academic and everyday settings and discourses. The paper interrogates “underachievement” in numeracy from perspectives of mathematics as a social practice. Much of the discourse in explaining underachievement in numeracy has focused on institutional considerations and practices (teacher knowledge, pedagogical issues, curriculum, methodologies and so forth). This is much to the exclusion of everyday considerations and practices.
The “boundaries and barriers” (p. 42) between school and home were investigated. The authors propose that the social must not be seen in simplistic terms, but rather in explicit epistemological terms and in configurations of “ideology and discourse, power relations, values, beliefs, social relations and social institutions” (p. 42). In particular, the social relations involved in social practices involve positioning and identities afforded in differential numeracy practices which are inherently social.
The home takes on a contradictory social role – as a place of everyday numeracy practices, but also a place where academic/institutional practices are supposed to be reinforced. The home thus can become a place where knowledges are at least implicitly contested.
The authors sought in their studies to replace “deficit and hierarchical” models of numeracy practice with models in which a “social practices” account highlights multiple practices and knowledge resources (p.47). It is here where the complex interrelations between school and home practices are acknowledged.
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