In chapter 6, Boaler delivers an account of the variety of assessments she investigates to observe “whether differences existed in the extent, nature or form of students’ understanding” (Boaler, 2002, p.84). Within these she develops two applied assessments which further her aim to investigate the notion of situated learning. “Lave and Wenger (1991) argue that learning should not be viewed as simply the transmission of abstract and decontextualised knowledge from one individual to another, but a social process whereby knowledge is co-constructed; they suggest that such learning is situated in a specific context and embedded within a particular social and physical environment (p.40)” (Wikipedia, 2011). At Amber Hill students have very little exposure to situated learning, unlike Phoenix Park students who are completely immersed in it within their classrooms.
Through the applied assessments Boaler makes a number of interesting observations about the students from both Amber Hill and Phoenix Park. In order to test students performance, at two different points in time Boaler provides two activities: the architectural activity and the planning a flat activity. As students in both schools completed these activities some significance differences regarding students’ mathematical understanding arise.
Before beginning both activities students had to complete related questions concerning the concepts that would be needed to solve the activity. In both cases, Amber Hill students scored higher. However, while completing the activities Phoenix Park significantly outperformed Amber Hill students. During the first activity, although students at Amber Hill were taking from the top set (meaning they were the strongest academically in that cohort), “students related to an inability to decide what to do when they were not given explicit instructions” (p.88). Even though students had learned the appropriate knowledge to solve the problem, when they had to make decisions as to what methods to chose to solve the problem they became lost (Boaler, 2002, p.88).
The second activity provided another insight into Amber Hill’s lack of mathematical understanding. While completing the producing a flat activity Amber Hill students showed difficulty in interpreting the situation and the goals and demands required of them. Students did what they thought was required of them, “ignoring the situation or context in which they were placed” (p.92). Students had the appropriate knowledge to solve the problems but seemed unable to interpret what they had to do; having “difficulty making use of the mathematics they learned in an applied situation” (p.93).
Finally, during the planning a flat activity students at Phoenix Park illustrated a significant degree of creativity when planning their flats. Their designs included unusual rooms and “were ingenious, entailing a creative use of space with interlocking rooms that saved on redundant hall or corridor space. In effect, the students often gave themselves a more demanding cognitive task, but managed to attend to the given rules and constraints of size and scale to produce impressive designs” (p.91). Students from Amber Hill showed much less creativity with designs that were “inaccurate, sketchy, and basic”, even though students seemed to really enjoy the activity (p.91).
I think Amber Hill is an example of a school where “when learning is removed from its context, the value of the knowledge and the relevance of that knowledge to the learner become depreciated” (Duffy & Cunningham, 1996). As Boaler points out students from Amber Hill had difficulty making use of their mathematics, not “due to a lack of mathematics knowledge, but the ways in which students interpreted the demands of the activity” (p.93). Learning is a social event, and in a classroom where students are expected only to regurgitate information instead of think for themselves it cannot be expected that quality learning will ensue. Even though students show much enthusiasm and motivation for the activity, they had not developed the skills to be successful.
Students at Phoenix Park showed much success with both applied assessments. The instruction they received throughout their mathematics education made them bettered prepared to use their mathematics skills, understanding and interpreting the problems they faced.
References:
Boaler, J. (2002). Experiencing School Mathematics. New York: Routledge.
Duffy, T. & Cunningham, D. (1996). Constructivism: Implications for the Design and Delivery of Instruction. In D. Jonassen (Ed.), Handbook of research on educational communications and technology. New York: Simon & Schuster.
Lave, J. & Wenger, E. (1991). Situated Learning. Legitimate peripheral participation, Cambridge: University of Cambridge Press.
Wikipedia. (2011). Situated Learning. Retrieved from http://en.wikipedia.org/wiki/Situated_learning on November 5, 2011.
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