Should Problem Solving Be Used as a Learning Device in Mathematics?

Owen, Elizabeth; Sweller, John

doi:10.2307/749520

Cited by 30 publications

(20 citation statements)

References 13 publications

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“…These results confirm the critical importance of linking instructional design in mathematics to our knowledge of cognitive architecture (see Lawson, 1990;Owen & Sweller, 1989;and Sweller, 1990 for an earlier debate on these issues). Those aspects of our cognitive architecture discussed in the present paper are quite uncontroversial.…”

Section: Discussionsupporting

confidence: 84%

Translating words into equations: a cognitive load theory approach

Pawley

Ayres

Cooper

et al. 2005

Educational Psychology

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The conditions under which explicit instruction in checking, combined with worked examples, may be beneficial in learning how to translate sentences into algebraic equations was examined from the perspective of cognitive load theory. In two experiments it was shown that Grade 8 and 9 students were initially disadvantaged by the inclusion of a checking method. However, after a more substantial period of acquisition, students with a low level of mathematical knowledge performed significantly better after receiving checking instructions than those who did not receive checking instructions. In contrast, higher knowledge students were continually disadvantaged by the inclusion of a checking method. The positive effect of checking for lower knowledge students and the negative effect for higher knowledge students in this domain is a further example of the expertise reversal effect.

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Section: Discussionsupporting

confidence: 84%

Translating words into equations: a cognitive load theory approach

Pawley

Ayres

Cooper

et al. 2005

Educational Psychology

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“…Owen and Sweller (1989) are skeptical about the role of these strategies in facilitating the transfer of learning, arguing instead that failure to transfer is more likely to result from the student's lack either of particular schema or of sufficiently automatized rules. Recent analyses of transfer suggest that this position should be revised to include a wider range of factors, including general problem-solving strategies, that can influence the presence and extent of transfer of learning.…”

Section: Transfer and Transfer Failurementioning

confidence: 96%

The Case for Instruction in the Use of General Problem-Solving Strategies in Mathematics Teaching: A Comment on Owen and Sweller

Lawson¹

1990

Journal for Research in Mathematics Education

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“…In other words, under many commonly found conditions, leaming and problem solving may be incompatible. (See Owen & Sweller, 1989, for a more detailed exposition of this position, Lawson, 1990 for a response, and Sweller, 1990, for a reply to Lawson). Two techniques have been used to simultaneously provide evidence for this suggestion and to test alternatives to conventional problem solving that are more in accord with the requirements of schema acquisition.…”

Section: Using Problem Solving As a Learning Techniquementioning

confidence: 99%

Some cognitive factors relevant to mathematics instruction

Sweller

Low

1992

Math Ed Res J

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Our understanding of cognitive processes has progressed sufficiently in the last few years to enable us to generate novel instructional techniques that can enhance substantially learning of subjects such as mathematics. This paper will review briefly some research intended to contribute to this process. There are two relevant aspects. Firstly, recent work has thrown light on schema acquisition while learning mathematics, and on techniques for detecting schemas in mathematics learners. Secondly, other research has assessed the distribution of cognitive resources while learning mathematics and other related subjects leading to the design of instructional techniques to facilitate schema acquisition. The Relevance of Schemas to Mathematica) ExpertiseCognitive research findings have revealed the importance of schema acquisition in successful leaming and problem solving in mathematics (see Sweller, 1988). A problem schema can be defined as a cognitive construct that allows problem solvers to recognise a problem as belonging to a specific category that requires particular moves for solution. This definition includes problem states, problem-solving operators, and their relations.Consider a problem such as, "If a boat travelled downstream in 120 minuten with a current of 5 kilometres per hour and the return trip against the same current took 3 hours, what was the speed of the boat in stil) water?" Irrespective of the person's skill in computation and their basic linguistic and factual knowledge (e.g., what "stil) water" means, that rivers have currents that run only downstream), this problem is beyond the capability of someone who does not know the specific relations between speed of boat, rate of current, and time involved in river current contrast problems. In the absence of such schematic knowledge, there is no context for computation and calculation. The person needs to be able to identify the problem as belonging to a given type (e.g., river current contrast) in order to determine what information from the text should be used, in what sequence, and through what operations (see Mayer, 1987, pp. 345-373).

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Should Problem Solving Be Used as a Learning Device in Mathematics?

Cited by 30 publications

References 13 publications

Translating words into equations: a cognitive load theory approach

Translating words into equations: a cognitive load theory approach

The Case for Instruction in the Use of General Problem-Solving Strategies in Mathematics Teaching: A Comment on Owen and Sweller

Some cognitive factors relevant to mathematics instruction

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