Quantitative reasoning in a reconceived view of transfer

Lobato, Joanne; Siebert, Daniel

doi:10.1016/s0732-3123(02)00105-0

Cited by 104 publications

(50 citation statements)

References 24 publications

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“…As described in the empirical context section, the class teacher assumed that students could build knowledge via conjecturing by themselves as Lobato and Siebert (2002) and Zimmerman (1998Zimmerman ( , 2000Zimmerman ( , and 2002) elaborated if they were fully engaged in OCA problem solving. With this assumption, she directed reflective discourse on the process and the constructs of OCA problem solving in a sense that Cobb and Boufi (1997, p. 258) suggested.…”

Section: Discussionmentioning

confidence: 99%

“…As a result of this instructional approach, learners were able to voice diverse views on relational similarities. One new perspective on the transfer of learning called actor-oriented transfer (Lobato & Siebert, 2002), supports the use of analogical reasoning in a broader sense rather than just the application of the aforementioned three analogies. Based on empirical evidence, Lobato and Siebert claim that a teacher should develop better understanding of how students find or construct relational similarity to design instruction rather than just distinct surface or structure in similarity from his/her point of view and give static tasks to promote transfer (pp.…”

Section: Re-conception Of Classical Analogymentioning

confidence: 99%

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Conjecturing via reconceived classical analogy

Lee

Sriraman

2010

Educ Stud Math

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Analogical reasoning is believed to be an efficient means of problem solving and construction of knowledge during the search for and the analysis of new mathematical objects. However, there is growing concern that despite everyday usage, learners are unable to transfer analogical reasoning to learning situations. This study aims at facilitating analogy use for conjecturing in discourse-rich mathematics classrooms. We reconceptualized one of the traditional perspectives on analogical reasoning, called classical analogy, as a more dynamic one by providing learners with the opportunity to choose a target object and its property. While shifting attention to particular aspects of mathematical activity, we observed and analyzed how students became aware of hidden relational similarities and utilized them while weakening others to make conjectures. The detailed analysis of the constructs and processes of several similarity-making and conjecturing activities supports the significance of reconceived classical analogy use in mathematics classrooms.

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Section: Discussionmentioning

confidence: 99%

Section: Re-conception Of Classical Analogymentioning

confidence: 99%

Conjecturing via reconceived classical analogy

Lee

Sriraman

2010

Educ Stud Math

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“…Izsák (2000) analyzed processes of notation variation and mapping variation that eighth-grade students used when constructing algebraic models of linear motions in a physical device, and Roschelle (1998) introduced registrations to characterize similar knowledge when analyzing students' qualitative reasoning about Newtonian motion simulated by a computer microworld. Other researchers (Lobato, Ellis, & Muñoz, 2003;Lobato & Siebert, 2002;Meira, 1995;Monk & Nemirovsky, 1994;Moschkovich, 1998;Nemirovsky, 1994;Schoenfeld, Smith, & Arcavi, 1993) also reported instances in which learning to focus on and use features of graphs and tables-including y-intercepts, x-intercepts, and slopes-and attributes of physical objects for solving problems has been a significant accomplishment for students.…”

Section: Selecting Attributesmentioning

confidence: 98%

"You Have to Count the Squares": Applying Knowledge in Pieces to Learning Rectangular Area

Izsák¹

2005

Journal of the Learning Sciences

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This article extends and strengthens the knowledge in pieces perspective (diSessa, 1988(diSessa, , 1993 by applying core components to analyze how 5th-grade students with computational knowledge of whole-number multiplication and connections between multiplication and discrete arrays constructed understandings of area and ways of using representations to solve area problems. The results complement past research by demonstrating that important components of the knowledge in pieces perspective are not tied to physics, more advanced mathematics, or the learning of older students. Furthermore, the study elaborates the perspective in a particular context by proposing knowledge for selecting attributes, using representations, and evaluating representations as analytic categories useful for highlighting some coordination and refinement processes that can arise when students learn to use external representations to solve problems. The results suggest, among other things, that explicitly identifying similarities and differences between students' past experiences using representations to solve problems and demands of new tasks can be central to successful instructional design.This case study applies core components of an epistemological perspective referred to as knowledge in pieces (diSessa, 1988(diSessa, , 1993 to answer an instance of the following research question: How can students coordinate their understandings of problem situations with those of external representations when learning to solve problems? DiSessa developed the knowledge in pieces perspective to explain emerging expertise in Newtonian mechanics. The perspective holds that knowledge elements are more diverse and smaller in grain size than those presented in

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“…A strategy referred to as unit analysis, dimensional analysis, or proportional analysis commonly occurs in engineering and science. Lobato describes proportional analysis as a valuable strategy implemented by expert problem solvers 14 . Proportional analysis or unit analysis is the use of units to derive relationships between variables to solve the problem.…”

Section: Problem Solving Strategiesmentioning

confidence: 99%

“…Proportional analysis or unit analysis is the use of units to derive relationships between variables to solve the problem. This strategy is particularly useful if the student does not remember equations required to solve the problem 14 .…”

Section: Problem Solving Strategiesmentioning

confidence: 99%

Connections Between Undergraduate Engineering Students’ Problem-solving Strategies and Perceptions of Engineering Problems

McGough¹,

Kirn²,

Faber³

2015 ASEE Annual Conference and Exposition Proceedings

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Lisa Benson is an Associate Professor of Engineering and Science Education at Clemson University, with a joint appointment in Bioengineering. Her research focuses on the interactions between student motivation and their learning experiences. Her projects involve the study of student perceptions, beliefs and attitudes towards becoming engineers and scientists, and their problem solving processes. Other projects in the Benson group include effects of student-centered active learning, self-regulated learning, and incorporating engineering into secondary science and mathematics classrooms. Her education includes a B.S.

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Quantitative reasoning in a reconceived view of transfer

Cited by 104 publications

References 24 publications

Conjecturing via reconceived classical analogy

Conjecturing via reconceived classical analogy

"You Have to Count the Squares": Applying Knowledge in Pieces to Learning Rectangular Area

Connections Between Undergraduate Engineering Students’ Problem-solving Strategies and Perceptions of Engineering Problems

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