Building and Understanding Multiplicative Relationships: A Study of Prospective Elementary Teachers

Simon, Martin; Blume, Glendon W.

doi:10.2307/749486

Cited by 71 publications

(65 citation statements)

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“…This study contributes to the discussion (e.g. Simon & Blume, 1994;Southwell & Penglase, 2005;Misailidou & Williams, 2002;Tatto, Schwillie, Senk, & Ingvarson, 2012) of strengths and weaknesses of pre-service teachers MCK of proportional reasoning.…”

Section: Introductionmentioning

confidence: 99%

Second-Year Pre-Service Teachers’ Responses to Proportional Reasoning Test Items

Livy

Herbert

2013

AJTE

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Section: Introductionmentioning

confidence: 99%

Second-Year Pre-Service Teachers’ Responses to Proportional Reasoning Test Items

Livy

Herbert

2013

AJTE

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“…These studies have demonstrated that a fully developed understanding of linear and area measurement requires the coordination of multiple ideas and that the process of coordination can vary from student to student. Moreover, Simon and Blume (1994) demonstrated that difficulties coordinating ideas related to linear and area measurement can persist well beyond elementary grades. They found that, in a group of 26 preservice teachers, many did not fully understand the multiplicative relation between linear and area measurements of rectangles.…”

Section: Students' Understandings Of Rectangular Areasmentioning

confidence: 99%

“…Classifications of situations that can be modeled by multiplication have consistently included rectangular areas (e.g., Greer, 1992;Schmidt & Weiser, 1995;Schwartz, 1988;Vergnaud, 1983Vergnaud, , 1988, and research on multiplication has used rectangles to illustrate multiplication of fractions and the commutative property (Greer, 1992). Some researchers have suggested, however, that students connect multiplication to areas of rectangles by reciting, but not understanding, the length times width formula (De Corte, Verschaffel, & Van Coillie, 1988;Nesher, 1992;Peled & Nesher, 1988;Simon & Blume, 1994). Several multiplication studies have taken place in classrooms (e.g., Confrey & Scarano, 1995;Hino, 2002;Izsák, 2004b;Lampert, 1986aLampert, , 1986bMechmandarov, 1987, as discussed by Nesher, 1988;Scarano & Confrey, 1996;Treffers, 1987), but only those by Hino and by Izsák have had a primary focus on arrays and rectangular areas.…”

Section: Research On Whole-number Multiplication Arrays and Rectangmentioning

confidence: 99%

"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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“…Eventhough the PSTs were confortable calculating the area and the perimeter of the presented rectangles in this study, there is evidence in the literature that teachersstruggle with the concepts of perimeter and area (Baturo & Nason, 1996;Fuller, 1997;Heaton, 1992;Ma, 1999). They show limited understanding and various misconceptions such as believing that there is a constant relationship between area and perimeter (Baturo & Nason, 1996;Simon & Blume, 1994;Ma, 1999). Below is an excerpt to demonstrate PSTs' responses to the sample question 3 in table 3.…”

Section: Figure 2 Geometric Shapes Used During Interviewsmentioning

confidence: 99%

Productive Struggle in a Geometry Class

Zeybek

2016

IJRES

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Struggle and its connection to learning are central to improve student learning and understanding of mathematics. A description of what a student's productive struggle looks like in the setting of classrooms can provide insight into how teaching can support or hinder the student's learning process. In order for any struggle to be productive, these struggles with mathematics must be documented. However, prior studies on student struggles are limited and have primarily focused on examining whether or not struggle occurred. Thus, the purpose of this study is to describe pre-service middle grade teachers' (PSTs) struggle types in details as well as to investigate how enagaging in a non-routine high level task (doing mathematics) fosters (or inhibits) productive struggle during instruction.

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Building and Understanding Multiplicative Relationships: A Study of Prospective Elementary Teachers

Cited by 71 publications

References 0 publications

Second-Year Pre-Service Teachers’ Responses to Proportional Reasoning Test Items

Second-Year Pre-Service Teachers’ Responses to Proportional Reasoning Test Items

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

Productive Struggle in a Geometry Class

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