Children’s use of realistic considerations in problem solving: some English evidence

Cooper, Barry; Harries, Tony

doi:10.1016/j.jmathb.2003.09.004

Cited by 24 publications

(21 citation statements)

References 9 publications

(9 reference statements)

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“…A physical representation may motivate participants to be involved in the problem they are solving and may help them construct a correct representation of the problem. Research that has investigated physical representation in the past also has similar conclusions about the representation's effectiveness (Cooper & Harries, ; De Lange, ; Freudenthal, ; Palm, ). Given its effectiveness here and the documented benefits in mathematical education and judgment and decision‐making literature (Aprea & Ebner, ; De Corte et al, ; Galesic et al, ; Garcia‐Retamero & Dhami, ; Garcia‐Retamero & Galesic, ; Garcia‐Retamero et al, ), physical representations will also be effective in reducing CH reliance in a wider range of nonlinear problems and contexts.…”

Section: Discussionmentioning

confidence: 82%

Reducing the Linear Perception of Nonlinearity: Use of a Physical Representation

Dutt

González

2011

Behavioral Decision Making

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Research shows that while judging accumulations of quantities over time (e.g., money in a bank account or CO 2 in Earth's atmosphere), people assume that the shape of the accumulation is similar to the shape of the inflow (i.e., people rely on a correlation heuristic). Relying on the correlation heuristic is particularly worrisome for Earth's climate, as judging the CO 2 accumulation according to its emissions (inflow) would underestimate the actual (nonlinear) increase. This misperception undermines the seriousness of climate problem and results in wait-and-see behavior. We report two experiments where the effectiveness of a physical representation is compared with graphical and text representations in reducing people's underestimation of nonlinear accumulation in different contexts and problems. A physical representation presents an accumulation using a picture that works as a metaphor. In the first experiment, participants drew the shape of an accumulation over time relying on physical or graphical representations in one of two contexts: carbon dioxide and marbles. Although the participants underestimated the accumulation in both contexts, underestimations were reduced in the physical representation compared with the graphical representation. In the second experiment, we extended the evaluation of physical representations against both text and graphical representations in two different climate problems (with linearly increasing or decreasing inflow). Again, underestimations of the accumulation were reduced in the physical representation compared with the other two representations, regardless of the nature of the problem. We discuss implications of using the physical representation for improving people's estimates of nonlinear CO 2 accumulation.

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Section: Discussionmentioning

confidence: 82%

Reducing the Linear Perception of Nonlinearity: Use of a Physical Representation

Dutt

González

2011

Behavioral Decision Making

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“…It seemed that working class children were more likely than service class children to introduce aspects of their everyday knowledge in ways that were not intended by the designers of the items and were thereby disadvantaged (Cooper & Dunne, 1998). Cooper & Harries (2003) proposed a continuum of context problems representing the range of extents to which students are expected to take account of extra-mathematical aspects of context. At one end of the spectrum, the extra-mathematical material is completely extraneous and the intention is that it be ignored.…”

Section: Evidence In Relation To Impacts On Students' Mathematical Unmentioning

confidence: 99%

Putting Context in Context: An Examination of the Evidence for the Benefits of ‘Contextualised’ Tasks

Beswick

2011

Int J of Sci and Math Educ

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This is completely the opposite of what Van den Heuvel-Panhuizen has argued for in several publications (e.g. Van den Heuvel-Panhuizen & Becker, 2003) and says in her text on page 142 in Van den Heuvel-Panhuizen (1999): Psychometric-based testing can never be a complete model for didactical assessment. Developing didactical assessment problems implies ignoring a number of traditional requirements for assessment problems and dispelling a number of misconceptions about mathematical problems which have long determined assessment, namely that assessment problems: should be unambiguous; should provide students with all the data needed; should only have one correct answer, and so on. The online version of the original article can be found at

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“…Cooper and Harries (2003) conducted a study on DWR problem for solving and interpreting. The participants of their study was 14 working class students who were 11-12 years old.…”

Section: Resultsmentioning

confidence: 99%

An Exami̇nati̇on of Preservi̇ce Mathemati̇cs Teachers’ Reali̇sti̇c Approaches Wi̇th Di̇vi̇si̇on Wi̇th Remai̇nder (Dwr) Problems

Arıkan¹,

Unal²

2016

IJOSES

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The purpose of this study was to investigate prospective mathematics teachers' realistic approaches during problem solving and posing. In advance of this study, pilot study had been implemented to see its necessity. According to findings of pilot study, the current study was required. The current study is a case study of qualitative research methods. 40 mathematics teacher candidates, who study at a state university in Istanbul, participated in this study. Questions were developed by Chen et al. (2005) were used in the study. Descriptive statistics and percent frequency methods were used in data analyzing. As a result, the study was of high importance for prospective teachers to recognize realistic problems.

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Children’s use of realistic considerations in problem solving: some English evidence

Cited by 24 publications

References 9 publications

Reducing the Linear Perception of Nonlinearity: Use of a Physical Representation

Reducing the Linear Perception of Nonlinearity: Use of a Physical Representation

Putting Context in Context: An Examination of the Evidence for the Benefits of ‘Contextualised’ Tasks

An Exami̇nati̇on of Preservi̇ce Mathemati̇cs Teachers’ Reali̇sti̇c Approaches Wi̇th Di̇vi̇si̇on Wi̇th Remai̇nder (Dwr) Problems

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