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CHILDREN’S APPROACHES TO MATHEMATICAL PROBLEM SOLVING

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CHILDREN’S APPROACHES TO MATHEMATICAL PROBLEM SOLVING

Author: Dianne Siemon

Publication Year: 1992

Abstract

This paper reports on one aspect of a study designed to explore the role of metacognition in fourth grade children's mathematical problem solving. A response mapping technique was developed to represent individual problem solving episodes in terms of Flavell' s (1981) model of cognitive monitoring. The consistency of the patterns observed in the individual models suggested a relationship between conceptual and procedural knowledge of a cognitive and metacognitive kind. A meta-model was proposed to describe andexplain the nature of this inferred relationship. The paper provides an outline of the response mapping technique, a summary of the meta-model, and an example of the response map data. The analysis supported the view that children's approaches to mathematical problem solving can be described in terms of the four generic approaches identified by the meta-model, that is, a Solver's approach (high conceptual-high procedural), a Diver's approach (high conceptual-low procedural), a Player's approach (low conceptual-high procedural), and a Survivor's approach (low conceptual-low procedural)

Type: research paper

DIANNE SIEMON
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Short Communications & Round Tables

The following documents are essential to read and complete when considering submitting a short communication or round table to the MERGA conference (available in the Submission section of this website).

MERGA Paper Template – to be used to write the abstracts which are then submitted to the MERGA conference website
MERGA Publication Agreement – to be submitted on the MERGA conference website at the time of the abstract submission

Submissions not exceeding one page are required for short communications and round tables. The submissions must be prepared using the conference template, and can include essential references. They will be reviewed by the Editorial Team and, if accepted, will be published in the conference proceedings as one-page abstracts (not as papers). Presenters are invited to prepare a paper for distribution at the conference, but these papers will not be included in the proceedings.

Short communications are suitable for reports on research in mathematics education that do not fully meet the requirements for published papers. These might include works in preliminary stages, reports of pilot projects, initial reviews of literature, ideas or suggestions for future study, and briefer discussions of particular issues. Short communications allow new researchers to obtain feedback on projects in a constructive and supportive environment, and foster the building of links between researchers with similar interests.

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Round tables are led by author(s) only, allocated the same time as research reports (in past, this was 40 minutes). The abstracts should make clear the interactive element of the proposed activity, with no more than 15 min of the session time in a presentation mode.

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MERGA Paper Template – to be used to write the papers which are then submitted to the MERGA conference website
MERGA Publication Agreement – to be submitted on the MERGA conference website at the time of the paper submission

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1. Reports of empirical investigations

When empirical investigations are reported (such as in an experimental intervention, confirmatory study, or action research, etc.), the paper should also include

a statement of rationale for methodologies used in collecting and analysing data;
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a theoretical discussion;
a position paper;
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a literature review, a meta-study;
an account of a new initiative;
a reflective critique of practice; or
any mixture of these or other recognised scholarly forms.

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Structure of research papers – All papers for publication in the conference proceedings should contain the following:

a statement of the problem/issue and a discussion of its significance;
a critical analysis of the research literature as it relates to the topic of the paper; and
conclusions and implications for mathematics education derived from the study.

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MERGA Paper Template (to be used to write the papers which are then submitted to the MERGA conference website)
MERGA Publication Agreement (to be submitted on the MERGA conference website at the time of the paper submission)

Presentation of groups of published papers related by theme in the form of a research symposium is encouraged. The symposium forum will be particularly suitable for presentations relating to a single large project or presentations that explore topical themes from different and/or related perspectives. Special Interest Groups [SIGs] are encouraged to consider the symposium option as a means for sharing and discussing current research.

A symposium should consist of no more than four presentations of about 15 minutes duration each. The written papers should be half the length of research papers as described for research papers. Both research report types – empirical or non-empirical – are acceptable as published symposium papers.

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The set of symposium papers (and the overview) will be blind reviewed by a review panel. The main purpose of the reviews is the same as for published papers, and the same criteria are used. The reviewers will be asked to consider the cohesiveness of the set of symposium papers. They will indicate whether the symposium as a whole, and each paper within it, should be “accepted”, “rejected” or if it “requires revision”. If it is deemed that one, some or all of the papers are in need of revision, the reviewers will outline which papers need to be revised and provide suggestions for the required changes. When the revisions are made, the symposium papers will be re-submitted and the set of papers will be sent to the same review panel for further consideration. As with research papers, the final decision about which symposium papers will be published is at the discretion of the Editorial Team.

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