Designing a detailed instructional framework: A teaching experiment in multiplication and division

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Designing a detailed instructional framework: A teaching experiment in multiplication and division

Designing a detailed instructional framework: A teaching experiment in multiplication and division

David Ellemor-Collins

Within a larger design research project, we developed an instructional framework for multiplication and division, to be refined through a teaching experiment with low-attaining primary students. We describe the instruction at multiple scales, from the broad organization into domains and phases, through the sequencing of small topics, to the details of specific instructional activities. We also map the multiple dimensions of mathematisation involved: progressions toward larger numbers, more abstract settings, more formal notations, more sophisticated strategies, and so on. The framework contributes to research on arithmetic instruction; and also to our developing notions of frameworks, learning trajectories, and instructional design.

Research Papers

The following four documents are essential to read and complete when considering to submit a research paper to the MERGA conference.

Research paper guidelines
Research paper template (to be used to write the paper which is then submitted to the MERGA conference website)
Author checklist
Publication Agreement (to be submitting on the MERGA conference website)

Research papers can take two major forms:

i. reports of empirical investigations; or

ii. reports that are not based on empirical research including:

– a theoretical discussion;

– a position paper;

– a report of scholarly enquiry in progress;

– 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.

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.

All papers must respect MERGA’s ethical guidelines relating to research work. Papers should be not more than the set length. (Formatting details and WORD template are available from the submissions). In addition, papers must be: readable; free of grammatical, spelling and typographical errors; and adhere strictly to style requirements advertised by the conference proceedings Editorial Team.

i. 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;
– a critical discussion of data findings in the light of the research literature; and
– in the literature review, prior work in the area should be acknowledged and an explanation of how the work reported in the paper builds on that earlier work should be included.

ii. Theoretical or position papers

When the work is a theoretical discussion, a position paper, a report of scholarly inquiry in progress, a review of literature, a theoretical study, a meta-study, an account of a new initiative, a reflective critique of practice or any mixture of these or other recognised scholarly forms, the material presented must be discussed critically, and alternative points of view relating to themes presented should be appropriately argued.
It is expected that presenting authors will have 40 minutes to present their work at the conference. At least 10 minutes must be allowed to field questions and comments from the audience.

Originality

Only research papers that are substantially different from work that has been published previously will be considered for publication in the conference proceedings and/or presentation at the conference.

Reviewing of research papers

Research papers will be blind reviewed by a panel of peers approved by the conference committee. The main purpose of the refereeing process is to contribute to the growth and development of quality practice in mathematics education research. Thus reviewers are asked to assist authors by providing helpful feedback and to comment on the suitability of papers for presentation at the conference. Accordingly, it will not be assumed that published papers presented at the conference will be as polished as articles in scholarly journals. Referees will be asked to assess papers being reviewed against the accepted norms for scholarly works presented at MERGA conferences, as set out above.

Each conference proceedings’ Editorial Team will exercise discretion over the reviewing process.

Reviewers’ comments will be returned to the authors. Authors whose papers are not accepted for publication may be invited by the editorial panel to present their paper at the conference, with an abstract (only) being published in the proceedings. Papers may be rejected outright, with no opportunity for presentation at the conference in an alternative form.

The MERGA website has detailed advice about criteria for reviewing of MERGA papers, review forms, and examples of strong and poor reviews of different types.

Presentation of research papers

Research papers are presented by author(s) only. A maximum of 30 minutes may be used for presenting the paper, and at least 10 minutes is then used for audience questions and open discussion.

Research Symposia

There are four essential documents to read and complete when considering to submit a research paper to the MERGA conference.

Symposia paper guidelines
Symposia paper template (to be used to write the paper which is then submitted to the MERGA conference website)
Author checklist
Publication Agreement (to be submitting on the MERGA conference website)

Presentation of groups of published papers related by theme in the form 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.

A brief overview of the symposium (limit one page), including a title, the names of presenters, an introduction to the theme/project, and a short introduction to each of the 3-4 contributions, must be submitted with the set of short papers.

The symposium proposer will also nominate a person to chair the symposium, and a discussant can also be named if desired. This information should accompany the collection of papers submitted for review.

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.

The date for submission of the collection of symposium papers is the same as for Early Bird papers. This date has been set for the benefit of the group of authors of symposia papers. Should the symposium papers require revision, the authors will have the time to make the corrections and resubmit the set of symposium papers to be re-reviewed by the original reviewers.

Presentation of symposia

Symposia are presented by author(s) only. At least 10 minutes must be allocated for audience questions and open discussion.

Designing a detailed instructional framework: A teaching experiment in multiplication and division

Designing a detailed instructional framework: A teaching experiment in multiplication and division

Short Communications

Presentation of short communications

Beth Southwell Practical Implications Award

Recent Winners

Applying for entry into the BSPIA

Judging of the BSPIA

History of the Award

Research Papers

Research papers can take two major forms:

i. Empirical investigations

ii. Theoretical or position papers

Originality

Reviewing of research papers

Presentation of research papers

Research Symposia

Early Career Research Award

Recent Winners

Applying for the Award

Early Bird Review Process