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INTEGRATING COMPUTERS INTO THE TEACHING OF CALCULUS: DIFFERENTIATING STUDENT NEEDS

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INTEGRATING COMPUTERS INTO THE TEACHING OF CALCULUS: DIFFERENTIATING STUDENT NEEDS

Author: Julie Ryan

Publication Year: 1992

Abstract

The study undertaken here looked at difficulties associated with the first
principles approach to the derivative of a function and concentrated in
particular on the first five lessons in calculus as experienced by a typical
group of nineteen year 10 students who were preparing to take calculus at
year 11. A traditional teaching approach was contrasted with an alternative
computer teaching approach and both approaches were analysedfor success
in terms of conceptual understanding, skill acquisition and student
perceptions of whether the work was easy to understand. The traditional first
principles approach was found to be too cognitively demanding for the
students who demonstrated a 'rush to rule' for meaning. Students undergoing
the computer treatment also demonstrated this rush to rule and therefore
very gradual development is recommended for students in their first
encounters with calculus.

Type: Research Paper

JULIE RYAN
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Short Communications & Round Tables

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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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The following documents are essential to read and complete when considering submitting a research paper to the MERGA conference (available in the Submission section of this website).

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

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a theoretical discussion;
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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.

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.

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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.

A brief overview of the symposium (limit one page), including a symposium title, 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. Please list the symposium convenors as the authors on the first page, and name the paper authors in the text description.

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.

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