List of Content

December 2008

Editorial

Theory

Maps and Math: Connecting Cartography, Art and Social Justice to mathematics
Brian R. Evans

Using Clinical Interview with Low-Performing Students in Mathematics
Eric Fuchs, Violetta Menil

The Transition from Pre-algebra to Algebra: Learning Theories-Based Instructional Tasks
William Baker, Bronislaw Czarnocha

Achilles and Tortoise – Teaching Experiment: Working within the Zone of Proximal Development. A Case Study
Bronislaw Czarnocha, Vrunda Prabhu

Corresponding Teaching-Research Workshop Tasks

Maps and Math Activities
Brian R. Evans

Examples of Clinical Interviews
Eric Fuchs, Violeta Menil

Instructional Sequence
William Baker, Bronislaw Czarnocha

(A&T) Essay Assignments and Student Response
Bronislaw Czarnocha, Vrunda Prabhu

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Editorial: Workshop in the Craft of Teaching-Research

This unusual issue of MTRJ brings together a workshop in the craft of teaching-research. How to do it? – is the theme of this issue which includes several collected examples of TR activity.

Each submission to this issue has two parts, the theoretical or descriptive part, and the corresponding set of examples, tasks or instructional sequences. The text of each article is linked to the corresponding example of the tasks, and vice-versa.

We start with the description of a simple classroom teaching experiment which joins together mathematics, art and social justice. It shows how a simple classroom research can be analyzed statistically (with the help of SPSS) giving it general educational research value.

This work is followed by Baker, Czarnocha contribution showing how to apply general learning theories available in the profession to the design of the instructional sequence in agreement with the development of concepts. The theories applied are duality theories, that is theories based on the duality of mathematical process and object such as Dubinsky‘s APOS theory and Sfard‘s reification theory integrated with Shuell/Shepard schema theory. The work by Fuchs and Menil introduces the technique of clinical interviews into regular remedial activities, where the interview becomes as much a teaching as an investigative tool. Emerging internal structure of teaching research interviews with dual roles is worth paying attention to.

The work by Czarnocha, Prabhu demonstrates how to use the Zone of Proximal Development in the design and analysis of essay assignments analyzing Zeno’s Achilles and Tortoise paradox.

This issue of MTRJoL is dedicated to colleagues, Teacher-Researchers interested in the development of the TR craft.