# On the instructional triangle and sources of justification for actions in mathematics teaching

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## Abstract

We elaborate on the notion of the instructional triangle, to address the question of how the nature of instructional activity can help justify actions in mathematics teaching. We propose a practical rationality of mathematics teaching composed of norms for the relationships between elements of the instructional system and obligations that a person in the position of the mathematics teacher needs to satisfy. We propose such constructs as articulations of a rationality that can help explain the instructional actions a teacher takes in promoting and recognizing learning, supporting work, and making decisions.

## Keywords

Mathematics Teaching Mathematics Teacher Mathematical Task Practical Rationality Mathematical Work## Notes

### Acknowledgments

The ideas reported in this paper have been developed in part with the support of National Science Foundation Grants ESI-0353285 and DRL-0918425 to the authors. All opinions are those of the authors and do not necessarily represent the views of the Foundation. The authors thank Ander Erickson and three anonymous reviewers for valuable comments on an earlier version.

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