**APA**

**In-text citation:** (Ruthven & Lavicza, 2011)

**Reference:** Ruthven, K., & Lavicza, Z. (2011). Didactical Conceptualization of Dynamic Mathematical Approaches: Example Analysis from the InnoMathEd Program. *International Electronic Journal of Mathematics Education, 6*(2), 89-110.

**AMA**

**In-text citation:** (1), (2), (3), etc.

**Reference:** Ruthven K, Lavicza Z. Didactical Conceptualization of Dynamic Mathematical Approaches: Example Analysis from the InnoMathEd Program. *INT ELECT J MATH ED*. 2011;6(2), 89-110.

**Chicago**

**In-text citation:** (Ruthven and Lavicza, 2011)

**Reference:** Ruthven, Kenneth, and Zsolt Lavicza. "Didactical Conceptualization of Dynamic Mathematical Approaches: Example Analysis from the InnoMathEd Program". *International Electronic Journal of Mathematics Education* 2011 6 no. 2 (2011): 89-110.

**Harvard**

**In-text citation:** (Ruthven and Lavicza, 2011)

**Reference:** Ruthven, K., and Lavicza, Z. (2011). Didactical Conceptualization of Dynamic Mathematical Approaches: Example Analysis from the InnoMathEd Program. *International Electronic Journal of Mathematics Education*, 6(2), pp. 89-110.

**MLA**

**In-text citation:** (Ruthven and Lavicza, 2011)

**Reference:** Ruthven, Kenneth et al. "Didactical Conceptualization of Dynamic Mathematical Approaches: Example Analysis from the InnoMathEd Program". *International Electronic Journal of Mathematics Education*, vol. 6, no. 2, 2011, pp. 89-110.

**Vancouver**

**In-text citation:** (1), (2), (3), etc.

**Reference:** Ruthven K, Lavicza Z. Didactical Conceptualization of Dynamic Mathematical Approaches: Example Analysis from the InnoMathEd Program. INT ELECT J MATH ED. 2011;6(2):89-110.

# Abstract

This paper examines examples of teaching approaches involving the use of dynamic mathematics software. These were nominated as successful approaches by four organizations participating in the InnoMathEd professional development program. The most common type of task reasoning structure was one which required students to quantitatively formulate a mathematical relationship expressed by a visual representation. The examples nominated by most of the organizations reflected a more didactic, guided-discovery orientation grounded in directed action, but those from one organization reflected a more adidactic, problem-solving orientation grounded in constrained solution. Instrumental demands on students varied substantially between examples, calling for very different levels of preparation and guidance. The core idea behind these dynamic approaches was one of manipulating displayed representations so as to highlight associated variation (or non-variation) of properties, and relations between different states or representations. Employing this type of user interaction to support visualization and observation was seen as creating a learning environment that encourages exploration and experimentation through which mathematical properties and relationships can be discovered.