**APA**

**In-text citation:** (Groth, 2010)

**Reference:** Groth, R. E. (2010). Teachers’ Construction of Learning Environments for Conditional Probability and Independence.

*International Electronic Journal of Mathematics Education, 5*(1), 32-35.

https://doi.org/10.29333/iejme/248
**AMA**

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

**Reference:** Groth RE. Teachers’ Construction of Learning Environments for Conditional Probability and Independence.

*INT ELECT J MATH ED*. 2010;5(1), 32-35.

https://doi.org/10.29333/iejme/248
**Chicago**

**In-text citation:** (Groth, 2010)

**Reference:** Groth, Randall E.. "Teachers’ Construction of Learning Environments for Conditional Probability and Independence".

*International Electronic Journal of Mathematics Education* 2010 5 no. 1 (2010): 32-35.

https://doi.org/10.29333/iejme/248
**Harvard**

**In-text citation:** (Groth, 2010)

**Reference:** Groth, R. E. (2010). Teachers’ Construction of Learning Environments for Conditional Probability and Independence.

*International Electronic Journal of Mathematics Education*, 5(1), pp. 32-35.

https://doi.org/10.29333/iejme/248
**MLA**

**In-text citation:** (Groth, 2010)

**Reference:** Groth, Randall E. "Teachers’ Construction of Learning Environments for Conditional Probability and Independence".

*International Electronic Journal of Mathematics Education*, vol. 5, no. 1, 2010, pp. 32-35.

https://doi.org/10.29333/iejme/248
**Vancouver**

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

**Reference:** Groth RE. Teachers’ Construction of Learning Environments for Conditional Probability and Independence. INT ELECT J MATH ED. 2010;5(1):32-5.

https://doi.org/10.29333/iejme/248
# Abstract

Although literature on challenges to students’ learning of data analysis and probability has steadily accumulated over the past few decades, research on challenges encountered in teaching the content area is in its beginning stages. The present study aims to help build this area of research by identifying some knowledge elements necessary for teaching conditional probability and independence. Artifacts of classroom practice, including written plans and lesson video, were used to identify challenges encountered by teachers in establishing productive learning environments for students first learning the concepts. It is proposed that enhanced common and specialized content knowledge may help teachers address the challenges identified. Some salient aspects include knowledge of: distinctions among major concepts, data displays with pedagogical value, and the roles of fractions and combinatorial ideas in the psychology of learning conditional probability and independence. The discussion of these and other relevant knowledge aspects is drawn upon to propose potentially productive directions for teacher education efforts and future research.