Measures and References: Statistical Reasoning

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Numerous measures exist to gain a full picture of a student's learning strengths and challenges. Following are examples of measures used to assess this Learner Factor. These measures should be administered and interpreted by experienced professionals.

Statistical Variation Measure (Watson et al., 2003): Questionnaire examining student understanding of statistical variation, including understanding of basic chance measurement and graph reading, variation in a chance setting (e.g., results of throwing a die), and variation in data and graphs. Students respond to multiple choice questions but also have space to explain their responses which allows for a more comprehensive measure of their understanding.

KeyMath-3 Diagnostic Assessment (Connolly, 2007): In the Data Analysis/Probability subtest, students interpret tables and tally charts, and estimate probability.


Amir, G. S., & Williams, J. S. (1999). Cultural influences on children's probabilistic thinking. The Journal of Mathematical Behavior, 18(1), 85-107.

Chiesi, F., Primi, C., & Morsanyi, K. (2011). Developmental changes in probabilistic reasoning: The role of cognitive capacity, instructions, thinking styles, and relevant knowledge. Thinking and Reasoning, 17(3), 315-350.

Connolly, A. J. (2007). KeyMath diagnostic assessment (3rd ed.). Minneapolis, MN: Pearson Assessments.

delMas, R. C. (2002). Statistical literacy, reasoning, and thinking: A commentary. Journal of Statistics Education, 10(2).

English, L. D., & Watson, J. M. (2015). Exploring variation in measurement as a foundation for statistical thinking in the elementary school. International Journal of STEM Education, 2(1), 1-20.

English, L. D., & Watson, J. M. (2016). Development of probabilistic understanding in fourth grade. Journal for Research in Mathematics Education, 47(1), 28-62.

Gal, I. (2005). Towards "Probability Literacy" for all citizens : Building blocks and instructional dilemmas. Exploring Probability in School: Challenges for Teaching and Learning, (April), 43-71.

Langrall, C. W., & Mooney, E. S. (2005). Characteristics of elementary school students' probabilistic reasoning. In G. A. Jones (Ed.), Exploring Probability in School: Challenges for Teaching and Learning (pp. 95-119). Boston, MA: Springer US.

Langrall, C. W., Makar, K., Nilsson, P., & Shaughnessy, J. M. (2017). Teaching and learning probability and statistics: An integrated perspective. In Jinfa Cai (Ed.), Compendium for research in mathematics education (pp. 490-525) Reston, VA, United States: National Council of Teachers of Mathematics.

Makar, K. (2014). Young children's explorations of average through informal inferential reasoning. Educational Studies in Mathematics, 86(1), 61-78.

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core standards mathematics. Washington, DC: Authors.

Obersteiner, A., & Bernhard, M. (2015). Primary school children's strategies in solving contingency table problems: The role of intuition and inhibition. ZDM Mathematics Education, 47, 825-836.

Vukovic, R. K., & Lesaux, N. K. (2013). The language of mathematics: Investigating the ways language counts for children's mathematical development. Journal of Experimental Child Psychology, 115(2), 227-244.

Watson, J. M., Kelly, B. A., Callingham, C. A., & Shaughnessy, J. M. (2003). The measurement of school students' understanding of statistical variation. International Journal of Mathematical Education in Science and Technology, 34(1), 1-29.

Watson, J. M. (2007). The role of cognitive conflict in developing students' understanding of average. Educational Studies in Mathematics, 65(1), 21-47.