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Prospective Mathematics Teachers’ Professional Noticing of Students’ Reasoning about Mean and Variability

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Abstract

This study examined prospective secondary mathematics teachers’ professional noticing of students’ reasoning about mean and variability as described in a current statistics curriculum in the USA. Six prospective mathematics teachers were asked to analyse students’ written solutions to statistics problems, constructed at the two levels described in the statistics curriculum. Findings indicated that prospective teachers had difficulties noticing students’ reasoning about variability. None of the prospective teachers explicitly interpreted the student’s limited understanding of variability when comparing data sets with unequal sample sizes. There was a gradation in their noticing skill, ranging from those who showed no evidence of differentiating between students’ different levels of reasoning and made general pedagogical decisions to those who differentiated between students’ developmental levels and decided how to respond based on students’ existing understanding as well as identifying the intrinsic statistical properties in students’ solutions. Implications for research and mathematics teacher education are discussed.

Résumé

Cette étude se penche sur la capacité professionnelle des futurs enseignants de mathématiques au secondaire à noter le raisonnement des élèves sur la moyenne et la variabilité, tel que décrit dans un programme actuel de statistiques aux États-Unis. Six futurs enseignants de mathématiques ont été invités à analyser les solutions écrites d’étudiants à des problèmes statistiques, élaborés selon les deux niveaux décrits dans le curriculum de statistiques. Les résultats indiquent que les futurs enseignants ont du mal à identifier le raisonnement des élèves sur la variabilité. Aucun des futurs enseignants n’a explicitement interprété la compréhension limitée de la variabilité chez les étudiants lorsque ceux-ci devaient comparer des ensembles de données de tailles inégales. Il y avait des degrés dans leur capacité d’observation, allant de ceux qui ne semblaient ne pas distinguer les différents niveaux de raisonnement des élèves et prenaient des décisions pédagogiques générales, à ceux qui tenaient compte des différents niveaux de développement des apprenants, choisissaient leur façon de répondre en fonction du niveau de compréhension actuelle des étudiants, et identifiaient les propriétés statistiques intrinsèques des solutions proposées par les étudiants. Certaines implications pour la recherche et la formation des enseignants de mathématiques sont également explorées.

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Notes

  1. Note that each of the 6 interpretation categories in Table 2 does not necessarily correspond to different PMTs’ interpretation because each PMT exhibited multiple categories of interpretation.

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Acknowledgements

This study is based on dissertation research conducted by Dongjo Shin at the University of Georgia and under the supervision of AnnaMarie Conner.

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  1. Gifted Education Center, Korea University, 315 Lyceum, 145 Anam-ro, Seongbuk-gu, Seoul, South Korea

    Dongjo Shin

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Correspondence to Dongjo Shin.

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Shin, D. Prospective Mathematics Teachers’ Professional Noticing of Students’ Reasoning about Mean and Variability. Can. J. Sci. Math. Techn. Educ. 20, 423–440 (2020). https://doi.org/10.1007/s42330-020-00091-w

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