Mathematical knowledge for teaching and the mathematical quality of instruction: a study of novice elementary school teachers

  • Rossella SantagataEmail author
  • Jiwon Lee


This study examines the association between mathematical knowledge for teaching and instructional quality in a sample of first-year elementary school teachers. Ten teachers completed the mathematical knowledge for teaching (MKT) survey at the end of teacher preparation. Three mathematics lessons taught during their first year of teaching were videotaped and scored using the Mathematical Quality of Instruction. Findings replicate prior studies that were conducted with more experienced teachers. A strong, positive and statistically significant association was found between teacher knowledge and the mathematics is clear and not distorted dimension of instructional quality. In addition, associations of moderate strength were found between MKT and other dimensions of instructional quality centered on the mathematics taught in the lesson. Analyses also revealed individual differences among teachers and raised the question of what other factors might impact instructional quality. Three cases studies highlight the role of lesson design, mathematics tasks, and participation structures that support or inhibit instructional quality and the use of knowledge during teaching. Conclusions suggest that preparation and induction programs should include a focus on individual teachers’ mathematical knowledge for teaching, the development of a student-centered vision of mathematics instruction, and tailored support during the first year of teaching.


Mathematical knowledge for teaching Instructional quality Novice teachers Elementary school teachers Video Mixed methods Case studies 



The authors thank the teachers for their participation and for opening their classroom door and making their instruction public. In addition, they are grateful to Janet Mercado and Cathery Yeh who assisted with data collection and organization; to Rosalind Alicia Ball who scored lesson videos for inter-rater reliability; and to several undergraduate research assistants who completed lesson transcriptions.


This research was supported by the National Science Foundation (REESE program) under Grant DRL-0953038. Any opinions, findings, and conclusions expressed in this material are those of the authors and do not necessarily reflect the views of the funding agency. Previous versions of this paper were presented at the 2017 biannual meeting of the Korea Society of Educational Studies in Mathematics (KSESM), Korea National University of Education, Cheongju, South Korea and the 2018 annual meeting of the Association of Mathematics Teacher Education, Houston, TX.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.UC Irvine School of EducationUniversity of California, IrvineIrvineUSA

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