Hitting the Conceptual Knowledge Wall: Pre-Service Teacher Responses to High-Stakes Mathematics Testing Failure

Oct 15, 2026

Research examines two pre-service teachers who initially failed to reach the 60% passing requirement on a Mathematics for Teaching Exam at the end of their first intermediate-level mathematics methods course. The exam serves as a graduation requirement within a teacher education program at a university in Ontario. The study contrasts divergent reactions—growth and learning versus anger and hostility—and analyzes how these responses shape later mathematics learning, including their unexpected effects on peers, and raises concerns about using a high-stakes test as a mandatory requirement.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages29

Reading Time1 h 13 min

AccessFree to download

Abstract

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Hitting the Conceptual Knowledge Wall: Pre-Service Teacher Responses to High-Stakes Mathematics Testing Failure Jennifer Holm Wilfrid Laurier University Ann Kajander Lakehead University Abstract The research reported here is part of a larger study and examines the cases of two individuals who were initially unable to achieve the required 60% passing grade on a Mathematics for Teaching Exam at the end of their first enrolment in an intermediate-level mathematics methods course. The exam is a graduation requirement of the teacher education program at a specific university in Ontario. The two individuals reacted in markedly different ways to the news that they had not met the mathematics requirement: one took itas an opportunity to grow and learn the mathematics she was aware she had never learned Canadian Journal of Education / Revue canadienne de l’éducation 43:3 (2020)©2020 Canadian Society for the Study of Education/ Société canadienne pour l’étude de l’éducation [www.cje-rce.ca](www.cje-rce.ca) in her past; the other became angry and hostile, blaming his professor for his lack of success. In this article, we present the contrasts in approach between the cases, and how the responses influenced the participants’ further mathematics learning. As well, the somewhat unexpected impact that these responses had on the subjects’peers is explored. Finally, we document concerns that were raised from the use of a high-stakes exam as a mandatory graduation requirement and consider reasons for the differing reactions. Keywords: pre-service education, mathematics education, mathematics for teaching, high stakes examination Résumé Les résultats présentés ici font partie d’une plus vaste étude qui examine les cas de deux personnes qui n’ont pas réussi à atteindre le seuil de réussite de 60% à un examen de mathématiques pour les futurs enseignants à la fin de leur premier cours de méthodologie des mathématiques de niveau intermédiaire. Les deux personnes ont réagi de manièrenettement différente à la nouvelle qu’elles n’avaient pas satisfait aux exigences en mathématiques : l’une d’entre elles l’a vu comme une occasion de grandir et d’apprendre les connaissances en mathématiques qu’elle savait n’avoir jamais acquises par le passé; l’autres’est quant à elle mise en colère et a démontré de l’hostilité, rejetant la responsabilité del’échec sur son professeur. Dans cet article, nous présentons les contrastes d’approche entre les deux cas, et la manière dont leur réponse a influencé leur apprentissage ultérieur des mathématiques. Nous explorons aussi l’impact quelque peu inattendu de ces réponses sur leurs pairs. Enfin, nous examinons les préoccupations soulevées par l’utilisation d’un examen à enjeux élevés comme condition d’obtention du diplôme et les raisons possibles des différentes réactions obtenues. Mots-clés : formation initiale, enseignement des mathématiques, mathématiques pour l’enseignement, examen à enjeux élevés Canadian Journal of Education / Revue canadienne de l’éducation 43:3 (2020) [www.cje-rce.ca](www.cje-rce.ca) Acknowledgement We would like to thank Lori Ruberto ofLakehead University for providing this translation of the abstract. Canadian Journal of Education / Revue canadienne de l’éducation 43:3 (2020) [www.cje-rce.ca](www.cje-rce.ca) Introduction Since the work of Shulman (1986), researchers have examined the knowledge teachers require in order to teach effectively. Ma (1999) used the term profound understanding of fundamental mathematics, and Ball and her colleagues (e.g., Ball et al., 2008) gave these understandings the broad umbrella term of mathematics knowledge for teaching. Our work follows these scholars in examining the mathematics knowledge for teaching of pre-service teachers. Given the links that have been established between teacher knowledge and student achievement (e.g., Baumert et al., 2010; Hill & Ball, 2004; Hill et al., 2005), we decided to make attaining a minimal le

FAQs

What is the main focus of the study?

The study analyzes contrasting responses by two pre-service teachers to failing a high-stakes Mathematics for Teaching Exam and how those responses influenced their later mathematics learning.

What passing requirement did the participants initially fail to meet?

They were initially unable to achieve the required 60% passing grade on the Mathematics for Teaching Exam.

How did the two participants respond after not passing the exam?

One participant used the failure as an opportunity to grow and learn mathematics she had not learned before, while the other became angry and hostile, blaming the professor and developing a negative outlook on the program.

Oct 15, 2026

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