Purposeful questioning is one of the most important elements to promote successful mathematics understanding (National Council of Teachers of Mathematics, 2014; Ontario Ministry of Education, 2011). Questioning helps teachers to elicit, interpret, and respond to student thinking (Stein et al., 2008) and supports students' understanding,…

This study examined "backward transfer," which we define as how students' ways of reasoning about previously encountered concepts are modified when learning about new concepts. We examined the backward transfer produced when students learned about quadratic functions. We were specifically interested in how backward transfer may vary for…

This paper employs Cultural Historical Activity Theory (CHAT) as an analytical heuristic in exploring the internationally prevalent situation of teaching out-of-field. Drawing on interview transcripts, we use CHAT to frame the activity of a young teacher teaching mathematics out-of-field in a small rural K-12 school in Australia. We identify and…

Natural language is known to play a crucial and specific role for children's learning in school mathematics. Not only does it carry special vocabulary, but subtle differences between natural languages may lead to surprising challenges, for instance, for learners who are not taught mathematics in their mother tongue. In this paper, the…

Generative artificial intelligence (AI)-powered conversation agents such as ChatGPT are increasingly being used in teacher education. Although ChatGPT can provide ample resources for lesson planning, little attention has been paid to how teacher candidates construct prompts and evaluate AI-generated outputs in real time to develop lesson plans.…

In this case study, we investigate how an inquiry-oriented interactive calculus textbook supported one U.S. college instructor's classroom teaching. We utilized analytical inquiry-oriented frameworks on observation data from a small classroom to capture textbooks' influence on the instruction conceptualized by the Teacher-Mathematics-Student face…

Researchers have increasingly utilized artificial intelligence to automatically analyze classroom dialogue, aiming to provide timely feedback to teachers due to its educational significance. However, traditional machine learning and deep learning models face challenges, such as limited performance and lack of generalizability, across various…

This investigation explored the role of artificial intelligence (AI)-powered gamification on mathematics cognition through a mixed-methods design, blending an intervention with a gamified learning application (app) and a survey to evaluate student engagement and performance. The study explores the nexus of gamification, AI, and mathematics…

The Standards for Mathematical Practice (SMPs; CCSSI, 2010) describe mathematical behaviors and habits that students should express during mathematics instruction. Teacher candidates should have knowledge about the SMPs and their implications for mathematical instruction. This study aims to share the validity evidence for interpretations of…

We present findings from an analysis of tests of teacher mathematical knowledge identified over a 20-year period of mathematics education literature. This analysis is part of a larger project aimed at developing a repository of instruments and their associated validity evidence for use in mathematics education. We report on how these tests are…

Previous research has shown the importance of affect when seeking knowledge about students' achievements. However, there are surprisingly few studies looking at students' expressed effort on a longertime scale. Using data spanning over almost three decades, in this paper, we analyze Swedish lower secondary school students' responses to items in…

Using teaching representations is one of the common means for preparing pre-service mathematics teachers (PSTs) to learn how to teach mathematics meaningfully. However, turning PSTs' attention to the mathematical objects that students engage with during the lesson is a challenging pursuit. This paper suggests using the Realization Tree Mediator…

With a focus on related rates problems, the present study reports on quantitative and covariational reasoning opportunities provided by five widely used calculus textbooks in the United States. There are three major results from this study. First, quantitative reasoning opportunities are plentiful, while covariational reasoning opportunities are…

Writing-related activities have long been identified as supporting students' mathematics mastery and overall math success (Bahls, 2012). To further understand student experiences using writing in college math coursework, the present mixed-methods study explored the perceptions of a group of students (N = 55) in Multivariate Calculus who…

As online learning platforms become more popular and deeply integrated into education, understanding their effectiveness and what drives that effectiveness becomes increasingly important. While there is extensive prior research illustrating the benefits of intelligent tutoring systems (ITS) for student learning, there is comparatively less focus…