Persistent inequities in mathematics teaching and learning for specific groups of learners are a key challenge for researchers and educators. The use of ability grouping has been common practice in New Zealand mathematics classrooms. However, many researchers (e.g. Boaler and Wiliam 2001; Zevenbergen in 2003) highlight the negative effects of…

We explore student performance on True-False assessments with statements in the conditional form "If P then Q" in order to better understand how students process conditional logic and to see whether logical misconceptions impede students' ability to demonstrate mathematical knowledge. We administered an online assessment to a population…

We present a validation study of fifteen new math anxiety scale items designed to augment the widely-used Revised Mathematics Anxiety Scale (RMARS). While the RMARS and other standard instruments measure students' anxiety in response to computation, test situations, and math course activities such as buying a textbook or watching a lecture, the…

Some views of elementary teacher preparation may include the idea that undergraduate mathematics courses are useful or even crucial for prospective teachers to have. This study sought to identify teacher candidates with mathematics degrees, in order to study their mathematical preparation. The identified prospective teachers were studied to…

What mathematical knowledge is required for teaching has been researched by many, with Ball et al. (J Teach Educ 59(5):389-407, 2008) and their practice-based theory of mathematical knowledge for teaching (MKT) primary among them. However, what is required in terms of mathematical knowledge for teacher educator training has been researched much…

This paper reports an ongoing effort to address the problem of instructional capacity for high school geometry from a systems improvement perspective. In an effort to understand the system that contains the high school geometry instructional capacity problem, we identified key stakeholders and conducted preliminary interviews to learn about the…

The document presents a set of categories for the analysis of the conceptualization of the congruence of polygons--a central theme in school mathematics--and details the application of the analytical tools used, derived from Grounded Theory, in this construction. This set of categories is called 'Interpretive Model of the Conceptualization of…

This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

This study examines pre-service teachers' (PSTs') views of tasks that engage students in mathematical argumentation. Data were collected in two different mathematics courses for elementary school education majors (n = 51 total PSTs). Analyzed were (a) written journals in which PSTs defined tasks that promote student engagement in argumentation,…

One of the main tendencies of mathematical development in 19th and 20th centuries seem to be on rigor and formalization. Rigor and formalization took place on axiomatic basis leading to more abstraction. Euclidean type of an axiomatic model became a model of mathematics even for constructively developed analysis. Even though rigor and axiomatic…

This study examined whether the efficacy of a 50 lesson mathematics intervention program focused on whole number concepts for at-risk kindergarten students, ROOTS, differed by group size and whether initial skill moderated intervention effects by group size. The study utilized a randomized block design with at-risk students (n = 1,251) within…

This research was carried out to examine middle school students' perceptions of mathematics self-efficacy and their concerns about mathematics. In the research, the Mathematics Anxiety Scale was used to determine students' anxiety levels and the Self-Efficacy Scale was used to determine the level of self-efficacy perceptions. The sample of the…

To allow prospective teachers to see mathematics as a useful tool to make sense of the world we redesigned a university mathematics content course for prospective elementary school teachers in the context of exploring income distribution in the United States. This allowed the prospective teachers to learn mathematics in a meaningful context and…

A typical mathematics assignment consists of one or two dozen practice problems relating to the same skill or concept, yet empirical evidence suggests that there is little or no long-term benefit from working more than a few problems of the same kind in immediate succession. Alternatively, randomized experiments in the laboratory and classroom…

Teacher noticing requires listening to student sense-making, interpreting the mathematical understandings teachers hear, and deciding how to respond based on what they notice in a specific interaction. Teachers manage what they notice about students in instructional interactions to both make key teaching decisions and adjust their interactions…