This article describes an activity that incorporates measurement in order to lead students to discover and explore fundamental concepts of calculus. Students are provided with an experientially real starting point involving measurement and are encouraged to engage in mathematical discussions in a low-stakes environment. I describe the activity as…

There is a vital need in the mathematics and science teaching and learning community at the secondary school level for assistance for teachers in adapting curricular materials to meet the many district, state, and national demands and to facilitate high-quality learning of students and their ability to transfer this learning and apply it as they…

In this paper I describe classroom experiences with pre-service secondary mathematics teachers (PSMTs) investigating and extending patterns embedded in the Pythagorean configuration. This geometric figure is a fruitful source of mathematical tasks to help students, including PSMTs, further develop habits of mind such as visualization,…

Many mathematics teacher educators encounter the challenge of creating or choosing mathematical tasks that evoke important mathematical insights and connections yet remain firmly grounded in school mathematics. This challenge increases substantially when trying to meet the needs of practicing secondary mathematics teachers pursuing graduate work…

Elementary Education pre-service teachers are noted for disliking and even fearing mathematics, so a teaching strategy that increases their enjoyment of mathematics learning must be a powerful one, indeed. When the same strategy can also support problem posing and assess mathematical knowledge and reasoning, providing an occasional alternative to…

This study investigated the effects upon elementary preservice teachers' mathematics teaching self-efficacy and interdisciplinary lesson design strategies, which resulted from an educational intervention that emphasized integrated music-mathematics instruction. The participating elementary preservice teachers (n = 152) were recruited for this…

This cross-cultural study investigated the relationship between attitudes toward statistics (ATS) and course achievement (CA) among Japanese college students. The sample consisted of 135 male and 134 female students from the first two-year liberal arts program of a four-year college in Tokyo, Japan. Attitudes about statistics were measured using…

This paper provides empirical findings from a study that examined how three grade 7-12 flipped mathematics educators utilized class time when implementing a flipped learning model. Additionally, the researchers investigated the educators' purposes for various in-class tasks as well as their general use of class time. The data revealed flipped…

The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

Mathematics anxiety is recognized as a significant performance impediment that affects students across multiple ethnic and economic backgrounds. However, research has yet to fully examine the possible differential effect of mathematics anxiety on underrepresented K-12 students. Specifically, given the long-standing achievement gap between African…

In the Western developed world, the language of 21st century competencies, also referred to as 21st century skills or competences, is a powerful means of drawing attention to links between the secondary school curriculum, post-secondary education, and the social and economic imperatives of the developed economies. This paper will analyze different…

There are specific topics in college calculus that can be major stumbling blocks for students. Having taught college calculus for four years to over a thousand students, we observed that even the students who have already taken pre-calculus or calculus during their high school careers had common misunderstandings. Students may remember a technique…

Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

This paper describes how the author's students (in-service and pre-service secondary mathematics teachers) enrolled in college geometry courses use the Geometers' Sketchpad (GSP) to gain insight to formulate, confirm, test, and refine conjectures to solve the classical airport problem for triangles. The students are then provided with strategic…

Traditionally, teacher education programs have placed little emphasis on preparing mathematics teachers to work with students who struggle in mathematics. Therefore, it is crucial that mathematics teacher educators explicitly prepare prospective teachers to instruct students who struggle with mathematics by providing strategies and practices that…