Preservice teachers commonly struggle with topics related to fractions, ratio, and proportion. The use of double number lines can facilitate the teaching in these areas and provide autonomy and flexibility in mathematical thinking. Moreover, double number lines support many topics in the curriculum, including unit rate, convenience scaling, and…

In this paper, I share an activity that reinforces students' understanding of translations, reflections, and rotations via body movement. As a result of this activity, students gain a different perspective compared to previous explorations on paper, communicate mathematics, and visualize transformations as rigid motions on the plane. Furthermore,…

This paper describes a project that sought to simultaneously facilitate the mathematical learning of both preservice teachers (PSTs) and schoolchildren. The project involved the organization of community Math Stations related to research-based number sense activities and was integrated within two university-level courses. This article describes…

As students learn to problem solve in authentic situations, they must also develop metacognitive tools to manage and regulate their problem-solving process. To foster process-focused metacognition utilized by mathematical thinkers and problem solvers, inquiry-based learning classroom practices and an adapted version of portfolio problems were…

Prospective teachers and cryptography students use programming, statistics and guile to enrich both their courses.

Preparing students placing into developmental mathematics for success in undergraduate mathematics and preparing future teachers for the increasing demands of K-12 school settings are both persistent, yet seemingly divergent, problems facing higher education. In this paper, we shed light on a model that attempts to address aspects of each problem…

Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities…

Why would anyone think of teaching and learning mathematics directly from primary historical sources? We aim to answer this question while sharing our own experiences, and those of our students across several decades. We will first describe the evolution of our motivation for teaching with primary sources, and our current view of the advantages…

We describe several service-learning initiatives implemented by the mathematics and education departments. College students with majors and minors in math and math education have helped to design and implement math events for elementary and middle school students. Formal and informal reflections on these service-related experiences have…

Secondary school mathematics teachers often need to answer the "Why do we do that?" question in such a way that avoids confusion and evokes student interest. Understanding the properties of number systems can provide an avenue to better grasp algebraic structures, which in turn builds students' conceptual knowledge of secondary mathematics. This…

In this article, the author suggests that to improve the teaching of mathematics in elementary schools, we must, when teaching content courses to prospective teachers, model the kind of teaching we want them to engage in. The author suggests ways to model this kind of teaching, which include the following: (1) challenge "all" students; (2)…

This article introduces a mathematical entity, the varimeter, that can be used to engage future mathematics teachers in reflection about the structure of measurement systems, thus aiding in the development of insight and understanding which may be beneficial to the future teachers when they work with their own students on measurement. Furthermore,…

This article is a reflection on an elementary pre-service teacher's intuitive idea offered as a mistaken solution strategy for counting matchsticks. It shows the difficulties in responding to flawed lines of intuitive reasoning arising in the classroom setting. A number of learning environments for teacher professional development are suggested…

Probability knowledge and skills are needed in science and in making daily decisions that are sometimes made under uncertain conditions. Hence, there is the need to ensure that the pre-service teachers of our children are well prepared to teach probability. Pre-service teachers' conceptions of probability are identified, and ways of helping them…

Research shows that preservice teachers can enhance their growth and development through interactions with children in the school setting as a component of their coursework in education. Additionally, preservice teachers feel they need more interactions with parents in their university preparation. Family Math Night has the potential to address…