The Riemann sum definition of integration is ubiquitous in college calculus courses. This, however, is not the only possible way to define an integral. Here, we present an alternative mean-based definition of integration. We conjecture that this definition is more accessible to students. In support of this proposition we first present a…

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…

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,…

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…

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…

The purpose of this study is to provide an account of preservice elementary mathematics teachers' understandings about irrational numbers. Three dimensions of preservice mathematics teachers' understandings are examined: defining rational and irrational numbers, placing rational and irrational numbers on the number line, and operations with…

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 describes a collaboration between two faculty members, one from mathematics and the other from education, to strengthen the preparation of pre-service elementary school teachers for teaching mathematics. The model used is a learning community which combines a mathematics content course offered by the mathematics department, with a…

It is possible to get prospective elementary school teachers to learn interesting mathematics well by not only requiring that they learn the material in a mathematics course but also requiring that they teach it as part of an enrichment program at the middle school level. This article discusses the reasons for such a course, and describes a…

In this paper, I will discuss two related activities that I have developed for use in a college geometry course directed at pre-service secondary and elementary school teachers. These activities ask students to develop geometry on pool tables and on cones. The two activities are closely related, and both ask students to relate computer models with…

This article describes an approach for introducing the unit concept in a mathematics content course designed for preservice elementary mathematics teachers. Classroom activities presented in the article emphasize the awareness, flexibility, and importance of the unit concept. Dialogue with selected preservice teachers is included and reveals some…

In this paper we discuss a variety of writing, reading and assessment techniques used in an elementary problem-solving class for pre-service K-8 teachers at Western Oregon University. We share our experience in teaching problem-solving strategies through selection and creation of quality word problems, problem-solving assessment and the Oregon…

In this study, twenty-eight prospective teachers enrolled in a mathematics course participated in regular writing activities in reflective notebooks. Students' writings and data collected from interviews and surveys were used to analyze the effects of the notebooks on students' perceptions of their learning and mathematics anxiety. Students…