With the current focus in mathematics education on the importance of developing students' conceptual understanding, fluency with the language of mathematics, critical thinking, and working mathematically, teachers are constantly expected to design challenging and investigative tasks that can engage and motivate students in their learning of…

There are many classroom activities that can be implemented with primary students that introduce and immerse them in ratio investigations. Some enjoyable tasks include finding the ratio of tongue rollers to non-tongue rollers in the classroom; left-hand dominant to right-hand dominant; right-thumb over left-thumb when clasping the hands to…

Hispanic English-language learners and other students learning English are failing in K-12 mathematics. The field has not responded with mathematics curricula designed for this population, especially at the middle grades. In response to this academic crisis, the Help with English Language Proficiency (HELP) Math program for middle school students…

Why should prospective elementary and high school teachers study group theory in college? This paper examines applications of abstract algebra to the familiar algorithm for converting fractions to repeating decimals, revealing ideas of surprising substance beneath an innocent facade.

The algebraic concepts and major ideas that govern Newton's laws of motion can often be a challenge for the majority of ninth-grade students. Therefore, to make learning these concepts less task-oriented and more enjoyable, the author developed lessons that allow students to construct and express their understanding of these ideas through…

In this paper we describe an interdisciplinary course on dynamics that is appropriate for nonscience majors. This course introduces ideas about mathematical modeling using examples based on pendulums, chemical kinetics, and population dynamics. The unique emphasis for a nonmajors course is on chemical reactions as dynamical systems that do more…

In the Netherlands, the "iceberg model," developed by the Freudenthal Institute, has been used to support teacher identification of informal and preformal representations that build students' understanding of formal mathematics. This article offers suggestions on how this model can be used to support professional development,…

To address the confusion resulting from difficulties with proportional reasoning among preservice physical science students, a cube-assembly activity was used to bring a sense of concreteness to abstract ideas. The activity took students from the concrete step of assembling cubes of various sizes and directly measuring their properties to slightly…

The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)

This study investigates pre-service mathematics teachers' concept images of radian and possible sources of such images. A multiple-case study was conducted for this study. Forty-two pre-service mathematics teachers completed a questionnaire, which aims to assess their understanding of radian. Six of them were selected for individual interviews on…

Data analysis plays a prominent role in various facets of modern life: Schools evaluate and revise programs on the basis of test scores; policymakers make decisions on the basis of information gleaned from polling data; supermarkets stock shelves on the basis of data collected at checkout lanes. Data analysis provides teachers with new tools and…

Mathematics and science are important for success in school, but learning mathematics and science can be a difficult task to some students. Efforts to improve students' learning of school mathematics and science have led to reform efforts in curriculum and instruction over the past decades (e.g., National Council of Teachers of Mathematics [NCTM],…

David Schwartz's classic book "How Much Is a Million?" can be the catalyst for sparking many interesting mathematical investigations. This article describes five episodes in which children in grades 2-5 all heard this familiar story read aloud to them. At each grade level, they were encouraged to think of their own way to explore the concept of…

For the past decade, students at California State University (CSU) campuses increasingly lack basic mathematics skills. To address this concern, Executive Order No. 665 (1998) called for CSU campuses to bring students to proficiency in mathematics. School districts have struggled to modify their mathematics curriculum, pedagogy, and assessment in…

"Focus in Grade 1: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 1 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate…