"Project work" is far from being a new phenomenon in the mathematics curriculum. Students reporting their findings of the "project" in a scrapbook format may be a novel approach. Asking learners to assess their "effort rating" is unusual self-assessment. But, there is far more detail in this account of project work.…

Composition has been described as essential for understanding functions (Carlson, Oehrtman, & Engelke, 2010; Cooney, Beckmann, & Lloyd, 2010). Studies of students' understanding of function composition have shown that students use multiplication and other operations in place of composition (Carlson et al., 2010; Horvath, 2010). While…

This study uses teacher research to examine teacher learning in the context of instructional coaching. The author, a mathematics instructional coach, engaged in an intense three-week coaching relationship with a high school Algebra teacher. A detailed description of the teaching and learning of quadratics that took place during this research…

This article seeks to address a pedagogical theory of introducing the classicist and the frequentist approach to probability, by investigating important elements in 9th grade students' learning process while working with a "TinkerPlots2" combinatorial problem. Results from this research study indicate that, after the students had seen…

Vocabulary presents a challenge to students in content area classes, making it difficult to understand new concepts and make connections to background knowledge. This article describes the 5 Cs, a tool developed to help content area teachers consider vocabulary as part of lesson planning. By selecting a set of key words for instruction, teachers…

This study investigated the development of the concept of variables in middle grades mathematics textbooks during four eras of mathematics education in the United States. Findings revealed that each of the middle grades mathematics curricula examined used variables, but in varied proportions and levels of complexity. Formal definitions for…

We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school…

Learning in the cellular phone environment enables utilizing the multiple functions of the cellular phone, such as mobility, availability, interactivity, verbal and voice communication, taking pictures or recording audio and video, measuring time and transferring information. These functions together with mathematics-designated cellular phone…

This article confronts the issue of why secondary and post-secondary students resist accepting the equality of 0.999... and 1, even after they have seen and understood logical arguments for the equality. In some sense, we might say that the equality holds by definition of 0.999..., but this definition depends upon accepting properties of the real…

In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and…

The incorporation of literacy strategies into content area instruction has been proposed as an effective way of improving student learning in the content areas. However, few studies have examined how teachers incorporate content literacy strategies into their instruction and the specific nature of implementation. As part of an ongoing professional…

One of the most rewarding accomplishments of working with preservice secondary school mathematics teachers is helping them develop conceptually connected knowledge and see mathematics as an integrated whole rather than isolated pieces. To help students see and use the connections among various mathematical topics, the authors have paid close…

This article presents an origami activity which can lead to rich tasks in several branches of mathematics. This activity is a good first step for preservice teachers to get to know one another, start talking to one another, and start discussing mathematics. It can also show them how mathematics teaching and learning have changed to a more…

Understanding counting rules is challenging for students; in particular, they struggle with determining when and how to implement combinations, permutations, and the multiplication rule as tools for counting large sets and computing probability. We present an activity--using ideas from the games of poker and pinochle--designed to help students…

Teachers have used graphic organizers successfully in teaching the writing process. This paper describes graphic organizers and their potential mathematics benefits for both students and teachers, elucidates a specific graphic organizer adaptation for mathematical problem solving, and discusses results using the "four-corners-and-a-diamond"…