Over decades and across grade levels, deaf/hard-of-hearing (d/hh) student performance in mathematics has shown a gap in achievement. It is unclear, however, exactly when this gap begins to emerge and in what areas. This study describes preschool d/hh children's knowledge of early mathematics concepts. Both standardized and nonstandardized measures…

About 80 middle and secondary school teachers participated in the professional development sequence as a part of a larger professional development project. Sessions provided participants with half-day experiences in an inquiry-oriented classroom taught by a master teacher, in which they experienced examples of inquiry lessons as both student and…

What better way to engage young students in physical science concepts than to have them engineer flying toy rockets? The integration of engineering into science classrooms is advocated by the "Next Generation Science Standards" (NGSS) and researchers alike (Brophy et al. 2008), as engineering provides: (1) A "real-world…

If you want to get the attention of a group of eighth grade math students, tell them they are going to build a life-size cardboard boat. To increase interest, follow up this statement by telling them that two to four of them will actually be rowing this boat across a small pond. Eighth grade math students at Oasis Charter Middle School in…

Several studies on learning mathematics for rural area's student indicate that students have difficulty in understanding the concept of division operation. Students are more likely to be introduced by the use of the formula without involving the concept itself and learning division separate the concrete situation of learning process. This…

Persevering in problem solving and constructing and critiquing mathematical arguments are some of the mathematical practices included in the Common Core State Standards for Mathematics (CCSSI 2010). To solve unfamiliar problems, students must make sense of the situation and apply current knowledge. Teachers can present such opportunities by…

This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…

The aim of this study is to reveal teacher candidates' preference regarding uses of verbal, symbolic, number line, and/or model representations of fraction divisions, and to investigate their skill of transferring from one representation type to the others. Case study was used as the research method in this study. The case that is examined within…

Pattern blocks are inexpensive wooden, foam, or plastic manipulatives developed in the 1960s to help students build an understanding of shapes, proportions, equivalence, and fractions (EDC 1968). The colorful collection of basic shapes in classic pattern block kits affords opportunities for amazing puzzle-like problem-solving tasks and for…

This article describes how a sixth-grade teacher's "missing word" task uncovered higher-level thinking and engaged her students in the Standards for Mathematical Practice. The role and selection of the task promotes higher-level thinking and connects to the Common Core State Standards for Mathematics. The task required students to apply…

In this study, we examined how curricular resources supported three expert teachers in their enactment of progressions. Using a video-stimulated interview process, we documented the multiple types of progressions identified, described, and enacted by the teachers. Results indicate that the teachers used four different types of…

Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

This paper reports a study on retention of core concepts in differential and integral calculus by examining the knowledge of two pre-service mathematics students. The study is conducted using a mixed method approach and the obtained data were analyzed using theory of three worlds of mathematics. The results showed that having good understanding of…

Generalizing--along with conjecturing, representing, justifying, and refuting--are forms of mathematical reasoning important in all branches of mathematics (Lannin, Ellis, and Elliott 2011). Increasingly, however, generalizing is recognized as the essence of thinking in algebra (Mason, Graham, and Johnston-Wilder 2010; Kaput, Carraher, and Blanton…

This paper provides a method for analysing undergraduate teaching of proof-based courses using Toulmin's model (1969) of argumentation. It presents a case study of one instructor's presentation of proofs. The analysis shows that the instructor presents different levels of detail in different proofs; thus, the students have an inconsistent set of…