Presently, research is questioning the value of homework, especially at the elementary level. One reason homework is considered important is that it allows for the opportunity to practice and reinforce skills. Currently, elementary students in the United States are assigned homework in mathematics three or more times a week. Since homework…

In this paper, an attempt is made to determine if peer collaboration increases student achievement in teaching elementary mathematics. Empirical evidence and philosophical problems with constructivist epistemology are considered. Two things are argued: first, it is reasonable to think, for elementary mathematics, peers collaboration is useful…

This article illustrates the kinds of mathematical discussions that should occur with students in classrooms. The authors use a sample from professional development to show discussions that focus on the relationships of events within a problem that led to each representation, the connections between the ways participants chose to represent those…

Using sticky notes and number lines, a hands-on activity is shared that anchors initial student thinking about absolute value. The initial point of reference should help students successfully evaluate numeric problems involving absolute value. They should also be able to solve absolute value equations and inequalities that are typically found in…

The authors examined the impact of manipulative-based instruction on 2 independent cohorts of preservice elementary teachers. In Study 1, 50 participants engaged in problem solving with operations on whole numbers and fractions using concrete and representational manipulatives over 5 classes. Pre- to posttest performance on a mathematics survey…

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…

The purpose of this study was to explore pre-service and in-service mathematics teachers' analyses of student learning in a video case of mathematics instruction via an online learning forum. The study was conducted in the context of three different mathematics methods courses in a 4-year college in the Midwestern United States. Twenty-six…

Since coastal communities are already subjected to the impacts of climate change, adaptation has become a necessity. This article presents competencies demonstrated by Canadian municipal employees during an adaptation process to sea level rise. To adapt, the participants demonstrated the following competencies: problem solving (highlighting…

Research, from all around the world, has shown that teachers' actions are informed by a variety of factors, including long-held and frequently unarticulated traditions about teaching and learning, systemic expectations of the processes of schooling, available textbooks, traditions of teacher education, school cultures, assessment traditions and…

How fast does a tank drain? Of course this depends on the shape of the tank and is governed by a physical principle known as Torricelli's law. This note investigates some connections between tank shape and a mathematical function related to the time required for the tank to drain completely. The techniques employed provide some interesting…

In algebra and precalculus courses, students are often asked to find extreme values of polynomial functions in the context of solving an applied problem; but without the notion of derivative, something is lost. Either the functions are reduced to quadratics, since students know the formula for the vertex of a parabola, or solutions are…

Encouraging children to think--independently and publicly--is possibly one of any teachers' most challenging and rewarding responsibilities. Young children's less-developed language and listening skills further complicate teachers' work at the early elementary level. Yet, the author has been fortunate to work with many teachers who have embraced…

In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 - 9 yields…

This study focuses on the knowledge exhibited by 30 elementary school in-service and pre-service teachers in solving non-routine mathematical problems and on their beliefs regarding these kinds of problems. Interviews were used to reveal teachers' knowledge and beliefs. The findings indicated that these teachers had difficulty in solving…

The publication in June of Sir Peter Williams' review of mathematics teaching in early years' settings and primary schools came at a time when the thoughts of many teachers were turning towards a well-earned summer break. However, the report has attracted much attention and promises a fundamental shake-up of attitudes and approaches to the…