This study investigated children's understanding of area measurement, including the concept of area and the area formula of a rectangle, as well as their strategic knowledge for solving area measurement problems. Twenty-two fourth-graders from three classes of a public elementary school in Taipei, Taiwan, participated in a one-on-one interview.…

Many studies have tested external supports for promoting productive collaboration, but relatively few have examined what features characterize naturally productive collaborative tasks. Two lines of research have come to distinct conclusions on the primary task feature associated with productive collaboration: demonstrability versus complexity.…

In this paper we investigate how competition among tutees in the context of learning by teaching affects tutors' engagement as well as tutor learning. We conducted this investigation by incorporating a competitive Game Show feature into an online learning environment where students learn to solve algebraic equations by teaching a synthetic…

Now in a fully updated second edition, "Unlocking Mathematics Teaching" is a comprehensive guide to teaching mathematics in the primary school. Combining theory and practice, selected experts outline the current context of mathematics education. They suggest strategies, activities and examples to help develop readers understanding and confidence…

Given the importance of algebra, middle school mathematics teachers have a responsibility to help students transition from understanding arithmetic to understanding the algebra that will be necessary for success in high school. One method of transition involves introducing algebraic concepts in concrete ways using meaningful contexts. The series…

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to…

It is important for teacher educators to understand new alternative certification middle and high school teachers' mathematical problem solving abilities and perceptions. Teachers in an alternative certification program in New York were enrolled in a proof-based algebra course. At the beginning and end of a semester participants were given a…

Content authenticity and correctness is one of the important challenges in eLearning as there can be many solutions to one specific problem in cyber space. Therefore, the authors feel it is necessary to map problems to solutions using graph partition and weighted bipartite matching. This article proposes an efficient algorithm to partition…

District-Charter Partnerships (DCP) is an initiative that is part of the Equity and Excellence for All agenda established by Mayor De Blasio. Its goal is to support meaningful collaboration between the district and charter sector in order to increase educator capacity and student learning in all New York City public schools. The District-Charter…

The present study examined the relationship between Oral Reading Fluency (ORF) scores and mathematics problem solving scores. The reading fluency scores were obtained from the Dynamic Indicator of Basic Early Literacy (DIBELS) assessment. The mathematics problem solving scores were obtained from the Indiana State Test of Education Progress Plus…

This study examines the connection between mathematical knowledge (described as a teacher's engagement in mathematical processes and actions on the products of those processes) used by a beginning secondary mathematics teacher (Fiona) in her personal mathematical problem solving and the mathematics in which she engaged her students in her…

Spatial and creative abilities are important for innovations in science, technology, engineering, and math (STEM) fields, but talents are rarely developed from these abilities by schools, including among gifted children and adolescents who have a high potential to become STEM innovators. This article provides an overview of each ability and makes…

This paper is based on an online graduate program for middle school science and mathematics teachers in Texas titled Integration of Science, Mathematics and Reflective Teaching (iSMART). Launching the program for its first cohort in fall 2010, the authors attempted to answer the following two questions in this paper: (a) How do the members of the…

The purpose of this quasi-experimental non-equivalent control group study was to test theories of constructivism and motivation, along with research-based teaching practices of differentiating instruction and instructing within a child's Zone of Proximal Development, in measuring the effect of computer-aided instruction on fifth grade students'…

The article demonstrates that multiple solution tasks (MSTs) in the context of geometry can serve as a research instrument for evaluating geometry knowledge and creativity. Geometry knowledge is evaluated based on the correctness and connectedness of solutions, whereas creativity is evaluated based on a combination of fluency, flexibility, and…