Mathematics textbooks are a predominant resource in primary school in Greece, as well as in many other countries. The present study reports on both a content analysis of Greek mathematics textbooks with regard to the types of word problems represented in them and a quantitative analysis of children's achievement in these problems. For the…

The purpose of this study was to deconstruct the relationship between visual static models and students' written solutions to fraction problems using a large sample of students' solutions. Participants in the study included 162 third-grade and 209 fourth-grade students from 17 different classrooms. Students' written responses to…

Much research has been conducted on how elementary students develop mathematical understanding and subsequently how teachers might use this information. This article builds on this type of work by investigating how one high-school algebra teacher designs and conducts a lesson on exponential functions. Through a lesson study format she studies with…

Mathematics educators have had a long standing interest in students' understanding of decimal numbers. Most studies of students' understanding of decimals have been conducted within Western cultural settings. Similar research in other countries is important for a number of reasons, perhaps most importantly because it can provide insights…

This study comes at an opportune moment for Japanese and U.S. educators, policymakers, and researchers given the trends of global policy and equity-based reform. Discussions of academic achievement in both societies allows us to examine mathematics education as a public good versus private commodity in order to best serve the needs of students.…

The National Council of Teachers of Mathematics [NCTM] noted that middle and high school students are expected to be able to both explain inequalities by using mathematical symbols and understand meanings by interpreting the solutions of inequalities. Unfortunately, research has revealed that not only do middle and high school students hold…

This paper explores sixty-six students' personal meaning and interpretation of the vertex of a quadratic function in relation to their understanding of quadratic functions in two different representations, algebraic and word problem. Several categories emerged from students' personal meaning of the vertex including vertex as maximum or…

In this article, we present and discuss an example of how teachers' discussions of mathematical knowledge for teaching (MKT) items elicited their beliefs about the knowledge needed to teach mathematics. One category of MKT is "horizon content knowledge," and this can be described as mathematical knowledge not directly deployed in…

Two classes of third grade students (n = 56) from an elementary school located on the western coast of the United States participated in this research study. A pretest-posttest control group design was utilized to examine changes between two groups of participating students' in mathematics achievement and dispositions, including beliefs about…

This paper examines how mathematical understandings might emerge through student-centred inquiry. Data is drawn from a research project on student-centred curriculum integration that situated mathematics within authentic problem-solving contexts and involved students in collaboratively constructed curriculum. The project involved case studies in…

We discuss an innovative task used in teacher education--Lesson Play--that involves presenting a lesson in the form of an interaction between a teacher and students. We describe the motivation for the development of this task and, through specific examples, describe the iterative design process in which the task was refined and improved. We…

The goal of the present article is to provide the teacher with an alternative perspective in writing multiple-choice questions. To the techniques and advice available in the literature on the topic, three further aspects are added whose provenance is an emerging line of research--the exemplification of concepts. The objective is to expand…

Research has shown students can identify practices considered appropriate for achieving when learning mathematics (Kershner & Pointon, 2000; McCullum, Hargreaves & Gripps, 2000). Yet, if you listen to students talking about the practices they consider important to succeed, and then observe the same students working in their mathematics…

Math Teachers' Circles have been spreading since their emergence in 2006. These professional development programs, aimed primarily at middle-level mathematics teachers (grades 5-9), focus on developing teachers' mathematical problem solving skills, in line with the Common Core State Standards-Standards of Mathematical Practice. Yet, to…

Teachers are tasked with supporting students' learning of abstract mathematical concepts. Students can represent their mathematical understanding in a variety of modes, for example: manipulatives, pictures, diagrams, spoken languages, and written symbols. Although most students easily pick up rudimentary knowledge through the use of concrete…