This paper uses a series of models to illustrate one of the fundamental processes of model building--that of enrichment and elaboration. The paper describes how a problem context is given which allows a series of models to be developed from a simple initial model using a queuing theory framework. The process encourages students to think about the…

Understanding how students translate between mathematical representations is of both practical and theoretical importance. This study examined students' processes in their generation of symbolic and graphic representations of given polynomial functions. The purpose was to investigate how students perform these translations. The result of the…

One aspect of professional development of mathematics teachers relates to the development of assessment skills. The aim of this study is to examine the effects of engaging prospective mathematics teachers in peer assessment, both as assessors and assessees, on the development of their assessment skills in general and assessment of geometrical…

This qualitative study examined middle school students' performance, solution strategies, difficulties and the underlying reasons for their difficulties in calculating the volume of a rectangular prism. The data was collected from 35 middle school students (6th, 7th and 8th grade students) enrolled in a private school in Istanbul, Turkey. The…

Students start to memorize arithmetic facts from early elementary school mathematics activities. Their fluency or lack of fluency with these facts could affect their efforts as they carry out mental calculations as adults. This study investigated participants' levels of brain activation and possible reasons for these levels as they solved…

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…

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…

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…

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…

Recent mathematics education reform calls for efforts to create collaborative and student-centered environments, where students have opportunities to reason and construct their understanding as part of a community of learners. Mathematics instruction should provide students opportunities to engage in mathematical inquiry and meaning making through…

In this paper, we present a framework used to analyze the extent to which assessments (i.e., chapter tests) accompanying three published elementary grades 3-5 curricula in the United States provide students with opportunities to engage with key mathematical processes. The framework uses indicators for five criteria to assess the processes of…

Students who are preparing to study science and engineering need to understand equation solving but adult students returning to study can find this difficult. In this paper, the design of an online resource, Equations2go, for helping students learn to solve linear equations is investigated. Students learning to solve equations need to consider…

The purpose of this study was to investigate the effect of instruction in alternative solutions on Taiwanese eighth-grade students' mathematical problem solving performance. This study was exploratory rather than experimental. Alternative-Solution Worksheet (ASW) was developed to encourage students' engagement with alternative solutions to…

In this study, we investigated to what extent arithmetic ability and self-regulated learning skills in the beginning of lower secondary school predicts measures of students' performance in mathematics at the end of lower secondary school. Arithmetic ability and self-regulated learning skills were tested the first two weeks in lower secondary…

In this paper we explore the relationship between language and developmental processes of logical tools through the analysis at different levels of some "linguistic-manipulative" activities in a primary school classroom. We believe that this kind of activities can spur in the children a reflection and a change in their language representation.…