In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are…

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…

Professional development (PD) programs often evaluate their impact on teachers' learning by assessing teachers either individually or in groups. The goal of this paper is to illustrate the variety of paths teachers might follow as a result of working in groups within online PD settings. Data are drawn from a PD program for grades 5-9…

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…

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…

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…

Over the past decade it has been frequently reported that East Asian students are outperforming their Western counterparts in international tests of mathematics at middle-school level. This paper probes classroom discourse in an attempt to shed some light on this phenomenon. Data were collected from a sample of Chinese Year 8 students in a normal…

This study investigated the development of the concept of variables in middle grades mathematics textbooks during four eras of mathematics education in the United States. Findings revealed that each of the middle grades mathematics curricula examined used variables, but in varied proportions and levels of complexity. Formal definitions for…

A secondary data analysis was conducted using a large dataset from a study related to online professional development for eighth grade teachers of mathematics. Using this data, the paper provides a snapshot of the current state of teachers' knowledge related to proportional reasoning and functions. The paper also considers how teachers' knowledge…

Moving from primary school (Year 6) to the next stage in schooling (Year 7 intermediate or middle school) can provide challenges for students, teachers, and parents. A study was carried out to investigate these challenges with a focus on mathematics for 65 students from six different urban primary schools in New Zealand. Qualitative data were…

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…

This longitudinal study analyzes middle school mathematics pre-service teachers' development of teaching goals. The Teaching Goals Inventory (TGI) (Angelo & Cross, 1993) was administered on four occasions: pre- and posttest summer 1, end posttest end of spring, and posttest end of summer 2. The data were analyzed for consistency and changes from…

Whether they are acknowledged or not, resources such as textbooks, curriculum guides, assessments, and professional development programs present messages about what is most important for students to learn and how students can best learn this. At times teachers feel obligated to enact these messages, but at other times they feel free to ignore…