Because talking about their mathematical ideas is difficult for emergent bilinguals if they do not have experience with the language used to represent those ideas, constructing math lessons wherein the materials and tasks support the development of fruitful talk is an important task for the teacher. Waiting until emergent bilinguals are fully…

Writing multiple-choice test items to measure student learning in higher education is a challenge. Based on extensive scholarly research and experience, the author describes various item formats, offers guidelines for creating these items, and provides many examples of both good and bad test items. He also suggests some shortcuts for developing…

It is great to see how the sharing of ideas sparks new ideas. In 2011 Lyon and Bragg wrote an "Australian Primary Mathematics Classroom" (APMC) article on the mathematics of kitchen gardens. In this article the authors show how the kitchen garden may be used as a starting point for proportional reasoning. The authors highlight different…

As a percussive dancer, Malke Rosenfeld makes rhythm with her feet while she dances, and she also helps elementary students make their own percussive dance steps by integrating mathematics into her lesson plans. To do this she uses the Jump Patterns tool, a tool she developed during the first six years of her teaching artist career to help…

In this article, Garcia and Davis describe problem analysis as the process of examining a given mathematics exercise to find ways in which the problem can be modified and extended to create a richer learning opportunity for students. Students are often reluctant to attempt what they perceive to be higher-order thinking problems, but problem…

Most teachers agree that if a student understands a particular mathematical topic well, he/she will probably be able to do problems correctly. The converse, however, frequently fails: students who do problems correctly sometimes do not actually have robust understandings of the topic in question. In this paper we explore this phenomenon in the…

The standing long jump was an Olympic event until 1912. In 1904, Ray Ewry set the world record for the longest standing long jump, which was about 11.5 feet, or 138 inches. Although the standing long jump is no longer an Olympic event, the Norwegians still include it in their National Competition, and Arne Tvervaag set a new world record at about…

This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data…

In this study, reflections of problem solving environment based on group work are presented. Samples of the study are 28 students studying on 9th grade of a secondary school in Trabzon. In this study a historical problem of Fibonacci in his book "Liber Abaci" arranged appropriately to the problem solving steps of Polya and a worksheet…

In this study, ways in which problem posing activities aid our understanding of children's learning of addition of unlike fractions and product of proper fractions was examined. In particular, how a simple problem posing activity helps teachers take a second, deeper look at children's understanding of fraction concepts will be discussed. The…

This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyse students' mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger…

This study examined the effects of a research-based intervention, schema-based instruction (SBI), implemented by experienced- (taught SBI in previous study; Jitendra et al., 2015) and novice-teacher implementers (taught SBI for the first time with professional development) on the mathematics outcomes of seventh-grade students. SBI is a…

The How Far Do You Think You Can Jump? activity (see EJ1174770) was completed in three different contexts: an after-school mathematics enrichment program at Woodland and Country Schools in Weston, Massachusetts; a small-group pull-out of second graders at Wren Elementary in Piedmont, South Carolina; and a family math night in Lafayette, Indiana.…

This research study aims to examine secondary school students' mathematical problem-solving attitudes in terms of certain variables. The study was carried out to determine whether the students' mathematical problem-solving attitudes differ or not in terms of the variables of gender, grade, attending nursery school, parents' education level and…

This article examines the shifts in attention and focus as one teacher introduces and explains an image that represents the processes involved in a numeric problem that his students have been working on. This paper takes a micro-analytic approach to examine how the focus of attention shifts through what the teacher and students do and say in the…