Changes to students' understanding of mathematical notation may be brought about by using technology within mathematics. Taking equality as a case study, the paper provides brief epistemological, historical, didactical, and computational reviews of its symbolic representation in pen-and-paper and technology-assisted mathematics, most especially in…

Ambitious teaching is a form of teaching that requires a high level of teacher responsiveness to what students do as they actively engage with the subject matter. Thus, a teacher enacting ambitious teaching is often confronted with uncertainties about how to advance students' learning while also building on students' contributions. In…

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…

In this paper we offer a review of sorts of the studies conducted around issues of problem posing in mathematics education research. We first ground the work on problem posing in the seminal work of Polya and of Brown and Walter, which influenced most studies on this subject. We then propose two perspectives taken on problem posing: the implicit…

The Mathematics for Computer Science mandatory course was conducted in a flipped classroom (FC) setting with an optional, voluntary, project-based learning (PBL) component. The objective of this study was to examine the effect of studying in an FC setting, with and without PBL, on students' problem-solving performance, conceptual understanding,…

There are many choices for learning mathematics for engineering students with courses available in face-to-face, blended and fully online modalities. Students are demanding more flexibility in their programs, however the temptation to misuse this flexibility to avoid mathematical studies until it is too late can be an unfortunate side effect. A…

As today's classrooms become more and more diverse, there is a growing need to explore the intersection between English Learners (ELs) and students with learning disabilities (LD) in the content-specific instruction of mathematics problem solving. The aim of this study was to determine which types of instructional scaffolds may be used by math…

The aim of this study is to know the differences of enhancement in mathematical problem solving ability (MPSA) between the students who received soft skill- based metacognitive learning (SSML) with the students who got conventional learning (CL). This research is a quasi experimental design with pretest-postest control group. The population in…

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 mathematical problem solving, American students are falling behind their global peers because of a lack of foundational and reasoning skills. A specific area of difficulty with problem solving is working non-routine, heuristic-based problems. Many students are not provided with effective instruction and often grow frustrated and dislike math.…

Research documents an income-based achievement gap in mathematics, yet children from lower-income backgrounds do not lag behind their more advantaged peers in high-level social reasoning tasks. The purpose here was to investigate whether modifying mathematics word problems to make them more socially based would impact the mathematics performance…

In this paper, the RBC+C framework (Hershkowitz, Schwartz, & Dreyfus, 2001) is used to analyse and describe construction and consolidation of mathematical knowledge by primary pupils in a whole-class setting. I describe a lesson that concerned what is commonly termed the Handshakes problem. One pupil spontaneously established a connection with…

This article focuses on a simple trigonometric problem that generates a strange phenomenon when different methods are applied to tackling it. A series of problem-solving activities are discussed, so that students can be alerted that the precision of diagrams is important when solving geometric problems. In addition, the problem-solving plan was…

This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.

In considering mathematics problem solving as a model-eliciting activity (Lesh & Doerr, 2003; Lesh & Harel, 2003; Lesh & Zawojewski, 2008), it is important to know "what" students are modeling for the problems: situations or solutions. This study investigated Grade 3 students' mathematization process by examining how they modeled different…