English language learners (ELLs) struggle with solving word problems for a number of reasons beyond math procedures or calculation challenges. As a result, ELLs may not only need math support but also reading and linguistic support. The purpose of this study was to assess the effectiveness of a math comprehension strategy called Dynamic Strategic…

We discuss a mathematics capstone course designed to help students grow in mathematical independence. We describe how the course is structured to support this goal and the major assignments: a course wiki, a group expository project, and an individual problem to solve and extend. Students learn to ask and answer their own questions, helping them…

Queensland rural and remote schools have difficulty in attracting experienced, in-field mathematics teachers. Thus, when such teachers arrive, much is expected of them to increase the mathematics knowledge of students. This paper looks at one such teacher who, against the high expectations placed upon him as an in-field teacher, experienced…

Imagine a mathematics classroom in which students engage in sharing ideas and reasoning through solutions to interesting mathematical problems. They are excited about mathematics and working on challenging problems that encourage collaboration and critical thinking. These are things that teachers want, but sometimes they do not know how to achieve…

Explaining appears to dominate primary teachers' understanding of mathematical reasoning when it is not confused with problem solving. Drawing on previous literature of mathematical reasoning, we generate a view of the critical aspects of reasoning that may assist primary teachers when designing and enacting tasks to elicit and develop…

Patterns and generalization are one of the most fundamental aspects of mathematics, which makes recent decades, mathematical tasks which include patterns, whether they are numerical or graphical, are mostly used, for example researching generalization. The aim of this paper is to investigate how a special kind of task concerning well-known…

Existing studies have quantitatively evidenced the relatedness between problem posing and problem solving, as well as the magnitude of this relationship. However, the nature and features of this relationship need further qualitative exploration. This paper focuses on exploring the interactions, i.e., mutual effects and supports, between problem…

The purpose of this article is to determine the levels of understanding for solving Stoichiometry problems from the aspect of macroscopic, microscopic and symbolic representations of high, average and low achieving students after infusion of metacognitive skills. Nine form four students aged sixteen years old from a secondary school in Kuala…

In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…

The aim of this research is to examine the mathematical thinking skills of licensed athletes engaged in individual and team sports. The research is designed as a survey model. The sample of the research is composed of 59 female and 170 male licensed athletes (n = 229) and (aged 14 to 52) licensed who do the sports of shooting, billiards, archery,…

Exploratory learning environments (ELEs) promote a view of learning that encourages students to construct and/or explore models and observe the effects of modifying their parameters. The freedom given to learners in this exploration context leads to a variety of learner approaches for constructing models and makes modelling of learner behavior a…

Educators usually mean different constructs when they speak of open tasks: some may refer to pure-mathematics investigative tasks while others may have authentic real-life tasks in mind; some may think of the answer being open while others may refer to an open method. On the other hand, some educators use different terms, e.g. open and open-ended,…

How can the best of mathematical problem-based learning be applied toward literature classes? Daniel Sussman, an English teacher at Moorestown Friends School in New Jersey, discusses how he uses problem solving tactics to encourage close, critical reading of fiction texts in his Jewish literature and poetry classes. He explores the challenges of…

The task of constructing a square is used to argue that looking for and pursuing several solution routes is a powerful principle to identify and analyse properties of mathematical objects, to understand problem statements and to engage in mathematical thinking activities. Developing mathematical understanding requires that students delve into…

With recent increased attention to engaging students in written mathematical communication, the Elementary Mathematical Writing Task Force has recommended specific types of and purposes for mathematical writing with the ultimate goals of communicating and reasoning: Exploratory, Informative/Explanatory, Argumentative, and Mathematically Creative.…