In this article, the author presents the Treasure Island problem and some inquiry activities derived from the problem. Trying to find where pirates buried a treasure leads to a surprising answer, multiple solutions, and a discussion of problem solving. The Treasure Island problem is an example of an inquiry activity that can be implemented in…

The challenge in education field these days rises as the cause of society's expectation for higher education. This increasingly complex expectation demands that higher education prepares the students to gain integrity. Higher education provides not only hard skills for the student, but also soft skills. By observing the hard skills side, in the…

PQcalc is an online calculator designed to support students in college-level science classes. Unlike a pocket calculator, PQcalc allows students to set up problems within the calculator just as one would on paper. This includes using proper units and naming quantities strategically in a way that helps finding the solution. Results of calculations…

We analyze the mathematical solutions of 7- to 8-year-old pupils while individually solving an arithmetic problem. The analysis was based on the "configuration of objects," an instrument derived from the onto-semiotic approach to mathematical knowledge. Results are illustrated through a number of cases. From the analysis of mathematical…

This study investigated 11 pre-service middle school teachers' solution strategies for exploring their knowledge of fraction division interpretations. Each participant solved six fraction division problems. The problems were organized into two sets: symbolic problems (involving numbers only) and contextual problems (involving measurement…

This article examines whether the 7 abilities found in a previous study carried out by the authors to constitute fraction understanding of sixth grade elementary school students determine hierarchical levels of fraction understanding. The 7 abilities were as follows: (a) fraction recognition, (b) definitions and mathematical explanations for…

There are strong classroom ties between mathematics and the sciences of physics and chemistry, but those ties seem weaker between mathematics and biology. Practicing biologists realize both that there are interesting mathematics problems in biology, and that viewing classroom biology in the context of another discipline could support students'…

The degrees of freedom (DOF) concept is a powerful tool that has been taught since at least the '70s in undergraduate curriculum, typically introduced in the context of a first course on material and energy balances. The concept, however, has not been widely applied beyond the material balance domain and in general is not taught as a unified…

Assessment and instruction are interwoven in mathematically rich formative assessment tasks, so employing these tasks in the classrooms is an exciting and time-efficient opportunity. To provide a window into how these tasks work in the classroom, this article analyzes summaries of student work on such a task and considers several students'…

Prospective teachers (PTs) need opportunities to develop fraction number sense, yet little research has explicated how this development occurs. Our research team collaboratively designed a task targeted at helping PTs develop fraction number sense through an exploration of fraction comparison strategies. This paper focuses on developing one…

This paper aims to revisit and clarify the term problem context and to develop a theoretical classification of the construct of levels of context use (LCU) to analyse how the context of a problem is used to formulate a problem in mathematical terms and to interpret the answer in relation to the context of a given problem. Two criteria and six…

A challenging problem in some developing countries such as Nigeria is inadequate training of students in effective problem solving using the core concepts of their disciplines. Related to this is a disconnection between their learning and socio-economic development agenda of a country. These problems are more vivid in statistical education which…

Teaching how to solve problems--from solving simple equations to solving difficult competition tasks--has been one of the greatest challenges for mathematics education for many years. Trying to find an effective method is an important educational task. Among others, the question arises as to whether a method in which students help each other might…

This research study examines preservice teachers' experiences of learning through game design. In particular, we investigate how their perceptions of digital games have evolved through the process of designing and building their own educational games. We are also concerned with the knowledge and reasoning skills that preservice teachers…

Although test scores from similar tests in multiple choice and constructed response formats are highly correlated, equivalence in rankings may mask differences in substantive strategy use. The author used an experimental design and participant think-alouds to explore cognitive processes in mathematical problem solving among undergraduate examinees…