Although findings from cognitive science have suggested learning benefits of confronting errors (Metcalfe, 2017), they are not often capitalized on in many mathematics classrooms (Tulis, 2013). The current study assessed the effects of examples focused on either common mathematical misconceptions and errors or correct concepts and procedures on…

Conditions under which group work leads to learning have been studied in collaborative settings. Little is known, however, about whether and how the interplay between collaboration and cooperation impinges on group learning. In this paper, we study this interplay in the context of mathematical problem-solving. We focus on how training students to…

Virtual resources team up to create a computational grid, which is used in computation-intensive problem solving. A majority of these problems require high performance resources to compute and generate results, making grid computation another type of high performance computing. The optimization in computational grids relates to resource…

The practice of grouping mathematics students by perceived levels of attainment, commonly referred to by teachers as ability grouping, is a contentious and long-standing topic of debate in education. Responses from a survey of 102 mathematics support teachers affirm the widespread use of ability grouping within New Zealand primary school…

Sternberg (2017) summarizes the history of identification of giftedness in the 20th century and presents a case for the shortcomings of measures such as IQ for problem-solving skills required in the 21st century. The Active Concerned Citizenship and Ethical Leadership (ACCEL) model is proposed to replace the outdated construct of IQ, particularly…

Two simple discrete-time models of mutation-induced cannibalism are introduced and investigated, one linear and one nonlinear. Both form the basis for possible classroom activities and independent investigative study. A range of classroom exercises are provided, along with suggestions for further investigations.

How can we teach inquiry? In this paper, I offer practical techniques for teaching inquiry effectively using activities built from routine textbook exercises with minimal advanced preparation, including rephrasing exercises as questions, creating activities that inspire students to make conjectures, and asking for counterexamples to reasonable,…

The ability to think and solve problems quickly is a necessary skill for success in education (Flanagan, Ortiz, Alfonso, & Mascolo, 2006; Proctor, 2011; Taub, Floyd, Keith, & McGrew, 2008). This leaves students who struggle with speeded tasks at greater risk for not meeting the educational demands in the classroom. Modern intellectual…

This study aimed to develop a survey instrument to measure student attitudes towards mathematics teaching-learning processes that is appropriate for the Indonesian context. This study consisted of two phases: Phase 1 (n = 320) was a pilot study to assess the suitability of the instrument items for Indonesian students. Phase 2 (n = 1001) was…

Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…

My charge in this study is to explore the lived experience of a high school teacher while immersed in a problem solving situation in a classroom setting. The main gist of this investigation is to textualize and, thereof, capture the essence of a teacher's encounter of failing to solve a mathematics problem during one of the classroom sessions. To…

The purpose of this study is to reveal factors considered by mathematics student teachers while posing modelling problems. The participants were twenty-seven mathematics student teachers and posed their modelling problems within their groups. The data were obtained from the modelling problems posed by the participants, their solutions on these…

The Mathematics students who perform truth-seeking process upon solving mathematical problems were unique. Therefore, the study deems it necessary to know students' mental structure and mechanism so that they can make the right decision by performing truth-seeking. However, no research has delved into the mental structures and mechanisms of…

This paper is based on the presumption that teaching multiple ways to solve the same problem has academic and social value. In particular, we argue that such a multifaceted approach to pedagogy moves towards an environment of more inclusive and personalized learning. From a mathematics education perspective, our discussion is framed around…

Mistakes can be a source of frustration for teachers and students in mathematics classrooms because they reveal potential misunderstandings or a lack of learning. However, increasing evidence shows that making mistakes creates productive pathways for learning new ideas and building new concepts (Boaler 2016; Borasi 1996). Learning through…