We present the results of a study analysing the cooperative behaviour of fifth-grade student pairs when they have to overcome a difficulty (a barrier) in a mathematical problem task. As analysing method we used content analysis as well as frequency-tests (chi-squared test, CFA, Freeman-Halton-test). Our results help to confirm and elaborate the…

Increasing student's critical thinking is the focus of many current education discussions. Experts in reading agree that the keys to building critical thinking include: engagement, novelty, cooperative learning, and discussion. Wiggins and McTighe (2005) insist that deep learning and critical thinking can be developed by using questions based on…

A focus on enrollments, rankings, uncertain budgets, and branding efforts to operate universities could have serious implications for discussions of sustainable solutions to complex problems and the decision-making processes of leaders. The Authentic Leadership Model for framing ill-defined problems in higher education is posited to improve the…

Sets in the game "Set" are lines in a certain four-dimensional space. Here we introduce planes into the game, leading to interesting mathematical questions, some of which we solve, and to a wonderful variation on the game "Set," in which every tableau of nine cards must contain at least one configuration for a player to pick up.

Solving equations in finite algebraically structures (semigroups with identity, groups, rings or fields) many times is not easy. Even the professionals can have trouble in such cases. Therefore, in this paper we proposed to solve in the various finite groups or fields, a binomial equation of the form (1). We specify that this equation has been…

We examined whether requiring an individual readiness assurance test (iRAT) before a team readiness assurance test (tRAT) would benefit students in becoming better problem solvers in physiology. It was tested in the form of tRAT scores, the time required to complete the tRAT assignment, and individual performance on the unit examinations. Students…

The purpose of this article is to explore how a group of four university physics students addressed mechanics problems, in terms of student direction of attention, problem solving strategies and their establishment of and ways of interacting. Adapted from positioning theory, the concepts "positioning" and "storyline" are used to describe and to…

Over the last few decades there has been a strong narrative "turn" within the humanities and social sciences in general and educational studies in particular. Especially Jerome Bruner's theory of narrative as a specific "mode of knowing" was very important for this growing body of work. To understand how the narrative mode works Bruner proposes to…

Two contestants debate the notorious probability problem of the sex of the second child. The conclusions boil down to explication of the underlying scenarios and assumptions. Basic principles of probability theory are highlighted.

A comparative analysis of 51 case problems used in five problem-based pedagogical models was conducted to examine whether there are differences in their characteristics and the implications of such differences on the selection and generation of ill-structured case problems. The five pedagogical models were: situated learning, goal-based scenario,…

The focus of this article is a theoretical discussion and analysis of the concept of intuition. The article investigates how intuition, in the psychological sense, is connected with concepts like problem-solving, reflective thinking, automatized thinking activities and understanding 'gestalt' or structure and meaning. Automatisms are based on…

The role of the body, particularly gesture, in supporting mathematical reasoning is an emerging area of research in mathematics education. In the present study, we examine undergraduate students providing a justification for a task about a system of alternating gears, which involves concepts of number relating to even/odd patterns. Some…

Counting problems have applications in probability and computer science, and they provide rich contexts for problem solving. Such problems are accessible to students, but subtleties can arise that make them surprisingly difficult to solve. In this paper, students' work on the Groups of Students problem is presented, and an important issue related…

Researchers are currently investigating how calculus students understand the basic concepts of first-year calculus, including the integral. However, much is still unknown regarding the "cognitive resources" (i.e., stable cognitive units that can be accessed by an individual) that students hold and draw on when thinking about the integral. This…

Problem posing (not only in lesson planning but also directly in teaching whenever needed) is one of the attributes of a teacher's subject didactic competence. In this paper, problem posing in teacher education is understood as an educational and a diagnostic tool. The results of the study were gained in pre-service primary school teacher…