Even after many decades of productive research, problem solving instruction is still considered ineffective. In this study we address some limitations of extant problem solving models related to the phenomenon of insight during problem solving. Currently, there are two main views on the source of insight during problem solving. Proponents of the…

The topic of inhibition in mathematics education is both well timed and important. In this commentary, we reflect on the role of inhibition in mathematics learning through four themes that relate to how inhibition is defined, measured, developed, and applied. First, we consider different characterizations of inhibition and how they may shape the…

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…

Structured abstract: Introduction: Difficulties in science and mathematics may stem from intuitive interference of irrelevant salient variables in a task. It has been suggested that such intuitive interference is based on immediate perceptual differences that are often visual. Studies performed with sighted participants have indicated that in the…

The ubiquity of the subject of percentages in our everyday life demands that math teachers and pre-service math teachers demonstrate a profound knowledge and thorough understanding of the concept of percentages. This work, which originated from one specific lesson in an 8th grade math class, studies the conceptual understanding and problem-solving…

We encounter ratios on a daily basis. They also play an important role as a basic construct of thinking in many areas of school mathematics. For example, a fraction can be interpreted as the ratio of a part to the respective whole. Many children appear to have difficulties with fractions and although the concept of ratios is crucial for this…

Many students encounter difficulties in science and mathematics. Earlier research suggested that although intuitions are often needed to gain new ideas and concepts and to solve problems in science and mathematics, some of students' difficulties could stem from the interference of intuitive reasoning. The literature suggests that overcoming…

According to the intuitive rules theory, students are affected by a small number of intuitive rules when solving a wide variety of science and mathematics tasks. The current study considers the relationship between students' Piagetian cognitive levels and their tendency to answer in line with intuitive rules when solving comparison tasks. The…

Presents a way of using counterintuitive mathematics problems to help keep students actively involved in mathematics education. (KHR)

The relationship between quantitative problem solving and commonsense has provided the basis for an expanding exploration for Colleran and O'Donoghue. For example the authors (Colleran et al., 2002, 2001) discovered the pivotal role commonsense plays in adult quantitative problem solving and suggest commonsense is an important "resource? in…

The paper discusses the interaction between intuitive biases of probabilistic thinking and mathematical knowledge. It would appear that students may answer numerical problems correctly but falter on simple descriptive solutions. Students appear to relinquish formal knowledge for simpler heuristics when attempting to describe the outcome of an…

Considers 33 preservice secondary mathematics teachers' solutions to a famous sampling problem with particular interest on the use of intuition and/or formal mathematics in reaching a conclusion. Considers the relationship of solution strategy to students' background in formal mathematics and gender. Discusses implications for teaching statistics…

In their work in science and mathematics education, the authors have observed that students intuitively react in similar ways to a wide variety of scientific tasks. These tasks differ with regard to their content area and/or to the reasoning required for their solution, but share some common, external features. We have identified three types of…

This article describes the factors to which the classroom teacher needs to attend to enhance the mathematical problem-solving abilities of students. Emphasis is placed upon the means necessary to develop the attribute of being a problem solver, rather than focusing on the goal of becoming a problem solver. (JJK)

In the international community of mathematics and science educators the intuitive rules theory developed by the Israeli researchers Tirosh and Stavy receives much attention. According to this theory, students' responses to a variety of mathematical and scientific tasks can be explained in terms of their application of some common intuitive rules.…