Reasoning and imagining are seen as very different acts of mind. Imagination connotes the counterfactual and the unruly; reasoning connotes a realistic and rule-bound activity. Good reasoning depends crucially on the vigorous exercise of imagination. Good informal reasoning is as difficult, and as dependent on imagination, as mathematical…

Reasoning and learning are closely related, both being the methods of solving problems, learning usually results from the process of reasoning. All inventions, discoveries, art, literature and advances in culture and civilization are based on thinking, reasoning and problem solving capacity of human being. A sound reasoning leads to better…

This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15-16 years old). Four levels of the development of constructing and using mathematical models were…

High schools may still be anchored to 20th century expectations, but what are the critical guideposts for a 21st century high school education? There are many specific skills and competencies that young people will need to succeed, but more than particular skills, they will need the cognitive capacity to educate themselves throughout their entire…

This paper provides an instrumental account of precalculus students' graphical process for solving polynomial inequalities. It is carried out in terms of the students' instrumental schemes as mediated by handheld graphing calculators and in cooperation with their classmates in a classroom setting. The ethnographic narrative relays an instrumental…

This study compared the behaviors of children who had been in a toddler day care program at least 13 months with children who had been there less than 6 months. The children who had been in the program longer were rated significantly higher in ability to get along with peers, problem solving, ability to abstract, and ability to plan. (JMB)

The study with 30 five-year-olds and 30 seven-year-olds demonstrated that children as young as five have an emerging ability to solve both verbal and perceptual proportional analogy problems and to detect the meaning of proportional metaphoric sentences. (Author/DB)

The findings of this study indicate that students can be taught to avoid specified verbal operations which block problem-solving processes without detriment to the processes themselves. (RC)

Supports the proposition that anxiety over intellectual performance is one antecedent of a reflective cognitive disposition. (Author/WY)

The relationship between a student's stated preference for solving a problem and his/her actual problem methodology, concrete or abstract, was studied. Comparisons were made between formal and nonformal students. (MP)

In this article we propose the following definition for advanced mathematical thinking: Thinking that requires deductive and rigorous reasoning about mathematical notions that are not entirely accessible to us through our five senses. We argue that this definition is not necessarily tied to a particular kind of educational experience; nor is it…

Investigated distribution of spatial visualization scores (Space Relations test of the Differential Aptitude Test) and mathematical problem-solving scores (Mental Arithmetic Problems) obtained by 161 male and 152 female 9th grade students. No significant sex-related differences were found between mean scores of tests of spatial visualization or…