Analogous thinking has been commonly discussed as being an inherent and distinguishing characteristic of human cognition (e.g., Gentner, 2010; Goldstone, Day, & Son, 2010; Holyoak, in press; Rittle-Johnson & Star, in press). Gentner (2003) has argued that as part of the human cognitive toolbox, comparison accompanied by the relational language to…

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…

The current study compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems. The data consisted of clinical interviews conducted with three pre-service secondary mathematics teachers and a newly registered graduate…

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…

This article describes the rich thinking that can go into solving a difficult equation. The authors also give some sources for challenging mathematical problems.

Abstraction is a major concept in computer science and serves as a powerful tool in software development. Pattern-oriented instruction (POI) is a pedagogical approach that incorporates patterns in an introductory computer science course in order to structure the learning of algorithmic problem solving. This paper examines abstraction processes in…

We comment on the paper "The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra" by Carolyn Kieran and Paul Drijvers. We look at aspects of Kieran and Drijvers' analysis with regard to "task-technique-theory" in the light of a model of abstraction in context…

This document sets forth the design of a test of reading comprehension. The exam requires students to read passages of written English text--either literary or informational--and to answer questions about what they have read. In some cases, the questions deal with facts in the text or vocabulary. In other cases, a complete answer requires a clear…

In this paper we report on a research aimed to identify and characterize secondary school students' reasoning and proof abilities when working with 3-dimensional geometric solids. We analyze students' answers to two problems asking them to prove certain properties of prisms. As results of this analysis, we get, on the one side, a characterization…

The teaching and learning of statistics has impacted the curriculum in elementary, secondary, and post-secondary education. Because of this growing movement to expand and include statistics into all levels of education, there is also a considerable interest in how to teach statistics. For statistics concepts that tend to be very difficult or…

Experiences in designing and teaching a reformed abstract algebra course are described. This effort was partially a result of a five year statewide National Science Foundation (NSF) grant entitled the Rocky Mountain Teacher Enhancement Collaborative. The major thrust of this grant was to implement reform in core mathematics courses that would…

Eight teachers were interviewed concerning how students verify conjectures. The study is a sequel to a previous study, "How Students Verify Conjectures" [Bergqvist, T. (2000). "How students verify conjectures." "Research reports in Mathematics Education" 3]. Teachers' expectations of students' reasoning and performance are examined, and also how…

In your interactions with secondary school students learning science, you have probably become aware of large differences in student ability to understand science concepts, conduct investigations, and/or solve specific problems. Some students are extremely capable, while others demonstrate peculiar and inappropriate reasoning strategies.…

Teachers tend to design worksheets to assist their students to develop their spatial skills. Many secondary schools students may not have sufficient concrete experiences to tackle abstract reasoning in geometrical concepts competently. In addition, students who are non-visual and spatial learners may have difficulties in learning geometrical…

Science is at heart a rational activity. Reasoning, being an important component of critical thinking has been successfully taught using Socratic methods. As an approach, the instructor or designer of instruction models an inquiring and probing mind focusing on providing questions and not answers. The main aim has been to allow learners to…