We examine a prospective high school teacher's instructional representations of rate of change and right triangle trigonometry to investigate his interpretation and understanding in relation to the development of proportional reasoning. Despite a constant effort by the subject to resort to "real life" examples in order to give meaning to his…

Examined inconsistencies in secondary school students' reasoning about the probability concept of equally likely events. Results of two studies suggest that the number of students who understand the concept of independence is much lower than the latest National Assessment of Educational Progress results indicate. (Contains 22 references.) (MDH)

Pragmatic and semantic problem solving are examined as processes that enhance acquisition of mathematical knowledge. It is suggested that development of mathematical cognition involves restructuring and that math teachers can help restructure children's knowledge systems by providing them with situations in which semantic and pragmatic problem…

Investigated the effect of problem wording on solving arithmetic word problems by first graders. Found that wording is a crucial component in solving difference problems. Results suggest that further research on word problem-solving processes focus on the interaction between linguistic comprehension and mathematical reasoning. (AA)

A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)

Twenty-four sixth-grade children participated in clinical interviews on ratio and proportion before receiving instruction in the domain. Student thinking was analyzed in terms of mathematical components critical to proportional reasoning. Two components, relative thinking and unitizing, were consistently related to higher levels of sophistication…

Mathematical tasks calling for relational thinking were given to 60 children of Indian, Pakistani, or Bangladeshi origin who had spent their school lives in England, 60 who had arrived within the past 3 years, and 60 British children. Differences in the ability to abstract, hypothesize, and generalize were studied. (KC)

Defines the mathematical concept of proportionality. Uses graphs of linear relationships to explore and make generalizations about the characteristics of proportional situations to help students critically evaluate problems involving proportions. (MDH)

Challenges the readers comprehension of mathematical induction by presenting four examples of arguments that misrepresent the concept. Discusses the reasons why the arguments lead to false conclusions. (MDH)

Describes several short geometry tasks that go beyond the simple recognition of figures and properties. Presents scoring rubrics and questions that might be useful to middle school teachers developing short open-ended questions that encourage and assess students' thinking. (ASK)

This paper examines the mathematical conversations of middle school students as they use computer-mediated graphic representations to construct a shared understanding of the basic concepts of probability under two conditions. The first condition used graphical representations to depict important abstract relationships visually, and the second…

Sixty-five Year 2 children with ages ranging from six to seven years participated in a teaching experiment to introduce functional thinking. The results show that young children are capable of generalising, can provide examples of relations and functions, can describe the inverse of such relationships and give valid reasons for how they found the…

Problems were presented to 13 university students in which letters were to be added or subtracted (e.g., B + D = ? or F - ? = D). After each problem, each subject gave a retrospective protocol indicating the way in which the problem was solved. Models of performance by each subject in each experimental session shared major properties; choices by…

This exploratory study had two goals: (1) to identify signs of abstraction and consolidation of abstractions of functional concepts in students in a situation-based curriculum; and (2) to use theoretical arguments as well as experimental evidence in order to shape notions of abstraction and consolidation of abstractions. The methodology was…

The purpose of this booklet is to explain examination registration procedures and to introduce the Psychometric Entrance Examination so that students will know what to expect, what types of questions they will be asked, and how they will be expected to answer. The aim of the examination is to evaluate a variety of cognitive abilities: verbal,…