Some potential difficulties involved in using "real-life situations" in teaching problem solving are illustrated with a racing car problem. The importance of developing mental images and the ability to abstract in the solution process is indicated. (MP)

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations (in particular "diagrams") of mathematical problems. As a paradigmatic…

This study sought to determine the basis for young children's understanding of fundamental addition and subtraction processes, and to expose any limitations on such arithmetic reasoning. Thirty-six two-year-olds and 36 three-year-olds participated in six experiments which examined children's relational quantity judgments about pairs of arrays in…

This study addressed the question: "What instructional techniques are most effective in helping students learn how to self-regulate their learning?" An integrated model based on current research in self-regulated learning (SRL) was used to explain changes in students' SRL. Five key instructional practices were identified and embedded…

Presents examples where mathematical and physical reasoning complement each other in interpreting and analyzing some basic science concepts using proof by contradiction and contrapositive. Examples involve the rotation of the moon, the stability of electrons and protons, the electron's orbit about the nucleus, and the earth's liquid core. (MDH)

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)

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…

Thinking-aloud protocols of human problem solvers working on geometry problems are presented and discussed. Protocols were obtained from six individuals working on nine different problems in which constructions were used. Nineteen protocols are presented with annotation and discussion, and other protocols are summarized. The primary purpose of the…

This study examined the development of the rational number concept as a ratio. Preliminary to the description of the study is an introduction discussing constructivism and equilibration. The study itself tests whether equilibration theory holds, and if so, what is the nature of its "phases" and whether these are found at each of the "periods" of…

This paper asserts that any intellectually responsible program to instruct young children in math, science, and technology must overcome at least three seemingly insurmountable obstacles: (1) adults' inability to discover, either by reflection or analysis, the means by which children acquire science and technology concepts; (2) the fact that young…

Examined is the relationship between junior high school students' directional reasoning about rates and numerical reasoning on proportion-related word problems. The relationship between the ability to solve context-free fraction exercises and the ability to solve mathematically similar word problems is discussed. (KR)

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)

Discusses prerequisites that help students develop multiple strategies for solving problems as recommended in the National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards." Presents two examples of activities involving addition, subtraction, and permutations that promote multiple strategies. Suggests ways to…