This article presents, in the context of solving a specific mathematical problem, an argument to indicate how problem posing can lead to a deeper understanding of what is involved in the act of problem solving. (DT)

Four problems concerning the maximum number of regions determined by circles and polygons are explored. (DT)

An algebra problem is analyzed, and several variations are suggested for further student inquiry. Practical applications of the problem are discussed. (DT)

Geometric models are used to study numerical relationships in summation formulas. (DT)

As part of a larger investigation of preservice teachers' use of, and movement amongst, various modes of representing exponential relationships, this report focuses on one case study, that of Mike, whose facility in moving amongst representational registers was not matched by conceptual understanding of the underlying mathematical ideas as he…

This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…

This paper presents an analysis of high school and starting college students' work with algebraic expressions and problems involving parameters. We suggest that parameters should be considered as general numbers that are used to make second order generalizations. The Three Uses of Variable model (3UV model) is then used as theoretical framework to…

This book demonstrates how K-2 students deepen their mathematical ideas when encouraged to represent and communicate their thinking. Numerous vignettes from actual classrooms and reflective comments from teachers provide a model for how show and tell can enhance classroom teaching and improve children's learning. Examples of students' work and…

This paper consists of a learning unit for college algebra in which the problem presents three different payment plans for a tuition plan to pay for college expenses. The details of each payment plan are presented, each followed by several exercises so that comparisons of the results can be made across payment plans. (MM)

This study investigates whether the National Council of Teachers of Mathematics (NCTM) professional standards are appropriate for a two-year college developmental mathematics courses. The NCTM professional standards of worthwhile mathematical tasks, classroom discourse, and teacher reflection were all part of this preparatory mathematics course.…

Our teaching conception acknowledges the teacher's central role as a decision maker, influenced by knowledge, beliefs, and emotions. We believe that teachers' education must be focused on teachers' awareness of the complexity of the teaching process, of the incidence of these factors in it, and of the importance of looking at theory as a strong…

As a result of questions arising from differences in performance on Algebra 1 final examinations by school during the 1999-2000 school year, students' middle school mathematics experiences have received renewed focus. Specific questions have arisen regarding whether all students are sufficiently prepared to handle algebraic content by grade 8 or…

This paper describes "The Migration Method," a new technique for graphing a quadratic function (one of the major foundations of undergraduate mathematics) and finding its zeroes. The method promotes a higher degree of conceptualization, reinforces the concept of symmetry, encourages mental visualization, and strengthens the ability to…

This paper examines the question of whether the introduction and use of the function machine representation as a scaffolding device helps undergraduates enrolled in a developmental algebra course to form a rich, foundational concept of function. It describes students' developing understanding of function as an input/output process and as an…

The major focus of this study is to trace the cognitive development of students throughout a mathematics course and to seek the qualitative differences between those of different levels of achievement. The aspect of the project described here concerns the use of concept maps constructed by the students at intervals during the course. From these…