Rational points in the plane were defined as points having both coordinated rational. Students solved several problems linking rational points with lines, circles, and other geometric figures. (SD)

A series of interesting mathematical applications for the greatest integer function are presented. (JT)

An activity is described as an example of an application that draws on the behavior of current in electrical circuits to create a symbolic algebra. Five worksheets are included, with discussion of their use. (MNS)

Discussed is an approach in which algebra and geometry are interwoven in a series of problems that develop one from another. The two main concepts are the algebraic concept of function and the geometric concept of the "family of quadrilaterals." (MNS)

This study concerned conceptual difficulties of college students learning programming and ways the teacher can simplify the process. An analysis of general strategies used in solving problems involving loops is given, with four types of hierarchical strategy categorized. Students had difficulty transforming their algebraic descriptions into…

Reports results obtained when 24 14-year-old students were presented with algebra tasks by a computer-based modeling system and, four months later, comparable paper and pencil tests together with detailed interviews. Comparison of the results revealed profound misunderstandings of algebraic notation and identified classes of strategies used by…

Methods of finding algebraic expressions to fit number patterns are explored. (DT)

This is a qualitative study of 22 9th graders performing generalizations on a task involving linear patterns. Our research questions were: What enables/hinders students' abilities to generalize a linear pattern? What strategies do successful students use to develop an explicit generalization? How do students make use of visual and numerical cues…

This book is a guide to the development of mathematical talent in students in grades K through 8. The first chapter is on developing mathematical promise and considers characteristics of students who are mathematically promising, the goals of mathematics instruction, how to find and/or create good problems, models for increasing the numbers and…

This study explores students algebraic and geometric approach in solving tasks in functions and the relation of these approaches with complex geometric problem solving. Data were obtained from 95 sophomore pre-service teachers, enrolled in a basic algebra course. Implicative statistical analysis was performed to evaluate the relation between…

This research study deals with the modes of representation that ninth-graders choose in order to communicate their problem solving paths and justifications, and the relation between these modes of representations and achievement level. The findings are based on analysis of 350 answers to problems that demanded communication of reasoning,…

The study proves that a didactical model based in a method to solve word problems of increasing complexity which uses a numerical approach was essential to develop the analytical ability and the competent use of the algebraic language with students from three different performance levels in elementary algebra. It is shown that before using the…

We deal with the study of the senses and the meanings generated in the representation of the unknowns in the resolution of word problems involving two unknown quantities. The discussed cases show the difficulties that the students beginning the algebra learning have to deal with when using the equality between "unknown things". For them,…

We explore how fourth grade (9 to 10 year olds) students can come to understand and use the syntactic rules of algebra on the basis of their understanding about how quantities are interrelated. Our classroom data comes from a longitudinal study with students who participated in weekly Early Algebra activities from grades 2 through 4. We describe…

During several years of experimentation, we accumulated a large collection of data on the analysis of problems generally encountered in algebra and on the reasoning developed by students at different levels when confronted with these problems. Analysis of this data led us to a new way of looking at differences among word problems, and to the…