Involving students in generating and solving their own problems is proposed. A method for generating problems by using a number puzzle is presented. Ideas for using the "what if not" technique are also given. (MNS)

Included in this section are brief articles on making up a story to explain a graph, the inverse of a function of a single variable, and exotic horse-race wagering and combinatorics. (MNS)

Presented is the second of a two part series on the use of exponential functions. Discussed, with examples, is the exponential growth of compound interest problems. (SL)

Worksheets are provided which lead students through an exploration of symmetry groups of geometric figures. (DT)

The organization of a basic algebra college course, in which lectures were combined with programmed learning instruction, is discussed. (DT)

There is a significant gap between theories of general psychological functions on one hand (e.g., memory) and theories of mathematical content knowledge on the other (e.g., content of algebra). To better guide the design of ground breaking and demonstrably better mathematics instruction, we need instructional principles and associated design…

One of the greatest challenges for mathematics teacher educators committed to reforming and improving mathematics education is to help preservice elementary and middle school teachers develop an appreciation for algebraic reasoning. Preservice teachers' views of algebra are typically derived from their experiences in middle school and high school…

This paper describes student difficulties in first-year calculus classes and suggests some instructional strategies to address these difficulties. Participants in this study were 200 low socio-economic background freshmen majoring in business in Brazil. Results show that the main difficulties are related to lack of understanding of algebraic…

The teaching and learning of early algebra draw heavily on arithmetic and the relationship between these two forms of activity is much debated. Drawing on interviews with 12 year old pupils we consider the ways in which some pupils used substitution of numbers for letters to extend their ability to manipulate algebraic expressions. We argue that…

Increasing numbers of mathematics educators, policy makers, and researchers believe that algebra should become part of the elementary education curriculum. Such endorsements require careful research. This paper presents the general results of a longitudinal classroom investigation of children's thinking and representations over two and a half…

This is a book about teaching maths to pupils with learning differences, not learning difficulties. Teaching and learning in schools is, and always has been, print based. Other ways of thinking--visual, kinaesthetic, practical--are discounted in the classroom. To become teachers, students must jump over a long series of hurdles, formal and…

Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…

This paper concerns a study of the performance of students in a linear algebra examination. Differences in performance of tasks requiring understanding of concepts with those that required only the use of routine procedures and factual recall were investigated. Central to the study was the use of a taxonomy based on Bloom's Taxonomy for…

This issue of Changing Schools explores what algebraic thinking is and why students need algebraic thinking. The efforts of Kansas and North Dakota to incorporate algebraic thinking into their state mathematics standards are described. Contents include: (1) "Algebraic Thinking: Preparing Students for Mastering Algebraic Concepts" (Vicki…

This book provides a resource for mathematics teachers to understanding the National Council of Teachers of Mathematics' (NCTM) standards and implementing these standards in their teaching. Five standards are overviewed: (1) number and operation; (2) algebra; (3) geometry; (4) measurement; and (5) data analysis and probability. Lesson plans are…