This article presents several activities (some involving graphing calculators) designed to guide students to discover several interesting properties of Fibonacci numbers. Then, we explore interesting connections between Fibonacci numbers and matrices; using this connection and induction we prove divisibility properties of Fibonacci numbers.

A conceptually sound, research-based method is presented to make sense of students' thinking about length. It is suggested that the levels of framework is an important tool for improving instruction and formative assessment as well as effectively diagnosing and remediating students' difficulties in learning about length. Some of the measurement…

The authors present an analysis of portfolio entries submitted by candidates seeking certification by the National Board for Professional Teaching Standards in the area of Early Adolescence/Mathematics. Analyses of mathematical features revealed that the tasks used in instruction included a range of mathematics topics but were not consistently…

This course guide is intended for classroom use by teachers of secondary level mathematics to Spanish-speaking students of English as a second language (ESL). Both mathematical instruction and acquisition of English mathematical terminology are emphasized. The book is divided into chapters that comprise a Spanish-English glossary of mathematical…

This paper examines students' self-motivation in mathematics learning between girls and boys using secondary analysis of the Third International Mathematics and Science Study (TIMSS) conducted in 2003 by the International Association for the Evaluation of Educational Achievement (IEA) involving eighth graders. Components of self-motivation include…

This paper describes a content upgrading course on Secondary School Algebra which was planned and conducted for in-service mathematics teachers who are trained to teach mathematics at lower secondary level (ages 13 to 14). In order to be an effective mathematics teacher, one needs to know a great deal of mathematical knowledge on top of good…

This paper summarizes our analysis of the complexity of ratio problems at Grades 6 and 7, and reports a two-year experiment related to the teaching and learning of rational numbers and proportionality in these grades. Two classes were followed and observed. Part of the teaching material was common to both classes, mainly the objectives and the…

This volume is a teacher's edition in a series of books that contain open-ended exploration activities and experiments. These activities allow and encourage students to set their own goals, use their own creativity and ideas, investigate the wonders of nature, learn about the workings of real businesses, and draw conclusions from their…

Team research is important in studying cognition as enactive. This paper contains four different pieces of research directed toward the evidences and artifacts of two students in Canada engaging in a sustained mathematical activity. These four portraits of mathematical cognition in action consider the conversation in which the activity occurs; the…

This book reinforces the outstanding work done by the National Council of Teachers of Mathematics (NCTM) in developing curriculum standards for students in kindergarten through fourth grade by discussing the 13 strands of mathematics and their implications for teachers and parents who work with students. It also provides some suggested resources…

Four preschool children with developmental delays were taught to name the numerical value of sets of geometric figures, the corresponding numeral, the corresponding number word, and the corresponding Roman numeral. Half of the stimuli were taught with instructive feedback and the other half without, as two conditions were established: the future…

The purpose of this document is to provide a framework around which systems and schools may build their mathematics curriculum. Important components of a mathematics education for the majority of students are identified. This document is presented in two parts. Part I, Principle for School Mathematics, addresses questions such as what is…

Counting books offer children the time and the tools to develop the understanding needed to solve problems. Stimulated by these books, children may use mathematic language and talk about mathematics as they get involved with materials to move and manipulate, as they use supportive aids found in illustrations, and as they interact with materials to…

A mathematics curriculum for moderately and severely retarded and autistic students and adults should possess 10 necessary characteristics, including provision for instruction based on assessment results, stress on functional application, focus on generalization of skills, and specific criteria for mastery of each skill. The functional but…

Mathematics activities and facts related to pi are presented in this issue of "Student Math Notes." Included are: (1) an exercise based on Buffon's needle problem in which pieces of toothpicks are dropped onto a ruled surface; (2) a calculation of pi to 200 decimal places; (3) exercises related to Biblical and ancient Chinese…