"The Simpsons" is an ideal source of fun ways to introduce important mathematical concepts, motivate students, and reduce math anxiety. We discuss examples from "The Simpsons" related to calculus, geometry, and number theory that we have incorporated into the classroom. We explore student reactions and educational benefits and difficulties…

Three issues about students' reasoning, proving and understanding proof in number patterns are investigated in this paper. The first is to elaborate the features of junior high students' reasoning on linear and quadratic number patterns. The second is to study the relationships between 9th graders' justification of mathematical statements about…

Research suggests component skill performance has a strong positive relationship with composite skill performance. This study examined the association between accuracy and fluency for the component-composite relationship within multiplication. One hundred and fifty-seven fifth-graders did one-minute assessments for single-digit, and multi-digit…

An alternating treatments design was used to compare the effects of baseline, interspersed brief problems, and interspersed brief problems plus token reinforcement on students' endurance while completing math worksheets. By pairing the completion of brief problems with token reinforcement, the role of problem completion as a conditioned reinforcer…

Literacy educators have been actively theorising the demands of literacy in New Times yet mathematics educators have taken little of this debate up. If, as literacy educators suggest, literacy demands are different in these New Times, what are the implications for numeracy or mathematics educators? This paper explores perceptions of young and…

Children's accounts of their participation in sociocultural activity related to number are essential for their teachers in order that they can assist children in building their formal learning in number on informally acquired numerical understandings. Children's participation in sociocultural activity related to number will differ from child to…

Math is about the relationship between numbers. Right answers are not the only thing to look for when examining students' work in mathematics. Looking at how children solve computation problems can give teachers insight into their thinking and help determine what math skills they already know and what they still need to learn. The author contends…

Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared)…

The Country Data Project was developed for eighth-grade students of Milwaukee public schools to make them understand the importance of numbers by making them interpret the full descriptions of people of various countries by analyzing the numbers summarizing the population distribution of the respective country. The results prove that the project…

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 booklet is a designed to introduce adult basic education/literacy instructors to a spiral sequencing approach that may be used to teach whole number skills. The booklet begins with a brief discussion of integration of numeracy into literacy instruction. Discussed next are the benefits of using a spiral sequence for numeracy facilitation and…

This paper posits that, as educators' attention turns to elementary mathematics as preparation for algebra, it is important to begin by examining the kind of elementary mathematics content teaching that is aligned with reform. The paper calls for a close examination of students' development of operation sense. The role of children's engagement…

This book is a compilation of recent research on the development of multiplicative concepts. The sections and chapters are: (1) Theoretical Approaches: "Children's Multiplying Schemes" (L. Steffe), "Multiplicative Conceptual Field: What and Why?" (G. Vergnaud), "Extending the Meaning of Multiplication and Division" (B. Greer); (2) The Role of the…