The characteristics of expert knowledge--interconnectedness, understanding, and ability to transfer--are inextricably linked, a point that is critically important for educators and constitutes a major theme of this paper. This paper explores how an analysis of the architecture of expert knowledge can inform the development of assessments to help…

This book features a comprehensive review of the Math Sense series and 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 whole numbers;…

The case study presented in this report was part of assessing a teaching proposal on ratio and proportion. A group of sixth-grade students of elementary education in Mexico participated in the implementation of the proposal. The girl of the case study was representative of those students in the group who had a lot of recourse to handling…

The Purposeful Algebraic Activity project aims to explore the potential of spreadsheets in the introduction to algebra and algebraic thinking. We discuss two sub-themes within the project: tracing the development of pupils' construction of meaning for variable from arithmetic-based activity, through use of spreadsheets, and into formal algebra,…

The Purposeful Algebraic Activity Project is a longitudinal study of the development of pupils' algebraic activity in the early years of their secondary schooling. Analysis of data from a spreadsheet-based teaching programme and from semi-structured interviews leads us to identify three features of the spreadsheet environment that appear to shape…

Our study concerns the analysis of teacher and student activities. Secondary school 6th grade students were confronted, for the first time, with solving equations. We used our cognitive models of students and experts (in algebraic calculations) for analyzing the teaching process and the cognitive functioning of students. Our model led us to…

The purpose of this report is to investigate the range of student responses in three domains--hypothesizing, organizing data, and algebraic generalization of patterns during their work on a spreadsheet-based activity. In a wider context, we attempted to investigate students' utilization schemes of spreadsheets in their learning of introductory…

In the United States, African Americans, Latinos, and Native Americans have lower success rates and higher drop-out rates in mathematics than other racial or ethnic groups. Given that quantitative competency serves increasingly as a vehicle for economic enfranchisement, these differential success rates make mathematics achievement a civil rights…

Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help 6-8 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…

Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help 3-5 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…

This paper explores the role of open-ended realistic division problem in the development of algebraic reasoning. A written test was administered to 672 students. From the results of this test students were selected for semi-structured interviews. The students were interviewed in pairs and were asked to explain to each other how they would solve…

We present classroom research on a variant of the guess-my-rule game, in which nine-year-old students make up linear functions and challenge classmates to determine their secret rule. We focus on issues students and their teacher confronted in inferring underlying rules and in deciding whether the conjectured rule matched the rule of the creators.…

This paper reports on part of a wider study on the teaching and learning of the conventions of formal algebraic notation. Through the analysis of paper tasks given to teachers I argue that not only does the inherent mathematical structure have an effect on the way in which an equation is manipulated but also the visual impact of notation itself.…

This study compared the effects of two different special educator roles within high school algebra classes containing special needs students. The special educator served as either in-room assistant or as co-teacher. The study was conducted for one chapter of algebra study over a 3-week period. No significant differences between groups were found…

This book is a compatible instructional component to any algebra textbook and was developed by University of Hawaii under the Dwight D. Eisenhower Mathematics and Science Education Improvement Act. The tasks align with the content and instructional approach used in daily classes that emphasize standards-based teaching and learning. The tasks…