Suggests ways early years educators can begin teaching young children to think algebraically and prepare them for success in algebra. Focuses on ways to promote mathematical patterns, mathematical situations and structures, models of quantitative relationship, and change. Describes how first-graders used real object representations to better…

Describes student historical research and student classroom presentation of the results of that research. Feedback from the student surveys verifies that active-learning mathematics history can motivate students to learn mathematics. (Author/DDR)

Describes an activity in which students use data analysis and mathematical modeling to obtain insight into a geometrical question. Explores a simple case of the isoperimetric inequalities. (KHR)

Introduces exercises on histograms and frequency density. Guides pupils to Discovering Important Statistical Concepts Using Spreadsheets (DISCUSS), created at the University of Coventry. Includes curriculum points, teaching tips, activities, and internet address (http://www.coventry.ac.uk/discuss/). (KHR)

Presents a project used to help students make connections between linear and exponential models and between arithmetic and geometric sequences. (KHR)

Recommends that numeracy be better coordinated and integrated across the curriculum and that teachers examine the image of mathematics presented to children. Discusses the value of eliciting children's ideas about and experiences with numbers and measuring. (DDR)

Explores algebraic thinking as children search for patterns while collecting, organizing, and graphing data and as they derive equations describing relationships found in the data. (ASK)

Discusses the vital place of proofs in geometry classes. Argues that, although inductive geometry with computer software certainly makes theorems come alive, proofs lead to insight and understanding that allow students to extend the concepts that they see in examples. Presents a theorem, its proof, and a computer exercise. (ASK)

Recommends that mathematics instruction should promote student discourse by orchestrating situations in which each individual's thinking is challenged and asking students to clarify and justify ideas. Provides a vignette of a heterogeneously grouped seventh-grade mathematics class to illustrate the process of mathematical discourse. (ASK)

Presents an overview of the geometry findings of the Third International Mathematics and Science Study (TIMSS) and ways to use problems from the study to assess students' understanding of geometry. (ASK)

Presents a unit for fourth and fifth grades on fractions and mixed numbers in which students have to decrease and increase the number of servings of different recipes. Describes students' strategies for multiplying fractions, and discusses how the use of a ratio table facilitated their thinking. (ASK)

Recommends conducting interviews with students in order to grasp their understanding of fractions and provides interview questions. Presents results of a study using those interview questions and concludes student responses fell into three main categories: (1) described a mental image of an object; (2) drew a model of the fraction using a circle…

In today's society, changes in technology have made estimation skills more important than ever in the development of mathematical power. Presents a schoolwide activity in which students participate in a mathematical contest on estimation. Concludes that, in devising their estimates, students have practiced their problem-solving and sense-making…

Presents a game called Push-Penny, played by pushing a coin and having it land on a line, used to teach students to develop intuitive feelings for the consequences of randomness, including data handling and the construction and use of tables and graphs. (ASK)

Argues that basic components of discrete mathematics can be introduced to students through gradual elaboration of experiences with iconic spreadsheet-based simulations of concrete materials. Suggests that the study of homogeneous and heterogeneous patterns of manipulative spreadsheet templates allows for appreciation of the development of…