Describes a model using a group of fifth-grade students to better understand the assessment standards. Discusses the activity, the lesson on tessellation, and instructional decisions from the perspective of the assessment standards. (ASK)

Presents the problem of points and the development of the binomial triangle, or Pascal's triangle. Examines various attempts to solve this problem to give students insight into the nature of mathematical discovery. (KHR)

Describes an investigation-based, lecture-free first-year algebra course in which students are responsible for compiling their own textbooks. Discusses the purpose and procedures of the activity. Includes student worksheets. (KHR)

Examines existing research literature which suggests that introducing computing tools can help students focus on the relevant aspects of a problem, function at higher levels of geometric understanding, distinguish between drawings and constructions, and develop and reason about conjectures on the basis of generalization of patterns. (KHR)

Investigates the use of mathematical modeling tasks in 11- and 12-year-old students and the development of mathematical thinking skills using practical modeling activities. Analyzes the development of students' mathematical thinking with interviews of a form of dynamic assessment. Reports that some students proved to be naturally mindful and…

Presents materials and methods that maintain student interest and encourage them to think creatively, develop mathematical reasoning, and look at problems from different perspectives, all within an open-ended approach to problem solving. Includes questions for discussion. (KHR)

Explains TIMA (Tools for Interactive Mathematical Activity), that were designed to provide elementary schools children with contexts in which they could enact mathematical operations. Discusses differences from drill and practice software; provides examples of how the TIMA were used by children to engage in cognitive play; and emphasizes the…

Examines four areas of difficulty with graphing and modeling, identifies confusions and misconceptions, and shows how these areas interact in the presence of data-collection devices. (KHR)

Proposes lotto games as a source of problems and exercises for classroom activities as well as applications of basic probability concepts in a practical setting which leads to a greater understanding of the remote chance anyone has of winning a lottery game. (KHR)

Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)

Discusses Einstein's special relativity theory and some of the developmental mathematics involved. Presents motivational classroom materials used in discussing relative-motion problems, evaluating a radical expression, graphing with asymptotes, interpreting a graph, studying variation, and solving literal and radical equations. (KHR)

Presents five articles addressing numbers and math instruction for young children: "Math Talk with Young Children: One Parent's Experience" (Fred E. Gross); "How Children Build Their Understanding of Numbers" (David Elkind); "Early Math: It's More than Numbers" (Ann S. Epstein); "Assessing Mathematical Learning: Observing and Listening to…

Explores how to know when children think mathematically, how to establish a setting that elicits mathematical thinking, and what to learn about children as a result. Fourth grade students think and talk mathematically while tackling a real-life PACKETS program. Addresses content standards involving proportional reasoning as well as the process…

Proposes some possible ways of using an interactive whiteboard as a means of stimulating pupils' thinking and active participation. (KHR)

Presents a classroom project in which children use bottles and sand to explore mathematics. (Author)