Presents a problem of tetras made with four cubes, mathematical ideas involved in this problem, and guiding questions for teachers. (KHR)

Presents mathematics activities to teach place value. (Author/YDS)

Describes a framework to help teachers decide when to use calculators with their students. (YDS)

Describes student work with linear and nonlinear relationships illustrating algebra skills and understanding which are important to introductory algebra. (YDS)

Explains big ideas in algebra that help students connect ideas with procedures in different mathematical topics to build a relational understanding of algebra. (Contains 10 references.) (YDS)

Includes three responses to David Lemire's article "Math Problem Solving and Mental Discipline." Contends that quality mathematics instruction should result in citizens capable of functioning productively in this highly technological, capitalistic, and democratic society. Proposes that mathematics is very relevant for real-life problem solving.…

From their experience with open-ended tests requiring higher-order thinking and problem-solving abilities, schoolchildren in the USSR learn to think before answering. U.S. students instead train for rapid response, learning how to take tests rather than how to solve problems. Tests should be part of the curriculum, not separate from it. (MLH)

Explores the relationship between mathematical concepts and the circumstances of learning as they relate to within-individual variation. Analyzes previous results on mathematical concepts in and out of school in terms of their similarities and differences. (RJC)

Describes activities that will help students calculate the volume of water carried by a river or stream and how to measure the amount of water wasted by leaky faucets. (MDM)

Describes a program to encourage students in grades one through three to draw illustrations for word problems and then use the pictures to help solve the problems. (MKR)

Describes four teaching activities to help children extend math problem-solving skills by using their own questions. Activities involve using a chart and symbols to develop equations adding up to 12, going on an imaginary shopping trip, using shapes to represent dollar amounts, using the date on a penny to engage in various mathematical…

Describes the incorporation of audio-taped notes about student work, a rubric for scoring aspects of students' problem solving, and student portfolios in a program of classroom assessment. (MKR)

Studied fifth-grade (n=10) teachers' and (n=20) students' beliefs about mathematical problem solving, attributions for the causes of performance in problem solving, and beliefs about the teaching and learning of problem solving in mathematics. Gives four general conclusions. (17 references) (Author/MKR)

Uses change (mostly pennies) in a one-liter plastic soda bottle to get students to practice estimation skills and creative thinking in an effort to determine the amount of money in the bottle. (MVL)

Makes the analogy between Wilfred Bion's theory of mental processes involving preconception and mathematical problem solving. (MDH)