Uses probability models in problem-solving activities based on an episode of the television show "Gunsmoke." (MKR)

Utilizing three exemplary problem-solving tasks within an arithmetic framework, this article discusses the four focal components deemed necessary for the improvement of mathematics teaching, namely task appropriateness, avenues of classroom discourse, the intellectual climate within the classroom, and proper and effective methods of analysis. (JJK)

Because of the importance of problem-solving skills in mathematics instruction of children with learning disabilities, this article offers guidance on teaching heuristic global strategies, including use of analogy, annotating problems, detail analysis, deletion of details, detail sorting, symbolizing operations, and designating formulas. (DB)

Describes an attempt to increase business calculus students' desire to learn by overcoming typical low levels of mathematical preparation and motivation utilizing a corporate structure managed by the students. Includes 10 sample problems from fictitious corporations. (JJK)

Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)

A personal experience is described concerning problem solving that incorporates the computer to help generate multiple examples of proposed conjectures as solutions. The positive potential of technology to allow students of mathematics to experience the process of discovering mathematics through conjecture and generalization is emphasized. (MDH)

Within the next two decades, calculators will be standard tools in mathematics classrooms. They should be used regularly but carefully in classroom instruction and testing to allow use of realistic data and exploration of mathematical concepts, but not to allow finding the answer without understanding the question. (MSE)

Considers the reasons that mathematical word problems are particularly difficult for remedial students. Describes the use of language-oriented teaching techniques in helping students to understand and solve word problems and to recognize that English and mathematics are two overlapping language systems. (PAA)

Uses ancient Egyptian numeration system in a new setting to extend the concepts of base, place value, and correspondence. Discusses similarities and differences between the Egyptian and decimal systems. Students are asked to propose changes to make the Egyptian system easier. (LDR)

Discusses a problem involving probability and uncertainty that students can investigate experimentally or theoretically and transforms the problem to a two-player game so that students can be introduced to some fundamental concepts of decision making. Includes computer programs used to analyze the problems. (MKR)

A review of six published studies on algebra interventions for students with learning disabilities revealed that successful interventions included instruction on domain-specific knowledge, as well as general problem-solving and self-regulation strategies. Promising practices include sequential introduction of work problems through concrete,…

This article extends and strengthens the knowledge in pieces perspective (diSessa, 1988, 1993) by applying core components to analyze how 5th-grade students with computational knowledge of whole-number multiplication and connections between multiplication and discrete arrays constructed understandings of area and ways of using representations to…

This study describes a conceptual teaching approach that helps students make connections between their everyday activities and mathematical word problems. It includes a brief review of the importance of teaching for understanding and describes four principles of conceptual teaching: (1) use cooperative groups; (2) allow students enough time to act…

This article explores the algebra that can be uncovered in many middle-grades mathematics tasks that, on first inspection, do not appear to be algebraic. It shows connections to the other four Standards that occur in traditional algebra problems, and it offers strategies for modifying activities so that they can be used to foster algebraic…

The activity developed in an integrated high school course that was team-taught by both mathematics and science teachers examines linear equations developed from relationships in biology. These equations provide students with opportunities to see the way mathematics could be used to describe biological relationships, and then apply to solve…