In February and May 1973, experimental forms of the mathematics game EQUATIONS were used in two seventh-grade classes which had been participating twice a week in EQUATIONS tournaments since the previous September. The purpose of the experimental games was to gain information as to the kinds of mathematical ideas players choose to concern…

Performance of 237 students in ten eighth-grade mathematics classes was assessed to measure their ability to solve (1) problems which involve only computation, and (2) problems which involve computation and recognition of the relevance of a particular mathematical idea indispensable to the solution of the problem. Pretest and/or posttest data were…

Presents a variety of examples through which kindergarten and primary grade children can engage in significant problem solving. The suggested activities use materials in a problem solving context to permit children to experiment, to create, and to make measurements. (PK)

This study investigated the performance of 14 Hispanic and Anglo ninth graders on several problem-solving tasks, with the focus on the interplay of language-related factors in translating several mathematical statements expressing relationships among variables into mathematical equations. (MNS)

What students need to know in a world where most computations are done by machine is discussed. Needed changes in the mathematics curriculum are then detailed in relation to mental arithmetic, numeration, decimals and fractions, paper-and-pencil computation, order of operations, problem solving, and instruction on calculator use. (MNS)

Provided are follow-up activities for having students explore the concept of line symmetry. Using a mirror to move a pattern; finding patterns with one, two, or four lines of symmetry; finding asymmetrical patterns; deciding if patterns are different; and solving the problem of finding all patterns possible are discussed. (MNS)

Presents research on cognitive skills demanded by elementary and secondary school mathematics textbooks, based on an original 10-level classification of thinking activities; reports a general decline both in the amount of material demanding student involvement and in the percentage of that material requiring higher-order thinking. (MCG)

The problem-solving skills of logical thinking, critical thinking, visualization, and communication skills are linked with some activities for students. Sample activities with logic, strategies and patterns, breaking fixed notions, open-minded problems, spatial visualization, and communication are described. (MNS)

Building on previous research on the tendency in students of diverse ages to overrely on proportionality in different domains of mathematics (e.g., geometry, probability), this study shows that--when confronted with missing-value word problems--Flemish primary school pupils strongly tend to apply proportional solution strategies, also in cases…

In this paper we report on some patterns of reasoning, which emerged during an activity of proving a mathematical statement performed by nine grade and university mathematics students. The statement in question involves drawing figures, working in arithmetic and in algebra. As for secondary students we detected fluency, flexibility and ability of…

Ways of giving students specifications to design computation exercises are revealed. Pupils are seen to benefit from the pride of ownership and familiarity with the vocabulary in developing word problems. (MP)

Proposes a model that displays the five components of the statistical problem-solving process. Focuses on the collection of coins in sets by mint location and fully describes the procedures. Includes ideas for data collection and analysis. (DDR)

Describes an interdisciplinary project encompassing English, history, public speaking, and mathematics that allows students to experience success with integrating mathematics into real world experiences. (DDR)

Presents findings from five studies measuring students' attitudes towards mathematics, perception of performance, perception of the importance of mathematical problem solving, and perception of problem difficulty. The interaction of affect and cognition and the implications for assessing and teaching mathematical problem solving to students with…

This study examined the effect of video-based contextualized advisement and competition on transfer of mathematics skills in a computer-based simulation game in which participants helped their "aunt and uncle" fix up a house. Participants were 123 seventh- and eighth-grade students. Results indicated an interaction between competition…