The purpose of this study was to determine (1) whether the development of combinatorial schema as defined by Piaget is dependent on, or independent of, instruction, and (2) whether or not a prescribed treatment compatible with contemporary learning theories can develop the combinatorial operational abilities of students who are in a transitional…

This report describes a program for improving students' comprehension of the language of mathematical problems. The targeted population consists of 5th and 6th grade multi-age students and multi-age learners with special needs at a middle school located outside a major city in a Midwestern community. Evidence for the existence of this problem…

Study analyzed the written protocols of 900 elementary mathematics students from 5 achievement levels utilizing a 15-item arithmetic and problem-solving test administered in grade 3 and again in grade 6. Correct solutions resulted from similar strategies regardless of the achievement level, yet incorrect solutions ensued from many incorrect…

Nineteen fifth and 11 sixth graders given preliminary instruction about a computer-based problem-solving game received additional problem-solving training, problem-solving and self-monitoring training, or no further training. The beneficial impact of the monitoring training is discussed as evidence of the importance of the monitoring strategy in…

Examined the quality of responses of six classes of grade six students to four questions requiring multiple and generalized solutions posed under varying conditions. Results indicated that this type of question can be useful in classrooms because students can respond at a variety of levels. (13 references) (MDH)

Twenty-four sixth-grade children participated in clinical interviews on ratio and proportion before receiving instruction in the domain. Student thinking was analyzed in terms of mathematical components critical to proportional reasoning. Two components, relative thinking and unitizing, were consistently related to higher levels of sophistication…

Describes a study that measured the ability of New Zealand students, grades five though eight, to locate information using library structures and systems through the standardization of six information skills tests. The paper and pencil tests were based on an information problem-solving perspective. (Author/LRW)

Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem…

In this study, we examined the use of cognitive tools provided in a problem-based hypermedia learning environment for sixth graders. Purposes were to understand how the built-in tools were used, and if tool use was associated with different problem-solving stages. Results showed that tools supporting cognitive processing and sharing cognitive load…

This study makes use of an action research paradigm to improve primary students' analyzing skills. It was conducted at the San Esteban Elementary School, Region I, Philippines, during the 6-week off campus practice teaching of one of the researchers. Sources of data include a thinking skills checklist, a set of Curriculum Support Materials (CSM),…

Since 1990, the January issue of "Teaching Pre K-8" has highlighted a school visit by the president of the National Council of Teachers of Mathematics. This article discusses Cathy Seeley's visit to a 6th grade classroom at the J. E. Pearce Middle School in Austin, Texas, where she participated in a math activity from the Connected…

Metacognition has been accorded a role in both mathematical problem solving and in the learning of mathematics. There has been consistent advocacy of the need for the promotion of metacognitive activity in both domains. Such advocacy can only be effective if the advocated process is well understood. In this paper we have four goals: to describe a…

Research is only beginning to show the benefits of the effective use of manipulatives with students who have disabilities. This article highlights how teachers can incorporate three manipulative instructional strategies to help students with high-incidence disabilities.

This paper reports on a pilot study of 34 sixth-grade students engaged in mathematical explorations that was carried out in the context of a national Logo project in Costa Rica. Students worked in pairs investigating a mathematical microworld written in Logo. The investigation had three phases: (1) open exploration of the microworld, during which…

The Helping Hands Project (HHP) is a program that aims at improving achievement in reading comprehension and in math problem-solving by helping the classroom teacher sustain instructional intensity. Implemented in grades four and six in two Newark School District elementary schools, HHP involved five teachers and 117 students. Ninety-two percent…