In solving mathematics problems in collaboration, students encounter a range of mathematical and social struggles. As teachers cannot possibly respond to every such struggle, they may need to respond to those with which students require most support. Yet, little is known about students' success in overcoming the various types of struggle they…

Mental models are representations of students' minds concepts to explain a situation or an on-going process. The purpose of this study is to describe students' mental model in solving mathematical patterns of generalization problem. Subjects in this study were the VII grade students of junior high school in Situbondo, East Java, Indonesia. This…

Manipulating algebraic expressions is guided by students' structure sense and the individual process of relating subexpressions to each other. This paper presents a framework for identifying the underlying cognitive processes of manipulating algebraic expressions, based on 'basic structures' and 'giving relevance'. A design-research case study…

To better understand the role that ways of reasoning play in students' success on integer addition and subtraction problems, we examined the relationship between students' flexible use of ways of reasoning and their performance on integers open number sentences. Within groups of students in 3 participant groups--39 2nd and 4th graders who had…

Although the average, or arithmetic mean, has a rich conceptual meaning, it is often defined simply as the outcome of a procedure. The purpose of this study was to compare the nature and extent of the procedural and conceptual understandings developed by two groups of students who received different forms of instruction, one based on the…

The mathematical behaviors of a group of seventh grade students were observed as part of a longitudinal study of how children build mathematical ideas. The children, having built representations of their solutions to a combinatorics task, were challenged by their teacher to explain and discuss their ideas, and to extend them to similar situations.…

The purpose of this exploratory, descriptive study was to examine how children process different tasks of comprehension presented in graphical form. During the Spring 1981, 8 fourth graders and 9 seventh graders were interviewed. The children were presented with graphs accompanied by six questions reflecting three levels of comprehension:…

The purpose of this exploratory study was to examine the problem-solving behaviors and perceptions of (n=27) seventh-grade students as they worked on solving a mathematical problem within a small-group setting. An assessment system was developed that allowed for this analysis. To assess problem-solving behaviors within a small group a Group…

This study explores the potential effectiveness of a new procedure for identifying and studying certain of the cognitive processes used during problem solving. The procedure is used in an attempt to categorize the types of conceptual thinking problem solvers employ, to study trial-and-error behavior, and to investigate problem solvers' abilities…

A study investigated the relationship between text organization and children's reading comprehension of expository material. Upgraded and downgraded versions of both macrostructures and microstructures were combined to produce four texts on the topic of insect-eating plants. Forty-three seventh grade students were randomly assigned to one of the…

Working in groups of three, seventh-grade students were video taped solving an applied mathematical problem. Audio tapes were made of each group discussing their session. Analysis focused on the first stage of Noddings (1984) model of problem solving for school mathematics: Creation of a representation. Some factors identified as impeding…

One year after sixth grade students participated in an instructional intervention experiment aimed at teaching reflective planning skills in writing, a followup study focused on evidence of reflectivity in attitudes and metacognitive knowledge concerning writing. This study was conducted with 16 experimental and 13 control students. Data were…

A study investigated children's and adults' abilities to derive inferences requiring the integration of two episodic premises (episodic inferences) and inferences requiring the integration of one episodic premise with extra-stimulus, semantic knowledge. Subjects, 95 kindergarten, third grade, seventh grade, and college students, watched either an…

Work in the design and construction of virtual environments (VEs) is described from the standpoint of semiotic theory. It is advocated that well-constructed visual worlds can create in a person the feelings and cognitions that arise from being in the natural world and that interactions with computer-constructed VEs are mediated through signs. The…

Open-ended learning environments (OELEs) like microworlds have been touted as one approach for blending learning theory and emerging technology to support the building of student-centered understanding. The learning process involves developing a theory-in-action--an intuitive theory that is generated and changed by learners as they reflect upon…