This article reports on the results of research, the objective of which was to document and analyze the manner in which students relate different representations when solving problems. A total of 20 students attending their first year of university studies took part in the study. In order to design the problem, the underlying information in each…

A study was conducted at the Technical University Berlin involving students who twice failed the written examination in the first semester course Linear Algebra for Engineers in order to better understand the reasons behind their failure. The study considered student understanding in terms of Bloom's taxonomy and the ways in which students…

Basic brain function is not a mystery. Given that neuroscientists understand the brain's basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain…

Equation problems elicited a strategy in which the subject attempted to isolate the X variables on one side of the equation, whereas word problems elicited a strategy in which the subject attempted to reduce the expression. These results suggest that problem format influences the type of strategy used to solve algebra problems. (Author/PN)

This paper reports a study that sought to explain student understanding of the concept of linear inequality as presented in a problem-solving setting. In the course of data analysis, the transition from arithmetic to algebra emerged as a critical issue. Therefore, the study examined the differences in the problem-solving activities of solvers who…

This study examined the problem-solving behaviors, strategies, and achievement of college students enrolled in a one-semester college algebra and statistics course, with respect to the content areas of quantitative literacy, connections between algebraic and graphical representations, and mathematical modeling. Four instructional units of this…

This paper examines the question of whether the introduction and use of the function machine representation as a scaffolding device helps undergraduates enrolled in a developmental algebra course to form a rich, foundational concept of function. It describes students' developing understanding of function as an input/output process and as an…

The major focus of this study is to trace the cognitive development of students throughout a mathematics course and to seek the qualitative differences between those of different levels of achievement. The aspect of the project described here concerns the use of concept maps constructed by the students at intervals during the course. From these…

Interviews students majoring in mathematics who had passed a required introductory course on algebraic structures on students' difficulties with basic concepts in group theory as part of a research project. Reports data concerning cyclic groups. (ASK)

This paper concerns a study of the performance of students in a linear algebra examination. Differences in performance of tasks requiring understanding of concepts with those that required only the use of routine procedures and factual recall were investigated. Central to the study was the use of a taxonomy based on Bloom's Taxonomy for…

Data indicate that relatively advanced science-oriented college students can experience serious difficulties in symbolizing certain meaningful relationships with algebraic equations. Reversal errors in formulating equations were seen to stem from two main sources: (1) a syntactic word order matching process and (2) a semantic static comparison…

The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…

The fragmentation of strategies that distinguishes the more successful elementary grade students from those least successful has been documented previously. This study investigated whether this phenomenon of divergence and fragmentation of strategies would occur among undergraduate students enrolled in a remedial algebra course. Twenty-six…

Three problem-solving strategies--working backward from the unknown, forward from the given, and mixed--were applied to interrelated algebra equations. The mixed strategy was most popular and most efficient with grouped variables. Memory load or information-processing load differences among the strategies were evident. (CP)

Team research is important in studying cognition as enactive. This paper contains four different pieces of research directed toward the evidences and artifacts of two students in Canada engaging in a sustained mathematical activity. These four portraits of mathematical cognition in action consider the conversation in which the activity occurs; the…