Knowledge assessments in undergraduate mathematics education commonly evaluate response correctness to determine learner proficiency. However, simultaneous evaluation of learner metacognition more accurately assesses the multiple dimensions of knowledge and has been shown to increase assessment validity and reliability. Research into…

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the…

This paper proposes an hypothsis describing how some college students incorrectly view semantically laden letters and provides both clinical and written data that supports that hypothesis. Several word problems were given to nine college math students. These students were then interviewed as they attempted to solve these problems. In addition to…

Because the failure rate for Math 110 (a college algebra course for non-science/technology-oriented majors at the University of Maryland) was so high, it was decided to offer selected registrants the opportunity to take a free refresher workshop series to improve their mathematics skills before they took the course. In summer 1985, 809 students…

Students enrolled in two sections of college algebra (Math 110) at the University of Maryland in spring 1984 were informed about assistance available from the Math Lab. They were also informed that a sticker would be attached to any one of the four semester exams when grades indicated that the student should pursue one or more of the Lab services.…

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…

This study concerned conceptual difficulties of college students learning programming and ways the teacher can simplify the process. An analysis of general strategies used in solving problems involving loops is given, with four types of hierarchical strategy categorized. Students had difficulty transforming their algebraic descriptions into…

Explores whether the differences in use of terminology were related to respective fields or to idiosyncratic characteristics of experience and education. Reports differences among college teachers, high school teachers, and college students from a 16-item survey on algebraic and graphing terminology used in mathematics and science. (YP)

The focus of this document is on students' understanding of symbolization processes in algebra, and specifically their understanding of semantically laden letters. In the first four sections, four inappropriate ways in which many college students use semantically laden letters are described. Evidence from clinical interview protocols demonstrate…

This article develops an algorithm to find all solutions to the problem, making all sums of a hexagram's nine lines the same. It shows how to exploit the geometric structure of the hexagram and its group of automorphisms. (YP)

Investigated was the relation between student ability to translate sentences into equations, equations into sentences, and student performance in formal operational reasoning, proportional reasoning, and introductory-level chemistry. Results indicate that students who lack formal operational skills may experience problems in the translation of…

A structured system of visual features is seen to parallel the propositional hierarchy of operations usually associated with the parsing of algebraic expressions. Women more than men were found to depend on these visual cues. Possible causes and consequences are discussed. Subjects were secondary and college students. (Author/DC)

Research supports the premise that various mathematical topics can be categorized as being performed better by the left or right brain hemisphere. Hemispheric lateralization is defined as a learner's preferred hemisphere of control. Torrence's "Human Information Processing Survey" was given to 170 black female college students enrolled in…

This study assessed the effectiveness of the remedial/developmental mathematics program developed at Ramapo College of New Jersey. Data was gathered from a random sample of 604 students who participated in the program for at least part of the three-year period 1981-84 and for whom both pretest and posttest scores were available in at least one…