Little research in the field of Mathematics Education is directed towards emotions of students beyond their emotions in problem-solving. In particular, the daily emotions of students in a mathematics class have been sparsely studied in the field of mathematics education. In order to fill this gap, this qualitative research aims to identify high…

This article presents results of a research study. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students overrelied on various combinations of whole-number principles as…

One of the important phenomena observed in the learning of mathematics is compartmentalization. This phenomenon occurs when a learner has two different, potentially contradictory schemes in his or her cognitive structure; in a typical case, a student deals with the same mathematical concept in an inconsistent or incoherent way, or activates a less…

Graphs without a time axis, such as velocity-versus-position graphs, offer interesting possibilities for exploring graphing and motion. Relations depicted by these graphs are not limited to functions. Interviews with a high school student named Olivia, who uses a motion detector to create such graphs, indicate that she uses thought experiments as…

This study investigated the knowledge base necessary for choosing appropriate statistical techniques in applied research. In this study, we compared knowledge used by six experts and six novices in two types of statistical tasks. The tasks were: 1) comparing research scenarios from the perspective of choosing a statistical technique, and 2) direct…

Students can learn to solve problems of qualitative integration and differentiation independently of their study of formal calculus or algebra. This exploratory study investigated the basic intuitions that elementary school children construct in their daily experience with physical and symbolic change. Elementary school children (n=18) were…

Interviews with (n=20) primary teachers, who had participated in inservice workshops on Cognitively Guided Instruction (CGI), revealed three patterns of CGI use--as mainstay, as supplement, and decreasingly--which seemed related to their beliefs about mathematics, learning, and CGI itself. (40 references) (MKR)

Analyzed questionnaire responses of 152 prospective secondary mathematics teachers, 10 of whom were interviewed, to investigate their knowledge of the concept of function. Results indicated that many did not have a modern concept of function, a limitation that influenced their pedagogical approach. (Contains 45 references.) (MDH)

Reports results of interviews in which students were asked to illustrate three interpretations of fractions: a unit subdivided into equal-sized parts; a set subdivided into equal-sized parts; and a ratio. Two areas of difficulty in giving reasonable representations are discussed. Proposes teaching suggestions to overcome these difficulties. (MDH)

Investigated the upper limits of (n=22) seventh-grade students' informal processes in solving first degree equations in one unknown prior to instruction. Results indicated the existence of a cognitive gap between arithmetic and algebra characterized as the students' inability to operate spontaneously with or on the unknown. (37 references)…

This paper addresses the evidence that secondary school students use to imply that they understand something in mathematics. As part of a larger study, an open-ended questionnaire probing several aspects of metacognitive self-knowledge, was administered to students (N=72) in four schools. Two previously identified types of understanding were…

Videotaped interviews of 29 Australian students from grades 1-3 were analyzed to assess and compare the processing loads of mathematical representations and strategies used by teachers and children to learn the concept of place value. Results indicated that some representations and strategies impose an unnecessary processing load that can…

The estimation processes used by fifth through eighth grade students as they responded to computational estimation test items were examined. Interview-based process descriptions were cross-validated using large group test data from an open-ended test and a multiple choice test. Five question formats were used to test different estimation…

The relationship between teachers' and students' personal constructs regarding intrinsic motivation in the mathematics class were examined in this study. Participants were six middle-school mathematics teachers and 30 students from 5 classes. Videotape, direct observation, individual interviews, and repertory grid tasks focused on the ways in…

This study considered the meaning that was given to knowing/doing mathematics in classrooms comprising the observational study conducted by the Wisconsin Center for Education Research during 1978-81. The study interprets the work of teachers and students, and considers what constitutes appropriate mathematical knowledge for children to learn. A…