This study was carried out in order to determine how the 3rd grade students of the Department of Elementary Mathematics Education structured their "if and only if propositions". The data were obtained by examining the students' answers given to the midterm exam questions and discussing the solutions with the students in the classroom.…

The number sequences describe a hierarchy of students' concepts of number. This research uses two defining cognitive structures of the number sequences--units coordination and the splitting operation--to model middle-grades students' abilities to write linear equations representing the multiplicative relationship between two unknowns. Results…

In the context of the sociocultural approach, the authors studied the problem of the development of the students' conceptual mental structures in the process of geometry teaching. An educational activity for the development of a generalized ability to solve geometry construction problems in electronic educational environment served as a…

It is widely documented that the density property of rational numbers is challenging for students. The framework theory approach to conceptual change places this observation in the more general frame of problems faced by learners in the transition from natural to rational numbers. As students enrich, but do not restructure, their natural number…

Cognitive scientists investigate mental models (how humans organize and structure knowledge in their minds) so as to understand human understanding of and interactions with the world. Cognitive and mental model research is concerned with internal conceptual systems that are not easily or directly observable. The goal of this research was to…

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…

Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for…

Describes the case of a woman who experienced disparity in mathematics classrooms between learning (which for her was necessarily relational) and its validation by a system that did not ratify meaningful learning but instead rewarded the behavioral products of rote or instrumental learning. (MKR)

Examines the mathematical proof schemes of students starting their studies at the University of Cordoba and relates these schemes to the meanings of mathematical proof in different institutional contexts. Concludes that deductive mathematical proof is difficult for these students. Suggests that the different institutional meanings of proof might…

In an effort to examine the impact of the changes being made at San Jose State University (California) in the calculus curriculum, multiple measures were collected and analyzed. This study focuses on the relationship between performance on a pretest and the class grade. Through written responses on the pretest, a belief and knowledge profile for…

Investigated the acquisition and maturation of the infinity concept in mathematics of students ages 13-15. Found the infinity concept is learned by students only when provided with appropriate guidance. (Author/MKR)

Presents a study designed to explore whether a student's use of the graphing calculator during instruction will affect their concept of function, how students' participation in a conceptual change assignment affects their concept of function, and how the graphing calculator and the conceptual change assignment interact with one another to…

This study examined how engaging calculus students in Writing to Learn Mathematics affected the types of conceptual and procedural errors that the students made on their examinations. Students in two sections of an introductory college calculus course in Fall 1994 were the respondents in this study. A classification system was developed that…

Students at concrete or formal operational reasoning levels made similarity judgments on geometric concepts and mathematical expressions on ratio, proportion, and similarity. Clear prototypical maps could be derived for both groups. Formal operational students structured subject matter content significantly more like subject matter experts than…

Studied were the misconceptions that preservice elementary teachers have about multiplication and division. Results indicated that they are influenced by the same primitive models as students; the most common errors made by both groups are quite similar. (MNS)