The present study examines secondary school students' geometrical figure apprehension based on Duval's theoretical framework regarding perceptual, operative, and discursive apprehension. The aim is to explore the cognitive structure of the geometrical figure apprehension dimensions (operative, discursive, and perceptual) in three grades of…

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

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 aim of this study is to examine pre-service mathematics teachers' conceptual structures about "geometry". Qualitative research methodology has been adopted in the study. The data of the study is obtained from mathematics teacher candidates who have been students at the faculties of education of an Anatolian university in the academic…

This study aimed to investigate the informal cognitive structures regarding "point" and "straight line"--two basic and undefined terms of geometry--in children registered in preschool--the previous step before in-class formal education process. The study was conducted with the participation of 50 children enrolled in nursery,…

The present research approached a problem which has a twofold aspect: the concept of angle and the techniques needed to represent how pupils construct that concept in their cognitive structure during their years in school. In order to access the knowledge of the concept of angle, we used the pathfinder associative networks. This technique provided…

This investigation is part of a combined research/curriculum development project in which children's learning is being examined in the context of developing and testing instructional units on 3-D geometry in grades 3, 4, and 5. There are two components to the article. First, the strategies and cognitive constructions that students utilize to…

Examines the nature of prior mathematical knowledge that facilitates the construction of useful problem representations in the domain of geometry. Indicates that high achievers build schemas that are qualitatively more sophisticated than low achievers, which in turn helps them construct representations that are conducive to understanding the…

Argues that the organization of cognitive structures for technical domains can be visualized as a network of connected thinkable models. Describes a taxonomy of models that has been developed and discusses the issue of how representations relate to human modes of perception and action. Contains 25 references. (DDR)

Presented is an alternative method for analyzing the van Hiele level of students' geometrical reasoning. The accuracy of students' answers may afford a description of acquisition and/or expertise for each of the van Hiele levels simultaneously rather than the traditional assignment and evaluation of one level at a time. (JJK)

Described is research which sought to prove the hypothesis that mental models tend to preserve their autonomy with regard to the originals they are meant to represent. The results of this investigation involving 200 Israeli students are presented. (CW)

A study was conducted in Israel to determine effects of external similarity in problem structure on students' responses. Fifty students from each of the 7th, 8th, 10th, and 12th grade levels were presented with three problems involving successive divisions that were similar in structure. The problems asked separately whether the processes of…

Research on intelligent tutoring seeks to develop systems for automating education and to explore epistemological issues concerning the nature of the knowledge presented by tutors and how that knowledge can be learned. The ACT theory of skill acquisition and its successor (PUPS--PenUltimate Production System) provides production-system models of…

Compared are the van Hiele levels of geometric thinking and the geometry curriculum recommended by the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics. Activities which illustrate the various levels are provided by grade level with procedures. (CW)

The main thesis of the paper is that geometry deals with mental entities (the so-called geometrical figures) which possess simultaneously conceptual and figural characters. The paper analyzes the internal tensions which may arise in figural concepts because of their double nature, developmental aspects, and didactical implications. (Author/MDH)