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Torner, Gunter – International Group for the Psychology of Mathematics Education, 2003

To probe beyond declarative knowledge about real numbers in secondary school, the authors interviewed students in Grades 9, 10 and 12. The main question seems to be whether the length of a decimal expansion is "indefinite" or "infinite." It blurs the mental representation of rational numbers as well. (Contains 3 footnotes.) [For complete…

Descriptors: Numbers, Grade 9, Cognitive Processes, Case Studies

Powell, Arthur B.; Maher, Carolyn A. – International Group for the Psychology of Mathematics Education, 2003

This report analyzes the discursive interactions of four students to understand what heuristic methods they develop as well as how and why they build isomorphisms to resolve a combinatorial problem set in a non-Euclidian context. The findings suggest that results of their heuristic actions lead them to build isomorphisms that in turn allow them to…

Descriptors: Heuristics, Problem Sets, Grade 12, High School Students

Wagner, David – International Group for the Psychology of Mathematics Education, 2003

Taking seriously the recent call for critical language awareness in mathematics classrooms, I propose that students engage with their teachers in the analysis of the discourse in their classrooms. To explore the potential for increased mathematical understanding, I analyze transcripts of students and a teacher listening to and responding to their…

Descriptors: Metalinguistics, Mathematics Instruction, Discourse Analysis, Classroom Communication

Di Martino, Pietro; Zan, Rosetta – International Group for the Psychology of Mathematics Education, 2003

In this communication we analyze a dichotomy that pervades research on attitude in mathematics education: the classification of attitude as positive/negative. After highlighting the ambiguity of the term "positive", and some problems related to it, we suggest that the positive/negative dichotomy is too simplistic to take into account the deep…

Descriptors: Mathematics Education, Student Attitudes, Attitude Measures, Negative Attitudes

Simon, Martin A. – International Group for the Psychology of Mathematics Education, 2003

I present a theoretical distinction that may prove useful in conceptualizing mathematics teacher education (and graduate education) and research on mathematics teacher education. Further, the distinction can contribute to developing frameworks on the design of mathematics curricula. The distinction between empirical activity and…

Descriptors: Graduate Study, Mathematical Concepts, Mathematics Teachers, Teacher Education

Sakonidis, H.; Klothou, A. – International Group for the Psychology of Mathematics Education, 2003

Assessment practices influence and are influenced by a number of educational as well as social factors. The present study looks at these practices of five primary teachers displayed in the mathematics classroom and in a relevant pedagogical discourse developed in the context of an interview. The results show that, on the whole, their practices…

Descriptors: Mathematics Education, Student Evaluation, Evaluation Methods, Elementary School Teachers

Shaughnessy, J. Michael; Canada, Dan; Ciancetta, Matt – International Group for the Psychology of Mathematics Education, 2003

This paper summarizes the thinking of 84 middle school mathematics students' about variability in three stochastics tasks that involve repeated trial. Differences in students' acknowledgment of variability were found, depending on whether the task was from a sampling environment, or a probability environment. Students tended to neglect variability…

Descriptors: Middle Schools, Probability, Sampling, Student Attitudes

Santos, Manuel; Aguero, Evelyn; Borbon, Alexander; Paez, Cristhian – International Group for the Psychology of Mathematics Education, 2003

Can textbook exercises be transformed into problem solving activities that encourage students to develop mathematical thinking? This study documents what high school students showed when they were explicitly asked to use technological tools to examine and solve a routine problem from different angles or perspectives. In this process, students…

Descriptors: Problem Solving, Secondary School Mathematics, High School Students, Mathematics Instruction

Singer, Mihaela – International Group for the Psychology of Mathematics Education, 2003

The paper is focused on recent researches in neuroscience and developmental psychology regarding mathematical abilities of infants. A model that tries to explain these findings is developed. The model underlies the mental operations that could be systematically trained to generate efficient school learning. The model is built from a cognitive…

Descriptors: Constructivism (Learning), Developmental Psychology, Cognitive Psychology, Teaching Methods

Stehlikova, Nada – International Group for the Psychology of Mathematics Education, 2003

In the study, a part of longitudinal research focused on the emergence of mathematical knowledge structures in a learner's mind is presented. It concentrates on the analysis of introspective data gained from the author's study of a non-standard arithmetic structure in terms of the model of abstraction in context (Hershkowitz, Schwarz and Dreyfus).…

Descriptors: Mathematics Education, Longitudinal Studies, Models, Interviews

Steinle, Vicki; Stacey, Kaye – International Group for the Psychology of Mathematics Education, 2003

Over a period of about 3 years, 3204 students in Grades 4 to 10 completed 9862 tests to identify and track their interpretation of decimal notation. Analysis of the longitudinal data demonstrates that different misconceptions persist among students to different degrees and in different patterns across the grades. Estimating the prevalence of…

Descriptors: Grade 5, Grade 6, Grade 7, Grade 8

Teppo, Anne R.; Esty, Warren W.; Kirkpatrick, Kay – International Group for the Psychology of Mathematics Education, 2003

Undergraduate students' written exams were analyzed from a freshman-level mathematics course that emphasized, among other topics, the study of mathematical logic. Findings indicate that on questions related to the negation of a conditional sentence, students performed much better when given natural-language contexts than they did on questions…

Descriptors: Undergraduate Students, Logical Thinking, Mathematical Logic, Courses

Tzur, Ron – International Group for the Psychology of Mathematics Education, 2003

Within an elaborated social-constructivist perspective, I conducted a teaching experiment with two fourth graders to study how a teacher and students can jointly produce the content-specific reversible fraction conception. Ongoing and retrospective analysis of the data revealed the non-trivial process by which students can abstract multiplicative…

Descriptors: Constructivism (Learning), Mathematics Instruction, Grade 4, Elementary School Mathematics

Thomas, Mike – International Group for the Psychology of Mathematics Education, 2003

It is becoming widely recognised that teachers' content knowledge has an important influence on their pedagogical content knowledge, and hence on the learning of students. In secondary schools, function is one of the fundamental concepts of mathematics. This paper considers the understanding of function exhibited by a group of teacher trainees in…

Descriptors: Fundamental Concepts, Pedagogical Content Knowledge, Knowledge Base for Teaching, Secondary School Mathematics

Schliemann, Analucia; Carraher, David; Brizuela, Barbara; Earnest, Darrell; Goodrow, Anne; Lara-Roth, Susanna; Peled, Irit – International Group for the Psychology of Mathematics Education, 2003

Increasing numbers of mathematics educators, policy makers, and researchers believe that algebra should become part of the elementary education curriculum. Such endorsements require careful research. This paper presents the general results of a longitudinal classroom investigation of children's thinking and representations over two and a half…

Descriptors: Mathematics Curriculum, Elementary School Mathematics, Grade 4, Algebra