- Professor Emerita, Mathematics Department,
Illinois State Universityedit
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▶ Presents new ideas and developments of major importance in mathematical education ▶ Publishes articles dealing with didactical, methodological and pedagogical subjects, rather than with specific programs for teaching mathematics ▶... more
▶ Presents new ideas and developments of major importance in mathematical education ▶ Publishes articles dealing with didactical, methodological and pedagogical subjects, rather than with specific programs for teaching mathematics ▶ Reflects the variety of research concerns within the field and the range of methods used to study them ▶ 100% of authors who answered a survey reported that they would definitely publish or probably publish in the journal again
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I taught a course on informal geometry — a content course — to students at The Florida State University who are prospective high school mathematics teachers. In the first week I asked them to bring or wear to the next class, something... more
I taught a course on informal geometry — a content course — to students at The Florida State University who are prospective high school mathematics teachers. In the first week I asked them to bring or wear to the next class, something which had geometry in it, and to come to class prepared to tell why they had chosen that particular item and to talk about its geometry.
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Page 1. Vol.2-744 PME-NA 2006 Proceedings CONNECTED REGISTERS FOR GEOMETRY: LEARNING TO GENERALIZE Jeffrey Barrett Illinois State University jbarrett@ilstu.edu Sharon McCrone Illinois State University Norma Presmeg Illinois State... more
Page 1. Vol.2-744 PME-NA 2006 Proceedings CONNECTED REGISTERS FOR GEOMETRY: LEARNING TO GENERALIZE Jeffrey Barrett Illinois State University jbarrett@ilstu.edu Sharon McCrone Illinois State University Norma Presmeg Illinois State University ...
Research Interests: Mathematics and Geometry
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A frequent message in mathematics education focuses on the benefits of multiple representations of mathematical concepts (Aspinwall and Shaw 2002). The National Council of Teachers of Mathematics, for instance, claims that “different... more
A frequent message in mathematics education focuses on the benefits of multiple representations of mathematical concepts (Aspinwall and Shaw 2002). The National Council of Teachers of Mathematics, for instance, claims that “different representations support different ways of thinking about and manipulating mathematical objects” (NCTM 2000, p. 360). A recommendation conveyed in the ongoing calculus reform movement is that students should use multiple representations and make connections among them so that they can develop deeper and more robust understanding of the concepts.
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... Page 2. 280 object, a representamen (which I prefer to call a sign vehiclePresmeg 2006) that stands for the object in some way, and an interpretant, which is the result of inter-preting the relationship between the sign vehicle and... more
... Page 2. 280 object, a representamen (which I prefer to call a sign vehiclePresmeg 2006) that stands for the object in some way, and an interpretant, which is the result of inter-preting the relationship between the sign vehicle and its object. ... Page 12. 290 Presmeg, NC (2006). ...
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In times of cultural change, education plays an especially important role. The writer suggests that even mathematics curricula, which have traditionally been considered culture-free, have a role to play in fostering mutual understanding... more
In times of cultural change, education plays an especially important role. The writer suggests that even mathematics curricula, which have traditionally been considered culture-free, have a role to play in fostering mutual understanding amongst members of different cultures, after a period of cultural upheavel. As indicated by the word "towards" in the subtitle, the writer does not regard this paper as providing ultimate solutions to problems which are extremely complex. Writing, as she is, about South African cultures and sub-cultures all of which are in a state of intense ferment at this time, she is aware of complexities and contradictions which are implicit in some of the issues (and of which are not confined to South African society). The analysis of elements which may contribute to a mathematics curriculum for mutual understanding is offered as a first approximation to an answer to the question of how pupils from diverse cultures can best learn mathematics together a...
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Researchers who have carried out studies pertaining to mental computation and everyday mathematics point out that adults and children reason intuitively based upon experiences within specific contexts; they use invented strategies of... more
Researchers who have carried out studies pertaining to mental computation and everyday mathematics point out that adults and children reason intuitively based upon experiences within specific contexts; they use invented strategies of their own to solve real-life problems. We draw upon research areas of mental computation and everyday mathematics to report on a study that investigated adults’ use of mental mathematics in everyday settings. In this paper, we report on one adult’s use of mental computation at work and highlight the role of context and context related parameters in his mental mathematical activities. El papel de los parámetros relacionados con el contexto en actos de cálculo mental en adultos Los investigadores que han realizado estudios relacionados con el cálculo mental y las matemáticas cotidianas señalan que los adultos y los niños razonan intuitivamente basándose en las experiencias de contextos específicos; usan estrategias inventadas por sí mismos para resolver p...
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With the increasing recognition that connections are an important component in the pedagogy of school mathematics (National Council of Teachers of Mathematics, 1989), there is a need for a theoretical framework that addresses the ways in... more
With the increasing recognition that connections are an important component in the pedagogy of school mathematics (National Council of Teachers of Mathematics, 1989), there is a need for a theoretical framework that addresses the ways in which the real experiences and cultural practices of students may be connected with mathematics classroom pedagogy. In this paper, the objective is to construct such a theoretical framework, drawing on literature from semiotics and ethnomathematics. Examples and evidence that suggest the efficacy of this framework in connecting school mathematics and mathematical ideas constructed from cultural practice are drawn from the literature and from data collected in a research project in a multicultural high school mathematics class. Seven high school students from African American, Caucasian, Asian American, and Hispanic American cultural backgrounds described their lives and cultural heritages as bases for the development of culturally responsive mathema...
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Japanese lesson study, in various adapted forms, is becoming increasingly significant in professional development of mathematics teachers in the USA. Our goal in the research reported in this paper was to investigate, in a three-tiered... more
Japanese lesson study, in various adapted forms, is becoming increasingly significant in professional development of mathematics teachers in the USA. Our goal in the research reported in this paper was to investigate, in a three-tiered teaching experiment, the cycles of learning of two researchers, six teachers, and the students in three grade 4 classes and three grade 5 classes, in a six-month long lesson study project in the first half of 2002. The learning processes evolved in each of the three tiers (students, teachers, and researchers) over the course of three iterations of a lesson on measurement taught respectively in grades 4 and 5 by the three grade 4 and three grade 5 teachers. This paper documents some of these shifts in learning in each of the three tiers and assesses this form of lesson study for professional development, through the eyes of the teachers. (Contains 2 footnotes, 1 figure and 2 tables.) [For complete proceedings, see ED500860.]
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This article introduces an instrument designed to determine students’ preferences for visual or analytic thinking for calculus tasks presented graphically and their understanding of the calculus derivative and antiderivative.
Evidence from two research projects, one with high school students and the other with graduate students in an Ethnomathematics course, is presented to suggest that the beliefs students hold about the nature of mathematics both enables and... more
Evidence from two research projects, one with high school students and the other with graduate students in an Ethnomathematics course, is presented to suggest that the beliefs students hold about the nature of mathematics both enables and constrains their ability to construct conceptual bridges between familiar everyday practices and mathematical concepts taught in school or university. Using a semiotic theoretical
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In this reaction to Section 1 of the book, some of the commonalities and differences in the approaches of the authors of these four chapters to emergent modeling are explored. Their conceptual frameworks and their use of evidence from... more
In this reaction to Section 1 of the book, some of the commonalities and differences in the approaches of the authors of these four chapters to emergent modeling are explored. Their conceptual frameworks and their use of evidence from their own research are examined from the point of view of children’s processes of transition, through pseudo-concepts, through chains of signification and construction of meaning, from activities in which they engage to increasingly mathematical practices and terminology. Finally, a triadic model of chaining of signifiers is used as a lens to interpret some of the research reported in these four chapters.
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... Various definitions of visualization have been used in the research literature. For us, visualization involves both external and internal representations (or images), and thus following Presmeg (200624. ... View all references) and... more
... Various definitions of visualization have been used in the research literature. For us, visualization involves both external and internal representations (or images), and thus following Presmeg (200624. ... View all references) and Presmeg (200624. Presmeg, NC 2006. ...
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This paper describes the need and rationale for a culture-inclusive course for prospective and practicing mathematics teachers. From the principles used in such a course as it was originally taught in 1993, up to the present, the graduate... more
This paper describes the need and rationale for a culture-inclusive course for prospective and practicing mathematics teachers. From the principles used in such a course as it was originally taught in 1993, up to the present, the graduate ethnomathematics course stresses as a key element students' ownership of their individual and personally meaningful cultural mathematics projects. The projects, personally chosen
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ABSTRACT The importance of students’ problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to... more
ABSTRACT The importance of students’ problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students’ mathematical content knowledge could be highly related to creativity in mathematics, too. This paper reports on a study that investigated USA and Chinese high school students’ mathematical content knowledge, their abilities in mathematical problem posing, and the relationships between students’ mathematical content knowledge and their problem-posing abilities in mathematics.
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ABSTRACT En: Suma Zaragoza 1999, n. 32, noviembre ; p. 17-22 Análisis sobre la efectividad del pensamiento basado en imágenes en la resolución de problemas, justificando que la visualización no siempre es efectiva. Se proponen estrategias... more
ABSTRACT En: Suma Zaragoza 1999, n. 32, noviembre ; p. 17-22 Análisis sobre la efectividad del pensamiento basado en imágenes en la resolución de problemas, justificando que la visualización no siempre es efectiva. Se proponen estrategias de aula para fomentar y hacer más efectivo el pensamiento basado en imágenes en los alumnos
Classroom oral communication is of utmost importance for student learning. In particular, how teachers question, listen, and respond to their students is crucial in students' understanding of mathematics. This study traced how two... more
Classroom oral communication is of utmost importance for student learning. In particular, how teachers question, listen, and respond to their students is crucial in students' understanding of mathematics. This study traced how two student teachers evolved in their teaching modes, that is, their interrelated questioning, listening, and responding approaches in the classroom. The relationships between the participants' beliefs about mathematics teaching and learning and their dominant teaching modes were also investigated. This research raised several questions for future research and has implications for teacher education. Research has indicated that many reform-oriented teacher education courses and field experiences do not significantly impact student teachers' beliefs about mathematics teaching and learning nor their subsequent classroom practices (e.g., Tabachnick & Zeichner, 1984). Researchers and teacher educators have been urged to investigate, support, and guide t...
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... Page 4. Editors Philip Clarkson Norma Presmeg Faculty of Education Illinois State University Australian Catholic University Department of Mathematics Fitzroy VIC 3065 313 Stevenson Hall Australia Normal IL 61790-4520 p. clarkson@... more
... Page 4. Editors Philip Clarkson Norma Presmeg Faculty of Education Illinois State University Australian Catholic University Department of Mathematics Fitzroy VIC 3065 313 Stevenson Hall Australia Normal IL 61790-4520 p. clarkson@ patrick. acu. ... 239 Wee Tiong Seah Index ...
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... Related Items: Show Related Items. Click on any of the links below to perform a new search. Title: Visualization in Multicultural Mathematics Classrooms. Authors: Presmeg, Norma C. ...
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... the various registers (Duval, 1999) of school trigonometry (Presmeg, 2006b). ... of such topics as ''Stu-dents' improper proportional reasoning'' (Modestou and Gagatsis, 2007), or ''Exploring young... more
... the various registers (Duval, 1999) of school trigonometry (Presmeg, 2006b). ... of such topics as ''Stu-dents' improper proportional reasoning'' (Modestou and Gagatsis, 2007), or ''Exploring young children's geometri-cal strategies'' (Gagatsis, Sriraman, Elia, & Modestou, 2006). ...
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... Many such pupils would like to choose careers in engineering or architecture; success in school mathematics is ... Kinds of visual imagery Images used by visualisers in this study were classified as Tollows ... Crispin T: Again,... more
... Many such pupils would like to choose careers in engineering or architecture; success in school mathematics is ... Kinds of visual imagery Images used by visualisers in this study were classified as Tollows ... Crispin T: Again, that's another pattern; actually I've got quite a few of them. ...