journal-articles

Children’s arithmetical thinking

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Göta Eriksson from Stockholm University has written an article in The Journal of Mathematical Behavior. The article is entitled: Arithmetical thinking in children attending special schools for the intellectually disabled, and it was available online yesterday. The entire article is available at the above link, but here is the abstract:

This article focuses on spontaneous and progressive knowledge building in “the arithmetic of the child.” The aim is to investigate variations in the behavior patterns of eight pupils attending a school for the intellectually disabled. The study is based on the epistemology of radical constructivism and the methodology of multiple clinical interviews. Theoretical models elucidate behavior patterns and the corresponding mental structures underlying them. The individual interviews of the pupils were video recorded. The results show that the activated behavior patterns, which are responses to well-adapted contexts presented by the researcher, are compatible with findings in Swedish compulsory schools. Six of the pupils’ mental structures in the study are numerical. A substantial implication for special education is the harmonization of the content in teaching with the children’s own ways of operating, which implies a triadic teaching process.

The effects of designing Webquests

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Erdogan Halat has written an article that has recently been published in International Journal of Mathematical Education in Science and Technology (IJMEST). The article is entitled: “The effects of designing Webquests on the motivation of pre-service elementary school teachers“, and here is the abstract:

The purpose of this study was to examine the effects of webquest-based applications on the pre-service elementary school teachers’ motivation in mathematics. There were a total of 202 pre-service elementary school teachers, 125 in a treatment group and 77 in a control group. The researcher used a Likert-type questionnaire consisting of 34 negative and positive statements. This questionnaire was designed to evaluate a situational measure of the pre-service teachers’ motivation. This questionnaire was used as pre- and post-tests in the study that took place in two semesters. It was administered to the participants by the researcher before and after the instruction during a single class period. The paired-samples t-test, the independent-samples t-test and analysis of covariance with agr = 0.05 were used to analyse the quantitative data. The study showed that there was a statistically significant difference found in participants’ motivation between treatment and control groups favouring the treatment group. In other words, the participants who designed the webquest-based applications indicated positive attitudes towards mathematics course than the others who did the regular course work.

The particular and the general

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Vicenç Font and Ángel Contreras wrote an article that was recently published in Educational Studies in Mathematics. The article is entitled “The problem of the particular and its relation to the general in mathematics education“, and here is the abstract:

Research in the didactics of mathematics has shown the importance of the problem of the particular and its relation to the general in teaching and learning mathematics as well as the complexity of factors related to them. In particular, one of the central open questions is the nature and diversity of objects that carry out the role of particular or general and the diversity of paths that lead from the particular to the general. The objective of this article is to show how the notion of semiotic function and mathematics ontology, elaborated by the onto-semiotic approach to mathematics knowledge, enables us to face such a problem.

Two IJSME articles

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Two articles has recently been published online in International Journal of Science and Mathematics Education. Here are the titles and abstracts:

  • Lene Møller Madsen and Carl Winsløw have written an article called “RELATIONS BETWEEN TEACHING AND RESEARCH IN PHYSICAL GEOGRAPHY AND MATHEMATICS AT RESEARCH-INTENSIVE UNIVERSITIES“. Abstract: We examine the relationship between research and teaching practices as they are enacted by university professors in a research-intensive university. First we propose a theoretical model for the study of this relationship based on Chevallard’s anthropological theory. This model is used to design and analyze an interview study with physical geographers and mathematicians at the University of Copenhagen. We found significant differences in how the respondents from the two disciplines assessed the relationship between research and teaching. Above all, while geography research practices are often and smoothly integrated into geography teaching even at the undergraduate level, teaching in mathematics may at best be ‘similar’ to mathematical research practice, at least at the undergraduate level. Finally, we discuss the educational implications of these findings.
  • Muammer Çalik, Alipaşa Ayas and Richard K. Coll wrote an article called “INVESTIGATING THE EFFECTIVENESS OF AN ANALOGY ACTIVITY IN IMPROVING STUDENTS’ CONCEPTUAL CHANGE FOR SOLUTION CHEMISTRY CONCEPTS“. Abstract: This paper reports on an investigation on the use of an analogy activity and seeks to provide evidence of whether the activity enables students to change alternative conceptions towards views more in accord with scientific views for aspects of solution chemistry. We were also interested in how robust any change was and whether these changes in conceptual thinking became embedded in the students’ long-term memory. The study has its theoretical basis in an interpretive paradigm, and used multiple methods to probe the issues in depth. Data collection consisted of two concept test items, one-on-one interviews, and student self-assessment. The sample consisted of 44 Grade 9 students selected from two intact classes (22 each), from Trabzon, Turkey. The interviews were conducted with six students selected because of evidence as to their significant conceptual change in solution chemistry. The research findings revealed statistically significant differences in pre-test and post-test scores, and pre-test and delayed post-test scores (p<0.05), but no differences between post-test and delayed test scores (p>0.05). This suggests that the analogy activity is helpful in enhancing students’ conceptual understanding of solution chemistry, and that these changes may be stored in the students’ long-term memory.

Structures of argumentation

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Christine Knipping wrote an article that was recently published online in ZDM. The article is entitled: A method for revealing structures of argumentations in classroom proving processes. Here is the abstract:

Proving processes in classrooms follow their own peculiar rationale. Reconstructing structures of argumentations in these processes reveals elements of this rationale. This article provides theoretical and methodological tools to reconstruct argumentation structures in proving processes and to shed light to their rationale. Toulmin’s functional model of argumentation is used for reconstructing local arguments, and it is extended to provide a ‘global’ model of argumentation for reconstructing proving processes in the classroom.

How is subjectivity understood?

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Tony Brown has written an article that was recently published online in Educational Studies in Mathematics. The article is entitled “Signifying “students”, “teachers” and “mathematics”: a reading of a special issue“, and here is the abstract:

This paper examines a Special Issue of Educational Studies in Mathematics comprising research reports centred on Peircian semiotics in mathematics education, written by some of the major authors in the area. The paper is targeted at inspecting how subjectivity is understood, or implied, in those reports. It seeks to delineate how the conceptions of subjectivity suggested are defined as a result of their being a function of the domain within which the authors reflexively situate themselves. The paper first considers how such understandings shape concepts of mathematics, students and teachers. It then explores how the research domain is understood by the authors as suggested through their implied positioning in relation to teachers, teacher educators, researchers and other potential readers.

ESM, July 2008

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Open-ended problems

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The International Journal for Mathematics Teaching and Learning has recently published an article called: “Teaching and Evaluating ‘Open-Ended’ Problems“. The article is written by Rama Klavir and Sarah Hershkovitz, and it is freely available in pdf format. Here is the abstract:

This paper focuses on an open-ended problem. The problem comprises a group of four numbers from which the students are asked to find the one that does not belong. Each of the numbers can be selected as not belonging, each one for different reasons. The problem was given to 164 fifth-grade students. The paper suggests tools for teachers to analyze and evaluate the work of their students when dealing with problems of this kind.

The system of coordinates and the concept of dimension

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Constantine Skordoulis et al. have written an article called “The system of coordinates as an obstacle in understanding the concept of dimension“. This article has recently been published online in International Journal of Science and Mathematics Education. Here is the abstract of the article:

The concept of dimension, one of the most fundamental ideas in mathematics, is firmly rooted in the basis of the school geometry in such a way that mathematics teachers rarely feel the need to mention anything about it. However, the concept of dimension is far from being fully understood by students, even at the college level. In this paper, we examine whether the Cartesian x-y plane is responsible for student difficulty in estimating the value of the dimension of an object, or is it only students misconceptions about dimension that lead them to a false estimation of the value of the dimension of various objects. A second question discussed in this paper examines whether the system of coordinates acts as an epistemological obstacle or whether it has only a didactical character.