journal-articles

Intuitive vs analytical thinking

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Uri Leron and Orit Hazzan have written an article called Intuitive vs analytical thinking: four perspectives. The article was recently published online in Educational Studies in Mathematics. Here is the abstract of their article:

This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives—mathematics, mathematics education, cognitive psychology, and evolutionary psychology—each offering a different view on mathematical thinking and learning and, in particular, on the source of mathematical errors and on ways of dealing with them in the classroom. The four perspectives represent four levels of explanation, and we see them not as competing but as complementing each other. In the classroom or in research data, all four perspectives may be observed. They may differentially account for the behavior of different students on the same task, the same student in different stages of development, or even the same student in different stages of working on a complex task. We first introduce each of the perspectives by reviewing its basic ideas and research base. We then show each perspective at work, by applying it to the analysis of typical mathematical misconceptions. Our illustrations are based on two tasks: one from statistics (taken from the psychological research literature) and one from abstract algebra (based on our own research).

Using graphing software in algebra teaching

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Kenneth Ruthven, Rosemary Deaney and Sara Hennesy have written an article that was published online in Educational Studies in Mathematics on Saturday. It is entitled: Using graphing software to teach about algebraic forms: a study of technology-supported practice in secondary-school mathematics. Besides having a focus on the use of graphing software, the article also discusses issues related to classroom teaching practice, teacher knowledge and teacher thinking. Here is the abstract of their article:

From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater depth through case study of two teachers each teaching two lessons of this type. The practitioner model developed in earlier research (Ruthven & Hennessy, Educational Studies in Mathematics 49(1):47–88, 2002; Micromath 19(2):20–24, 2003) provided a framework for synthesising teacher thinking about the contribution of graphing software. Further analysis highlighted the crucial part played by teacher prestructuring and shaping of technology-and-task-mediated student activity in realising the ideals of the practitioner model. Although teachers consider graphing software very accessible, successful classroom use still depends on their inducting students into using it for mathematical purposes, providing suitably prestructured lesson tasks, prompting strategic use of the software by students and supporting mathematical interpretation of the results. Accordingly, this study has illustrated how, in the course of appropriating the technology, teachers adapt their classroom practice and develop their craft knowledge: particularly by establishing a coherent resource system that effectively incorporates the software; by adapting activity formats to exploit new interactive possibilities; by extending curriculum scripts to provide for proactive structuring and responsive shaping of activity; and by reworking lesson agendas to take advantage of the new time economy.

Measuring teachers’ beliefs about mathematics

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M.A. Lazim and M.T. Abu Osman have written an article called Measuring Teachers’ Beliefs about Mathematics: A Fuzzy Set Approach. The article was published in the current issue of International Journal of Social Sciences. Here is the abstract of their article:

This paper deals with the application of a fuzzy set in measuring teachers’ beliefs about mathematics. The vagueness of beliefs was transformed into standard mathematical values using a fuzzy preferences model. The study employed a fuzzy approach questionnaire which consists of six attributes for measuring mathematics teachers’ beliefs about mathematics. The fuzzy conjoint analysis approach based on fuzzy set theory was used to analyze the data from twenty three mathematics teachers from four secondary schools in Terengganu, Malaysia. Teachers’ beliefs were recorded in form of degrees of similarity and its level of agreement. The attribute ‘Drills and practice is one of the best ways of learning mathematics’ scored the highest degree of similarity at 0.79860 with level of ‘strongly agree’. The results showed that the teachers’ beliefs about mathematics were varied. This is shown by different levels of agreement and degrees of similarity of the measured attributes.

TMME, No 1/2 2009 is here!

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I gave a pre-announcement of this two days ago, but now the first number of The Montana Mathematics Enthusiast for 2009 is ready for everyone to read. The feature themes in this double-issue is statistics education, and mathematics education research in the southern hemisphere. The first section of the issue has a number on articles on this:

Other feature articles in this double-issue include:

IJSME, February 2009

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International Journal of Science and Mathematics Education has already released the February issue (Number 1) of 2009. The issue contains the following articles:

ESM, January 2009

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Working for learning

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Pat Drake has written an article that was recently published online in Journal of Mathematics Teacher Education. The article is entitled Working for learning: teaching assistants developing mathematics for teaching. Here is the abstract of the article:

This article derives from a case study of 10 secondary school teaching assistants (TAs) who did not have conventional pre-qualifications in mathematics but who undertook an honours degree in mathematics education studies at a Higher Education Institution in England whilst continuing to work as TAs in school. Work-based learning was thus undertaken in parallel with advancement through the hierarchical undergraduate mathematics curriculum. Lave and Wenger’s work on communities of practice is used as a framework to explore the TAs’ learning of mathematics alongside their professional work in schools. This case illustrates how and where institution-based undergraduate teaching relates to work in school, and where it does not, thus signalling the importance of the TAs’ informal learning strategies in bringing together these experiences.

ZDM, No 1-2, 2009

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A new issue of ZDM was published on Friday. It is a double issue, with the following theme: Interdisciplinarity in Mathematics Education: Psychology, Philosophy, Aesthetics, Modelling and Curriculum. Guest editor of this issue is Bharath Sriraman, the editor of The Montana Mathematics Enthusiast. The issue contains not less than 22 articles:

If you don’t have full access to Springer (so that you can read these articles), you might want to pay attention to the article by Doorman and Gravemeijer, which is an Open Access article (i.e. freely available for all to read). 

A comparison of curricular effect

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The new issue of Instructional Science (January, 2009) has an article related to mathematics education: A comparison of curricular effects on the integration of arithmetic and algebraic schemata in pre-algebra students, by Bryan Moseley and Mary E. (“Betsy”) Brenner. Here is their article abstract:

This research examines students’ ability to integrate algebraic variables with arithmetic operations and symbols as a result of the type of instruction they received, and places their work on scales that illustrate its location on the continuum from arithmetic to algebraic reasoning. It presents data from pre and post instruction clinical interviews administered to a sample of middle school students experiencing their first exposure to formal pre-algebra. Roughly half of the sample (n = 15) was taught with a standards-based curriculum emphasizing representation skills, while a comparable group (n = 12) of students received traditional instruction. Analysis of the pre and post interviews indicated that participants receiving a standards-based curriculum demonstrated more frequent and sophisticated usage of variables when writing equations to model word problems of varying complexity. This advantage was attenuated on problems that provided more representational support in which a diagram with a variable was presented with the request that an expression be written to represent the perimeter and area. Differences in strategies used by the two groups suggest that the traditional curriculum encouraged students to continue using arithmetic conventions, such as focusing on finding specific values, when asked to model relations with algebraic notation.