beliefs

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.

The development of beliefs and practice

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Despina Potari  and Barbara Georgiadou–Kabouridis have written an article called A primary teacher’s mathematics teaching: the development of beliefs and practice in different “supportive” contexts. The article was recently published online in Journal of Mathematics Teacher Education. Here is the article abstract:

This article refers to a longitudinal case study of a primary school teacher over a period of 4 years. The focus is on the development of the teacher’s beliefs regarding mathematics teaching and learning from the last year of her university studies up to the third year of teaching mathematics in school. This development has been investigated within three different contexts, which have been distinguished in terms of the kind of support provided to this teacher. Two dominant beliefs emerged which have been traced through the period of the study from both the teacher’s reflections and actions. The first belief drew on the idea that what was considered an easy mathematical task by an adult could also be easily understood by children, while the second was that children learn mathematics through their actual involvement in a variety of teaching activities. The results indicate the way that teacher’s experiences from her university studies, actual classroom practice and inservice education interact and influence her beliefs and professional development.

Using history of mathematics

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Charalambos Y. Charalambous, Areti Panaoura and George Philippou have written an article called Using the history of mathematics to induce changes in preservice teachers’ beliefs and attitudes: insights from evaluating a teacher education program. The article was published online in Educational Studies in Mathematics on Tuesday. Here is the abstract of their article:

Scholars and teacher educators alike agree that teachers’ beliefs and attitudes toward mathematics are key informants of teachers’ instructional approaches. Therefore, it has become clear that, in addition to enriching preservice teachers’ (PSTs) knowledge, teacher education programs should also create opportunities for prospective teachers to develop productive beliefs and attitudes toward teaching and learning mathematics. This study explored the effectiveness of a mathematics preparatory program based on the history of mathematics that aimed at enhancing PSTs’ epistemological and efficacy beliefs and their attitudes toward mathematics. Using data from a questionnaire administered four times, the study traced the development of 94 PSTs’ beliefs and attitudes over a period of 2 years. The analysis of these data showed changes in certain dimensions of the PSTs’ beliefs and attitudes; however, other dimensions were found to change in the opposite direction to that expected. Differences were also found in the development of the PSTs’ beliefs and attitudes according to their mathematical background. The data yielded from semi-structured follow-up interviews conducted with a convenience sample of PSTs largely corroborated the quantitative data and helped explain some of these changes. We discuss the effectiveness of the program considered herein and draw implications for the design of teacher education programs grounded in the history of mathematics.

Elementary prospective teachers’ mathematical beliefs

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Susan L. Swars, Stephanie Z. Smith, Marvin E. Smith and Lynn C. Hart have written an article called A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs. The article was published online in Journal of Mathematics Teacher Education on Thursday. Here is the abstract of their article:

The universal emphasis in mathematics education on teaching and learning for understanding can require substantial paradigmatic shifts for many elementary school teachers. Consequently, a pressing goal of teacher preparation programs should be the facilitation of these changes during program experiences. This longitudinal, mixed methods study presents a thorough investigation of the effects of a distinctive teacher preparation program on important constructs related to prospective teacher preparedness to teach mathematics for understanding, including mathematics pedagogical and teaching efficacy beliefs, mathematics anxiety, and specialized content knowledge for teaching mathematics. The results indicate that the programmatic features experienced by the prospective teachers in this study, including a developmental two-course mathematics methods sequence and coordinated developmental field placements, provided a context supporting teacher change. These shifts are interpreted through the nature and timing of the experiences in the program and a model of teacher change processes. The findings provide insights for mathematics educators as to the outcomes of these programmatic features.

Belief enactment

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Danish colleague Jeppe Skott has written an interesting article about research concerning teachers’ beliefs. The article is entitled Contextualising the notion of ‘belief enactment’, and it was published online in Journal of Mathematics Teacher Education on Wednesday. Skott is a prominent researcher within the field of mathematics education research in the Nordic countries, and he has a critical view on the notion of research on teachers’ beliefs, as well as the approach to this area of research. Here is the abstract of his article:

For more than 20 years, belief research has been based on the premise that teachers’ beliefs may serve as an explanatory principle for classroom practice. This is a highly individual perspective on belief–practice relationships, one that does not seem to have been influenced by the increasingly social emphases in other parts of mathematics education research. In this article, I use the notions of context and practice to develop a locally social approach to understanding the belief–practice relationships. It is a corollary of the approach taken that the high hopes for belief research with regard to its potential impact on mathematics instruction need to be modified.

ZDM, No 5, 2008

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For some reason, ZDM has published two December issues this year. I have already covered one of them, which is actually No 6, but I have not covered No 5 (both are December issues). ZDM, No 5 has a focus on Empirical Research on Mathematics Teachers and their Education, and it is a very interesting issue (for me at least), with 14 articles:

So, if you (like me) you are interested in research related to mathematics teachers and/or mathematics teacher education, this would certainly be an issue to take a closer look at!

A large part of the articles in this issue are related to the international comparative study: “Mathematics Teaching in the 21st Century (MT21)”. This study, according to the editorial, is the first study that has a focus on “how teachers are trained and how they perform at the end of their education”.

Mathematical enculturation

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Jacob Perrenet and Ruurd Taconis have written an article called Mathematical enculturation from the students’ perspective: shifts in problem-solving beliefs and behaviour during the bachelor programme. The article was published online in Educational Studies in Mathematics on Tuesday, and it is an Open Access article, so it is freely available to anyone! Here is the article abstract:

This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and behaviour. At the end of their bachelor programme, as experienced bachelor students, they again fill in the questionnaire. As an educational exercise in academic reflection, they have to explain their individual shifts in beliefs, if any. Significant shifts for the group as a whole are reported, such as the growth of attention to metacognitive aspects in problem-solving or the growth of the belief that problem-solving is not only routine but has many productive aspects. On the one hand, the changes in beliefs and behaviour are mostly towards their teachers’ beliefs and behaviour, which were measured using the same questionnaire. On the other hand, students show aspects of the development of an individual problem-solving style. The students explain the shifts mainly by the specific nature of the mathematics problems encountered at university compared to secondary school mathematics problems. This study was carried out in the theoretical framework of learning as enculturation. Apparently, secondary mathematics education does not quite succeed in showing an authentic image of the culture of mathematics concerning problem-solving. This aspect partly explains the low number of students choosing to study mathematics.