Philosophy of Mathematics and Education Research Papers

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Carson, R. and Rowlands, S. (2005), “Mechanics as the Logical Point of Entry for the Enculturation into Scientific Thinking”, Science & Education, 14(3-5).
Force in modern classical mechanics is unique, both in terms of its logical character and the conceptual difficulties it causes. Force is well defined by a set of axioms that not only structures mechanics but science in general. Force is also the dominant theme in the ‘misconceptions’ literature and many philosophers and physicists alike have expressed puzzlement as to its nature. The central point of this article is that if we taught mechanics as the forum to discuss the nature of mechanics itself, then we would serve to better secure a learner’s understanding and appreciation of both science and mathematics. We will attempt to show that mechanics can provide the opportunity for students to enter this meta-discourse by engaging in Socratic discussion, entertaining thought experiments, comparisons made between force as defined within mechanics as a modern axiomatic system with Newton’s quantitative definition of force, how the concepts of force prior to Galileo and Newton can be used as a teaching aid with respect to student intuitive ideas and how mathematics was brought to bear on what is given empirically. Mechanics provides this opportunity and pedagogically may require it due to its axiomatic nature

Rowlands, S. and Carson, R. (2004), “Our response to Adam, Alangui and Barton's ``A Comment on Rowlands & Carson `Where would Formal, Academic Mathematics stand in a Curriculum informed by Ethnomathematics? A Critical Review'~'' Educational Studies in Mathematics, 56(2-3), 329-342.
There is a disparity between the historical Vygotsky and the diversity of ‘our Vygotsky’. This disparity is complex because it not only involves the interpretation of text but also mistranslation, construction of meaning and the legitimisation of current trends. This article attempts to throw light on the historical Vygotsky by unpacking this disparity with the ZPD in particular and argues that the ZPD should be seen as part and parcel of a scientific method in the quest to change psychology into an abstract theoretical framework, similar in structure to Marx’s Capital. In relation to Vygotsky, the issues of interpretation, translation, the logic of Capital and the ‘scientifically correct method’ are discussed. In particular, the ZPD is discussed in the context of teaching mathematics as a formal, academic discipline.

Rowlands, S. and Carson, R. (2002), ‘Where Would Formal, Academic Mathematics Stand in a Curriculum Informed by Ethnomathematics? A Critical review of Ethnomathematics’, Educational Studies in Mathematics, 50(1), 79-102.
This paper is a critical review of the ethnomathematics literature and classifies ethnomathematics according to where it might stand in relation to the teaching of formal, academic mathematics. This paper investigates what it sees as four possibilities: ethnomathematics should replace academic mathematics, ethnomathematics should be a supplement to the mathematics curriculum, ethnomathematics should be used as a springboard for academic mathematics and ethnomathematics should be taken into consideration when preparing learning situations. We argue that it is only through the lens of formal, academic mathematics sensitive to cultural differences that the real value of the mathematics inherent in certain cultures and societies be understood and appreciated.