History+of+Mathematics+in+Education

= = In the past several decades, various mathematics educators have seen the different roles the history of mathematics can take through its introduction into the education of mathematics teachers - Freudenthal [1] for example conceived it as giving a background to the teachers’ mathematical knowledge, while others concentrated on offering a possible pathway to the deepening of teachers’ reflection capabilities through an in-depth study of the development of mathematical concepts through history [2]. One of the approaches, developed by Hsieh and Hsieh [3], and Philippou and Christo [4] dealt with using the history of mathematics as a particular tool and context to develop beliefs and attitudes in mathematics.

Through the projects already completed by our academic team members and partners, we have been able to build upon expertise and experiences in order to link the history of mathematics as a focus for cooperation and collaboration as well as serving as an initiator for the creation of conceptual landscapes we hope our teachers and colleagues will use in their training and continuing professional development.

This project also builds upon the model of **//collaborative teaching practice //**. Collaborative teaching practice is the practice developed in different countries (most prominently Japan, Hungary, and more recently the United States and England) and sometimes also closely linked and/or referred to as ‘lesson study’. The collaborative teaching practice in this project is understood as a way of peer-discussion and the collective teaching tool is based on the simple cycle as follows:
 * plan the lesson together, discussing the potential research activities/foci of research
 * do individual research and share responsibilities for producing resources
 * meet or correspond and share the findings of research as well as produced resources
 * teach collaboratively or film the session
 * assess the filmed lessons as a team, adopting certain resources and approaches for further use and/or development, and rejecting others
 * communicate within the project and wider community the reflections on ‘what works’ in the classroom and resources used.

 Part of the project is on using the original sources – there will be two such units of work which you can choose to develop in your school:
 * Comparison of geometry textbooks from 18th and 19th centuries with those of today
 * Working on Newton’s mathematical writing (sixth formers and their teachers only).

As the picture is worth a ‘thousand words’ so is the original piece of mathematics worth a thousand textbooks trying to explain it. It is, however, not easy to find an original piece of mathematics – the roots of many mathematical concepts are buried under many a syllabus, educational programme, and mathematical textbook’s own order of exposition. All work that is being developed by our student teachers and teachers from your department will contribute to a website which will have these original ‘pieces’ of mathematics as the starting point for a study by your students - current and future.

If you wish to take part in developing these units, please get in touch by email with the project leader at s.lawrence2@bathspa.ac.uk.

[1] Freudenthal H, (1981). “//Should a mathematics teacher know something about the history of mathematics?//” In __For the Learning of Mathematics__, 2, 1: 30-33. [2] Arcavi A, Bruckheimer M, & Ben-Zvi R, (1982). “//Maybe a mathematics teacher can profit from the study of the history of mathematics//.” In __For the Learning of Mathematics__, 3, 1: 30-37. Arcavi A, Bruckheimer M, & Ben-Zvi R, (1987). “//History of mathematics for teachers: The case of irrational numbers//.” In __For the Learning of Mathematics__, 7, 2: 18-23. Swetz F J, (1995). “//To know and to teach: Mathematical pedagogy// //from a historical point// // context // .” In __Educational Studies in Mathematics__, 29: 73-88. [3] Hsieh C -J, and Hsieh F -J, (2000). “//What are teachers’ view of mathematics? An investigation of how they evaluate formulas in mathematics//.” In W -S Horng and F - L Lin (eds.) __Proceedings of HPM 2000 conference__, 1: 98-111. [4] Philippou G N, and Christou C, (1998a). “//Beliefs, teacher education and history of mathematics//.” In A Olivier and K Newstead (eds.) __Proceedings of PME__ 22, 4: 1-9. Philippou G N, and Christou C, (1998b). “//The effect of a preparatory mathematics program in changing prospective teachers’ attitudes towards mathematics//.” In __Educational Studies in Mathematics__, 35: 189-206.