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Geoffrey Howson

My pleasure at being sent for review this collection of papers on symbolism in mathematics was somewhat diminished when I saw that the first article was by Josette Adda and the last by Derek Woodrow. This was not due to any lack of respect for these two authors; rather, it indicated that readers were being offered not a structured survey of the problems of symbolism within mathematics education but an ad hoc collection of articles arranged alphabetically by author. In fact, although the nine articles vary considerably in quality, the overall standard is quite high, and any mathematics educator will find two or three of interest. Nevertheless, I very much felt the absence of a framework that would help the reader to identify more clearly the sa lient problems and to recognize fruitful avenues for research. In particular, the actual role of symbols within mathematics and within mathematical activity would seem to me to be given insufficient attention, although, almost of necessity, most authors touch on it.

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Anna Sierpinska, Jeremy Kilpatrick, Nicolas Balacheff, A. Geoffrey Howson, Anna Sfard and Heinz Steinbring

As mathematics education has become better established as a domain of scienti fic research (if not as a scientific discipline), exactly what this research is and what its results are have become less clear. The hi story of the past three International Congresses on Mathematical Education demonstrates the need for greater clarity. At the Budapest congress in 1988, in particular, there was a general feeling that mathematics educators from different parts of the world. countries, or even areas of the same country often talk past one another. There seems to be a lack of consensus on what it means to be a mathematics educator. Standards of scientific quality and the criteria for accepting a paper vary considerably among the more than 250 journals on mathematics education published throughout the world.