Memoir and study of mathematics. A didactic approach to the anthropological character.
(Mémoire et étude des mathématiques. Une approche didactique à caractère anthropologique.)

*(French)*Zbl 1256.97001
Paideia. Éducation, Savoir, Société. Rennes: Presses Universitaires de Rennes (PUR) (ISBN 978-2-7535-0934-4/pbk). 219 p. (2009).

The book aims at linking “memory” phenomena and mathematics education in a broad approach, including historical, didactical, anthropological and philosophical accounts.

By “memory”, the author refers to a variety of sociological and psychological features, ranging from individual long-term memory as defined by psychologists (the capacity to store and recall experiences or knowledge, or to learn procedures), to “institutional” memory (the survival of theories in a given social group, here mostly the mathematicians’ community).

A few interesting methodological avenues are suggested here and there that might prove useful to educational studies. For instance (p. 56), take French students learning to solve equations such as \(\ln (x^{2})+\ln (x)=2\). At first, they are taught to proceed as follow: \[ 2\ln (x) +\ln(x) = 2 \; ; \;3\ln (x) = 2\ln (e) \]

\[ \ln (x^{3}) = \ln (e^{2}) \; ; \; x^{3} = e^{2} \; ; \; x = \, ^{3}\sqrt{e^{2}} \]

A few months later however, they may take advantage of newly learned properties of \(\ln(.)\), as well as fractional powers. Matheron shows that when asked to remember a classroom experience after this new material is learned, they show false memories about how they performed the task the first time, which gives interesting insight into the process of mathematical evolution in the classroom.

Other interesting examples include historical reminiscence of once forgotten theories, or the pervasiveness and possibly noxious characteristic of “recall situations”, in which the teacher urges pupils to remember past educational events or mathematical facts.

The text remains essentially theoretical, favoring a philosophical standpoint with few clear practical applications. Unfortunately too, the author goes without the most relevant knowledge, discarding from the very beginning the vast psychological literature on memory. For instance, although issues addressed in the book would indeed benefit from her thorough work on oblivion and memory modification by subsequent experiences, Elizabeth Loftus is not even mentioned\(\ldots\).

By “memory”, the author refers to a variety of sociological and psychological features, ranging from individual long-term memory as defined by psychologists (the capacity to store and recall experiences or knowledge, or to learn procedures), to “institutional” memory (the survival of theories in a given social group, here mostly the mathematicians’ community).

A few interesting methodological avenues are suggested here and there that might prove useful to educational studies. For instance (p. 56), take French students learning to solve equations such as \(\ln (x^{2})+\ln (x)=2\). At first, they are taught to proceed as follow: \[ 2\ln (x) +\ln(x) = 2 \; ; \;3\ln (x) = 2\ln (e) \]

\[ \ln (x^{3}) = \ln (e^{2}) \; ; \; x^{3} = e^{2} \; ; \; x = \, ^{3}\sqrt{e^{2}} \]

A few months later however, they may take advantage of newly learned properties of \(\ln(.)\), as well as fractional powers. Matheron shows that when asked to remember a classroom experience after this new material is learned, they show false memories about how they performed the task the first time, which gives interesting insight into the process of mathematical evolution in the classroom.

Other interesting examples include historical reminiscence of once forgotten theories, or the pervasiveness and possibly noxious characteristic of “recall situations”, in which the teacher urges pupils to remember past educational events or mathematical facts.

The text remains essentially theoretical, favoring a philosophical standpoint with few clear practical applications. Unfortunately too, the author goes without the most relevant knowledge, discarding from the very beginning the vast psychological literature on memory. For instance, although issues addressed in the book would indeed benefit from her thorough work on oblivion and memory modification by subsequent experiences, Elizabeth Loftus is not even mentioned\(\ldots\).

Reviewer: Nicolas Gauvrit (Paris)