‘Experimental pedagogy’ in Germany, elaborated for mathematics – a case study in searching the roots of PME

Abstract

PME, the International Group for the Psychology of Mathematics Education, was founded in 1976, at the Third International Congress on Mathematical Education in Karlsruhe, organised by the International Commission on Mathematics Instruction (ICMI). While PME is thus beyond coming of age and is reflecting its further orientation – due to the present “social turn” – the origins of investigating psychological aspects of mathematics learning have not yet been systematically studied. I am undertaking here a first such approach, concentrating on Germany, where the first pertinent monographs were published in 1913 and 1916. Different endeavours, focussing in particular on the notion of error, merged into the characteristic approach of ‘experimental pedagogy’. Given the key function of ICMI for founding PME, an additional aspect is whether the forerunner of ICMI: the Internationale Mathematische Unterrichtskommission (IMUK), founded in 1908, had an impact upon promoting research into the psychology of mathematics education. The pertinent research was effected by psychology; doing research themselves was still outside the horizon of mathematics educators. Perspectives of future research, in particular comparative ones, are outlined.

Keywords:

• history of mathematics education
• emergence of empirical studies on learning mathematics
• experimental pedagogy in Germany

Notes

1. This is a substantially extended version of a Research Report presented at PME35 in 2011 (Schubring 2011).

2. Prosopography, the method for investigating biographies of groups, constitutes one of the basic methods of research into social history. See Lawrence Stone's “Prosopography”, Daedalus 100.1 (1971), pp 46–71.

3. In a comment by Trüper on the report of a conference, given by the teacher Fels from Essen, on a calculating machine for instruction in the Hilfsschulen: Die Kinderfehler, 151.

4. The title of this journal confirms the dominant conception to concentrate investigation of cognitive capacities on children regarded as abnormal: In the first series, 1905 to 1907, it was published by an association devoted to experimental pedagogy and didactics with special regard to the education of “schwachbegabte und abnorme” children. In the second series, it was renamed, still featuring the pathological orientation: “Zeitschrift für experimentelle Pädagogik, psychologische und pathologische Kinderforschung mit Berücksichtigung der Sozialpädagogik und Schulhygiene”. In 1911, it merged with the “Zeitschrift für pädagogische Psychologie und Jugendkunde”.

5. I will continue to use the German term Anlage, since it expresses more strongly the ideology of predisposition.

6. “Die schwache Anlage zum Rechnen, die wir als Rechenschwäche oder Arithmoasthenie bezeichnen, gibt sich sowohl in der größeren Zahl der falschen oder unsichern, spontan oder auf Aufforderung berichtigten doer überhaupt entfallenden Lösungen als insbesondere und am konsequentesten in der auffälligen Langsamkeit des Prozesses der richtigen Lösungen kund”.

7. In English, there is no good equivalent for the German term Didaktik – the term ‘didactic’ even having a negative connotation, while French and Italian languages have such a term.

8. Since in this period English was not yet “the language of mathematics”, there was no acronym and no fixed name for IMUK/CIEM in English. Sometimes, one finds as English name: International Commission on the Teaching of Mathematics.

9. “Über die Ursachen der frühern oder spätern Entfaltung der Geistesknospen bei einzelnen Kindern wissen wir noch gar nichts”.

10. Fettweis quotes several doctoral dissertations on Rechenfehler of the 1920s and 1930s, but adds no significant results from them.

11. Actually, Ranschburg had mentioned such “remedies”, but in a much more restrained manner (Ranschburg 1916, 69).