Der Mathematikunterricht in der Grundschule. Eine empirische Untersuchung über verschiedene Modelle zur Grundlegung des mathematischen Denkens in den ersten Schuljahren
Klaus-Ulrich Wasmuth (1973): Der Mathematikunterricht in der Grundschule. Eine empirische Untersuchung über verschiedene Modelle zur Grundlegung des mathematischen Denkens in den ersten Schuljahren. Dissertation, Universität zu Köln.
Begutachtet durch U. Lehr und C. Menze.
Ergebnisse der empirischen Untersuchung sind in Auswahl dargestellt in: "Mengenlehre in der Grundschule?" Pädagogische Rundschau 1974.- Summary dazu: Some results of an empirical study of mathematics in the first grade of primary school are presented as a contribution to the discussion of the problern "set theory in primary education". 734 pupils who were educated in 26 different school-classes in Cologne were tested in 1971172. In the context of this study the term "set theory" substantially and methodologically means the new form of mathematics which often is referred to as the "New Math" in the sense of Z.P. Dienes. Set theory was taught in 10 classes of the sample, following a textbook of Neunzig-Sorger: "Wir lernen Mathematik"(i970). As controlgroups 8 classes were tested, who learned mathematics according to Resag-Bärmann's "Westermann Mathematik für die Grundschule" (1971) and 8 classes who followed Fricke-Besuden: "Mathematik in der Grundschule" (1967) While Neunzig-Sorger's textbook can be regarded as the most consequent Iransposition of Dienes' thoughts into a mathematics-curriculum for primary schools in the GFR available in 1970, the concept in Bärmann's text can be understood as a development of Wittmann's 'ganzheitliches Rechnen' (wholistics approach to teaching arithmetics). This cannot be characterized as set theory in the meaning mentioned above, although Wittmann frequently refers to the concept of set. Fricke-Besuden's book is based on numbers and arithmetic operations primarily; it can be distinguished from Bärmann's text, however, in so far as it relies on the concepts of length and distance (Cuisenaire rods) in order to demonstrate arithmetics operations. In addition to this , results of our samples could be compared to J. Laus' data ("Die Bildung des Zahlensbegriffs in den ersten drei Schuljahren", Stuttgart 1969), which were collected of pupils who had never experienced any pre-numerical training in the formation of number-concepts; this allowed for comparisons with the aspect of "set theory and number concept." Results of the study show that an over-emphasis on set theory and logic combined with a reduced realization of numerical relations and arithmetical Operations in favour of pointing out formal structures did not yield any desired effects - at least up to the end of the first grade. A Iack of arithmetical skills was stated in comparison to the control-groups, which could not be compensated by a more successful "mathematization" of calculation. Even the base for number-concepts was formed in a better way following Bärmann's curriculum instead of Neunzig-Sorger's. Pupils taught according to Neunzig-Sorger's text came out to be more efficient when solving tasks which required recognition of generalized structural relations; in comparison to those who had followed Bärmann's textbook they were not even more efficient in transfer of learned operations on sets and logical unknown material. On the other hand, comparisons with Laux's results yield impressive evidence for the Statement that attempts to ban set and set theory from primary education are untenable and unjustified. This is confirmed, moreover, by some significantly worse results of those pupils who - according to Fricke-Besuden's conception - had Cuisenaire rods as their only illustrating material.