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The following active and completed projects focus on the theme of "*early mathematical education*":

**1 "Early education of mathematically gifted children: Osnabrücker Zwergen-Mathe-Olympiade (ZMO) (Osnabrück's Math Olympics for Infants) & Meisterhaft in Mathe (MiM) (Masterly in Math)" (project manager: Prof. Schwank, ZMO since 2001; MiM: since 2008)**

** Funding:** Universitätsgesellschaft of the University of Osnabrück and local businesses

Doctoral thesis project in the context of MiM: Dipl.-Math. Jörg Erik Kinner, doctoral student and staff member at the Institute for Cognitive Mathematics

**Project description: **The ZMO has been on offer annually since 2001 for third grades of all primary schools (about 120 schools) in the town and the administrative district of Osnabrück. It consists of two rounds: firstly, an application round in which each class creates an inventive mathematical application contribution on a given subject (so far over 10,000 children of 88 schools participated), and secondly, a mathematical brain sports round to which all participating classes can send one girl and one boy as ambassador / spokesperson each (there were 1030 ZMO-math-children so far, of which, about 515 were girls and 515 boys). The conception of the ZMO-tasks and the analysis of their solutions by children demand and allow varied specific insights into the mathematical rationale of the children. As one outstanding result children were not found to have been sufficiently trained in their mathematical thinking during their math courses in school, and they were not found to be able to use other representative modes than mathematics that is easy to write down in the formal system (that is less continuative in relation to complex tasks for this age). Another dramatic result refered to the fact that girls in contrast with boys were significantly less often present among the highest performers. We have to reconsider the mathematical education at primary school. Particularly in regard to the use of appropriate, the rationalness promoting materials, and the educational activities to give girls a better understanding of mathematical thinking.

Currently a second investigation for some of the former ZMO-children is conducted in the context of Mathe-Monate im Mathe-Jahr (math-month in the year of mathematics) for children of the school grades 4 to 7 (some of the former ZMO-children who achieved a gold or diamond certificate will be targetted; additionally, children are allowed to participate who produce a particular letter of recommendation from their math teacher).

**Project's beginning: **ZMO: 2001; MiM: 2008

**Key publications:**

Blocksdorf, K. & Schwank, I. (2006): Die Osnabrücker Zwergen-Mathe-Olympiade [ZMO] [The Osnabrück's Math Olympics for Infants [ZMO]]. In Beiträge zum Mathematikunterricht 2006, 131-134. Hildesheim: Franzbecker. [article in German]

Schwank, I. (2008): Mathematiklernen: Die verkannte Bedeutung des sprachlosen Denkens [Learning mathematics: The misjudged importance of thinking without speech]. In S. Kliemann (Ed.), Diagnostizieren und Fördern in der Sekundarstufe I – Schülerkompetenzen erkennen, unterstützen und ausbauen [Diagnosing and support for school grades 5 to 10 – to recognise, support and enlarge competencies of students], 174-185. Berlin: Cornelsen Scriptor. [book and book chapter in German]

Schwank, I. (in preparation): Zwergen-Mathe-Olympiade – Ein Wettbewerb für die 3. Grundschulklassen in Stadt und Landkreis Osnabrück [Math Olympics for Infants– a contest for children of the third school grade in the town and in the administrative district of Osnabrück]. Osnabrück: Forschungsinstitut für Mathematikdidaktik. [book in German]

**2 "Early mathematical education of less gifted children & fundamental research into basic understanding of number and number operations" (project manager: Prof. Schwank, since 2005) **

**Funding:** Forschungsinstitut für Mathematikdidaktik e.V. (Research Institute for Mathematics Education) and local businesses

**Project description:** Children are occationally discovered showing great difficulties with mathematical internal representations, although they behave intelligently in other areas. This study is set out to achieve a better understanding of the strengths and weaknesses of their particular performances (including processes of their interactions) against the background of results from basic research, and to develop and evaluate clearly laid out training steps.

**Project's beginning: **2005

**Key publications:**

Schwank, I. (2005): Die Schwierigkeit des Dazu-Denkens [The difficulty of thinking about how to add something to something]. In M. von Aster / J.-H. Lorenz (Eds.), Rechenstörungen bei Kindern. – Neurowissenschaft, Psychologie, Pädagogik [Developmental Dyscalculia in Children – neuroscience, psychology, education science], 93-133. Göttingen: Vandenhoeck & Ruprecht. [book and book chapter in German]

Schwank, I. (2007): Minisymposium D15: Neurowissenschaftliche Grundlagen mathematischen Denkens [Minisymposium D15: Neuroscientific basics of mathematical thinking]. In Beiträge zum Mathematikunterricht 2007, 348-349. Hildesheim: Franzbecker. [article in German]

Schwank, I. (2007): Kann eine Idee wie ''Number Race'' funktionieren [Is it possible for an idea like "Number Race" to work]? In Beiträge zum Mathematikunterricht 2007, 360-363. Hildesheim: Franzbecker. [article in German]

**3 "VorMath: Vorschul-Mathematik" (Preschool Mathematics) (project manager: Prof. Schwank, since 2007) **

**Funding:** Forschungsinstitut für Mathematikdidaktik e.V. (Research Institute for Mathematics Education) and local businesses

Doctoral thesis project in the context of VorMath2: Dipl.-Psych. Dana Heinze, doctoral student and staff member at the Institute for Cognitive Mathematics

**In cooperation with:**VorMath1: St. Marien – Kindergarten (nursery school), Bad Laer; St. Petri – Kindergarten (nursery school), Melle; Grundschule am Salzbach (primary school), Bad Laer; Grundschule Eggermühlen (primary school)

VorMath2: nursery and primary schools in the town of Osnabrück

**Project description:** Previous research showed that the task of correcting badly or sketchy and incoherently built mathematical internal representations is very difficult indeed. Accordingly, adequate mathematical internal representations should be constructed early in a child's educational progress, which can be achieved by approaching the activity in a playful way. The present study serves as the beginning of a long-term study. This long-term study aims to follow the participating children (currently 28, plus an additional cohort in the summer) in their development until (for the time being) the third school grade, this also in comparison to the other children in the corresponding school classes.

Not all children show a comparable convenient starting position at the beginning of their time in primary school. Therefor VorMath2 is intended to investigate how children – especially children with difficulties in the mathematical field – can be supported in their preschool age, (that is, relatively early), in such a way, that all children achieved a minimum standard of their mathematical precursor skills when they start school.

**Project's beginning: **2007