Abstract
Recent psychological studies as well as research findings in mathematics education highlight the significance of early number skills for the child’s achievement in mathematics at the end of primary school. In this context, the ongoing 3-year longitudinal study discussed in this chapter, investigates the development of early numeracy understanding of 408 children from 1 year prior to school until the end of Grade 1. The study seeks to identify children who struggle with respect to their mathematics learning after the first year of school and compare their achievements with their number concept development 1 year prior to school as well as immediately prior to school entry (Grade 1). Initial findings suggest that children’s understanding and skills with respect to number and counting are important precursors for later school success. The children who were identified as low-achievers in mathematics at the end of Grade 1, also demonstrated less knowledge and skills than their peers prior to school.
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Notes
- 1.
Migration background in this context means that the children speak at least one language other than German at home.
- 2.
However, it is important to note that not all arithmetic learning difficulties can be put on a level with dyscalculia.
- 3.
A fourth measuring point was included in order to acknowledge the fact that the group of low-achieving children might change towards the end of junior primary school, i.e. that children who show slower (mathematical) development than the majority of their peers might perform more weakly at the end of Grade 1 than at the end of Grade 2.
- 4.
The FYSMI is conducted in the first year of school, which in Australia is the preparatory grade preceding Grade 1. This preparatory year is compulsory and children are aged between 4 years 9 months and 6 years. In Germany in contrast, formal schooling starts with Grade 1 when children are 6 years old. While the vast majority of German five-year-olds attend kindergarten, this is not compulsory and involves fees to be paid by the parents.
- 5.
This instrument is a German adaptation of the Australian Early Years Interview (Department of Education, Employment and Training 2001).
- 6.
In order to base the statistical analyses on a complete and coherent data set, all student data that was incomplete with the respect to all measuring points or clearly incorrect due to mistakes during the data collection and recording were omitted.
- 7.
The framework of “growth points” reflects the analysis of “available research on key stages of levels in young children’s mathematics learning, as well as frameworks developed by other authors and groups to describe learning” (Clarke et al. 2002, p. 12). The framework was developed to describe mathematical growth of children from 5 to 8 years of age. According to the ENRP researchers “growth points can be considered primary stepping stones along the way to understanding important mathematical ideas” (Clarke et al. 2003, p. 69). To illustrate this concept, the growth point descriptors for counting (interview part A) are given below (Clarke et al. 2002, p. 124).
A. Counting: 0. Not apparent; 1. Rote counting; 2. Counting collections up to 20 objects; 3. Counting by 1 s (forward/backward from variable starting points between 1 and 100; knows numbers before/after); 4. Counting from 0 by 2, 5, and 10 s; 5. Counting from x (where x > 0) by 2, 5, and 10 s; 6. Extending and applying counting skills.
References
Anderson, A., Anderson, J., & Thauberger, C. (2008). Mathematics learning and teaching in the early years. In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives on mathematics in early childhood education (pp. 95–132). Charlotte: Information Age Publishing.
Aunola, K., Leskinen, E., Lerkkanen, M.-K., & Nurmi, J.-E. (2004). Developmental dynamics of mathematical performance from preschool to grade 2. Journal of Educational Psychology, 96, 762–770.
Baroody, A. J., & Wilkins, J. (1999). The development of informal counting, number, and arithmetic skills and concepts. In J. Copley (Ed.), Mathematics in the early years (pp. 48–65). Reston: NCTM.
Clarke, D., Cheeseman, J., Gervasoni, A., Gronn, D., Horne, M., McDonough, A., Montgomery, P., Roche, A., Sullivan, P., Clarke, B., & Rowley, G. (2002). Early numeracy research project final report. Melbourne: Mathematics Teaching and Learning Centre, Australian Catholic University.
Clarke, D., Cheeseman, J., McDonough, A., & Clarke, B. (2003). Assessing and developing measurement with young children. In D. Clements & G. Bright (Eds.), Learning and teaching measurement. NCTM Yearbook (pp. 68–80). Reston: NCTM.
Clarke, B., Clarke, D., & Cheeseman, J. (2006). The mathematical knowledge and understanding young children bring to school. Mathematics Education Research Journal, 18(1), 78–103.
Clarke, B., Clarke, D., Grüßing, M., & Peter-Koop, A. (2008). Mathematische Kompetenzen von Vorschulkindern: Ergebnisse eines Ländervergleichs zwischen Australien und Deutschland. Journal für Mathematik-Didaktik, 29(3/4), 259–286.
Clements, D. (1984). Training effects on the development and generalization of Piagetian logical operations and knowledge of number. Journal of Educational Psychology, 76, 766–776.
Cooper, T. J., Heirdsfield, A., & Irons, C. J. (1996). Children’s mental strategies for addition ans subtraction word problems. In J. Mulligan & M. Mitchelmore (Eds.), Children’s learning number (pp. 147–162). Adelaide: AAMT.
Dehane, S. (1992). Varieties of numerical abilities. Cognition, 44, 1–42.
Department of Education, Employment and Training (DEET). (2001). Early numeracy interview booklet. Melbourne: Department of Education, Employment and Training.
Dornheim, D. (2008). Prädikatoren von Rechenleistung und Rechenschwäche. Berlin: Logos.
Fuson, K. C. (1988). Children’s counting and concepts of number. New York: Springer.
Fuson, K. C., Secada, W. G., & Hall, J. W. (1983). Matching, counting, and the conservation of number equivalence. Child Development, 54, 91–97.
Ginsburg, H., Inoue, N., & Seo. K. (1999). Young children doing mathematics: Observations of everyday activities. In J. Copley (Ed.), Mathematics in the early years (pp. 88–99). Reston: NCTM.
Grüßing, M., & Peter-Koop, A. (2008). Effekte vorschulischer mathematischer Förderung am Ende des ersten Schuljahres: Erste Befunde einer Längsschnittstudie. Zeitschrift für Grundschulforschung, 1(1), 65–82.
Kaufmann, S. (2003). Früherkennung von Rechenstörungen in der Eingangsklasse der Grundschule und darauf abgestimmte remediale Maßnahmen. Frankfurt a. M.: Lang.
Krajewski, K. (2005). Vorschulische Mengenbewusstheit von Zahlen und ihre Bedeutung für die Früherkennung von Rechenschwäche. In M. Hasselhorn, W. Schneider, & H. Marx (Eds.), Diagnostik von Mathematikleistungen (pp. 49–70). Göttingen: Hogrefe.
Krajewski, K. (2008). Vorschulische Förderung mathematischer Kompetenzen. In F. Petermann & W. Schneider (Eds.), Angewandte Entwicklungspsychologie (pp. 275–304). Göttingen: Hogrefe.
Krajewski, K., & Schneider, W. (2009). Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a 4-year longitudinal study. Learning and Instruction, 19(6), 513–526.
Krajewski, K., Küspert, P., & Schneider, W. (2002). DEMAT 1 +. Deutscher Mathematiktest für erste Klassen. Göttingen: Hogrefe.
Krajewski, K., Liehm, S., & Schneider, W. (2004). DEMAT 2 +. Deutscher Mathematiktest für zweite Klassen. Göttingen: Hogrefe.
Krajewski, K., Grüßing, M., & Peter-Koop, A. (2009). Die Entwicklung mathematischer Kompetenzen bis zum Beginn der Grundschulzeit. In A. Heinze & M. Grüßing (Eds.), Mathematiklernen vom Kindergarten bis zum Studium. Kontinuität und Kohärenz als Herausforderung für den Mathematikunterricht (pp. 17–34). Münster: Waxmann.
Peter-Koop, A., & Grüßing, M. (2011). Elementarmathematisches Basisinterview KiGa. Offenburg: Mildenberger.
Peter-Koop, A., & Grüßing, M. (2014). Early enhancement of kindergarten children potentially at risk in learning school mathematics—Design and findings of an intervention study. In U. Kortenkamp, C. Benz, B. Brandt, G. Krummheuer, S. Ladel, & R. Vogel (Eds.), Early Mathe-matics learning: Selected papers of the POEM 2012 (S. 307–322). New York: Springer.
Peter-Koop, A., Wollring, B., Spindeler, B., & Grüßing, M. (2007). Elementarmathematisches Basisinterview (Zahlen und Operationen). Offenburg: Mildenberger.
Peter-Koop, A., Grüßing, M., & Schmitman gen. Pothmann, A. (2008). Förderung mathematischer Vorläuferfähigkeiten: Befunde zur vorschulischen Identifizierung und Förderung von potenziellen Risikokindern in Bezug auf das schulische Mathematiklernen. Empirische Pädagogik, 22(2), 208–223.
Piaget, J. (1952). The child’s conception of number. London: Routledge.
Resnick, L. B. (1983). A developmental theory of number understanding. In H. Ginsburg (Ed.), The development of mathematical thinking (pp. 109–151). New York: Academic Press.
Resnick, L. B. (1989). Developing mathematical knowledge. American Psychologist, 44(2), 162–169.
Sophian, C. (1995). Representation and reasoning in early numerical development. Child Development, 66, 559–577.
Stern, E. (1997). Ergebnisse aus dem SCHOLASTIK-Projekt. In F. E. Weinert & A. Helmke (Eds.), Entwicklung im Grundschulalter (pp. 157–170). Weinheim: Beltz.
van Luit, J., van de Rijt, B., & Hasemann, K. (2001). Osnabrücker Test zur Zahlbegriffsentwicklung (OTZ). Göttingen: Hogrefe.
Weinert, F. E., & Helmke, A. (Eds.) (1997). Entwicklung im Grundschulalter. Weinheim: Beltz.
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Peter-Koop, A., Kollhoff, S. (2015). Transition to School: Prior to School Mathematical Skills and Knowledge of Low-Achieving Children at the End of Grade 1. In: Perry, B., MacDonald, A., Gervasoni, A. (eds) Mathematics and Transition to School. Early Mathematics Learning and Development. Springer, Singapore. https://doi.org/10.1007/978-981-287-215-9_5
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