- Introduction.
One of the directions in preparing younger schoolchildren for studying in the middle grades of school is to improve combinatorial actions. Our work shows that successful learning of mathematics presupposes that children have developed actions of a combinatorial nature [8, p.261 – 285].
This experimental work is aimed at determining the conditions that contribute to the formation of combinatorial actions in schoolchildren studying in the second grade of primary school.
1.1.Study of combinatorial actions in primary school students.
English L.D. studied the features of finding solutions in combinatorial problems of varying complexity. A 1991 study compared the characteristics of actions performed by 7-year-old children and 4-6-year-old children. The results of the experiments indicate that 7-year-old children more often use a systematic approach to finding a solution associated with variation than 5-year-old children.
In a 1993 study , combinatorial problems were solved by schoolchildren aged seven to twelve. It turned out that, as in the 1991 experiments, 7-year-old children actually use a systematic strategy within which 3 parameters vary.
References
1. English L.D. (1991). Young children's combinatoric strategies. Educational Studies in Mathematics, 22 (5), 451- 474.2. English L.D. (1993). Children’s strategies for solving two- and three-dimensional combinatorial problems. Journal for Research in Mathematics Education, 24(3), 255-273.
3. English L.D. (2005). Combinatorics and the Development of Children's Combinatorial Reasoning. In: Jones G.A. (eds) Exploring Probability in School. Mathematics Education Library, vol 40. Springer, Boston, MA.Pages 121-141.
4. Krpec, R. (2014). The development of combinatorial skills of the lower primary school pupils through organizing the sets of elements. Acta mathematica, 17, 117 – 123.
5. Maher, C., & Yankelewitz, D. (2010). Representations as tools for building arguments. In Maher, C., Powell, A., & Uptegrove, E. (Eds.), Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms (pp. 17– 26). New York, NY: Springer.
6. White, H. Department of Psychology , University of California , USA (1984). The Development of Combinatorial Reasoning: The Role of Cognitive Capacity. The Journal of Genetic Psychology: Research and Theory on Human Development, 145, (2), 185 - 193.
7. Poddiakov A.N. (2011). Multivariable Objects for Stimulation of Young Children's Combinatorial Experimentation and Causal-Experimental Thought Psychology in Russia: State of the Art, 4, 397- 420
8. Zak A.Z. Thinking of a junior school student. – St. Petersburg: Assistance, 2004. 828 с.