Research Article

Improving combinatorial actions in children of 9 years

324 - 332, 15.01.2020
https://doi.org/10.17051/ilkonline.2020.644570

Abstract

 The aim
of the study was to determine the conditions for the improving of combinatorial
actions in children of 9 years old (3rd grade 9 years old elementary
school students). The original «Combination-2» educational program may become a
condition for improving combinatorial actions. It was supposed to establish
such conditions. The program includes 30 types of non-standard tasks with
extracurricular content. Each type of task had three structural versions of the
tasks: find the answer, find the question, find part of the initial conditions.
Solving these problems requires combinatorial actions. The control group
consisted of 91 children, the experimental group — of 96. These children
participated in 30 group classes for 30
weeks (weekly, from September to May). 
The study showed that the “Combination-2” lessons contribute to the
improving of combinatorial actions in children. In further studies, it is
planned to determine the extent to which the “Combination-2” program
contributes to the improving of combinatorial actions in children of 10 years
old.

References

  • Břehovský, J., Příhonská, J. (2017). Combinatorial problems of mathematics for elementary school. 16th Conference of Applied Mathematics. Applimat. Journal of Applied Mathematics and Engineerings, 206-214. Břehovský, J., Příhonská, J. (2018). The ability of primary school pupils to solve combinatorial tasks. In 17th Conference on Applied Mathematics. Source: Aplimat (pp. 127-136). 13 September 2019 retrieved from http://evlm.stuba.sk/APLIMAT2018/proceedings/Papers/0127_Brehovsky_Prihonska.pdf Davydov V. V. (2008). Lekcii po obshhej psikhologii [in Russian: Lectures in General Psychology]. Moscow: Academia. Eizenberg, M. M., & Zaslavsky, O. (2003). Cooperative problem solving in combinatorics: the inter-relations between control processes and successful solutions. The Journal of Mathematical Behavior, 22(4), 389-403. https://doi.org/10.1016/j.jmathb.2003.09.001 English, L. D. (1991). Young children's combinatoric strategies. Educational studies in Mathematics, 22(5), 451-474. https://doi.org/10.1007/BF00367908 English, L. D. (1993). Children's strategies for solving two-and three-dimensional combinatorial problems. Journal for research in Mathematics Education, 255-273. https://doi.org/10.2307/749347 English, L. D. (2005). Combinatorics and the development of children's combinatorial reasoning. In Exploring probability in school (pp. 121-141). Springer, Boston, MA. https://doi.org/10.1007/0-387-24530-8_6 Fischbein, E., & Grossman, A. (1997). Schemata and intuitions in combinatorial reasoning. Educational studies in Mathematics, 34(1), 27-47. Herzog, M., Ehlert, A., & Fritz, A. (2017). Kombinatorikaufgaben in der dritten Grundschulklasse. Journal für Mathematik-Didaktik, 38(2), 263-289. https://doi.org/10.1007/s13138-017-0118-8 Hidayati, Y. M., Sa'dijah, C., & Qohar, S. A. (2019). Combinatorial Thinking to Solve the Problems of Combinatorics in Selection Type. International Journal of Learning, Teaching and Educational Research, 18(2). https://doi.org/10.26803/ijlter.18.2.5 Höveler, K. (2016). Children’s combinatorial counting strategies and their relationship to mathematical counting principles. In Makalah disajikan dalam 13th International Congress on Mathematical Education Hamburg (pp. 231-245). Dortmund: TU Dortmund. 1 September 2019 retrieved from https://www.mathematik.tu-dortmund.de/sites/karina-hoeveler/download/TSG17_PA_Hoeveler.pdf Höveler, K. (2017). Children’s combinatorial counting strategies and their relationship to conventional mathematical counting principles. In Teaching and learning discrete mathematics Worldwide: Curriculum and research (pp. 81-92). Springer, Cham. https://doi.org/10.1007/978-3-319-70308-4_6 Inhelder, B., & Piaget, J. (1969). The psychology of the child. New York: Basic Books. Krekić-Pinter, V., Ivanović, J., Namestovski, Ž., & Major, L. (2015). Strategy and Methods for Solving Combinatorial Problems in Initial Instruction of Mathematics. International Journal of Modern Education Research, 2(6), 77-87. 30 August 2019 retrieved from http://article.aascit.org/file/pdf/9100785.pdf Krpec, R. (2014). The development of combinatorial skills of the lower primary school pupils through organizing the sets of elements. ACTA MATHEM ATICA 17, 103. 09 September 2019 retrieved from http://www.nmk.fpv.ukf.sk/2014/proceedings/13_krpec_fulltext.pdf Maher C. A., Yankelewitz D. (2011). Representations as tools for building arguments. In Combinatorics and Reasoning. Representing, justifying and building isomorphisms (pp. 17-25). Dordrecht, Springer Netherlands. https://doi.org/10.1007/978-94-007-0615-6_3 Palmér, H., & van Bommel, J. (2016). Exploring the role of representations when young children solve a combinatorial task. ICT in mathematics education: the future and the realities, 47. 08 September 2019 retrieved from http://ncm.gu.se/media/smdf/Published/No11_Madif10/047056_madif_001_palmer.pdf Palmér, H., & van Bommel, J. (2018). The role of and connection between systematization and representation when young children work on a combinatorial task. European Early Childhood Education Research Journal, 26(4), 562-573 Poddiakov, A. N. (2011). Multivariable objects for stimulation of young children's combinatorial experimentation and causal-experimental thought. Psychology in Russia, 4, 397. https://doi.org/10.11621/pir.2011.0027 Temnikova M. (2018). Combinatorial mathematical tasks in the education in mathematics for grades 1-4. European Scientific Journal, 2, 46-55. https://doi.org/10.19044/esj.2018.c5p18 van Bommel, J., & Palmér, H. (2017). Paper or and digital: A study on combinatorics in preschool class. In NORMA17 The Eighth Nordic Conference on Mathematics Education, Stockholm, 30 May–2 June 2017. Svensk förening för MatematikDidaktisk Forskning-SMDF. 13 September 2019 retrieved from http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A1181427&dswid=7604 van Bommel, J., & Palmér, H. (2018). Enhancing young children’s understanding of a combinatorial task by using a duo of digital and physical artefacts. Early years, 1-14. https://doi.org/10.1080/09575146.2018.1501553 White, H. (1984). The development of combinatorial reasoning: the role of cognitive capacity. The journal of genetic psychology, 145(2), 185-193. https://doi.org/10.1080/00221325.1984.10532266 Zak A. (2004). Myshlenie mladshego shkol’nika [in Russian: Thinking of the younger school student]. St. Peterburg: sodeystvije. Zak A. (2016). Razvitie avtorskogo myshlenia u mladshih shkol’nikov [in Russian: Development of author’s thinking in younger schoolchildren]. Moscow: Biblio-Globus.

324 - 332, 15.01.2020
https://doi.org/10.17051/ilkonline.2020.644570

Abstract

References

  • Břehovský, J., Příhonská, J. (2017). Combinatorial problems of mathematics for elementary school. 16th Conference of Applied Mathematics. Applimat. Journal of Applied Mathematics and Engineerings, 206-214. Břehovský, J., Příhonská, J. (2018). The ability of primary school pupils to solve combinatorial tasks. In 17th Conference on Applied Mathematics. Source: Aplimat (pp. 127-136). 13 September 2019 retrieved from http://evlm.stuba.sk/APLIMAT2018/proceedings/Papers/0127_Brehovsky_Prihonska.pdf Davydov V. V. (2008). Lekcii po obshhej psikhologii [in Russian: Lectures in General Psychology]. Moscow: Academia. Eizenberg, M. M., & Zaslavsky, O. (2003). Cooperative problem solving in combinatorics: the inter-relations between control processes and successful solutions. The Journal of Mathematical Behavior, 22(4), 389-403. https://doi.org/10.1016/j.jmathb.2003.09.001 English, L. D. (1991). Young children's combinatoric strategies. Educational studies in Mathematics, 22(5), 451-474. https://doi.org/10.1007/BF00367908 English, L. D. (1993). Children's strategies for solving two-and three-dimensional combinatorial problems. Journal for research in Mathematics Education, 255-273. https://doi.org/10.2307/749347 English, L. D. (2005). Combinatorics and the development of children's combinatorial reasoning. In Exploring probability in school (pp. 121-141). Springer, Boston, MA. https://doi.org/10.1007/0-387-24530-8_6 Fischbein, E., & Grossman, A. (1997). Schemata and intuitions in combinatorial reasoning. Educational studies in Mathematics, 34(1), 27-47. Herzog, M., Ehlert, A., & Fritz, A. (2017). Kombinatorikaufgaben in der dritten Grundschulklasse. Journal für Mathematik-Didaktik, 38(2), 263-289. https://doi.org/10.1007/s13138-017-0118-8 Hidayati, Y. M., Sa'dijah, C., & Qohar, S. A. (2019). Combinatorial Thinking to Solve the Problems of Combinatorics in Selection Type. International Journal of Learning, Teaching and Educational Research, 18(2). https://doi.org/10.26803/ijlter.18.2.5 Höveler, K. (2016). Children’s combinatorial counting strategies and their relationship to mathematical counting principles. In Makalah disajikan dalam 13th International Congress on Mathematical Education Hamburg (pp. 231-245). Dortmund: TU Dortmund. 1 September 2019 retrieved from https://www.mathematik.tu-dortmund.de/sites/karina-hoeveler/download/TSG17_PA_Hoeveler.pdf Höveler, K. (2017). Children’s combinatorial counting strategies and their relationship to conventional mathematical counting principles. In Teaching and learning discrete mathematics Worldwide: Curriculum and research (pp. 81-92). Springer, Cham. https://doi.org/10.1007/978-3-319-70308-4_6 Inhelder, B., & Piaget, J. (1969). The psychology of the child. New York: Basic Books. Krekić-Pinter, V., Ivanović, J., Namestovski, Ž., & Major, L. (2015). Strategy and Methods for Solving Combinatorial Problems in Initial Instruction of Mathematics. International Journal of Modern Education Research, 2(6), 77-87. 30 August 2019 retrieved from http://article.aascit.org/file/pdf/9100785.pdf Krpec, R. (2014). The development of combinatorial skills of the lower primary school pupils through organizing the sets of elements. ACTA MATHEM ATICA 17, 103. 09 September 2019 retrieved from http://www.nmk.fpv.ukf.sk/2014/proceedings/13_krpec_fulltext.pdf Maher C. A., Yankelewitz D. (2011). Representations as tools for building arguments. In Combinatorics and Reasoning. Representing, justifying and building isomorphisms (pp. 17-25). Dordrecht, Springer Netherlands. https://doi.org/10.1007/978-94-007-0615-6_3 Palmér, H., & van Bommel, J. (2016). Exploring the role of representations when young children solve a combinatorial task. ICT in mathematics education: the future and the realities, 47. 08 September 2019 retrieved from http://ncm.gu.se/media/smdf/Published/No11_Madif10/047056_madif_001_palmer.pdf Palmér, H., & van Bommel, J. (2018). The role of and connection between systematization and representation when young children work on a combinatorial task. European Early Childhood Education Research Journal, 26(4), 562-573 Poddiakov, A. N. (2011). Multivariable objects for stimulation of young children's combinatorial experimentation and causal-experimental thought. Psychology in Russia, 4, 397. https://doi.org/10.11621/pir.2011.0027 Temnikova M. (2018). Combinatorial mathematical tasks in the education in mathematics for grades 1-4. European Scientific Journal, 2, 46-55. https://doi.org/10.19044/esj.2018.c5p18 van Bommel, J., & Palmér, H. (2017). Paper or and digital: A study on combinatorics in preschool class. In NORMA17 The Eighth Nordic Conference on Mathematics Education, Stockholm, 30 May–2 June 2017. Svensk förening för MatematikDidaktisk Forskning-SMDF. 13 September 2019 retrieved from http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A1181427&dswid=7604 van Bommel, J., & Palmér, H. (2018). Enhancing young children’s understanding of a combinatorial task by using a duo of digital and physical artefacts. Early years, 1-14. https://doi.org/10.1080/09575146.2018.1501553 White, H. (1984). The development of combinatorial reasoning: the role of cognitive capacity. The journal of genetic psychology, 145(2), 185-193. https://doi.org/10.1080/00221325.1984.10532266 Zak A. (2004). Myshlenie mladshego shkol’nika [in Russian: Thinking of the younger school student]. St. Peterburg: sodeystvije. Zak A. (2016). Razvitie avtorskogo myshlenia u mladshih shkol’nikov [in Russian: Development of author’s thinking in younger schoolchildren]. Moscow: Biblio-Globus.
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Details

Primary Language English
Authors

Anatoly Zak This is me

Publication Date January 15, 2020

Cite

APA Zak, A. (n.d.). Improving combinatorial actions in children of 9 years. İlköğretim Online324-332. https://doi.org/10.17051/ilkonline.2020.644570
AMA Zak A. Improving combinatorial actions in children of 9 years. İOO.:324-332. doi:10.17051/ilkonline.2020.644570
Chicago Zak, Anatoly. “Improving Combinatorial Actions in Children of 9 Years”. İlköğretim Onlinen.d., 324-32. https://doi.org/10.17051/ilkonline.2020.644570.
EndNote Zak A Improving combinatorial actions in children of 9 years. İlköğretim Online 324–332.
IEEE A. Zak, “Improving combinatorial actions in children of 9 years”, İOO, pp. 324–332, doi: 10.17051/ilkonline.2020.644570.
ISNAD Zak, Anatoly. “Improving Combinatorial Actions in Children of 9 Years”. İlköğretim Online. n.d. 324-332. https://doi.org/10.17051/ilkonline.2020.644570.
JAMA Zak A. Improving combinatorial actions in children of 9 years. İOO.;:324–332.
MLA Zak, Anatoly. “Improving Combinatorial Actions in Children of 9 Years”. İlköğretim Online, pp. 324-32, doi:10.17051/ilkonline.2020.644570.
Vancouver Zak A. Improving combinatorial actions in children of 9 years. İOO. :324-32.