Algorithm-based mathematics from the perspective of gifted students: A case study

Abstract

An algorithm in mathematics is the design of a simple, clear, and specific order of the way to solve a problem. Designing an algorithm in accordance with the rules on the solution of a well-defined sample problem will enable students to consciously manage their own learning processes in solving the problem. The study aims to prepare algorithmic activities in accordance with the learning outcomes of the 4th-grade mathematics curriculum and to obtain the opinions of gifted students about these activities. The research was conducted using a case study design, one of the qualitative research designs. The study group consisted of 17 students studying at the 4th grade level of Science and Art Centre (SAC) in Afyonkarahisar province located in the west of Turkiye. The algorithmic activities were prepared with Lucidchart, a Web 2.0 tool that can prepare algorithms in a digital environment. In order to obtain the students' opinions about the activities carried out, a semi-structured interview form was prepared. The students were interviewed before and after the implementation of the activities. In the interview form, students' knowledge levels about algorithms were analyzed with Wilcoxon Signed Rank test. Students' algorithmic thinking awareness and their views on algorithm-based mathematics activities were analyzed by content analysis. As a result of the data analysis, while the students' knowledge level of the algorithm was low before the application, it increased to a high level after the application and revealed a significant difference. Accordingly, students were able to explain algorithmic thinking skills by producing many codes (rhythmic counting, calculating each path, Lego, experiment, artificial intelligence, instruction, etc.). The use of algorithms in mathematical activities was found to be fun, instructive, facilitating, interesting, revealing of prior knowledge, endearing, and a guide to mathematics. On the other hand, the use of algorithms was found to be tiring and boring due to its limitations in terms of step-by-step progress and immediate achievement of the result. The use of algorithms in mathematics teaching can improve students' algorithmic thinking skills and contribute to the development of their mathematical skills. In addition, it is suggested that these activities should be disseminated through the use of Web 2.0 tools.

Keywords

• Mathematics education
• Algorithm
• Gifted student
• Student opinion

Özel Yetenekli Öğrencilerin Gözünden Algoritma Temelli Matematik: Bir Durum Çalışması

Abstract

Araştırmanın amacı, 4. sınıf matematik dersi öğretim programında yer alan kazanımlara uygun algoritmik etkinlikler hazırlamak ve bu etkinliklere ilişkin özel yetenekli öğrencilerin görüşlerini almaktır. Araştırma nitel araştırma desenlerinden durum çalışması deseni ile yürütülmüştür. Çalışma grubunu Bilim ve Sanat Merkezi (BİLSEM) 4. sınıf düzeyinde öğrenim gören 17 öğrenci oluşturmaktadır. Yürütülen etkinliklere yönelik öğrencilerin görüşlerinin alınabilmesi için yarı yapılandırılmış görüşme formu hazırlanmıştır. Görüşme sorularına ait veriler içerik analiziyle çözümlenmiştir. Algoritmik etkinlikler dijital ortamda algoritma hazırlanabilecek bir Web 2.0 aracı olan Lucidchart ile hazırlanmıştır. Etkinlikler uygulanmadan önce ve uygulandıktan sonra öğrencilerle görüşmeler yapılmıştır. Verilerin analizi sonucunda, yapılan ön görüşmelerde öğrencilerin algoritma ile ilgili bilgi düzeyleri sınırlı düzeydeyken son görüşmelerde bilgi düzeylerinin arttığı görülmüştür. Buna bağlı olarak öğrenciler çok sayıda kod üreterek (ritmik sayma, her yolu hesaplamak, lego, deney, yapay zekâ, yönerge vb.) algoritmik düşünme becerisini açıklayabilmiştir. Matematik etkinliklerinde algoritma kullanmanın eğlenceli, öğretici, kolaylaştırıcı, ilginç, ön bilgileri açığa çıkarıcı, matematiği sevdirici ve yönlendirici olduğu belirlenmiştir. Bunun yanında algoritmanın adım adım ilerleme ve hemen sonuca ulaşma konusunda sınırlılıklarından dolayı yorucu ve sıkıcı olduğu ortaya çıkmıştır. Matematik derslerinde algoritma kullanılması öğrencilerin algoritmik düşünme becerilerini geliştireceği gibi matematiksel becerilerinin gelişimine de katkı sunabilir. Ayrıca bu etkinliklerin Web 2.0 araçları kullanılarak yaygınlaştırılması önerilmektedir.

Keywords

• Matematik eğitimi
• Algoritma
• Özel yetenekli öğrenci
• Öğrenci görüşleri

References

1. Aho, A. V. (2012). Computation and computational thinking. Computer Journal, 55(7), 832-835. https://doi.org/10.1093/comjnl/bxs074
2. Alkan, A. (2019). The effect of code game lab software on the level of problem solving skills in programming language teaching. Mehmet Akif Ersoy University Journal of Education Faculty, 50, 480-493. https://doi.org/10.21764/maeuefd.486061
3. Atabay, E. (2019). Okul öncesi dönem çocuklarına oyunlaştırma ile algoritma eğitimi verilmesi [Giving algorithm education with the gamification to preschool period children]. Master thesis. Süleyman Demirel University, Isparta.
4. Ataman, A. (2000). Üstün yetenekli çocuklar. Özel eğitime giriş [Gifted children. Introduction to special education]. Anadolu Üniversitesi Yayınları.
5. Avcu, Y. E., & Yaman, Y. (2022). Effectiveness of the differentiated instructional design for value education of gifted: A mixed study. Journal of Gifted Education and Creativity, 9(1), 1-23.
6. Brown, W. (2015). Introduction to algorithmic thinking. Retrieved from: https://raptor.martincarlisle.com/Introduction%20to%20Algorithmic%20Thinking.doc
7. Bundy, A. (2007). Computational thinking is pervasive. Retrieved from: http://www.inf.ed.ac.uk/publications/online/1245.pdf
8. Can, A. (2019). SPSS ile bilimsel araştırma sürecinde nicel veri analizi [Quantitative data analysis in scientific research process with SPSS] (7th Edition). Pegem Akademi.

9. Coufal, P., Hornik, T., Hubalovsky, S., & Musilek, M. (2017). Simulation of the automatic parking assist system as a method of the algorithm development thinking. International Journal of Education and Information Technologies, 11, 37-43.
10. Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Sage Publications.
11. Copur, K. D. (2020). Algoritmik düşünme öğretimi sürecinde web 2.0 araçlarının kullanımı [Use of web 2.0 tools in algorithmic thinking teaching process]. Master thesis. Erciyes University, Kayseri.
12. Dasso, A., Funes, A., Riesco, D. E., Montejano, G. A., Peralta, M., & Salgado, C. (2005, April 14-15). Teaching programming. I Jornadas de Educación en Informática y TICs en Argentina, Buenos Aires, República Argentina.
13. Demir, U., & Cevahir, H. (2020). Investigation of the relationship between algorithmic thinking capability and problem solving skills: The case of vocational and technical anatolian high school. Kastamonu Education Journal, 28(4), 1610-1619. https://doi.org/10.24106/kefdergi.4179
14. Dogan, U., & Kert, S. B. (2016). Bilgisayar oyunu geliştirme sürecinin, ortaokul öğrencilerinin eleştirel düşünme becerilerine ve algoritma başarılarına etkisi. Bogazici University Journal of Education, 33(2), 21-42.
15. Fernández, E., García, T., Arias-Gundín, O., Vázquez, A., & Rodriguez, C. (2017). Identifying gifted children: Congruence among diferent IQ measures. Frontiers in Psychology, 8(1239), 1-10. https://doi.org/10.3389/fpsyg.2017.01239
16. Galezer, J., Beeri, C., Harel, D., & Yehudai, A. (1995). A high-school program in computer-science. Computer, 28(10), 73-80. https://doi.org/10.1109/2.467599
17. Gardner, H. E. (2011). Leading minds: An anatomy of leadership. Hachette UK.
18. Guler, C. (2021). Algorithmic thinking skills without computers for prospective computer science teachers. Kuramsal Eğitimbilim Dergisi [Journal of Theoretical Educational Science], 14(4), 570-585.
19. Guven, Y. (2018). 5. sınıf bilişim teknolojileri ve yazılım dersi öğretmen rehber kitabı [5th grade information technologies and software course teacher guide book], 1, 163-164, Ministry of National Education.
20. Hamdaoui, N., Khalidi Idrissi, M., & Bennani, S. (2015). “Resorting to IMS-LD to standardize the learning process of Serious Game design in education,” International Journal of Education and Information Technologies, 9, 36-45.
21. Hromkovič, J. (2006, November 7-11). Contributing to general education by teaching informatics. International Conference on Informatics in Secondary Schools-Evolution and Perspectives, Vilnius, Lithuania.
22. Hsu, C. C., & Wang, T. I. (2018). Applying game mechanics and student-generated questions to an online puzzle-based game learning system to promote algorithmic thinking skills. Computers & Education, 121, 73-88. https://doi.org/10.1016/j.compedu.2018.02.002
23. Hubalovsky, S., & Korinek, O. (2015). Evaluation of algorithmic thinking of students using control testing environment. International Journal of Education and Information Technologies, 9, 205-208.
24. Karakus, F., & Baki, A. (2020). From chaotic to order: Using chaos game in mathematics teaching. Turkish Journal of Computer and Mathematics Education. Advanced publication. http://doi.org/10.16949/turkbilmat.541136
25. Kodla & Oyna. (2022, April 15). ALGORİTMA nedir sorusuna en güzel örnek... [The best example of what is ALGORITHM] [Video]. YouTube. https://youtu.be/xoqQKFtfzvM
26. Komarudin, K., Suherman, S., Puspita, L., Arrafiansyah, R., & Hasanah, U. (2020). Program course lab 2.4 mathematics learning media for increasing of creativity domain at Higher Order Thinking Skills (HOTS). Journal of Gifted Education and Creativity, 7(3), 131-136.
27. Kordaki, M. (2013). High school computing teachers' beliefs and practices: A case study. Computers & Education, 68, 141-152. https://doi.org/10.1016/j.compedu.2013.04.020
28. Korkmaz, O. (2012). The impact of critical thinking and logico-mathematical intelligence on algorithmic design skills. Journal of Educational Computing Research, 46(2), 173-193.
29. Korkmaz, O., Cakır, R., Ozden, M. Y., Oluk, A., & Sarioglu, S. (2015). Investigation of individuals’ computational thinking skills in terms of different variables. Ondokuz Mayis University Journal of Faculty of Education, 34(2), 68-87.
30. Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. University of Chicago Press.
31. Kucuk Demir, B., & Duzen Karatepe, U. (2022). Investigation of the effects of mathematics-centered stem activities on students’ creative thinking skills and student opinions. Journal of Gifted Education and Creativity, 9(1), 25-41.
32. Kucukkara, M. F. (2019). Etkinlik temelli algoritma eğitiminin 5-6 yaş çocuklarının problem çözme becerisine etkisi [The effect of activity based algorithm education on the problem-solving skills of 5-6 years old children]. Master thesis. Bolu Abant İzzet Baysal University, Bolu.
33. Mayer, R. E. (1981). The psychology of how novices learn computer-programming. Computing Surveys, 13(1), 121-141.
34. McMillan, J. H. (2000). Educational research: Fundamentals for consumer. Longman.
35. McMillan, J. H., & Schumacher, S. (2014). Research in education: Evidence-based inquiry (7th ed.). Pearson Education Inc.
36. Miller, R. C. (1990). Discovering mathematical talent. Council for Exceptional Children, ERIC Clearinghouse on Disabilities and Gifted Education. ERIC Document Reproduction Service No: ED 321487.
37. Ministry of National Education [MoNE] (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics curriculum (primary and secondary school grades 1, 2, 3, 4, 5, 6, 7 and 8]. Retrieved from: https://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329
38. Ministry of National Education [MoNE] (2021). Çerçeve programlar: Bilim ve sanat merkezleri Matematik dersi öğretim programı [Framework programmes: Science and art centres Mathematics curriculum]. Retrieved from: Mebbis/Bilsem Modülü: https://bilsem.meb.gov.tr/BLS00002.aspx
39. Navas-Sánchez, F. J., Carmona, S., Alemán-Gómez, Y., Sánchez-González, J., Guzmán-de-Villoria, J., Franco, C., et al (2016). Cortical morphometry in frontoparietal and default mode networks in math-gifted adolescents. Human Brain Mapping, 37(5), 1893-1902.
40. Oluk, A., Korkmaz, O., & Oluk, H. A. (2018). Effect of Scratch on 5th graders’ algorithm development and computational thinking skills. Turkish Journal of Computer and Mathematics Education, 9(1), 54-71.
41. Ozlu-Unlu, O., Arslanoglu, A., & Yikmis, A. (2022). Özel gereksinimli bireylere matematik öğretiminde somut-yarı somut-soyut öğretimin kanıta dayalı uygulama olarak belirlenmesi [Identifying concrete-representational-abstract instruction as an evidence-based practice in teaching mathematics to individuals with special needs]. Ankara University Faculty of Educational Sciences Journal of Special Education, 23(4), 931-960. https://doi.org/10.21565/ozelegitimdergisi.938438
42. Papadakis, S., & Kalogiannakis, M. (2019). Evaluating a course for teaching introductory programming with Scratch to pre-service kindergarten teachers. International Journal of Technology Enhanced Learning, 11(3), 231-246. https://doi.org/10.1504/Ijtel.2019.100478
43. Patton, M. Q. (2002). Qualitative research and evaluation methods. Sage.
44. Pfeifer, S. I. (2012). Current perspectives on the indentifcation and assessment of gifted students. Journal of Psychoeducational Assessment, 30(1), 3-9. https://doi.org/10.1177/0734282911428192
45. Polya, G. (1962). Mathematical discovery: On understanding, learning and teaching problem solving (Vol I). Wiley Press.
46. Psycharis, S., & Kallia, M. (2017). The effects of computer programming on high school students’ reasoning skills and mathematical self-efficacy and problem solving. Instructional Science, 45(5), 583-602.
47. Renzulli, J. S. (2012). Reexamining the role of gifted education and talent development for the 21st Century: a four-part theoretical approach. Gifted Child Quarterly, 56, 150-159. https://doi.org/10.1177/0016986212444901
48. Saeli, M., Perrenet, J., Jochems, W. M., & Zwaneveld, B. (2011). Teaching programming in secondary school: a pedagogical content knowledge perspective. Informatics in Education, 10(1), 73-88.
49. Sonmez, D. (2018). İlkokul matematik öğretiminde öğrencilerin duyuşsal farkındalıklarını artırmada matematiksel oyunların kullanımı [The use of mathematical games to improve students’ affective awareness in primary school mathematics teaching]. Master thesis. Yıldız Teknik University, İstanbul.
50. Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics?. Journal of Secondary Gifted Education, 17(1), 20-36.
51. Talu, N. (1999). Çoklu zekâ kuramı ve eğitime yansımaları [Multiple intelligence theory and its reflections on education]. Hacettepe University Journal of Education, 15, 164-172.
52. The Scientific and Technological Research Council of Türkiye [STRCT] (2022). Ortaokul Öğrencileri Araştırma Projeleri Yarışması Proje Rehberi 2204-B [Secondary school students research projects competition project guide 2204-B], Retrieved from: https://tubitak.gov.tr/sites/default/files/2750/ortaokul_proje_rehberi_2022_v3.pdf
53. Topal, A. (2015). Ortaokul 6. sınıf öğrencilerinin standart bir algoritmayla çözülebilen ve çözülemeyen problemlerde kullandıkları matematiksel düşüncelerinin incelenmesi [The examination of mathematical reasoning used by 6th grade students to solve process-constrained and process-open questions]. Master thesis. Gaziantep University, Gaziantep.
54. Umay, A. (2003). Matematiksel muhakeme yeteneği [Mathematical reasoning ability]. Hacettepe University Journal of Education, 24, 234-243.
55. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2021). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim [Elementary and Middle School Mathematics-Teaching Developmentally] (S. Durmuş, Çev. Ed.). Nobel Yayıncılık.
56. Wing, J. M. (2006). Computational thinking. Communications of the ACM, 49(3), 33-35. https://doi.org/10.1145/1118178.1118215
57. Yildirim, B. (2019). Ortaokul 6. Sınıf öğrencilerinin kesirlerle bölme algoritması oluşturma sürecinin incelenmesi [An investigation into the development process of the division algorithm in fractions by 6'th grade students’]. Master thesis. Bolu Abant İzzet Baysal University, Bolu.
58. Yildirim, C. (2018). Matematiksel düşünme [Mathematical thinking] (14th Edition). Remzi Kitabevi.
59. Yildirim A., & Simsek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in social science] (6th Edition). Seçkin Yayıncılık.
60. Yildiz, M. N. (2020). Algoritma öğretiminde kutu oyunu kullanılmasının ilkokul öğrencilerinin algoritma başarısına etkisinin incelenmesi [Investigation of algorithm achievements on primary school students by using the board game in algorithm teaching]. Master thesis. Bahçeşehir University, İstanbul.
61. Yi, T., & Mogilski, J. (2015). “Customizing course redesign and flipped classroom models to improve learning environment,” International Journal of Education and Information Technologies, 9, 135-142.
62. Yurtbakan, E., & Aydogdu-Iskenderoglu, T. (2023). The effect of STEM for gifted activities’ mathematical problem-posing skills of gifted primary school students. Journal of Gifted Education and Creativity,10(2), 97-112.
63. Yunkul, E., Durak, G., Cankaya, S., & Misirli, Z. A. (2017). The effects of scratch software on students’ computational thinking skills. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 11(2), 502-517. https://doi.org/10.17522/balikesirnef.373424