Teaching The Order of Operations Topic to Fourth-Graders Using Code.org

Abstract

Coding education has been included in the education programs of many countries and is taught to students in schools or outside of school hours to gain them learning outcomes. This study attempts to use coding as a context for mathematical learning at grade level 4 to support and enhance students’ mathematics learning. It examines the codes that emerged as a result of the order of operations topic learning process with coding. A case study approach was used in the study, and participants consist of three fourth-grade students with high, medium, and low achievements in mathematics. The data were collected through video records, photographs, worksheets, and observation notes and analyzed using a constant comparative coding method. In the applications, the participants first learned coding through the code.org platform. Then the expressions from the order of operations were studied with coding. As a result of data analysis, the codes were merged under the themes of code.org, student, and mathematical process. The analysis results showed that this coding activity enabled students to learn through modeling by concretizing the subject and developed their mathematical competencies by participating in many cognitive skills such as reasoning, analyzing, exploring, and verifying. Besides, it was found that problem-solving and generalizing from mathematical thinking skills were used in this learning activity.

Keywords

• coding
• computational thinking
• fourth-graders
• the order of operations topic

Code.org ile Dördüncü Sınıf Öğrencilerine İşlem Önceliği Konusunun Öğretilmesi

Abstract

Kodlama eğitimi birçok ülkenin eğitim programlarına dâhil edilmiştir ve öğrencilere okul saatlerinde veya okul dışı saatlerde kodlama eğitimi verilmektedir. Bu çalışma, dördüncü sınıf öğrencilerinin matematik öğrenimini desteklemek ve geliştirmek için kodlamayı bir bağlam olarak kullanmayı amaçlamaktadır. Çalışmada, işlem önceliği konusunun kodlama ile öğretilmesi süreci incelenmektedir. Durum çalışması deseninde gerçekleştirilen araştırmanın katılımcıları üç dördüncü sınıf öğrencisinden oluşmaktadır. Veriler video kayıtları, fotoğraflar, çalışma yaprakları ve gözlem notları aracılığıyla toplanmış ve karşılaştırmalı analiz yöntemi kullanılarak analiz edilmiştir. Uygulamalarda katılımcılar önce code.org platformu üzerinde kodlama yapmayı öğrenmiş, daha sonra işlem önceliği konusu kodlama ile çalışılmıştır. Verilerin analizi sonucunda ortaya çıkan kodlar; code.org, öğrenci ve matematiksel süreç olmak üzere üç temada toplanmıştır. Analiz sonuçları, bu kodlama etkinliğinin konuyu somutlaştırdığını, öğrencilerin modelleme yoluyla öğrenmelerini sağladığını, akıl yürütme, analiz etme, keşfetme, doğrulama gibi birçok bilişsel etkinlikte bulunarak matematiksel yeterliliklerini geliştirdiğini göstermiştir. Ayrıca öğrencilerin bu öğrenme etkinliğinde matematiksel düşünme süreçlerinden genelleme yapma ve problem çözme becerilerini kullandıkları tespit edilmiştir.

Keywords

• bilgi işlemsel düşünme
• dördüncü sınıf öğrencileri
• işlem önceliği konusu
• kodlama

References

1. Arfe, B., Vardanega, T., & Ronconi, L. (2020). The effects of coding on children's planning and inhibition skills. Computers & Education, 148, 103807. https://doi.org/10.1016/j.compedu.2020.103807
2. Barr, D., Harrison, J., & Conery, L. (2011). Computational thinking: A digital age skill for everyone. Learning & Leading with Technology, 38(6), 20-23.
3. Benton, L., Hoyles, C., Kalas, I., & Noss, R. (2017). Bridging primary programming and mathematics: Some findings of design research in England. Digital Experiences in Mathematics Education, 3(2), 115–138. https://doi.org/10.1007/s40751-017-0028-x
4. Bernardo, M. A., & Morris, J. D. (1994). Transfer effects of a high school computer programming course on mathematical modeling, procedural comprehension, and verbal problem solution. Journal of Research on Computing in Education, 26(4), 523-536. https://doi.org/10.1080/08886504.1994.10782108
5. Blando, J. A., Kelly, A. E., Schneider, B. R., & Sleeman, D. (1989). Analyzing and modeling arithmetic errors. Journal of Research in Mathematics Education, 20(3), 301- 308. https://www.jstor.org/stable/749518
6. Bocconi, S., Chioccariello, A., Dettori, G., Ferrari, A., & Engelhardt, K. (2016). Developing computational thinking in compulsory education–Implications for policy and practice. ). In Kampylis, P., & Punie, Y.(Eds.). Publications Office of the European Union.
7. Brennan, K., & Resnick, M. (2012). New frameworks for studying and assessing the development of computational thinking. In Proceedings of the 2012 annual meeting of the American educational research association (vancouver: Canada). http://scratched.gse.harvard.edu/ct/files/AERA2012.pdf
8. Bybee, R. W. (2013). The case for STEM education, challenges and opportunities. NSTA Press.

9. Calder, H. & Rhodes, K. (2021). Coding and learning mathematics: How did collaboration help the thinking? In Y. H. Leong, B. Kaur, B. H. Choy, J. B. W. Yeo, & S. L Chin (Eds.), Excellence in Mathematics Education: Foundations and Pathways (Proceedings of the 43 rd annual conference of the Mathematics Education Research Group of Australasia), pp. 139-146. Singapore: MERGA.
10. Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (second edition). Sage publications.
11. Creswell, J. W., Hanson, W. E., Clark Plano, V. L., & Morales, A. (2007). Qualitative research designs: Selection and implementation. The counseling psychologist, 35(2), 236-264. https://doi.org/10.1177/0011000006287390
12. Creswell, J. & Miller, D. L. (2000). Determining validity in qualitative inquiry. Theory Into Practice, 39(3), 124-130. https://doi.org/10.1207/s15430421tip3903_2
13. Di Lieto, M. C., Inguaggiato, E., Castro, E., Cecchi, F., Cioni, G., Dell’Omo, M., … Dario, P. (2017). Educational robotics intervention on executive functions in preschool children: A pilot study. Computers in Human Behavior, 71, 16– 23. https://doi.org/10.1016/j.chb.2017.01.018
14. Falloon, G. (2016). An analysis of young students’ thinking when completing basic coding tasks using Scratch Jnr. on the iPad. Journal of Computer Assisted Learning, 32(6), 576–593. https://doi.org/10.1111/jcal.12155
15. Fessakis, G., Gouli, E., & Mavroudi, E. (2013). Problem solving by 5–6 years old kindergarten children in a computer programming environment: A case study. Computers & Education, 63, 87-97. https://doi.org/10.1016/j.compedu.2012.11.016
16. Florez, F. B., Casallas, R., Hernandez, M., Reyes, A., Restrepo, S., & Danies, G. (2017). Changing a generation’s way of thinking: Teaching computational thinking through programming. Review of Educational Research, 87(4), 834–860. https://doi.org/10.3102/0034654317710096.
17. Gadanidis, G. (2014). Young children, mathematics and coding: A low floor, high ceiling, wide walls learning environment. In D. Polly (Ed). Cases on technology integration in mathematics education (p. 312-344). IGI Global.
18. Gadanidis, G. (2015). Coding as a Trojan Horse for mathematics education reform. Journal of Computers in Mathematics and Science Teaching, 34(2), 155-173.
19. Geist, E. (2016). Robots, programming and coding, oh my!. Childhood Education, 92(4), 298-304. https://doi.org/10.1080/00094056.2016.1208008
20. Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. Hawthorne, NY: Aldine.
21. Glidden, P. L. (2008). Prospective elementary teachers’ understanding of order of operations. School Science and Mathematics, 108(4), 130-136. https://doi.org/10.1111/j.1949-8594.2008.tb17819.x
22. Hayes, J., & Stewart, I. (2016). Comparing the effects of derived relational training and computer coding on intellectual potential in school‐age children. British Journal of Educational Psychology, 86(3), 397-411. https://doi.org/10.1111/bjep.12114
23. Holmes, K., Prieto-Rodriguez, E., Hickmott, D., & Berger, N. (2018). Using coding to teach mathematics : results of a pilot project. Integrated Education For The Real World: 5Th International Stem In Education Conference: Post-Conference Proceedings, Queensland University Of Technology, Brisbane, Australia, 21St To 23Rd November 2018, 152-158.
24. Hoyles, C. & Noss, R. (1987). Synthesizing mathematical conceptions and their formalization through the construction of a Logo‐based school mathematics curriculum. International Journal of Mathematical Education in Science and Technology, 18(4), 581-595. https://doi.org/10.1080/0020739870180411
25. Hoyles, C., & Noss, R. (1992). A pedagogy for mathematical microworlds. Educational studies in Mathematics, 23(1), 31–57.
26. Hutchison, A., Nadolny, L., & Estapa, A. (2016). Using coding apps to support literacy instruction and develop coding literacy. The Reading Teacher, 69(5), 493-503. https://doi.org/10.1002/trtr.1440
27. Kalelioglu, F. (2015). A new way of teaching programming skills to K-12 students: Code.org. Computers in Human Behavior, 52, 200-210. https://doi.org/10.1016/j.chb.2015.05.047
28. Kalelioglu, F., & Gülbahar, Y. (2014). The effects of teaching programming via Scratch on problem solving skills: A discussion from learners' perspective. Informatics in Education, 13(1), 33-50.
29. Linchevski, L., & Livneh, D. (1999). Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40(2), 173–196. https://doi.org/10.1023/A:1003606308064
30. Lincoln, Y. S., & Guba, E. G. (1986). But is it rigorous? Trustworthiness and authenticity in naturalistic evaluation. New directions for evaluation, 30, 73-84.
31. Ministry of National Education [MoNE], (2018). Mathematics curriculum (primary and secondary school grades 1, 2, 3, 4, 5, 6, 7 and 8). Ankara.
32. Miller, J. (2019). STEM education in the primary years to support mathematical thinking: Using coding to identify mathematical structures and patterns. ZDM, 51(6), 915-927. https://doi.org/10.1007/s11858-019-01096-y
33. Moreno-León, J., Robles, G., & Román-González, M. (2016). Code to learn: Where does it belong in the K-12 curriculum? Journal of Information Technology Education, 15, 283–303. http://www.informingscience.org/Publications/3521
34. Moreno León, J., Román González, M., García Perales, R., & Robles, G. (2021). Programar para aprender Matemáticas en 5º de Educación Primaria: implementación del proyecto ScratchMaths en España. Revista de Educación a Distancia (RED), 21(68). https://doi.org/10.6018/red.485441
35. Palumbo, D. B., & Michael Reed, W. (1991). The effect of BASIC programming language instruction on high school students’ problem solving ability and computer anxiety. Journal of Research on Computing in Education, 23(3), 343-372. https://doi.org/10.1080/08886504.1991.10781967
36. Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. Basic Books. http://www.medientheorie.com/doc/papert_mindstorms.pdf
37. Popat, S., & Starkey, L. (2019). Learning to code or coding to learn? A systematic review. Computers & Education, 128, 365-376. https://doi.org/10.1016/j.compedu.2018.10.005
38. 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. https://doi.org/10.1007/s11251-017-9421-5
39. Resnick, M., Maloney, J., Monroy-Hernandez, A., Rusk, N., Eastmond, E., Brennan, K., et al. (2009). Scratch: Programming for all. Communications of the ACM, 52(11), 60–67. https://doi.org/10.1145/1592761.1592779.
40. Roman-Gonzalez, M., Perez-Gonzalez, J. C., & Jimenez-Fernandez, C. (2017). Which cognitive abilities underlie computational thinking? Criterion validity of the computational thinking test. Computers in Human Behavior, 72, 678–691. https://doi.org/10.1016/j.chb.2016.08.047
41. Saez-Lopez, J. M., Roman-Gonzalez, M., & Vazquez-Cano, E. (2016). Visual programming languages integrated across the curriculum in elementary school: A two year case study using “Scratch” in five schools. Computers & Education, 97, 129–141. https://doi.org/10.1016/j.compedu.2016.03.003
42. Savard, A., & Highfeld, K. (2015). Teachers’ talk about robotics: Where is the mathematics? In M. Marshman, V. Geiger, & A. Bennison (Eds.), Proceedings of the 38th annual conference of the mathematics education research group of Australasia (pp. 540–546). Sunshine Coast: MERGA.
43. Taylor, M., Harlow, A., & Forret, M. (2010). Using a computer programming environment and an interactive whiteboard to investigate some mathematical thinking. Procedia-Social and Behavioral Sciences, 8, 561-570. https://doi.org/10.1016/j.sbspro.2010.12.078
44. Vanderbeek, G. (2007). Order of operations and RPN. MAT Exam Expository Papers, 46. https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1045&context=mathmidexppap
45. Wing, J. M. (2006). Computational thinking. Commun. ACM, 49, 33–35. https://doi.org/10.1145/1118178.1118215
46. Wing, J. M. (2008). Computational thinking and thinking about computing. Philosophical Transactions. Series A, Mathematical. Physical, and Engineering Sciences, 366(1881), 3717-3725. http://dx.doi.org/10.1098/rsta.2008.0118