Education Quarterly Reviews
Published: 15 December 2022
8th Graders’ Interpretation of Equal Sign in Scratch: Pan Balance Activities
Nazım Özkan, Meriç Özgeldi, Erman Uzun
Ministry of Education (Turkey), Mersin University (Turkey)
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Keywords: Equal Sign, Scratch, Programming, Algebra Teaching
The purpose of this study was to investigate how the 8th graders interpreted the equal sign in the pan balance activities they created on Scratch. Five eighth graders (4 girls and 1 boy) in Turkey participated in this study. Case study was employed as a qualitative research method. Data was gathered through the Scratch files created by the students and the think-aloud protocol interviews with them. The questions used in the activities were prepared in accordance with the test created by Matthews et al. (2012). For data analysis, content and descriptive analysis methods were employed. Findings showed that participants interpreted the operational questions as operational and relational questions as relational through using Scratch. Another significant finding emerged in Scratch activities was the fact that in order for the code block to provide an equation, the pan balance was supposed to balance. Employing Scratch in the class teachings may provide variety in learning environments for teaching of equal sign.
Akkan, Y. (2009). İlköğretim öğrencilerinin aritmetikten cebire geçiş süreçlerinin incelenmesi [Investigation of the primary school students’ transition processes from arithmetic to algebra] [Unpublished doctoral thesis]. Karadeniz Technical University.
Akkaya, R., & Durmuş S. (2006). İlköğretim 6-8. sınıf öğrencilerinin cebir öğrenme alanındaki kavram yanılgıları [Misconceptions of elementary school students in grades 6-8 on learning algebra]. Hacettepe University Journal of Education, 31(31), 1-12.
Akyüz, G., & Hangül, T. (2014). 6. Sınıf öğrencilerinin denklemler konusunda sahip oldukları yanılgıların giderilmesine yönelik bir çalışma [A study on overcoming misconceptions of 6th graders about equations]. Journal of Theoretical Educational Science, 7(1), 16-43. http://dx.doi.org/10.5578/keg.6176
Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students' understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9(3), 221-247. https://doi.org/10.1080/10986060701360902
Ar, N. A. (2012, July 11-13). Bilgisayar destekli eğitimde Logo programlama dili [Logo programming language in computer education] [Paper presentation]. International Educational Technology Conference IETC 2012, National Central University, Taoyuan, Taiwan.
Baki, A. (2000). Bilgisayar donanımlı ortamda matematik öğrenme [Learning mathematics within a computer-based environment]. Hacettepe University Journal of Education, 19, 186-193.
Baiduri, B. (2015). Mathematics education students’ understanding of equal sign and equivalent equation. Asian Social Science, 11(25), 15-24. https://doi.org/10.5539/ass.v11n25p15
Baratta, W. (2011). Linear Equations: Equivalence= Success. Australian Mathematics Teacher, 67(4), 6-11.
Behr, M., Erlwanger, S., & Nichols, E. (1980). How children view the equals sign. Mathematics Teaching, 92(1), 13-15.
Byrd, C. E., McNeil, N. M., Chesney, D. L., & Matthews, P. G. (2015). A specific misconception of the equal sign acts as a barrier to children's learning of early algebra. Learning and Individual Differences, 38, 61-67.https://doi.org/10.1016/j.lindif.2015.01.001
Calao, L. A., Moreno-León, J., Correa, H. E., & Robles, G. (2015, September). Developing mathematical thinking with scratch. In European conference on technology enhanced learning (pp. 17-27). Springer, Cham. https://doi.org/10.1007/978-3-319-24258-3_2
Calder, N. (2010). Using Scratch: An integrated problem-solving approach to mathematical thinking. Australian Primary Mathematics Classroom, 15(4), 9-14.
Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Heinemann, Portsmouth.
Çatlak, Ş., Tekdal, M., & Baz, F. Ç. (2015). Scratch yazılımı ile programlama öğretiminin durumu: Bir doküman inceleme çalışması [The status of teaching programming with Scratch: A document review work]. Journal of Instructional Technologies & Teacher Education, 4(3), 13-25.
Çelik, H. S., & Masal, E. (2018). 7. sınıf öğrencilerinin denklem ve eşitlik konusundaki öğrenmelerine öğrenci bileşeni açısından bir bakış [A glance at the equation and equality learning of 7th grade students in terms of student knowledge]. Sakarya University Journal of Education, 8(2), 168-186. https://doi.org/10.19126/suje.418532
Doğan Temur, Ö., & Sancak, G. (2012). Dördüncü sınıf öğrencilerinin eşit ı̇şaretini nasıl algıladıklarının ı̇ncelenmesi [An investigation of how fourth grade students perceive equal sign]. National Education Quarterly Journal of Education and Social Sciences, 194, 240-252.
Erol, O. (2015). Scratch ile programlama öğretiminin bilişim teknolojileri öğretmen adaylarının motivasyon ve başarılarına etkisi [The effects of teaching programming with scratch on pre-service information technology teachers’ motivation and achievement] [Unpublished doctoral thesis]. Anadolu University.
Falkner, K. P., Levi, L., & Carpenter, T. P. (1999). Children's understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6, 232-236. https://doi.org/10.5951/TCM.6.4.0232
Gökdağ, K., Özgeldi, M., & Yakın, İ. (2022). Unveiling students’ explorations of tessellations with Scratch through mathematical aesthetics. International Journal of Mathematical Education in Science and Technology, 1-19. https://doi.org/10.1080/0020739X.2021.2021306
Kakavas, K., & Zacharos, K. (2019). Teaching the concept of angle through programming with Scratch. Educational Journal of the University of Patras UNESCO Chair. https://doi.org/10.26220/une.2946
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317-326. https://doi.org/10.1007/BF00311062
Kilhamn, C., & Bråting, K. (2019, February). Algebraic thinking in the shadow of programming. In Eleventh Congress of the European Society for Research in Mathematics Education (No. 7). Freudenthal Group; Freudenthal Institute; ERME.
Knuth, E. J., Alibali, M. W., McNeil, N. M., Weinberg, A., & Stephens, A. C. (2005). Middle school students' understanding of core algebraic concepts: Equivalence & variable1. ZDM-Mathematics Education, 37(1), 68-76. https://doi.org/10.1007/BF02655899
Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297-312. https://doi.org/10.2307/30034852
Lai, A. F., & Yang, S. M. (2011, September). The learning effect of visualized programming learning on 6 th graders' problem solving and logical reasoning abilities. In 2011 International Conference on Electrical and Control Engineering (pp. 6940-6944). IEEE. https://doi.org/10.1109/ICECENG.2011.6056908
Lewis, C. M., & Shah, N. (2012, February). Building upon and enriching grade four mathematics standards with programming curriculum. In Proceedings of the 43rd ACM technical symposium on Computer Science Education 57-62. https://doi.org/10.1145/2157136.2157156
Matthews, P., Rittle-Johnson, B., McEldoon, K., & Taylor, R. (2012). Measure for measure: What combining diverse measures reveals about children's understanding of the equal sign as an indicator of mathematical equality. Journal for Research in Mathematics Education, 43(3), 316-350. https://doi.org/10.5951/jresematheduc.43.3.0316
Oksuz, C. (2007). Children’s understanding of equality and the equal symbol. International Journal for Mathematics Teaching and Learning, 13, 1-19.
Patton, M. Q. (2018). Nitel araştırma ve değerlendirme yöntemleri [Qualitative research and evaluation methods ] (M. Bütün, & S. B. Demir, Trans.). Ankara: Pegem Akademi.
Rittle-Johnson, B., Matthews, P. G., Taylor, R. S., & McEldoon, K. L. (2011). Assessing knowledge of mathematical equivalence: A construct-modeling approach. Journal of Educational Psychology, 103(1), 85-104. https://doi.org/10.1037/a0021334
Sáez-López, J. M., Román-González, M., & Vázquez-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
Scratch (2017, April 12). Scratch About. Retrieved April 12, 2017, from https://scratch.mit.edu/about/
Steinberg, R. M., Sleeman, D. H., & Ktorza, D. (1991). Algebra students' knowledge of equivalence of equations. Journal for research in mathematics education, 22, 112-121. https://doi.org/10.5951/jresematheduc.22.2.0112
Stephens, A. C., Knuth, E. J., Blanton, M. L., Isler, I., Gardiner, A. M., & Marum, T. (2013). Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings. The Journal of Mathematical Behavior, 32(2), 173-182. https://doi.org/10.1016/j.jmathb.2013.02.001
Şimsek, E., Xenidou-Dervou, I., Karadeniz, I., & Jones, I. (2019). The conception of substitution of the equals sign plays a unique role in students' algebra performance. Journal of Numerical Cognition, 5(1), 24-37. https://doi.org/10.5964/jnc.v5i1.147
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
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed). New Jersey: Pearson Education.
Yaman, H., Toluk, Z., & Olkun, S. (2003). İlköğretim öğrencileri eşit işaretini nasıl algılamaktadırlar? [How the elementary school students would perceive equal sign?]. Hacettepe University Journal of Education, 24, 142-151.
Yıldırım, A., & Şimşek, H. (2013). Nitel araştırma yöntemleri [Qualitative research methods]. Ankara: Seçkin Yayıncılık.
Yıldız, P., & Atay, A. (2019). Ortaokul beşinci sınıf öğrencilerinin eşit işaretine ilişkin anlamaları [Investigating middle school fifth grade students’ understanding of equal sign]. Journal of Ahi Evran University Institute of Social Sciences, 5(2), 426-438. https://doi.org/10.31592/aeusbed.602915