Examining the Quality of the Elementary School Mathematics Tasks Recommended for Distance Education

Year 2023, Volume: 52 Issue: 1, 1 - 32, 30.04.2023

Hande Gülbağcı Dede , Deniz Özen Ünal , Zuhal Yılmaz

https://doi.org/10.14812/cuefd.950622

Abstract

As a result of the COVID-19 pandemic, distance education started at K-12 levels in the spring semester of the 2019-2020 school year. The Ministry of National Education had also published instructional tasks to be used in distance education at all grade levels in order to create mathematics learning opportunities for students and to provide resources for teachers. Well-structured and high-quality instructional tasks play an important role in students' learning mathematics. The aim of this study is to examine the quality of the elementary school mathematics tasks recommended for distance remedial education from multiple perspectives, in particular their cognitive demand levels. A total of 85 tasks focusing on 79 critical objectives in grades 1-4 mathematics were examined using document analysis. Results of this study showed that the majority of the tasks were at low cognitive demand level, cognitive demand levels did not show a balanced distribution, and some tasks had mathematical errors.

Keywords

Cognitive demand, Distance Education, Elementary School, Task

Uzaktan Eğitim için Önerilen İlkokul Matematik Etkinliklerinin Niteliğinin Değerlendirilmesi

Abstract

COVID-19 salgını ile birlikte 2019-2020 akademik yılının bahar döneminden itibaren tüm öğretim kademelerinde uzaktan eğitime geçilmiştir. Milli Eğitim Bakanlığı da öğrencilere matematik öğrenme fırsatları oluşturmak ve öğretmenlere kaynak sağlamak adına tüm sınıf düzeylerinde uzaktan eğitimde kullanılmak üzere öğretim etkinlikleri yayınlanmıştır. İyi yapılandırılmış ve nitelikli öğretim etkinlikleri öğrencilerin matematiği öğrenmesinde önemli bir rol oynamaktadır. Bu çalışmanın amacı da ilkokul matematik dersine yönelik yayınlanmış olan ilkokul matematik etkinliklerinin başta bilişsel istem düzeyi olmak üzere farklı açılardan incelenmesi ve niteliğinin ortaya konmasıdır. Doküman analizi yöntemiyle yürütülen çalışmada 1-4. sınıf düzeyi matematik alanındaki 79 kritik kazanıma ait 85 etkinlik incelenmiştir. Analiz sonucunda etkinliklerin birçoğunun düşük bilişsel istem düzeyinde olduğu, bilişsel istem düzeylerinin dengeli bir dağılım sergilemediği, ve bazı etkinliklerin matematiksel hatalar barındırdığı görülmüştür.

Keywords

Bilişsel istem, Etkinlik, İlkokul, Uzaktan Eğitim

References

• Bailey, D. H., Siegler, R. S., & Geary, D. C. (2014). Early predictors of middle school fraction knowledge. Developmental Science, 17(5), 775–785. https://doi.org/10.1111/desc.12155
• Barlow, A. T., Edwards, C. M., Robichaux-Davis, R., & Sears, R. (2020). Enhancing and transforming virtual ınstruction. Mathematics Teacher: Learning and Teaching PK-12, 113(12), 972–982. https://doi.org/10.5951/MTLT.2020.0283
• Bayazit, I. (2013). Quality of the tasks in the new Turkish elementary mathematics textbooks: The case of proportional reasoning. International Journal of Science and Mathematics Education, 11(3), 651–682. https://doi.org/10.1007/s10763-012-9358-8
• Bingölbali, E., & Özmantar, M. F. (2015). Matematiksel kavram yanılgı: Sebepleri ve çözüm arayışları. E. Bingölbali, & M. F. Özmantar (Ed.), İlköğretimde karşılaşılan matematiksel zorluklar ve çözüm önerileri içinde (5. bs.) (ss. 313–348). Pegem Yayınevi.
• Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of railside school. Teachers College Record, 110, 8–9.
• Boston, M. D. (2012). Assessing instructional quality in mathematics. The Elementary School Journal, 113, 76–104. https://doi.org/10.1086/666387
• Boston, M. D. (2017). Instructional quality assessment classroom observation tool: Rater packet. Unpublished document.
• Boston, M., Candela, A. G., & Dixon, J. K. (2019). Making sense of mathematics for teaching to inform instructional quality. Solution Tree Press.
• Boston, M. D., & Smith, M. S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers' classrooms. Journal for Research in Mathematics Education, 40(2), 119–156. https://doi.org/10.2307/40539329
• Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27–40. https://doi.org/10.3316/QRJ0902027
• Bozkurt, A. (2018). Ortaokul 6. sınıf matematik ders kitabındaki etkinliklerin amaç, öğrenci çalışma biçimi ve uygulanabilirlik yönleriyle değerlendirilmesi. Elektronik Sosyal Bilimler Dergisi, 17(66), 535-548. https://doi.org/10.17755/esosder.342636
• Britannica. (2020, March 19). Leap year. https://www.britannica.com/science/leap-year-calendar
• Cheung, A. C., & Slavin, R. E. (2013). The effectiveness of educational technology applications for enhancing mathematics achievement in K-12 classrooms: A meta-analysis. Educational Research Review, 9, 88–113. https://doi.org/10.1016/j.edurev.2013.01.001
• Doğan Coşkun, S., & Işıksal Bostan, M. (2019). An in-service primary teacher’s implementation of mathematical tasks: The case of length measurement and perimeter instruction. International Journal of Mathematical Education in Science and Technology, 50(4), 486–505. https://doi.org/10.1080/0020739X.2018.1522675
• Dorn, E., Hancock, B., Sarakatsannis, J., & Viruleg, E. (2020, June 1). COVID-19 and student learning in the United States: The hurt could last a lifetime. McKinsey and Company. https://www.mckinsey.com/industries/public-and-social-sector/our-insights/covid-19-and-student-learning-in-the-united-states-the-hurt-could-last-a-lifetime
• Doyle, W. (1988). Work in mathematics classes: The context of students' thinking during instruction. Educational Psychologist, 23(2), 167–180. https://doi.org/10.1207/s15326985ep2302_6
• Engin, Ö., & Sezer, R. (2016). 7. sınıf matematik ders kitabındaki ve programdaki etkinliklerin bilişsel istem düzeylerinin karşılaştırılması. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (42), 24 –46.
• Estrella, S., Zakaryan, D., Olfos, R., & Espinoza, G. (2020). How teachers learn to maintain the cognitive demand of tasks through lesson study. Journal of Mathematics Teacher Education, 23(3), 293–310. https://doi.org/10.1007/s10857-018-09423-y
• Gonzales, N. A. (1994). Problem posing: A neglected component in mathematics courses for prospective elementary and middle school teachers. School Science and Mathematics, 94(2), 78–84. https://doi.org/10.1111/j.1949-8594.1994.tb12295.x
• Güzel, M., Bozkurt, A., & Özmantar, M.F. (2020). Öğretimsel dokümanlardaki etkinliklerin amaçlarının ortaokul matematik öğretmenlerinin perspektifinden incelenmesi. Cumhuriyet Uluslararası Eğitim Dergisi, 9(3), 875–896. http://dx.doi.org/10.30703/cije.668064
• Hadar, L. L. (2017). Opportunities to learn: Mathematics textbooks and students’ achievements. Studies in Educational Evaluation, 55, 153–166. https://doi.org/10.1016/j.stueduc.2017.10.002
• Hattie, J., Fisher, D., Frey, N., Gojak, L. M., Moore, S. D., & Mellman, W. (2016). Visible learning for mathematics, grades K-12: What works best to optimize student learning. Corwin Press.
• Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549. https://doi.org/10.5951/jresematheduc.28.5.0524
• Hill, H. C. (2010). The nature and predictors of elementary teachers' mathematical knowledge for teaching. Journal for Research in Mathematics Education, 41(5), 513–545. https://doi.org/10.5951/jresematheduc.41.5.0513
• Huinker, D., & Bill, V. (2017). Taking action: Implementing effective mathematics teaching practices in k-grade 5. National Council of Teachers of Mathematics.
• Kajander, A., & Lovric, M. (2009). Mathematics textbooks and their potential role in supporting misconceptions. International Journal of Mathematical Education in Science and Technology, 40(2), 173–181. https://doi.org/10.1080/00207390701691558
• Kazak, S. (2020). Etkinliklerin teknoloji bağlamında değerlendirilmesi. Y. Dede, M.F. Doğan, & F. A. Tutak (Ed.), Matematik eğitiminde etkinlikler ve uygulamaları içinde (ss. 145–163). Pegem Yayınevi.
• Lannin, J. K., & Chval, K. B. (2013). Challenge beginning teacher beliefs. Teaching Children Mathematics, 19(8), 508–515. https://doi.org/10.5951/teacchilmath.19.8.0508
• Milli Eğitim Bakanlığı. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Milli Eğitim Bakanlığı.
• Milli Eğitim Bakanlığı. (2020, 25 Ağustos). 18 Eylül'e kadar sürecek uzaktan eğitim döneminin yol haritası [Basın bülteni]. https://www.meb.gov.tr/18-eylule-kadar-surecek-uzaktan-egitim-doneminin-yol-haritasi/haber/21499/tr Miles, M, B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage Publication.
• Munter, C. (2014). Developing visions of high-quality mathematics instruction. Journal for Research in Mathematics Education, 45(5), 584–635. https://doi.org/10.5951/jresematheduc.45.5.0584
• National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
• National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all.National Council of Teachers of Mathematics.
• Ni, Y., Zhou, D. H. R., Cai, J., Li, X., Li, Q., & Sun, I. X. (2018). Improving cognitive and affective learning outcomes of students through mathematics instructional tasks of high cognitive demand. The Journal of Educational Research, 111(6), 704–719. https://doi.org/10.1080/00220671.2017.1402748
• Oliver, J. (1998). How we try to measure time: Calendars. Mathematics in School, 27(5), 2–6.
• Özgen, K., Aydın, M., Geçici, M. E., & Bayram, B. (2019). An investigation of eighth grade students’ skills in different problem posing types. International Journal For Mathematics Teaching and Learning, 20(1), 106–130.
• Özmantar, M. F., & Bingölbali, E. (2009). Sınıf öğretmenleri ve matematiksel zorlukları. GaziantepÜniversitesi Sosyal Bilimler Dergisi, 8(2), 401–427.
• Özmantar, M. F., & Bingölbali, E. (2015). Etkinlik tasarımı ve temel tasarım prensipleri. E. Bingölbali, & M. F. Özmantar (Ed.), İlköğretimde karşılaşılan matematiksel zorluklar ve çözüm önerileri içinde (5. bs.) (ss. 1–30). Pegem Yayınevi.
• Reçber, H., & Sezer, R. (2018). 8. sınıf matematik ders kitabındaki etkinliklerin bilişsel düzeyinin programdakilerle karşılaştırılması. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Dergisi, 51(1), 55–76. https://doi.org/10.30964/auebfd.405848
• Reimer, K., & Moyer, P. S. (2005). Third-graders learn about fractions using virtual manipulatives: A classroom study. Journal of Computers in Mathematics and Science Teaching, 24(1), 5–25.
• Reys, B., & Fennell, S. (2003). Who should lead mathematics instruction at the elementary school level? A case for mathematics specialists. Teaching Children Mathematics, 8(5), 277–282.
• Rich, K. M. (2020). Virtual manipulatives in elementary mathematics: A critical integrative review of research. In D. Schmidt-Crawford (Ed.), Proceedings of Society for Information Technology & Teacher Education International Conference (pp. 1387–1393). Association for the Advancement of Computing in Education (AACE). Sevimli, E., & Kul, Ü. (2015). Matematik ders kitabı içeriklerinin teknolojik uygunluk açısından değerlendirilmesi: Ortaokul örneği. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 9(1), 308–331. https://doi.org/10.17522/nefefmed.11253
• Schoenfeld, A. H. (2002). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31, 13–25. https://doi.org/10.3102/0013189X031001013
• Smith, M. S., & Stein, M. K. (1998). Reflections on practice: Selecting and creating mathematical tasks: From research to practice. Mathematics teaching in the middle school, 3(5), 344–350. https://doi.org/10.5951/MTMS.3.5.0344
• Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91–104. https://doi.org/10.1207/s15327833mtl0602_2
• Stein, M. K., Grover, B., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33, 455–488. https://doi.org/10.3102/00028312033002455
• Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50–80.
• Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268–275. https://doi.org/10.5951/MTMS.3.4.0268
• Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E. A. (2000). Implementing standards-based mathematics instruction. Teachers College Press.
• Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I., & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23, 691–697. https://doi.org/10.1177/0956797612440101
• Stigler, J. W., & Hiebert, J. (2004). Improving mathematics teaching. Educational Leadership, 61(5), 12–17.
• Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory based instruction: Toward a theory of teaching. Educational Researcher, 41(5), 147–156. https://doi.org/10.3102/0013189X12442801
• Tekkumru-Kisa, M., Stein, M. K., & Doyle, W. (2020). Theory and research on tasks revisited: Task as a context for students’ thinking in the era of ambitious reforms in mathematics and science. Educational Researcher, 49(8), 606–617. https://doi.org/10.3102/0013189X20932480
• Toluk Uçar, Z. (2011). Öğretmen adaylarının pedagojik içerik bilgisi: Öğretimsel açıklamalar. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 2(2), 88–102.
• Toprak, Z., & Özmantar, M. F. (2019). Türkiye ve Singapur 5. sınıf matematik ders kitaplarının çözümlü örnekler ve sorular açısından karşılaştırmalı analizi. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 10(2), 539–566. http://dx.doi.org/10.16949/turkbilmat.490210
• Usluoğlu, B. (2020). İlkokul 3 ve 4. sınıf matematik ders kitaplarındaki etkinliklerin yenilenmiş Bloom taksonomisine göre incelenmesi [Yayınlanmamış yüksek lisans tezi]. Kırıkkale Üniversitesi.
• Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M., & Brass, A. (2019). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Pearson.
• Wills, T. (2020). Teaching math at a distance, grades K-12: A practical guide to rich remote instruction. Corwin Press.
• Wu, H. (2009). What’s sophisticated about elementary mathematics. American Educator, 33(3), 4–14.
• Yabaş, D., & Altun, S. (2020). Matematiksel görevlerin uygulanmasında iletişim stratejileri ve bilişsel talep kavramı: Sınıf-içi yansımalar. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 35(4), 759–779. https://doi.org/10.16986/HUJE.2019056303
• Yalçın, S. (2019). İlkokul üçüncü sınıf matematik ders kitaplarının içerdiği etkinlikler ve sorular bağlamında incelenmesi. Erzincan Üniversitesi Eğitim Fakültesi Dergisi, 22(1), 18–34. https://doi.org/10.17556/erziefd.463013
• Yeşildere-İmre, S. (2020). Matematiksel etkinliklerin tasarım ilkeleri. Y. Dede, M. F. Doğan, & F. A. Tutak (Ed.), Matematik eğitiminde etkinlikler ve uygulamaları içinde (ss. 165-185). Pegem Yayınevi.
• Yıldırım, A., & Şimşek, H. (2018). Sosyal bilimlerde nitel araştırma yöntemleri (11. bs.). Seçkin Yayıncılık.
• Yıldızlı, H., & Sarı, M. H. (2017). Sınıf öğretmenlerinin geometrik cisimlere ilişkin alan bilgilerinin incelenmesi. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 30(2), 601–636. https://doi.org/10.19171/uefad.368975