An examination of the cognitive demand levels posed by problems in the middle grades mathematics textbooks

Yıl 2024, , 294 - 321, 24.09.2024

Tuğba Horzum , Anıl Ayseli Duran

https://doi.org/10.47806/ijesacademic.1522050

Öz

This research investigated the cognitive demand levels of mathematics tasks within the middle school mathematics textbooks endorsed by the Ministry of National Education for the academic year of the 2023-2024. To achieve this, a qualitative research method was utilized, and document analysis was performed. In this direction, the textbooks were analyzed using descriptive analysis. The tasks within the textbooks were examined through the lens of Smith and Stein’s (1998) theoretical framework. The findings indicate that the majority of mathematics tasks in middle school mathematics textbooks exhibit a low level of cognitive demand. It was found that over 80% of the tasks fell into the categories of memorization and procedures without connections levels. It has been revealed that tasks at the levels of procedures with connections and doing mathematics, which are high cognitive demand levels, are uncommon. This shows that textbooks do not sufficiently support the potential of students to develop mathematical thinking and problem-solving skills. Based on these results, various suggestions have been made for textbooks. The most important of these suggestions include ensuring that students are cognitively exposed to higher level tasks and increasing the number of tasks that will improve their mathematical thinking skills. Thus, it will be possible for students to have a more effective learning process by deepening their mathematical understanding.

Anahtar Kelimeler

cognitive demand levels, mathematics tasks, mathematics textbooks

Etik Beyan

This study analyzed textbooks that are publicly available at https://www.kimyadenizi.com/mat-ort/. Consequently, there were no ethical issues associated with the conduct of the research, and there was no requirement for ethics committee approval.

Destekleyen Kurum

Yok

Proje Numarası

-

Teşekkür

-

Kaynakça

• Adleff, A. K., Ross, N., König, J., & Kaiser, G. (2023). Types of mathematical tasks in lower secondary classrooms in Germany: Statistical findings from a latent class analysis based on general mathematical competencies. Educational Studies in Mathematics, 114(3), 371-392. https://doi.org/10.1007/s10649-023-10254-9
• Agterberg, D. A., Oostdam, R. J. & Janssen, F. J. J. M. (2022). From speck to story: relating history of mathematics to the cognitive demand level of tasks. Educational Studies in Mathematics, 110, 49–64. https://doi.org/10.1007/s10649-021-10093-6
• Aktan, O. (2019). İlkokul matematik öğretim programı dersi kazanımlarının yenilenen Bloom Taksonomisine göre incelenmesi [Investigation of primary school mathematics curriculum lesson acquisitions according to renewed Bloom Taxonomy]. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi 48(1), 15-36. https://doi.org/10.9779/pauefd.523545 (Turkish)
• Alayont, F., Karaali, G., & Pehlivan, L. (2023). Analysis of calculus textbook problems via Bloom's Taxonomy. PRIMUS, 33(3), 203-218. https://doi.org/10.1080/10511970.2022.2048931
• Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math anxiety. Psychonomic Bulletin & Review, 14, 243-248. https://doi.org/10.3758/BF03194059
• Ayres, P. (2006). Impact of reducing intrinsic cognitive load on learning in a mathematical domain. Applied Cognitive Psychology, 20(3), 287-298. https://doi.org/10.1002/acp.1245
• Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is—or might be—the role of curriculum materials in teacher learning and instructional reform? Educational researcher, 25(9), 6-14. https://doi.org/10.3102/0013189X025009006
• Barnett, J. H., Can, C., & Otero, D. E. (2024). Tagging opportunities to learn: A coding scheme for student tasks. The Mathematics Enthusiast, 21(1), 225-268. https://doi.org/10.54870/1551-3440.1625
• Basyal, D., Jones, D. L., & Thapa, M. (2023). Cognitive demand of mathematics tasks in Nepali middle school mathematics textbooks. International Journal of Science and Mathematics Education, 21(3), 863-879. https://doi.org/10.1007/s10763-022-10269-3
• Bayazıt, 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, 651-682. https://doi.org/10.1007/s10763-012-9358-8
• Borromeo Ferri, R. (2018). Task competency: For your instructional flexibility. Learning how to teach mathematical modeling in school and teacher education (pp. 41-75). Springer, Cham. https://link.springer.com/chapter/10.1007/978-3-319-68072-9_3
• Boston, M. D., & Smith, M. S. (2011). A ‘task-centric approach to professional development: Enhancing and sustaining mathematics teachers’ ability to implement cognitively challenging mathematical tasks. ZDM, 43, 965-977. https://doi.org/10.1007/s11858-011-0353-2
• 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., & Yılmaz, Ş. (2020). An examination of the activities in 8th-grade mathematics textbooks based on the levels of cognitive demand. İlköğretim Online, 19(1), 133-146. https://doi.org/10.17051/ilkonline.2020.647122
• Charalambous, C. Y., Delaney, S., Hsu, H. Y., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12(2), 117–151. https://doi.org/10.1080/10986060903460070
• Creswell, J. W. (2012). Educational research: Planning, conducting and evaluating qualitative and quantitative research (5th ed.). Boston: Pearson
• Deringöl, Y., & Guseinova, E. (2023). Problem-posing activities in primary school mathematics textbooks in Russia and Azerbaijan, Mimbar Sekolah Dasar, 9(3), 535-551. https://doi.org/10.53400/mimbar-sd.v9i3.44863
• Duran, A. A. (2024). Liselere geçiş sistemi matematik sorularının bilişsel istem düzeyleri bağlamında değerlendirilmesi [Evaluation of high school entrance system mathematics questions in terms of cognitive demand levels]. Necmettin Erbakan Üniversitesi Ereğli Eğitim Fakültesi Dergisi, 6(1), 65-85. https://dergipark.org.tr/tr/pub/neueefd/issue/85157/1328984 (Turkish)
• Ecemiş, U. O. (2017). A comparison of cognitive demand levels of tasks in 5th grade mathematics textbook used in Singapore, the United States, and Turkey. EJMS European Journal of Multidisciplinary Studies Articles, 5(1), 469-469.
• Ekol, G., & Mlotshwa, S. (2022). Investigating the cognitive demand levels in probability and counting principles learning tasks from an online mathematics textbook. Pythagoras, 43(1), 1-8. https://doi.org/10.4102/pythagoras.v43i1.677
• Engin, Ö., & Sezer, R. (2016). 7. sınıf matematik ders kitabındaki ve programdaki etkinliklerin bilişsel istem düzeylerinin karşılaştırılması [Comparison of cognitive demand levels of tasks in the 7th grade textbook and those in the curriculum]. Buca Eğitim Fakültesi Dergisi, 42, 24–46. https://dergipark.org.tr/tr/download/article-file/432037 (Turkish)
• 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, 293–310. https://doi.org/10.1007/s10857-018-09423-y
• Fukuda, M., & Manalo, E. (2024). Promoting learners’ self-regulated textbook use for overcoming impasses in solving mathematics exercises. Research in Mathematics Education, 26(1), 133-155. https://doi.org/10.1080/14794802.2022.2154825
• Gillette, G., & Sanger, M. J. (2014). Analysing the distribution of questions in the gas law chapters of secondary and introductory college chemistry textbooks from the United States. Chemistry Education Research and Practice, 15(4), 787-799. https://doi.org/10.1039/C4RP00115J
• Hadar, L. L., & Ruby, T. L. (2019). Cognitive opportunities in textbooks: The cases of grade four and eight textbooks in Israel. Mathematical Thinking and Learning, 21(1), 54-77. https://doi.org/10.1080/10986065.2019.1564968
• 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/10.2307/749690
• Hsu, W. (2013). Examining the types of mathematical tasks used to explore the mathematics instruction by elementary school teachers. Creative Education, 4(6), 396-404. http://dx.doi.org/10.4236/ce.2013.46056
• Hsu, H. Y., & Silver, E. A. (2014). Cognitive complexity of mathematics instructional tasks in a Taiwanese classroom: An examination of task sources. Journal for Research in Mathematics Education, 45(4), 460-496. https://doi.org/10.5951/jresematheduc.45.4.0460
• Hussain, S. (2018). Comparison of problem-solving strategies in middle-grade mathematics textbooks. International Journal of Research, 5(4), 3175-3180. https://journals.pen2print.org/index.php/ijr/article/view/13263/12481
• Incikabi, S., Sadak, M., & Incikabi, L. (2023). Identifying mathematical literacy demands in Turkish, Singaporean and Australian textbooks. Acta Educationis Generalis, 13(1), 147-169. https://doi.org/10.2478/atd-2023-0008
• Indiyanti, I., Asmarani, D., & Sutopo, S. (2023). Development of hots-based math textbooks to improve critical thinking skills. Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah di Bidang Pendidikan Matematika, 9(2), 156-170. https://doi.org/10.29407/jmen.v9i2.20033
• Ismail, F. N., & Rosli, R. (2022). Mathematics education textbook research trends: A systematic literature review. International Journal of Advanced Research in Education and Society, 4(3), 122-133. https://doi.org/10.55057/ijares.2022.4.3.12
• Jackson, K., Garrison, A., Wilson, J., Gibbons, L., & Shahan, E. (2013). Exploring relationships between setting up complex tasks and opportunities to learn in concluding whole-class discussions in middle-grades mathematics instruction. Journal for Research in Mathematics Education, 44(4), 646-682. https://doi.org/10.5951/jresematheduc.44.4.0646
• Jiang, T., & Li, S. (2023). Secondary school students’ use and perceptions of textbooks in mathematics learning: A large-scale investigation in China. Frontiers in Psychology, 14, 1132184. https://doi.org/10.3389/fpsyg.2023.1132184
• Jones, D. L., & Tarr, J. E. (2007). An examination of the levels of cognitive demand required by probability tasks in middle grades mathematics textbooks. Statistics Education Research Journal, 6(2), 4-27. https://mospace.umsystem.edu/xmlui/handle/10355/2500
• Kaur, B., & Chin, S. L. (2022). Nature of mathematics tasks and what teachers do. Current Opinion in Behavioral Sciences, 46, 101169. https://www.sciencedirect.com/science/article/pii/S2352154622000754
• Köğce, D. ve Baki, A. (2009). Matematik öğretmenlerinin yazılı sınav soruları ile ÖSS sınavlarında sorulan matematik sorularının Bloom taksonomisine göre karşılaştırılması [A Comparision of high-school mathematics teachers’ examination questions and mathematics questions in the university entrance exams according to Bloom’s Taxonomy]. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 26(26), 70-80. https://dergipark.org.tr/tr/pub/pauefd/issue/11117/132949 (Turkish)
• Lee, E. (2022). An analysis of the levels of cognitive demand and questioning types in textbook tasks: Focused on grade 5 and 6 mathematics textbooks. Korean Association For Learner-Centered Curriculum And Instruction, 22(24), 275-290. https://doi.org/10.22251/jlcci.2022.22.24.275
• Lin, C. (2023). The development of student’s thinking ability in arithmetic. In: Intellectual Development and Mathematics Learning. Springer, Singapore. https://doi.org/10.1007/978-981-19-8757-1_5
• Merriam, S. B. (2013). Qualitative research: A guide to design and implementation (S. Turan, trans). Nobel Publishing.
• Miles, M. B., & Huberman, A. M. (2015). Nitel veri analizi [Qualitative data analysis]. (S. Akbababa Altun & A. Ersoy Çev.). Pegem Akademi. (Turkish)
• MoNE. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics curriculum (Primary and middle school, grades 1, 2, 3, 4, 5, 6, 7 and 8)]. Ministry of National Education. https://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329 (Turkish)
• National Council of Teachers of Mathematics [NCTM], (2000). Principles and standards for school mathematics. Reston, VA: Author.
• Özgeldi, M., & Esen, Y. (2010). Analysis of mathematical tasks in Turkish elementary school mathematics textbooks. Procedia - Social and Behavioral Sciences, 2(2), 2277–2281. https://doi.org/10.1016/j.sbspro.2010.03.322
• Özkale, A., & Aprea, C. (2023). Designing mathematical tasks to enhance financial literacy among children in Grades 1–8. International Journal of Mathematical Education in Science and Technology, 54(3), 433–450. https://doi.org/10.1080/0020739X.2022.2157342
• Parrish, C. W., & Bryd, K. O. (2022). Cognitively demanding tasks: Supporting students and teachers during engagement and implementation. International Electronic Journal of Mathematics Education, 17(1), em0671. https://doi.org/10.29333/iejme/11475
• Peng, A., & Song, N. (2015). Design and implementation of mathematics textbooks in support of effective teaching for secondary schools: A Chinese case. Research in Mathematical Education, 19(4), 247-265. https://doi.org/10.7468/jksmed.2015.19.4.247
• Polat, S., & Dede, Y. (2023). Trends in cognitive demands levels of mathematical tasks in Turkish middle school mathematics textbooks: Algebra learning domain. International Journal for Mathematics Teaching and Learning, 24(1), 40-61. https://doi.org/10.4256/ijmtl.v24i1.476
• Purba, A., & Riskyka, R. (2021). The development of comparison in mathematics textbook and problem-based learning to improve mathematical problem-solving ability of junior high school students. Budapest International Research and Critics Institute-Journal (BIRCI-Journal), 4(4), 11369-11378. https://doi.org/10.33258/birci.v4i4.3200
• Radmehr, F. (2023). Toward a theoretical framework for task design in mathematics education. Journal on Mathematics Education, 14(2), 189-204. https://doi.org/10.22342/jme.v14i2.pp189-204
• Raditya, A., Iskandar, R. S. F., & Suwarno, S. (2020). Questions analysis in mathematics textbook from competency-based curriculum up to curriculum 2013. Desimal: Jurnal Matematika, 3(2), 89-98. http://dx.doi.org/10.24042/djm.v3i2.5973
• Reçber, H., & Sezer, R. (2018). 8. sınıf matematik ders kitabındaki etkinliklerin bilişsel düzeyinin programdakilerle karşılaştırılması [Cognitive demand levels of tasks in 8th grade textbook and mathematics program]. Ankara Universitesi Egitim Bilimleri Fakultesi Dergisi, 51(1), 55–76. https://doi.org/10.30964/auebfd.405848 (Turkish)
• Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211-246. https://doi.org/10.3102/00346543075002211 Roth, K., & Givvin, K. B. (2008). Implications for math and science instruction from the TIMSS 1999 video study. Principal Leadership, 8(9), 22–27. https://www.researchgate.net/publication/234682210_Implications_for_Math_and_Science_Instruction_from_the_TIMSS_1999_Video_Study
• Ruk, J. (2020). A conceptualized framework for assessing factors that maintain and lower cognitive demand during task enactment. In: Sacristán, A.I., Cortés-Zavala, J.C. & Ruiz-Arias, P.M. (Eds.). (2020). Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Mexico. Cinvestav / AMIUTEM / PME-NA. https:/doi.org/10.51272/pmena.42.2020
• Sianturi, I. A. J., Ismail, Z., & Yang, D. C. (2021). A cross‐national comparison of mathematical problems on numbers and operations‐related topics in five countries. School Science and Mathematics, 121(2), 72-84. https://doi.org/10.1111/ssm.12451
• Sievert, H., van den Ham, A. K., Niedermeyer, I., & Heinze, A. (2019). Effects of mathematics textbooks on the development of primary school children's adaptive expertise in arithmetic. Learning and Individual Differences, 74, 101716. https://doi.org/10.1016/j.lindif.2019.02.006
• 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
• Son, J. W., & Kim, O. K. (2015). Teachers’ selection and enactment of mathematical problems from textbooks. Mathematics Education Research Journal, 27, 491-518. https://doi.org/10.1007/s13394-015-0148-9
• Stein, M. K., Grover, B. W., & 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(2), 455–488. https://doi.org/10.2307/1163292
• 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. https://doi.org/10.1080/1380361960020103
• 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. A. & Silver, E. A. (2000). Implementing standards-based mathematics instructions: A casebook for professional development. New York: Teachers College.
• Stylianides, A. J., & Stylianides, G. J. (2008). Studying the classroom implementation of tasks: High-level mathematical tasks embedded in ‘real-life’contexts. Teaching and Teacher Education, 24(4), 859-875. https://doi.org/10.1016/j.tate.2007.11.015
• Sunzuma, G., & Luneta, K. (2023). An evaluation of secondary school mathematics textbooks in light of sustainable education in Zimbabwe. LUMAT: International Journal on Math, Science and Technology Education, 11(1), 118–139. https://doi.org/10.31129/LUMAT.11.1.1886
• Takker, S., & Pournara, C. (2022). Knowledge demands placed on mathematics teachers by textbooks: Case of decimal fractions. Asian Journal for Mathematics Education, 1(3), 285-305. https://doi.org/10.1177/27527263221111569
• Ubuz, B., & Sarpkaya, G. (2014). İlköğretim 6. sınıf cebirsel görevlerin bilişsel istem seviyelerine göre incelenmesi: Ders kitapları ve sınıf uygulamaları [The investigation of algebraic tasks in sixth grades in terms of cognitive demands: mathematics texbook and classroom implementations]. İlköğretim Online, 13(2), 594–606. https://search.trdizin.gov.tr/tr/yayin/detay/221023/ (Turkish)
• Üredi, L., & Ulum, H. (2020). İlkokul matematik ders kitaplarında bulunan ünite değerlendirme sorularının Yenilenmiş Bloom Taksonomisine göre incelenmesi [Evaluation of unit evaluation questions in primary school mathematics course books according to the Revised Bloom’s Taxonomy]. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 16(2), 432-447. https://doi.org/10.17860/mersinefd.693392 (Turkish)
• Wakhata, R., Mutarutinya, V., & Balimuttajjo, S. (2023, April). Exploring the impact of Stein et al.’s levels of cognitive demand in supporting students’ mathematics heuristic problem-solving abilities. Frontiers in Education, 8, 949988. https://doi.org/10.3389/feduc.2023.949988
• Weinberg, A., Wiesner, E., Benesh, B., & Boester, T. (2012). Undergraduate students’ self-reported use of mathematics textbooks. Primus, 22(2), 152-175. https://doi.org/10.1080/10511970.2010.509336 Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89, 41-65. https://doi.org/10.1007/s10649-015-9595-1
• Yabaş, D., & Altun, S. (2020). Matematiksel görevlerin uygulanmasında iletişim stratejileri ve bilişsel talep kavramı: Sınıf içi yansımalar [Communication strategies and cognitive demand in mathematical task enactment: reflections from the classroom]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 35(4), 759-779. https://www.doi.org/10.16986/HUJE.2019056303 (Turkish)
• Yang, D.-C., & Lin, Y.-C. (2015). Examining the differences of linear systems between Finnish and Taiwanese textbooks. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1265-1281. https://doi.org/10.12973/eurasia.2015.1483a
• Yıldırım, A., & Şimsek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in social sciences]. Seçkin Publishing. (Turkish)
• Yükselen, A., & Kepceoğlu, İ. (2021). Türkiye, Singapur ve Avustralya ortaokul matematik ders kitaplarında yüzdeler konusundaki soruların bilişsel istem düzeylerinin ve çözüm adımlarının karşılaştırmalı analizi [Turkey, Singapore and Australia secondary school comparative analysis of questions in the field of percent in mathematics textbooks]. Balıkesir Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 24(46), 961–976. https://doi.org/10.31795/baunsobed.802743 (Turkish)
• Zan, R., & Di Martino, P. (2007). Attitude toward mathematics: Overcoming the positive/negative dichotomy. The Montana Mathematics Enthusiast, 3(1), 157-168. https://www.researchgate.net/publication/228759042