Research Article
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Analysing the Tasks in Middle School Mathematics Textbooks According to the Levels of Cognitive Demand

Year 2024, Volume: 8 Issue: 3, 477 - 502, 30.11.2024

Abstract

This study aims to investigate and categorize the tasks in middle school mathematics textbooks based on their cognitive demand levels. The goal is to examine how these tasks align with educational objectives aimed at fostering students' critical thinking and problem-solving abilities. This research employed the document analysis method. This study evaluated the mathematical tasks in 5th to 8th grade textbooks used in schools in Türkiye, using Smith and Stein’s (1998) framework for classifying mathematical tasks. The data were examined using the content analysis method. The results indicated that most tasks in these textbooks were concentrated at the levels of procedures without connections and procedures with connections. Additionally, the proportion of tasks requiring higher-order cognitive skills, specifically, doing mathematics tasks, was relatively low. Based on these findings, future textbook revisions should integrate more high cognitive demand tasks to both strengthen students' procedural skills and foster complex problem-solving and critical thinking abilities.

Ethical Statement

In this study, all the rules specified to be followed within the scope of "Higher Education Institutions Scientific Research and Publication Ethics Directive" were complied with. None of the actions specified under the heading "Actions Contrary to Scientific Research and Publication Ethics", which is the second part of the directive, have been taken.

References

  • Antonijević, R. (2016). Cognitive activities in solving mathematical tasks: The role of a cognitive obstacle. Eurasia Journal of Mathematics, Science and Technology Education, 12(9), 2503-2515.
  • Boston, M. D., Madler, K., & Cutone, C. (2017). Implementing tasks that promote reasoning and problem solving. In D. A. Spangler & J. J. Wanko (Ed.), Enhancing classroom practice with research behind principles to actions (pp. 13-26). NCTM.
  • Bowen, G. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9, 27-40.
  • Bozkurt, A., & Yılmaz, Ş. (2020). An examination of the activities in 8th grade mathematics textbooks based on the levels of cognitive demand. Elementary Education Online, 19(1), 133-146.
  • Böge, H., & Akıllı, R. (2019). Ortaokul ve imam hatip ortaokulu matematik ders kitabı 8. sınıf [Mathematics textbook for middle school and imam hatip middle school 8th grade]. MEB.
  • Chapman, O. (2013). Mathematical-task knowledge for teaching. Journal of Mathematics Teacher Education, 16, 1-6.
  • Çağlayan, N., Dağıstan, A., & Korkmaz, B. (2019). Ortaokul ve imam hatip ortaokulu matematik ders kitabı 6. sınıf [Mathematics textbook for middle school and imam hatip middle school 6th grade]. MEB.
  • Cırıtcı, H., Gönen, İ., Araç, D., Özarslan, M., Pekcan, N., & Şahin, M. (2019). Ortaokul ve imam hatip ortaokulu matematik ders kitabı 5. sınıf [Mathematics textbook for middle school and imam hatip middle school 5th grade]. MEB.
  • Cichy, I., Kaczmarczyk, M., Wawrzyniak, S., Kruszwicka, A., Przybyla, T., Klichowski, M., & Rokita, A. (2020). Participating in physical classes using eduball stimulates acquisition of mathematical knowledge and skills by primary school students. Frontiers in Psychology, 11, 1-11.
  • Dede, Y., Doğan, M. F., & Aslan-Tutak, F. (Ed.). (2020). Matematik eğitiminde etkinlikler ve uygulamaları [Activities and application in mathematics education]. Pegem.
  • Dorner, C., & Ableitinger, C. (2022). Procedural mathematical knowledge and use of technology by senior high school students. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), 1-14.
  • Doyle, W. (1980) Student mediating responses in teaching effectiveness (ED187698). ERIC. https://eric.ed.gov/?id=ED187698
  • Doyle, W. (1983). Academic work. Review of Educational Research, 53(2), 159-199.
  • Doyle, W. (1988). Work in mathematics classes: The context of students' thinking during instruction. Educational Psychologist, 23(2), 167-180.
  • Engin, Ö., & Sezer, R. (2016). 7. sınıf matematik ders kitabındaki ve programdaki etkinliklerin bilişsel istem düzeylerinin karşılaştırılması [Comparison of 7th grade mathematics textbook and program activities' cognitive demand levels]. The Buca Faculty of Education Journal, 42, 24-46.
  • Foster, C. (2013). Teaching with tasks for effective mathematics learning. Research in Mathematics Education, 15(3), 309–313.
  • Foster, C. (2018). Developing mathematical fluency: Comparing exercises and rich tasks. Educational Studies in Mathematics, 97, 121-141.
  • 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. Johnson, H. L., Coles, A., & Clarke, D. (2017). Mathematical tasks and the student: navigating “tensions of intentions” between designers, teachers, and students. ZDM Mathematics Education, 49(6), 813-822.
  • Keskin Oğan, A., & Öztürk, S. (2019). Ortaokul ve imam hatip ortaokulu matematik ders kitabı 7. sınıf [Mathematics textbook for middle school and imam hatip middle school 7th grade]. MEB.
  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. National Research Council, Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. National Academy.
  • Leiss, D., Plath, J., & Schwippert, K. (2019). Language and mathematics - Key factors influencing the comprehension process in reality-based tasks. Mathematical Thinking and Learning, 21(2), 131–153.
  • Lee, E. J. (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.
  • Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM Mathematics Education, 49(6), 937-949.
  • Mayring, P. (2015). Qualitative content analysis: Theoretical background and procedures. In A. Bikner-Ahsbahs, C. Knipping, N. Presmeg (Eds.), Approaches to qualitative research in mathematics education. Advances in mathematics education. Springer.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage.
  • National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. Author.
  • National Research Council (NRC). (2012). Education for life and work: Developing transferable knowledge and skills in the 21st century. The National Academies.
  • Ni, Y., Zhou, D., Cai, J., Li, X., Li, Q., & Sun, I. (2018). Improving cognitive and affective learning outcomes of students through mathematics instructional tasks of high cognitive demand. The Journal of Educational Research, 111, 704-719.
  • Plath, J., & Leiss, D. (2018). The impact of linguistic complexity on the solution of mathematical modelling tasks. ZDM Mathematics Education, 50, 159-171.
  • 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.
  • Ponte, J. P., Branco, N., & Quaresma, M. (2014). Exploratory activity in the mathematics classroom. In Y. Li, E. Silver, & S. Li. (Eds.), Transforming mathematics instruction: Multiple approaches and practices. Springer.
  • Radford, L. (2008). Theories in mathematics education: A brief inquiry into their conceptual differences. Working Paper. Prepared for the ICMI Survey Team 7, 1-17.
  • Reçber, H., & Sezer, R. (2018). 8. sınıf matematik ders kitabındaki etkinliklerin bilişsel düzeyinin programdakilerle karşılaştırılması [Comparison of 8th grade mathematics textbook activities' cognitive level with those in the curriculum]. Ankara University Journal of Faculty of Educational Sciences, 51(1), 55-76.
  • Schmidt, W. H., Houang, R. T., & Cogan, L. S. (2002). A coherent curriculum: The case of mathematics. American Educator, 26(2), 10-26.
  • Seah, R., & Horne, M. (2021). Developing reasoning within a geometric learning progression: Implications for curriculum development and classroom practices. Australian Journal of Education, 65, 248-264.
  • 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.
  • Smith, M. S., & Stein, M. K. (2011). 5 Practices for orchestrating productive mathematical discussions. Corwin.
  • 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.
  • 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.
  • Toluk Uçar, Z. (2020). Matematiksel etkinlik kavramının teorik ve felsefi temelleri [Theoretical and philosophical foundations of the concept of mathematical activity]. In Y. Dede, M. F. Doğan, F. Aslan-Tutak (Eds.), Matematik eğitiminde etkinlikler ve uygulamaları [Theoretical and philosophical foundations of the concept of mathematical activity] (pp. 17-42). Pegem.
  • Ubuz, B., Erbaş, A. K., Çetinkaya, B., & Özgeldi, M. (2010). Exploring the quality of the mathematical tasks in the new Turkish elementary school mathematics curriculum guidebook: The case of algebra. ZDM Mathematics Education, 42, 483–491.
  • Ubuz, B., & Sarpkaya, G. (2014). İlköğretim 6. sınıf cebirsel görevlerin bilişsel istem seviyelerine göre incelenmesi: Ders kitapları ve sınıf uygulamaları [Examining primary school 6th grade algebraic tasks according to cognitive demand levels: Textbooks and classroom practices]. Elementary Education Online, 13(2), 595-606.
  • Van de Walle, J. A., Karp, K., S., & Bay-Williams, J. M. (2023). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Pearson.
  • Watson, A., & Mason, J. (2006). Seeing an exercise as a single mathematical object: Using variation to structure sense-making. Mathematical Thinking and Learning, 8(2), 91–111.
  • Wess, R., Klock, H., Siller, H., & Greefrath, G. (2021). Measuring professional competence for the teaching of mathematical modelling. In Leung, F. K. S., Stillman, G. A., Kaiser, G., & Wong, K. L. (Eds.), International perspectives on the teaching and learning of mathematical modelling. Springer.

Ortaokul Matematik Ders Kitaplarındaki Görevlerin Bilişsel İstem Düzeylerine Göre Analizi

Year 2024, Volume: 8 Issue: 3, 477 - 502, 30.11.2024

Abstract

Bu çalışma, ortaokul matematik ders kitaplarındaki matematiksel görevleri, bilişsel istem düzeylerine göre ayrıntılı bir biçimde incelemeyi ve sınıflandırmayı amaçlamaktadır. Bu görevlerin, öğrencilerin eleştirel düşünme, problem çözme ve matematiksel akıl yürütme becerilerini geliştirmeye yönelik olarak tasarlanan eğitim hedefleriyle nasıl bir uyum gösterdiğini ortaya çıkarmayı hedeflemektedir. Çalışmanın deseni doküman analizidir ve ders kitaplarında yer alan matematiksel görevlerin niteliğini derinlemesine incelemektedir. Bu çalışma kapsamında, 5., 6., 7. ve 8. sınıf ders kitaplarında yer alan matematiksel görevler, Stein ve Smith (1998) tarafından geliştirilen matematiksel görev sınıflandırma çerçevesi esas alınarak değerlendirilmiştir. Veriler, içerik analizi yöntemiyle incelenmiş ve görevlerin bilişsel düzeylerine göre dağılımları değerlendirilmiştir. Sonuçlar, ders kitaplarında yer alan matematiksel görevlerin çoğunlukla bağlantısız yöntemler ve bağlantılı yöntemler düzeylerinde yoğunlaştığını göstermiştir. Buna karşın, özellikle üst bilişsel beceriler gerektiren matematik yapma görevlerinin oranının düşük olduğu belirlenmiştir. Bu nedenle, gelecekteki ders kitabı revizyonlarının, öğrencilerin sadece işlemsel becerilerini değil, aynı zamanda karmaşık problem çözme ve eleştirel düşünme yeteneklerini de geliştirecek daha fazla bilişsel istem gerektiren görevleri içerecek şekilde düzenlenebilir.

Ethical Statement

Bu çalışmada "Yükseköğretim Kurumları Bilimsel Araştırma ve Yayın Etiği Yönergesi" kapsamında uyulması gerektiği belirtilen tüm kurallara uyulmuştur. Yönergenin ikinci bölümü olan "Bilimsel Araştırma ve Yayın Etiğine Aykırı Eylemler" başlığı altında belirtilen eylemlerin hiçbiri gerçekleştirilmemiştir.

References

  • Antonijević, R. (2016). Cognitive activities in solving mathematical tasks: The role of a cognitive obstacle. Eurasia Journal of Mathematics, Science and Technology Education, 12(9), 2503-2515.
  • Boston, M. D., Madler, K., & Cutone, C. (2017). Implementing tasks that promote reasoning and problem solving. In D. A. Spangler & J. J. Wanko (Ed.), Enhancing classroom practice with research behind principles to actions (pp. 13-26). NCTM.
  • Bowen, G. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9, 27-40.
  • Bozkurt, A., & Yılmaz, Ş. (2020). An examination of the activities in 8th grade mathematics textbooks based on the levels of cognitive demand. Elementary Education Online, 19(1), 133-146.
  • Böge, H., & Akıllı, R. (2019). Ortaokul ve imam hatip ortaokulu matematik ders kitabı 8. sınıf [Mathematics textbook for middle school and imam hatip middle school 8th grade]. MEB.
  • Chapman, O. (2013). Mathematical-task knowledge for teaching. Journal of Mathematics Teacher Education, 16, 1-6.
  • Çağlayan, N., Dağıstan, A., & Korkmaz, B. (2019). Ortaokul ve imam hatip ortaokulu matematik ders kitabı 6. sınıf [Mathematics textbook for middle school and imam hatip middle school 6th grade]. MEB.
  • Cırıtcı, H., Gönen, İ., Araç, D., Özarslan, M., Pekcan, N., & Şahin, M. (2019). Ortaokul ve imam hatip ortaokulu matematik ders kitabı 5. sınıf [Mathematics textbook for middle school and imam hatip middle school 5th grade]. MEB.
  • Cichy, I., Kaczmarczyk, M., Wawrzyniak, S., Kruszwicka, A., Przybyla, T., Klichowski, M., & Rokita, A. (2020). Participating in physical classes using eduball stimulates acquisition of mathematical knowledge and skills by primary school students. Frontiers in Psychology, 11, 1-11.
  • Dede, Y., Doğan, M. F., & Aslan-Tutak, F. (Ed.). (2020). Matematik eğitiminde etkinlikler ve uygulamaları [Activities and application in mathematics education]. Pegem.
  • Dorner, C., & Ableitinger, C. (2022). Procedural mathematical knowledge and use of technology by senior high school students. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), 1-14.
  • Doyle, W. (1980) Student mediating responses in teaching effectiveness (ED187698). ERIC. https://eric.ed.gov/?id=ED187698
  • Doyle, W. (1983). Academic work. Review of Educational Research, 53(2), 159-199.
  • Doyle, W. (1988). Work in mathematics classes: The context of students' thinking during instruction. Educational Psychologist, 23(2), 167-180.
  • Engin, Ö., & Sezer, R. (2016). 7. sınıf matematik ders kitabındaki ve programdaki etkinliklerin bilişsel istem düzeylerinin karşılaştırılması [Comparison of 7th grade mathematics textbook and program activities' cognitive demand levels]. The Buca Faculty of Education Journal, 42, 24-46.
  • Foster, C. (2013). Teaching with tasks for effective mathematics learning. Research in Mathematics Education, 15(3), 309–313.
  • Foster, C. (2018). Developing mathematical fluency: Comparing exercises and rich tasks. Educational Studies in Mathematics, 97, 121-141.
  • 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. Johnson, H. L., Coles, A., & Clarke, D. (2017). Mathematical tasks and the student: navigating “tensions of intentions” between designers, teachers, and students. ZDM Mathematics Education, 49(6), 813-822.
  • Keskin Oğan, A., & Öztürk, S. (2019). Ortaokul ve imam hatip ortaokulu matematik ders kitabı 7. sınıf [Mathematics textbook for middle school and imam hatip middle school 7th grade]. MEB.
  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. National Research Council, Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. National Academy.
  • Leiss, D., Plath, J., & Schwippert, K. (2019). Language and mathematics - Key factors influencing the comprehension process in reality-based tasks. Mathematical Thinking and Learning, 21(2), 131–153.
  • Lee, E. J. (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.
  • Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM Mathematics Education, 49(6), 937-949.
  • Mayring, P. (2015). Qualitative content analysis: Theoretical background and procedures. In A. Bikner-Ahsbahs, C. Knipping, N. Presmeg (Eds.), Approaches to qualitative research in mathematics education. Advances in mathematics education. Springer.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage.
  • National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. Author.
  • National Research Council (NRC). (2012). Education for life and work: Developing transferable knowledge and skills in the 21st century. The National Academies.
  • Ni, Y., Zhou, D., Cai, J., Li, X., Li, Q., & Sun, I. (2018). Improving cognitive and affective learning outcomes of students through mathematics instructional tasks of high cognitive demand. The Journal of Educational Research, 111, 704-719.
  • Plath, J., & Leiss, D. (2018). The impact of linguistic complexity on the solution of mathematical modelling tasks. ZDM Mathematics Education, 50, 159-171.
  • 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.
  • Ponte, J. P., Branco, N., & Quaresma, M. (2014). Exploratory activity in the mathematics classroom. In Y. Li, E. Silver, & S. Li. (Eds.), Transforming mathematics instruction: Multiple approaches and practices. Springer.
  • Radford, L. (2008). Theories in mathematics education: A brief inquiry into their conceptual differences. Working Paper. Prepared for the ICMI Survey Team 7, 1-17.
  • Reçber, H., & Sezer, R. (2018). 8. sınıf matematik ders kitabındaki etkinliklerin bilişsel düzeyinin programdakilerle karşılaştırılması [Comparison of 8th grade mathematics textbook activities' cognitive level with those in the curriculum]. Ankara University Journal of Faculty of Educational Sciences, 51(1), 55-76.
  • Schmidt, W. H., Houang, R. T., & Cogan, L. S. (2002). A coherent curriculum: The case of mathematics. American Educator, 26(2), 10-26.
  • Seah, R., & Horne, M. (2021). Developing reasoning within a geometric learning progression: Implications for curriculum development and classroom practices. Australian Journal of Education, 65, 248-264.
  • 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.
  • Smith, M. S., & Stein, M. K. (2011). 5 Practices for orchestrating productive mathematical discussions. Corwin.
  • 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.
  • 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.
  • Toluk Uçar, Z. (2020). Matematiksel etkinlik kavramının teorik ve felsefi temelleri [Theoretical and philosophical foundations of the concept of mathematical activity]. In Y. Dede, M. F. Doğan, F. Aslan-Tutak (Eds.), Matematik eğitiminde etkinlikler ve uygulamaları [Theoretical and philosophical foundations of the concept of mathematical activity] (pp. 17-42). Pegem.
  • Ubuz, B., Erbaş, A. K., Çetinkaya, B., & Özgeldi, M. (2010). Exploring the quality of the mathematical tasks in the new Turkish elementary school mathematics curriculum guidebook: The case of algebra. ZDM Mathematics Education, 42, 483–491.
  • Ubuz, B., & Sarpkaya, G. (2014). İlköğretim 6. sınıf cebirsel görevlerin bilişsel istem seviyelerine göre incelenmesi: Ders kitapları ve sınıf uygulamaları [Examining primary school 6th grade algebraic tasks according to cognitive demand levels: Textbooks and classroom practices]. Elementary Education Online, 13(2), 595-606.
  • Van de Walle, J. A., Karp, K., S., & Bay-Williams, J. M. (2023). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Pearson.
  • Watson, A., & Mason, J. (2006). Seeing an exercise as a single mathematical object: Using variation to structure sense-making. Mathematical Thinking and Learning, 8(2), 91–111.
  • Wess, R., Klock, H., Siller, H., & Greefrath, G. (2021). Measuring professional competence for the teaching of mathematical modelling. In Leung, F. K. S., Stillman, G. A., Kaiser, G., & Wong, K. L. (Eds.), International perspectives on the teaching and learning of mathematical modelling. Springer.
There are 45 citations in total.

Details

Primary Language English
Subjects Mathematics Education
Journal Section Research Article
Authors

Şenol Namlı 0000-0003-1252-4058

Bilal Özçakır 0000-0003-2852-1791

Publication Date November 30, 2024
Submission Date June 6, 2024
Acceptance Date November 1, 2024
Published in Issue Year 2024 Volume: 8 Issue: 3

Cite

APA Namlı, Ş., & Özçakır, B. (2024). Analysing the Tasks in Middle School Mathematics Textbooks According to the Levels of Cognitive Demand. Türk Akademik Yayınlar Dergisi (TAY Journal), 8(3), 477-502.

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