Cognitively Demanding Tasks: Supporting Students and Teachers during Engagement and Implementation

Christopher W. Parrish; Kelly O. Bryd

doi:10.29333/iejme/11475

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Christopher W. Parrish ¹ ^* , Kelly O. Bryd ¹

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¹ University of South Alabama, USA^* Corresponding Author

Abstract

A clear relationship exists between the consistent selection and implementation of cognitively demanding tasks and students’ conceptual understanding of mathematics. However, mathematics teachers often struggle to maintain the cognitive demand of implemented tasks, with a number of factors identified as contributing to this decline. As many students have limited opportunity to engage with cognitively demanding tasks, the percentage of students proficient in mathematics remains low and unchanged. Given that the consistent opportunity to engage with cognitively demanding tasks is key to increasing the percentage of students proficient in mathematics, understanding the role of tasks in the mathematics classroom is of essence to both mathematics students and the field of mathematics education. As such, the purpose of this paper is to describe the role of cognitively demanding tasks in the mathematics classroom, the barriers to task implementation, and the supports for students and teachers related to either their engagement with or implementation of cognitively demanding tasks.

Keywords

cognitively demanding tasks
student supports
teacher supports
professional development

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Review Article

INT ELECT J MATH ED, Volume 17, Issue 1, February 2022, Article No: em0671

https://doi.org/10.29333/iejme/11475

Publication date: 03 Jan 2022

Article Views: 2504

Article Downloads: 1565

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Ader, E. (2020). Investigating elementary school teachers’ development of mathematical task implementation quality. Education and Science. 45(203), 1-25. https://doi.org/10.15390/EB.2020.8544
Arbaugh, F., & Brown, C. (2005). Analyzing mathematical tasks: A catalyst for change? Journal of Mathematics Teacher Education, 8, 499-536. https://doi.org/10.1007/s10857-006-6585-3
Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teachers College Record, 110(3), 608-645. https://www.tcrecord.org/content.asp?contentid=14590
Boston, M. D. (2013). Connecting changes in secondary mathematics teachers’ knowledge to their experiences in a professional development workshop. Journal of Mathematics Teacher Education, 16(1), 7-31. https://doi.org/10.1007/s10857-012-9211-6
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://www.jstor.org/stable/40539329
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. The International Journal on Mathematics Education, 43(6-7), 965-977. https://doi.org/10.1007/s11858-011-0353-2
Bouck, E. C., Park, J., Bouck, M., Alspaugh, J., Spitzley, S., & Buckland, A. (2019). Supporting middle school students in tier 2 math labs: Instructional strategies. Current Issues in Middle Level Education, 24(2), 18-32. https://doi.org/10.20429/cimle.2019.240203
Charalambous, C. Y. (2010). Mathematical knowledge for teaching and task unfolding: An exploratory study. The Elementary School Journal, 110(3), 247-278. https://doi.org/10.1086/648978
Clarke, D., Cheeseman, J., Roche, A., & van der Schans, S. (2014). Teaching strategies for building student persistence on challenging tasks: Insights emerging from two approaches to teacher professional learning. Mathematics Teacher Education and Development, 16(2), 46-70. https://eric.ed.gov/?id=EJ1052607
Creager, M. A., Snider, R. B., & Parrish, C. W. (2021). Learning to launch cognitively demanding tasks: A practice-based unit for secondary methods. Mathematics Teacher Educator, 9(2), 127-144. https://doi.org/10.5951/MTE.2019.0002
DiNapoli, J. (2018). Supporting secondary students’ perseverance for solving challenging mathematics tasks. In T. D. Hodges, G. J. Roy, & A. M. Tyminski (Eds.), Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 890-897). http://www.pmena.org/pmenaproceedings/PMENA%2040%202018%20Proceedings.pdf
DiNapoli, J. (2019). “Getting better at sticking with it”: Examining perseverance improvement in secondary mathematics students. In S. Otten, A. G. Candela, Z. de Araugo, C. Haines, & C. Munter (Eds.), Proceedings of the 41st Annual Meeting of the North American Chapter of the International group of the Psychology of Mathematics Education (pp. 1386-1395). https://www.pmena.org/pmenaproceedings/PMENA%2041%202019%20Proceedings.pdf
Doyle, W. (1983). Academic work. Review of Educational Research, 53(2), 159-199. https://doi.org/10.3102/00346543053002159
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
Foley, G. D., Khoshaim, H. B., Alsaeed, M., & Er, S. N. (2012). Professional development in statistics, technology, and cognitively demanding tasks: Classroom implementation and obstacles. International Journal of Mathematical Education in Science and Technology, 43(2), 177-196. https://doi.org/10.1080/0020739X.2011.592616
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, H., & 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
Jackson, K. J., Shahan, E. C., Gibbons, L. K., & Cobb, P. A. (2012). Launching complex tasks. Mathematics Teaching in the Middle School, 18(1), 24-29. https://doi.org/ 10.5951/mathteacmiddscho.18.1.0024
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
Lalley, J. P., & Miller, R. H. (2006). Effects of pre-teaching and re-teaching on math achievement and academic self-concept of students with low achievement in math. Education, 126(4), 747-755. https://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=21701257&site=eds-live
National Center for Education Statistics. (2019). 2019 mathematics state snapshot report, Alabama, grade 8, public schools. https://nces.ed.gov/nationsreportcard/subject/publications/stt2019/pdf/2020013AL8.pdf
National Council of Teachers of Mathematics. (1980) An agenda for action.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics.
National Council of Teachers of Mathematics. (1991) Professional standards for teaching mathematics.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all.
National Council of Teachers of Mathematics. (2019). Catalyzing change in high school mathematics: Initiating critical conversations.
National Council of Teachers of Mathematics. (2020a). Catalyzing change in early childhood and elementary mathematics: Initiating critical conversations.
National Council of Teachers of Mathematics. (2020b). Catalyzing change in middle school mathematics: Initiating critical conversations.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics.
Ni, Y., Zhou, D. 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
Norton, A., & Kastberg, S. E. (2012). Learning to pose cognitively demanding tasks through letter writing. Journal of Mathematics Teacher Education, 15(2), 109-130. https://doi.org/10.1007/s10857-011-9193-9
Parrish, C. W., & Martin, (2020). Cognitively demanding tasks and the associated learning opportunities within the MathTwitterBlogosphere. International Journal of Mathematical Education in Science and Technology, 1-39. https://doi.org/10.1080/0020739X.2020.1772388
Pesek, D. D., & Kirshner, D. (2000). Inference of instrumental instruction in subsequent relational learning. Journal for Research in Mathematics Education, 31(5), 524-540. https://doi.org/10.2307/749885
Russo, J., & Hopkins, S. (2017). CLASS challenging tasks: Using cognitive load theory to inform the design of challenging mathematical tasks. Australian Primary Mathematics Classroom, 21, 21-27. https://files.eric.ed.gov/fulltext/EJ1138041.pdf
Russo, J., & Hopkins, S. (2019). Teaching primary mathematics with challenging tasks: How should lessons be structured? The Journal of Educational Research, 112(1), 98-109. https://doi.org/10.1080/00220671.2018.1440369
Smith, M., Bill, V., & Hughes, E. (2008). Thinking through a lesson: Successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14(3), 132-138. https://doi.org/10.5951/MTMS.14.3.0132
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 mathematical 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, 268-275. https://doi.org/10.5951/MTMS.3.4.0268
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/10.3102/00028312033002455
Stein, M. K., Smith, M. S., Arbaugh, F., Brown, C. A., & Mossgrove, J. (2004). Characterizing the cognitive demands of mathematical tasks: A task-sorting activity. Professional development guidebook (A supplement to the National Council of Teachers of Mathematics 2004 Yearbook). National Council of Teachers of Mathematics.
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E., A. (2009). Implementing standards-based mathematics instruction: A casebook for professional development (Vol. 2). Teachers College Press.
Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. Teachers College Press.
Stylianides, A. J., & Stylianides, G. J. (2008). Studying the classroom implementation of tasks: High-level mathematical tasks embedded in “real-life” contexts. Teacher and Teacher Education, 24(4), 859-875. https://doi.org/10.1016/j.tate.2007.11.015
Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A., & Walker, N. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 18, 123-140. https://doi.org/10.1007/s10857-014-9279-2
Sullivan, P., Mousley, J., & Jorgensen, R. (2009). Tasks and pedagogies that facilitate mathematical problem solving. In B. Kaur (Ed.), Mathematical problem solving (pp. 17-42). Singapore/ USA/ UK World Scientific Publishing: Association of Mathematics Educators. https://doi.org/10.1142/9789814277228_0002
Tarr, J. E., Reys, R. E., Reys, B. J., Chavez, O., Shih, J., & Osterlind, S. J. (2008). The impact of middle-grades mathematics curricula and the classroom learning environment on student achievement. Journal for Research in Mathematics Education, 39(3), 247-280. https://doi.org/10.2307/30034970
Tekkumru Kisa, M., & Stein, M. K. (2015). Learning to see teaching in new ways: A foundation for maintaining cognitive demand. American Educational Research Journal, 52(1), 105-136. https://doi.org/10.3102/0002831214549452
Watt, S. J., Kaldenberg, E., & Therrien, B. (2013). The effects of preteaching on students at risk for and with math learning disabilities. Journal of Evidence-Based Practices for Schools, 14(2), 134-159. https://psycnet.apa.org/record/2014-55912-002
Watt, S., J., & Therrien, W. J. (2016). Examining a preteaching framework to improve fraction computation outcomes among struggling learners. Preventing School Failure: Alternative Education for Children and Youth, 60(4), 311-319. https://doi.org/10.1080/1045988X.2016.1147011
Wilhelm, A. G. (2014). Mathematics teachers’ enactment of cognitively demanding tasks: Investigating links to teachers’ knowledge and conceptions. Journal for Research in Mathematics Education, 45(5), 636-674. https://doi.org/10.5951/jresematheduc.45.5.0636
Wilhelm, A. G., & Woods, D. M. (2020). Learning to launch complex tasks: How instructional visions influence the exploration of the practice. National Council of Teachers of Mathematics, 8(3), 105-119. https://doi.org/10.5951/MTE.2020.0010

How to cite this article

APA

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

Vancouver

Parrish CW, Bryd KO. Cognitively Demanding Tasks: Supporting Students and Teachers during Engagement and Implementation. INT ELECT J MATH ED. 2022;17(1):em0671. https://doi.org/10.29333/iejme/11475

AMA

Parrish CW, Bryd KO. Cognitively Demanding Tasks: Supporting Students and Teachers during Engagement and Implementation. INT ELECT J MATH ED. 2022;17(1), em0671. https://doi.org/10.29333/iejme/11475

Chicago

Parrish, Christopher W., and Kelly O. Bryd. "Cognitively Demanding Tasks: Supporting Students and Teachers during Engagement and Implementation". International Electronic Journal of Mathematics Education 2022 17 no. 1 (2022): em0671. https://doi.org/10.29333/iejme/11475

Harvard

Parrish, C. W., and 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

MLA

Parrish, Christopher W. et al. "Cognitively Demanding Tasks: Supporting Students and Teachers during Engagement and Implementation". International Electronic Journal of Mathematics Education, vol. 17, no. 1, 2022, em0671. https://doi.org/10.29333/iejme/11475