إستراتيجية تدريسية مقترحة قائمة على ممارسات تدريس الرياضيات الفعّال للمجلس الوطني لمعلِّمي الرياضيات (NCTM)

Sarah Abdulhadi  Al-Otaibi; Naem Mohammed  Al-amri

doi:10.35516/edu.v51i3.6897

Authors

Sarah Abdulhadi Al-Otaibi Riyadh Education Directorate, Saudi Arabia https://orcid.org/0009-0006-1130-0801
Naem Mohammed Al-amri Department of Curricula and Teaching Methods, College of Education, King Saud University, Saudi Arabia https://orcid.org/0009-0003-1070-6533

DOI:

https://doi.org/10.35516/edu.v51i3.6897

Keywords:

Instructional strategy, effective mathematics teaching practices, National Council of Teachers of Mathematics (NCTM)

Abstract

Objectives: The study aims to design a proposed instructional strategy based on effective mathematics teaching practices.

Methods: A qualitative approach was followed to achieve the study's objective. Qualitative data was used in designing the instructional strategy through the Delphi method, gathering the opinions of nineteen experts.

Results: The thematic analysis of the data revealed a set of themes distributed across the three stages of the strategy: planning, implementation, and evaluation. The planning stage included coherence, learning objectives, success criteria, prior knowledge, vocabulary, error anticipation, purpose, nature of the task, questions, multiple representations, assessment, and classroom structure. The implementation stage included lesson launch, educational activities, questioning, task execution, mathematical dialogue, and lesson closure. The evaluation stage included diagnostic assessment, formative assessment, summative assessment, and teacher self-reflection. Based on these results, the proposed instructional strategy was designed.

Conclusions: The research concluded with several recommendations, most notably: supporting and encouraging teachers to implement the procedural steps of the instructional strategy, which represent essential practices that support the achievement of mathematical success for all students. It also recommends the development of teacher guides by experts at the Curriculum Development Center, presenting lessons in specific steps that align with effective mathematics teaching practices.

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References

Alarabiat, A., & Ramos, I. (2019). The Delphi Method in Information Systems Research (2004-2017). Electronic Journal of Business Research Methods, 17(2), 86-100. DOI: 10.34190/JBRM.17.2.04

Almarode, J., Fisher, D., Assof, J., Moore, S. D., Hattie, J., & Frey, N. (2019). Teaching Mathematics in the Visible Learning Classroom, Grades 6-8. Corwin Press.

Boston, M. D., & Wilhelm, A. G. (2017). Middle school mathematics instruction in instructionally focused urban districts. Urban Education, 52(7), 829-861.‏ https://doi.org/10.1177/0042085915574528

Boston, M. D., Madler, K., & Cutone, C. (2017). Implementing Tasks That Promote Reasoning and Problem Solving. In D.A. Spangler & J.J. Wanko (Eds), Enhancing Professional Practice with Research Behind Principles to Actions (13-26). Reston, VA: NCTM.‏

Boston, M., Dillon, F., Smith, M. S., & Miller, S. (2017). Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 9-12. Reston, VA: NCTM.‏

Brady, Shane R. (2016). The Qualitative Method. In L. Jason & D. Glenwick (Eds.), Handbook of Methodological Approaches to Community-Based Research: Qualitative, Quantitative, and Mixed Methods (pp.61-68). UK: Oxford University Press.

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative research in psychology, 3(2), 77-101. ‏DOI: 10.1191/1478088706qp063oa

Clements, D. H., Sarama, J., Baroody, A. J., Kutaka, T. S., Chernyavskiy, P., Joswick, C., ... & Joseph, E. (2021). Comparing the efficacy of early arithmetic instruction based on a learning trajectory and teaching-to-a-target. Journal of Educational Psychology, 113(7), 1323. https://doi.org/10.1037/edu0000633

Cox, D. C., Meicenheimer, J., & Hickey, D. (2017). Eliciting and Using Evidence of Student Thinking Giving Students Voice. In D.A. Spangler & J.J. Wanko (Eds), Enhancing Professional Practice with Research Behind Principles to Actions (89-97). Reston, VA: NCTM

Cross, D. I. (2009). Creating optimal mathematics learning environments: Combining argumentation and writing to enhance achievement. International Journal of Science and Mathematics Education. 7(5), 905-930.‏ https://getd.libs.uga.edu/pdfs/cross_dionne_i_200708_phd.pdf

Daro, P., Mosher, F. A., & Corcoran, T. (2011). Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction.‏ CPRE Research Reports. https://files.eric.ed.gov/fulltext/ED519792.pdf

Di Teodoro, S., Donders, S., Kemp-Davidson, J., Robertson, P., & Schuyler, L. (2011). Asking good questions: Promoting greater understanding of mathematics through purposeful teacher and student questioning. The Canadian Journal of Action Research, 12(2), 18-29. DOI: https://doi.org/10.33524/cjar.v12i2.16

Fyfe, E. R., DeCaro, M. S., & Rittle‐Johnson, B. (2014). An alternative time for telling: When conceptual instruction prior to problem solving improves mathematical knowledge. British journal of educational psychology, 84(3), 502-519.‏ DOI: 10.1111/bjep.12035

Ghousseini, H., Lord, S., & Cardon, A. (2017). Supporting math talk in small groups. Teaching children mathematics, 23(7), 422-428.‏ https://doi.org/10.5951/teacchilmath.23.7.0422

Hartati, N., & Yogi, H. P. S. (2019). Item analysis for a better quality test. English Language in Focus (ELIF), 2(1), 59-70.‏

Hiebert, J., & Grouws, D. A. (2007). The Effects of Classroom Mathematics Teaching on Students’ Learning. In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (371-404). Charlotte, NC: Information Age.

Hodges, T. E., & Johnson, M … (2017). Representation as Tool for Mathematical Understanding. In D.A. Spangler & J.J. Wanko (Eds), Enhancing Professional Practice with Research Behind Principles to Actions (27-36). Reston, VA: NCTM.‏

Huinker, D. (2018). Principles to Actions: Moving to a Framework for Teaching Mathematics. Teaching Children Mathematics, 25(3),133-137. https://doi.org/10.5951/teacchilmath.25.3.0133

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. DOI: https://doi.org/10.5951/mathteacmiddscho.18.1.0024

Jacobs, V. R., & Ambrose, R. C. (2008). Making the most of story problems. Teaching children mathematics, 15(5), 260-266.‏ https://doi.org/10.5951/TCM.15.5.0260

Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for research in mathematics education, 169-202.‏ https://doi.org/10.5951/jresematheduc.41.2.0169

Kanold, T. D., Kanold-McIntyre, J., Larson, M. R., Barnes, B., Schuhl, S., & Toncheff, M. (2018). Mathematics instruction and tasks in a PLC at work. Solution Tree Press.‏

Kazemi, E., & Stipek, D. (2009). Promoting conceptual thinking in four upper-elementary mathematics classrooms. Journal of education, 189(1-2), 123-137.‏ DOI: 10.1086/499693

Maxwell, J. (2009). Designing a Qualitative Study. In Leonard Bickman & Debra J. Rog (Eds.), The Sage handbook of applied social research methods (2nd ed., 214–253). Thousand Oaks, CA: Sage.

McClain, K. (2002). Teacher's and students' understanding: The role of tools and inscriptions in supporting effective communication. Journal of the Learning Sciences, 11(2-3), 217-249. ‏ DOI: 10.1207/S15327809JLS11,2-3n_4

McGatha, M. B., Bay-Williams, J. M., Kobett, B. M., & Wray, J. A. (2018). Everything You Need for Mathematics Coaching: Tools, Plans, and a Process That Works for Any Instructional Leader, Grades K-12. Corwin Press

Miles, R. H., & Williams, L. A. (2017). Your Mathematics Standards Companion, Grades 6-8: What They Mean and How to Teach Them. Corwin Press. ‏

National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics (NCTM). (2014). Principles to Action Ensuring Mathematical Success for All. Reston, VA: Author.

Peterson, B. E., & Viramontes, R. (2017). Key Questions to Guide Teachers in Supporting Productive Struggle in Learning Mathematics. In D.A. Spangler & J.J. Wanko (Eds), Enhancing Professional Practice with Research Behind Principles to Actions (73-87). Reston, VA: NCTM.

Reinke, L. T., Schmidt, L. W., Myers, A., & Polly, D. (2022). Developing Student Teachers’ Skills at Eliciting Students’ Mathematical Thinking Using the Coaching Cycle. The Teacher Educator, 57(2), 215-237.‏ https://doi.org/10.1080/08878730.2021.1990454

Samsuddin, A. F., & Retnawati, H. (2018, September). Mathematical representation: the roles, challenges and implication on instruction. In Journal of Physics: Conference Series, 1097(1), 012152). IOP Publishing.‏ DOI: 10.1088/1742-6596/1097/1/012152

Schuhl, S., Kanold, T. D., Deinhart, J., Larson, M. R., & Toncheff, M. (2020). Mathematics Unit Planning in a PLS at WorkTM, Grades 3-5. Reston, VA: NCTM.

Sekayi, D., & Kennedy, A. (2017). Qualitative Delphi Method: A four round process with a worked example. The Qualitative Report, 22(10), 2755-2763. shorturl.at/uvx16

Smith, M., Bill, V., & Raith, M. L. (2018). Promoting a conceptual understanding of mathematics. Mathematics Teaching in the Middle School, 24(1), 36-43. https://doi.org/10.5951/mathteacmiddscho.24.1.0036

Smith, M, & Stein, M. K. (2018). 5 Practices for Orchestrating Productive Mathematics Discussion (2nd ed). Reston, VA: NCTM. ‏

Smith, M. S., Steele, M. D., & Raith, M. L. (2017). Taking action: Implementing effective mathematics teaching practices in grades 6-8. Reston, VA: NCTM.

Spangler, Denise., & Wanko, Jeffrey. (2017). Enhancing Classroom Practice with Research Behind Principles to Action. Reston, VA: NCTM. ‏

Staples, M., & King, S. (2017). Facilitating meaningful mathematical discourse. In D. A. Spangler & J. J. Wanko (Eds.), Enhancing Classroom Practice with Research behind Principles to Actions (pp 37–48). Reston, VA: NTM.

Stein, M.K., Meikle, E. (2017). The Nature and Role of Goals in and for Mathematics Instruction. In D.A. Spangler & J.J. Wanko (Eds), Enhancing Professional Practice with Research Behind Principles to Actions (1-12). Reston, VA: NCTM.‏

Terwel, J., van Oers, B., van Dijk, I., & van den Eeden, P. (2009). Are representations to be provided or generated in primary mathematics education? Effects on transfer. Educational research and Evaluation, 15(1), 25-44.‏ DOI: 10.1080/13803610802481265

Warshauer, H. K. (2015). Strategies to support productive struggle. Mathematics Teaching in the Middle School, 20(7), 390-393. https://doi.org/10.5951/mathteacmiddscho.20.7.0390

Warshauer, H. K. (2014). Productive struggle in teaching and learning middle school mathematics. Journal of Mathematics Education, 17(4), 3-28.

Webb, D. C., Boswinkel, N., & Dekker, T. (2008). Beneath the tip of the iceberg: Using representations to support student understanding. Mathematics teaching in the middle school, 14(2), 110-113.‏ https://doi.org/10.5951/MTMS.14.2.0110

‏Wood, M. B. &, Hackett, M. (2017). Repurposing Teacher Questions. In D.A. Spangler & J.J. Wanko (Eds), Enhancing Professional Practice with Research Behind Principles to Actions (49-60). Reston, VA: NCTM

Yee, S. P., & Bostic, J. D. (2014). Developing a contextualization of students’ mathematical problem solving. The Journal of Mathematical Behavior. 36, 1-19. DOI:‏ 10.1016/j.jmathb.2014.08.002

Yimam, M., & Dagnew Kelkay, A. (2022). Evaluation of the effects of discourse-based mathematics instruction on eleventh grade students’ conceptual and procedural understanding of probability and statistics. Cogent Education, 9(1), 2007742.‏ https://doi.org/10.1080/2331186X.2021.2007742