Instructional Design: Teaching Algebraic Equations to Grade 8 Students with Involvement of Mathematical Reasoning in Cambridge IGCSE Curriculum
DOI:
https://doi.org/10.37640/jim.v3i1.1035Keywords:
Algebraic equations, English instructions, Instructional design, Mathematical reasoningAbstract
Mathematics tends to be a subject that is not favored due to a misunderstanding of the whole concept. The author believes that through involvement of mathematical reasoning skills and proper instructional strategies, students understanding can be transformed and students will be able to relearn the concept. The aim of this paper is to help teachers to recreate their lesson plans in a form of an instructional design with the involvement of mathematical reasoning, specifically in learning and relearning algebraic equations (constructivism), that can further diminish the anxiety and frustration students experience due to misconceptions in their algebraic comprehension. Through a combination of theories related to the teaching and learning of algebra in secondary school and frameworks regarding instructional strategies, the betterment of mathematical reasoning is expected to go along the relearning process, and the students will be equipped to move forward in learning mathematics. This instructional design will provide a variety of learning activities ideas, including a sample lesson plan along with other supporting documents for learning activities that teachers can use in the classroom.
References
Battista, M. T. (2017). Reasoning and sense making in the mathematics classroom, grades 6-8. NCTM.
Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. Springer.
Cambridge International Examinations. (2016). IGCSE Mathematics Syllabus 0580. Cambridge International General Certificate of Secondary Education.
Cafarella, B. V. (2014). Exploring best practices in developmental math. Research and Teaching in Developmental Education, 30(2), 35-64.
Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French and German classrooms: Who gets an opportunity to learn what?. British educational research journal, 28(4), 567-590. https://doi.org/10.1080/0141192022000005832
Ignacio, N. G., Nieto, L. J. B., & Barona, E. G. (2006). The affective domain in mathematics learning. International Electronic Journal of Mathematics Education, 1(1), 16-32.
Kaur, B., & Toh, T. L. (Eds.). (2012). Reasoning, Communication and Connections in Mathematics: Yearbook 2012, Association of Mathematics Educators (Vol. 4). World Scientific.
Kirkpatrick, D. L. (1994). Evaluating Training Programs: The Four Levels. Berrett-Koehler.
Kontorovich, I. (2020). Theorems or procedures? Exploring undergraduates’ methods to solve routine problems in linear algebra. Mathematics Education Research Journal, 32, 589-605. https://doi.org/10.1007/s13394-019-00272-3
Kurt, S. (2017). ADDIE model: Instructional design. Educational Technology, 29.
Kuchemann, D. E. (1981). Algebra. In Hark K (Ed). Children’s understanding of Mathematics. Marry
Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169-186. https://doi.org/10.1007/s10649-017-9773-4
McTighe, J., & Wiggins, G. (2005). Understanding by Design. ASCD.
Molina, M., Rodríguez-Domingo, S., Cañadas, M. C., & Castro, E. (2017). Secondary school students’ errors in the translation of algebraic statements. International Journal of Science and Mathematics Education, 15(6), 1137-1156. https://doi.org/10.1007/s10763-016-9739-5
Musanti, S. I., Celedón-Pattichis, S., & Marshall, M. E. (2009). Reflections on language and mathematics problem solving: A case study of a bilingual first-grade teacher. Bilingual Research Journal, 32(1), 25-41. https://doi.org/10.1080/15235880902965763
Ontario Ministry of Education (2013). Paying attention to algebraic reasoning, K-12: Support document for paying attention to mathematical education. Queen's Printer for Ontario.
Partami, I., Padmadewi. N., & Artini, L. P. (2019). Differentiated Instruction in Multicultural Classroom of Primary Years Program in Gandhi Memorial Intercontinental School-Bali. Jurnal Pendidikan Bahasa Inggris Indonesia, 7(1), 1-11. https://doi.org/10.23887/jpbi.v7i1.2717
Parwati, N., & Suharta, I. (2020). Effectiveness of the implementation of cognitive conflict strategy assisted by e-service learning to reduce students' mathematical misconceptions. International Journal of Emerging Technologies in Learning (iJET), 15(11), 102-118. https://doi.org/10.3991/ijet.v15i11.11802
Prideaux, J. (2019). The constructivist Approach to Mathematics Teaching and the Active Learning Strategies used to Enhance Students Understanding. Mathematical and Computing Sciences Masters. Fisher Digital Publications.
National Council of Teachers of Mathematics. (2008). Principles and standards for school mathematics. NCTM.
Ramdani, Y. (2011). Enhancement of Mathematical Reasoning Ability at Senior High School by The Application of Learning with Open Ended Approach. In Seminar and the Fourth National Conference on Mathematics Education. Universitas Negeri Yogyakarta.
Sarwadi, H. R. H., & Shahrill, M. (2014). Understanding students’ mathematical errors and misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research, 2014(2014), 1-10. https://doi.org/10.5899/2014/metr-00051
Thorpe, J. A. (2018). Algebra: What should we teach and how should we teach it?. In Research issues in the learning and teaching of algebra (pp. 11-24). Routledge. https://doi.org/10.4324/9781315044378-2
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics teaching developmentally. Pearson.
Wagner, S. (1983). What are these things called variables?. The mathematics teacher, 76(7), 474-479.
Yuni, Y., Alghadari, F., Wulandari, A., & Huda, S. A. A. (2021). Student Thinking Levels in Solving Open-Ended Geometric-Function Problem by Algebraic Representation Approach. In 1st Annual International Conference on Natural and Social Science Education (ICNSSE 2020) (pp. 333-341). Atlantis Press. https://doi.org/10.2991/assehr.k.210430.050
Zazkis, R., Liljedahl, P., & Chernoff, E. J. (2008). The role of examples in forming and refuting generalizations. ZDM, 40(1), 131-141. https://doi.org/10.1007/s11858-007-0065-9
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