Investigating Pedagogical Content Knowledge and Decision-Making on Algebraic Tasks

Authors

  • Ajeng Gelora Mastuti IAIN Ambon, Maluku, Indonesia

DOI:

https://doi.org/10.15642/jrpm.2023.8.1.1-17

Keywords:

Pedagogical Content Knowledge, Decision-making, Algebraic tasks

Abstract

Pedagogical Content Knowledge (PCK) tasks and decision-making are closely related to teaching and learning mathematics. This study aims to investigate teacher PCK in decision-making on different algebra tasks and to see activity in teacher-student interactions. This research is qualitative, with a research approach used as a case study. The participants in this study were only one teacher with different characteristics in mathematics tasks. Data collection consisted of primary research data from class observations, teacher interview transcripts, and researcher notes, while documents such as teacher notes were secondary data. Data analysis was carried out directly based on class observations and interviews. The findings in this study reveal teacher PCK through teacher decision-making regarding algebraic tasks in Swartz & Perkins (2016) three theories of thinking: generating ideas, clarifying ideas, and assessing the reasonableness of ideas.

Downloads

Download data is not yet available.

References

Abdillah, A., & Mastuti, A. G. (2018). Munculnya Kreativitas Siswa Akibat Ill Structured Mathematical Problem. Matematika Dan Pembelajaran, 6(1), Article 1. https://doi.org/10.33477/mp.v6i1.442

Berisha, V., & Bytyqi, R. (2020). Types of mathematical tasks used in secondary classroom instruction. International Journal of Evaluation and Research in Education (IJERE), 9(3), 751. https://doi.org/10.11591/ijere.v9i3.20617

Bringula, R., Reguyal, J. J., Tan, D. D., & Ulfa, S. (2021). Mathematics self-concept and challenges of learners in an online learning environment during COVID-19 pandemic. Smart Learning Environments, 8(1), Article 1. https://doi.org/10.1186/s40561-021-00168-5

Chapman, O. (2013). Mathematical-task knowledge for teaching. Journal of Mathematics Teacher Education, 16(1), 1–6. https://doi.org/10.1007/s10857-013-9234-7

Chirove, M., & Ogbonnaya, U. I. (2021). The relationship between grade 11 learners’ procedural and conceptual knowledge of algebra. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(4), 368–387. https://doi.org/10.23917/jramathedu.v6i4.14785

Darling-Hammond, L., Flook, L., Cook-Harvey, C., Barron, B., & Osher, D. (2020). Implications for educational practice of the science of learning and development. Applied Developmental Science, 24(2), Article 2. https://doi.org/10.1080/10888691.2018.1537791

Demosthenous, E., Christou, C., & Pitta-Pantazi, D. (2021). Mathematics Classroom Assessment: A Framework for Designing Assessment Tasks and Interpreting Students’ Responses. European Journal of Investigation in Health, Psychology and Education, 11(3), 1088–1106. https://doi.org/10.3390/ejihpe11030081

Fukaya, T., Suzuki, M., Ozawa, I., & Nakagoshi, T. (2022). An Examination of Related Factors of Mathematical Pedagogical Content Knowledge in Elementary School Teachers: Focusing on Conceptions of Teaching and Learning and Test Utilization Strategy. SAGE Open, 12(4), 21582440221131264. https://doi.org/10.1177/21582440221131263

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

Hurrell, D. (2021). Conceptual Knowledge OR Procedural Knowledge or Conceptual Knowledge AND Procedural Knowledge: Why the Conjunction is Important to Teachers. Australian Journal of Teacher Education, 46(2), 57–71. https://doi.org/10.14221/ajte.2021v46n2.4

Johnson, H. L., Coles, A., & Clarke, D. (2017). Mathematical tasks and the student: Navigating “tensions of intentions” between designers, teachers, and students. ZDM, 49(6), Article 6. https://doi.org/10.1007/s11858-017-0894-0

Kim, S., Raza, M., & Seidman, E. (2019). Improving 21st-century teaching skills: The key to effective 21st-century learners. Research in Comparative and International Education, 14(1), Article 1. https://doi.org/10.1177/1745499919829214

Kuennen, E. W., & Beam, J. E. (2020). Teaching the mathematics that teachers need to know: Classroom ideas for supporting prospective elementary teachers’ development of mathematical knowledge for teaching. The Mathematics Enthusiast, 17(2–3), 771–805. https://doi.org/10.54870/1551-3440.1503

Li, Y., & Schoenfeld, A. H. (2019). Problematizing teaching and learning mathematics as “given” in STEM education. International Journal of STEM Education, 6(1), Article 1. https://doi.org/10.1186/s40594-019-0197-9

Mastuti, A. G., Abdillah, A., & Rijal, M. (2022). Teachers Promoting Mathematical Reasoning in Tasks. JTAM (Jurnal Teori Dan Aplikasi Matematika), 6(2), Article 2. https://doi.org/10.31764/jtam.v6i2.7339

Mastuti, A. G., Abdillah, A., Sehuwaky, N., & Risahondua, R. (2022). Revealing students’ critical thinking ability according to Facione’s theory. Al-Jabar: Jurnal Pendidikan Matematika, 13(2), Article 2. https://doi.org/10.24042/ajpm.v13i2.13005

Mastuti, A. G., Kaliky, S., & Arman, J. (2022). Mathematical Communication and Students’ Epistemological Beliefs of Linear Systems with Three Variables. JTAM (Jurnal Teori Dan Aplikasi Matematika), 6, 963. https://doi.org/10.31764/jtam.v6i4.9772

Mastuti, A. G., & Prayitno, L. L. (2023). Exploring high school teacher’s design of rich algebra tasks. Jurnal Elemen, 9(1), 1–14. https://doi.org/10.29408/jel.v9i1.5851

Ormond, C. A. (2021). Teaching Classroom Mathematics: Linking Two Pedagogical Models for Promoting Student Engagement and Conceptual Connections. Australian Journal of Teacher Education, 46(4), 35–62. https://doi.org/10.14221/ajte.2021v46n4.3

Ozan, C., & Kıncal, R. Y. (2018). The Effects of Formative Assessment on Academic Achievement, Attitudes toward the Lesson, and Self-Regulation Skills. Educational Sciences: Theory & Practice. https://doi.org/10.12738/estp.2018.1.0216

Papadopoulos, I. (2020). Using tasks to bring challenge in mathematics classroom. Journal of Pedagogical Research, 4(3), Article 3. https://doi.org/10.33902/JPR.2020063021

Stehle, S. M., & Peters-Burton, E. E. (2019). Developing student 21st Century skills in selected exemplary inclusive STEM high schools. International Journal of STEM Education, 6(39), Article 39. https://doi.org/10.1186/s40594-019-0192-1

Stylianou, D. (2013). An Examination of Connections in Mathematical Processes in Students’ Problem Solving: Connections between Representing and Justifying. Journal of Education and Learning, 2. https://doi.org/10.5539/jel.v2n2p23

Sullivan, P., Knott, L., & Yang, Y. (2015). The Relationships Between Task Design, Anticipated Pedagogies, and Student Learning. In A. Watson & M. Ohtani (Eds.), Task Design In Mathematics Education: An ICMI study 22 (pp. 83–114). Springer International Publishing. https://doi.org/10.1007/978-3-319-09629-2_3

Swartz, R. J., & Perkins, D. N. (2016). Teaching Thinking: Issues and Approaches. Routledge. https://doi.org/10.4324/9781315626468

Timothy, V., Watzka, B., Stadler, M., Girwidz, R., & Fischer, F. (2022). Fostering Preservice Teachers’ Diagnostic Competence in Identifying Students’ Misconceptions in Physics. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-022-10311-4

Vermeulen, C., & Meyer, B. (2017). The Equal Sign: Teachers’ Knowledge and Students’ Misconceptions. African Journal of Research in Mathematics, Science and Technology Education, 21, 1–12. https://doi.org/10.1080/18117295.2017.1321343

Wu, H.-H. (2018). The Content Knowledge Mathematics Teachers Need (pp. 43–91). https://doi.org/10.1007/978-3-319-61434-2_4

Yurniwati, Y., & Kustandi, C. (2022). Determination and Comparison Pedagogical Content Knowledge of Pre-Service and In-Service Elementary School Teachers in Mathematics. Journal of Further and Higher Education, 22, 117. https://doi.org/10.33423/jhetp.v22i4.5161

Downloads

Published

2023-06-30

How to Cite

Mastuti, A. G. (2023). Investigating Pedagogical Content Knowledge and Decision-Making on Algebraic Tasks. JRPM (Jurnal Review Pembelajaran Matematika), 8(1), 1–17. https://doi.org/10.15642/jrpm.2023.8.1.1-17

Issue

Section

Articles