April 2024

Volume 07 Issue 04 April 2024
An Innovative Model to Promote Secondary Students' Critical Thinking Skills in Algebra Learning
Wei Liu
Hillcrest Christian College VIC Australia
DOI : https://doi.org/10.47191/ijsshr/v7-i04-28

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ABSTRACT

This research aims to explore a learning model based on 21st-century skills and the Australian curriculum to cultivate students’ critical thinking skills in junior secondary mathematics algebra learning. This study used a mixed method. Quantitative data was collected through a questionnaire that provided information about perceptions of the challenges in learning algebra. Qualitative data was collected through semi-interviews with secondary mathematics teachers, which provided an opportunity for teachers to evaluate their understanding of critical thinking skills for algebra, it further clarified teachers’ expectations of mastering the key algebraic contents. Based on the data from the questionnaire and semi-interview, a practical model for embedding critical thinking skills and strategies in learning algebra was designed. The mathematical curriculum in Victoria and Australia were explored as they provided the basis of the model.

KEYWORDS:

Critical thinking Algebraic learning Critical- Algebraic model Algebraic learning framework

REFERENCES
1) National Council for Excellence in Critical Thinking (NCECT) (2017). Retrieved from https://www.criticalthinking.org/pages/the-national-council-for-excellence-in-critical-thinking/406

2) Organisation for Economic Co-operation and Development (2018). Programme for International Students Assessment (PISA), https://www.oecd.org/pisa/

3) Dwyer, C.P., Hogan, M. J., & Stewart, I. (2014). An integrated critical thinking framework for the 21st century. Thinking Skills and Creativity,12, 67-77.

4) Cheng, M.H.M., & Wan, Z.H. (2017). Exploring the effects of classroom learning environment on critical thinking skills and disposition: a study of Hong Kong 12th graders in liberal studies. Thinking Skills and Creativity,24, 152-163.

5) Liu,W.(2023). Exploring Chinese secondary teachers’ perception of critical thinking in mathematics teaching. Asian Conference on Education & International Development 2023

6) Australian Curriculum, Assessment and Reporting Authority (ACARA)(2016). Australian curriculum mathematics.URL: https://australiancurriculum.edu.au/f-10-curriculum/mathematics?

7) Fox, E., & Riconscente, M. (2008). Metacognition and self-regulation in James, Piaget, and Vygotsky. Educational Psychology Review, 20(4), 373-389. doi: 10.1007/s10648-008-9079

8) Gredler, M. (2009). Learning and instruction: Theory into practice (6th Ed.). Upper Saddle River, NJ: Merrill Pearson.

9) Pehkonen, E., Näveri, L., & Laine, A. (2013). On teaching problem solving in school mathematics. CEPS Journal: Center for educational Policy Studies Journal, 3(4), 9-23.

10) Cobb, P., Wood, T., Yackel, E. & McNeal, B. (1992). Characteristics of classroom mathematics tradition: an interactional analysis. American Educational Research Journal, 29, 573-604.

11) Henningsen, M. and 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, 25(5), 524-549

12) Zohar,A., & Dori, Y. J.(2003). Higher order thinking skills and low achieving students: are they mutually exclusive? Journal of the Learning Science, 12,145-181. Http://dx.doi.org/10.1207/S15327809JLS1202_1

13) Aizikovitsh-Udi,E., & Cheng, D.(2015). Developing critical thinking skills from dispositions to abilities: mathematics education from early childhood to high school. Creative Education, 6,455-462.

14) Fuad,J.,Ardana,W., Sulton,& Kuswandi,D.(2015). Increasing critical thinking skill through class debate. 1st UPI International Conference on Sociology Education (UPI ICSE 2015). 38-42.

15) Tee,K.N., Leong, K.E., Rahim, S.S.A.(2018). The Mediating Effects of Critical Thinking Skills on Motivation Factors for Mathematical Reasoning Ability. Asia-Pacific Edu Res, 27(5),373–382. https://doi.org/10.1007/s40299-018-0396-z

16) Osarenren, N., & Asiedu, A.S. (2007). Counselling implications on the role of the new mathematics teacher in the teaching and learning mathematics. International Journal of Educational Research, 3 (1), 13-20.

17) Alwadai, M.A. (2014). Islamic teachers’ perceptions of improving critical thinking skills in Saudi Arabian elementary school. Journal of Education and Learning, 3(4), 37-48.

18) Moore, T. (2004). The critical thinking debate: how general are general thinking skills? Higher Education: Research and Development,23(1),3-18.

19) Van Gelder,T., Bisset,M. & Cummings,G.(2004). Cultivating expertise in informal reasoning. Teaching,45(1),1-6.

20) Ennis, R. H. (1989). Critical thinking and subject specificity: Clarification and needed research. Educational Researcher,18(3), 4-10.

21) Case, R. (2005). Moving critical thinking to the main stage. Education Canada, 45(2), 45-49.

22) Silva, E. (2008). Measuring skills for the 21st Century. Washington, DC: Education Sector.

23) Swartz, R., & Parks, S.(1994). Infusing the Teaching of Critical and Creative Thinking into Content Instruction. A Lesson Design Handbook for the Elementary Grades, Critical Thinking Books & Software, California, 5–20.

24) Browne, M.N., & Keeley, S.M.,( 2004). Asking the Right Questions: A Guide to Critical Thinking, Prentice Hall, Englewood Cliffs, N.J.

25) Maričić, S., Špijunović, K. & Malinović Jovanović, N. (2013). The Role of Tasks in the Development of Students' Critical Thinking in Initial Teaching of Mathematics. In J. Novotna, H. Moraova Eds.).Task and tools in elementary mathematics (pp. 204–212). Prague, the Czech Republic: Charles University: Faculty of Education.

26) McPeck, J. E. (2016). Critical thinking and education. Routledge.

27) Davies, W. Martin (2006) 'An 'infusion' approach to critical thinking: Moore on the critical thinking debate', Higher Education Research & Development, 25: 2, 179 — 193

28) New South Wales Department of Education and Training (NSW DET)(2003). Quality Teaching in NSW Public Schools: Discussion paper. Sydney: Author. URL:http://www.darcymoore.net/wp-content/uploads/2012/02/qt_EPSColor.pdf

29) Kong,S.C.(2015). An experience of a three-year study on the development of critical thinking skills in a flipped sedcondary classrooms with pedagogical and technological support. Comoputers and Education,89(1),16-31.

30) Tunca,N.(2015). The regression level of constructivist learning environment characteristics on classroom environment characteristics supporting critical thinking. Eurasian Journal of Educational Research,60,181-200.

31) Huang,H.,F., Su,A., Ricci, F.,A., Mnatsakanian,M.(2016). Mathematical teaching strategies: pathways to critical thinking and metacognition. Internationl Journal of Research in Education and Science,2(1), 190-200.

32) Ennis, R. H., & Weir, E. E. (1985). The Ennis-Weir Critical Thinking Essay Test: An Instrument for Teaching and Testing. Retrieved from http://faculty.education.illinois.edu/rhennis/tewctet/Ennis-Weir_Merged.pd

33) Muthmainnah, M., Priatna, N., & Priatna, B. A. (2017). Analysis of students’ error in algebraic thinking test. Journal of Physics: Conference Series, 895(1), 1-5. Doi: 10.1088/1742-6596/895/1/012089

34) Paul, R. (1993). Critical thinking: What every person needs to survive in a rapidly changing world (3rdrev. ed.). Rohnert Park, CA: Center for Critical Thinking and Moral Critique, Sonoma State University

35) Paul, R., Willsen, J., & Binker, A. J. A. (1993). Critical thinking. Santa Rosa, CA: Foundation for Critical Thinking.

36) Paul, R., & Elder, L. (2010). International Critical Thinking Test. Foundation for Critical Thinking.

37) Duron, R., Limbach, B., & Waugh, W., (2006). Critical Thinking Framework For Any Discipline. International Journal of Teaching and Learning in Higher Education 17(2), 160-166.

38) Su, H.F., Ricci, F.A., & Mnatsakanian, M. (2016). Mathematical teaching strategies: Pathways to critical thinking and metacognition. Journal of Research in Education and Science (IJRES), 2 (1), 190-200.

39) National Council of Teachers of Mathematics (2000 ).Principles and Standards for Mathematics. (Reston: VA). https://www.itws.org/NCTM-ContentProcessCoreStandards.pdf

40) Permatasari,D.,Azka,R., & Fikriya,H.O.(2021). Exploring students’ algebraic thinking in generational activities and their difficulties. Journal Tadris Matematika,14(1),53-68. DOI 10.20414/betajtm.v14i1.418

41) Andini, W., & Suryadi, D. (2017). Student obstacles in solving algebraic thinking problems. Journal of Physics: Conference Series, 895(1), 1-6. Doi: 10.1088/1742-6596/895/1/012091

42) Fakhrunisa, F., & Hasanah, A. (2020). Students’ algebraic thinking: A study of mathematical modelling competencies. Journal of Physics: Conference Series, 1521(3), 1-6. Doi: 10.1088/1742-6596/1521/3/032077

43) Rahardjoni,A.S.,Hasanah, I. N., & Nugraheni,M.S.(2020).Developing critical thinking competence in algebraic thinking using augmented reality for junior high school. PRISMA, Prosiding Seminar Nasional Matematika 3, 497-503.

44) Britt, M. S., & Irwin, K. C. (2008). Algebraic thinking with and without algebraic representation: A three-year longitudinal study. ZDM - International Journal on Mathematics Education, 40(1), 39–53. Doi: 10.1007/s11858-007-0064-x

45) Patton, B., & Santos, E. (2012). Analyzing algebraic thinking using “guess my number” problems. International Journal of Instruction, 5(1), 5–22.

46) Siew, N. M., Geofrey, Jolly, & Lee, B. N. (2018). Students’ Algebraic Thinking and Attitudes towards Algebra: The Effects of Game-Based Learning using Dragonbox 12+ App. The Electronic Journal of Mathematics and Technology. 10(1), ISSN 1933-2823

47) Kieran, C. (1992). The Learning and Teaching of School Algebra. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 390-419). New York: Macmillan Publishing Company.

48) Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 139–151.

49) Van Amerom, B. A. (2003).Focusing on Informal Strategies When Linking Arithmetic to Early Algebra. Educational Studies in Mathematics, 54(1), 63-75.

50) Stacey, K. & Chick, H.(2004). Solving the problem with algebra The Future of the Teaching and Learning of Algebra: The 12th ICMI Study ed Stacey K, Chick H and Kendal M (Boston: Kluwer) pp.1–20

51) Rohati, Kusumah,Y.S., Kusnandi & Marlina.(2022). How Teachers Encourage Students’ Mathematical Reasoning during the Covid-19 Pandemic? Journal Pendidikan Indonesia,11(4), 715-726, https://doi.org/10.23887/jpiundiksha.v11i4.52756

52) Rohati, R.; Kusumah, Y.S.; Kusnandi, K. (2023).Exploring Students’ Mathematical Reasoning Behavior in Junior High Schools: A Grounded Theory. Educ. Sci. 13, 252. https://doi.org/10.3390/ educsci13030252

53) Gonser,S.(2020). How to Encourage Independent Thinking in Math. https://www.edutopia.org/article/how-encourage-independent-thinking-math

54) Junarti ,Ahamad, Y,T.,Amin, A.K. (2023). Building student's mathematical connection ability in abstract algebra: the combination of analogic-construction-abstraction stages. Journal of Education, Teaching, and Learning, 8( 1), P 80-97

55) Liu,W.,Osmond, D., & Affas,H.(2023).Pedagogical practice study about designing mathematics Investigation tasks for senior students in Australia. International Journal of Social Science And Human Research, 6(11),7146-7157. DOI: 10.47191/ijsshr/v6-i11-77

56) Heleni, S., & Zulkarnain. (2018). The Influence of Mathematical Thinking Ability with Modified MOORE Method on Learning Outcomes of Basic Mathematic II Chemical Education Students. Journal of Educational Sciences, 2(2), 33-41.
Volume 07 Issue 04 April 2024

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