Mathematics Teachers' Conceptual Knowledge of Algebra: A Literature Review/ Pengetahuan Konseptual Algebra Guru Matematik: Satu Kajian Literatur

Authors

  • Nor Adibah Abdullah Fakulti Pendidikan, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

DOI:

https://doi.org/10.11113/sh.v12n1.1048

Keywords:

Conceptual understanding, algebra, mathematics teachers, school, conceptual study

Abstract

Conceptual knowledge is one of the mathematical knowledge areas which should be mastered by mathematics teachers besides factual, procedural, and metacognitive knowledge. Teachers are prone to cast conceptual knowledge aside and prioritise procedural knowledge without understanding the concepts which influence the options of mathematical strategies and models in the context of problem solving. A literature review was conducted to discuss past research findings in identifying secondary school teachers' conceptual knowledge in the algebra topic. 68 past research articles were referred to and chosen based on the research purpose which was to investigate mathematics teachers' conceptual knowledge level and its implementation in several mathematical topics quantitatively and qualitatively in local and international contexts.  There have been a lot of researches conducted on teachers' conceptual knowledge in several mathematical topics, however there is still a lack of research in investigating teachers' conceptual knowledge on the algebra topic. Most of the past research findings showed that the teachers' conceptual knowledge level was at a low level in several mathematical  topics therefore a similar research is also needed in the algebra topic. This study can be extended to a more improved research in spite of the research sample, design or research methodology, instruments, and other factors.

 

References

Aksoy, Y., Bayazit, I., & Dönmez, S. M. K. (2015). Prospective Primary School Teachers' Proficiencies In Solving Real-World Problems: Approaches, Strategies And Models. EURASIA Journal of Mathematics, Science & Technology Education, 11(4), 827-839.

Alenazi, A. (2016). Examining Middle School Pre-Service Teachers’ Knowledge Of Fraction Division Interpretations. International Journal of Mathematical Education in Science and Technology, 47(5), 696-716.

Bair, S. L., & Rich, B. S. (2011). Characterizing the Development Of Specialized Mathematical Content Knowledge For Teaching In Algebraic Reasoning And Number Theory. Mathematical Thinking and Learning, 13(4), 292-321.

Banerjee, R., & Subramaniam, K. (2012). Evolution of a Teaching Approach For Beginning Algebra. Educational Studies in Mathematics, 80(3), 351-367.

Baroody, A. J., Feil, Y., & Johnson, A. R. (2007). An alternative Reconceptualization Of Procedural And Conceptual Knowledge. Journal For Research In Mathematics Education, 38(2), 115-131.

Borko, H., & Whitcomb, J. A. (2008). Teachers, Teaching, And Teacher Education: Comments On The National Mathematics Advisory Panel’s Report. Educational researcher, 37(9), 565-572.

Burroughs, E. A., & Yopp, D. (2010). Prospective Teachers' Understanding Of Decimals With Single Repeating Digits. Investigations in Mathematics Learning, 3(1), 23-42.

Byun, M. (2015). Enhancing Pre-Service Teachers' Knowledge Of Fractions Through The Model Method. (Doctor of Philosophy), Southern Illinois University Carbondale, Carbondale, Illinois, United States.

Capraro, M. M., An, S. A., Ma, T., Rangel-Chavez, A. F., & Harbaugh, A. (2012). An Investigation Of Preservice Teachers’ Use Of Guess And Check In Solving A Semi Open-Ended Mathematics Problem. The Journal of Mathematical Behavior, 31(1), 105-116.

Capraro, M. M., & Joffrion, H. (2006). Algebraic Equations: Can Middle-School Students Meaningfully Translate From Words To Mathematical Symbols? Reading Psychology, 27(2-3), 147-164.

Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and Algebra In Early Mathematics Education. Journal for research In Mathematics Education, 87-115.

Cave, A., & Brown, C. W. (2010). When Learning Is At Stake: Exploration Of The Role Of Teacher Training And Professional Development Schools On Elementary Students’ Math Achievement. Paper presented at the National Forum of Teacher Education Journal.

Chapman, O. (2012). Prospective Elementary School Teachers’ Ways Of Making Sense Of Mathematical Problem Posing. Pna, 6(4), 135-146.

da Ponte, J. P., & Chapman, O. (2008). Preservice Mathematics Teachers’ Knowledge and Development (Vol. 2). New York: Routledge.

Effandi Zakaria, Norazah Mohd, & Sabri Ahmad. (2007). Trend Pengajaran dan Pembelajaran Matematik. Kuala Lumpur: Utusan Publications & Distributors.

Effandi Zakaria, & Norliza Zaini. (2009). Conceptual and Procedural Knowledge Of Rational Numbers In Trainee Teachers. European Journal of Social Sciences, 9(2), 202-217.

Feldman, Z. (2012). Describing Pre-Service Teachers' Developing Understanding Of Elementary Number Theory Topics. (Doctor of Philosophy), Boston University, Boston, Massachusetts.

Frederick, M. F., & Kirsch, R. L. (2011). Conceptual Mathematics Knowledge. In J. W. C. III & N. P. O’Brien (Eds.), The Greenwood Dictionary of Education (2nd Ed.) (pp. 94). Santa Barbara, California: Greenwood.

Groth, R. E. (2014). Prospective Teachers' Procedural And Conceptual Knowledge Of Mean Absolute Deviation. Investigations in Mathematics Learning, 6(3), 51-69.

Groth, R. E., & Bergner, J. A. (2006). Preservice Elementary Teachers' Conceptual And Procedural Knowledge Of Mean, Median, And Mode. Mathematical Thinking and Learning, 8(1), 37-63.

Hannigan, A., Gill, O., & Leavy, A. M. (2013). An Investigation Of Prospective Secondary Mathematics Teachers’ Conceptual Knowledge Of And Attitudes Towards Statistics. Journal of Mathematics Teacher Education, 16(6), 427-449. doi: 10.1007/s10857-013-9246-3

Hayata, C. A. (2012). The development Of Algebraic Reasoning In Undergraduate Elementary Preservice Teachers. (Doctor of Philosophy), University of North Texas, Denton, Texas.

Ismail Salleh. (2008). Pendekatan Pengajaran Algebra Sekolah Menengah: Konseptual Atau Prosedural. (Sarjana Pendidikan), Universiti Pendidikan Sultan Idris.

Jacobbe, T., & Carvalho, C. (2011). Teachers’ Understanding of Averages. In C. Batanero, G. Burrill & C. Reading (Eds.), Teaching Statistics in School Mathematics Challenges for Teaching and Teacher Education , 14, 199-209. Netherlands: Springer.

Kahle, D. K. B. (2008). How Elementary School Teachers’mathematical Self-Efficacy And Mathematics Teaching Self-Efficacy Relate To Conceptually And Procedurally Oriented Teaching Practices. (Doctor of Philosophy), The Ohio State University, Columbus, Ohio.

Kajander, A. (2010). Elementary Mathematics Teacher Preparation In An Era Of Reform: The Development And Assessment Of Mathematics For Teaching. Canadian Journal of Education, 33(1), 228-255.

Kastberg, S., & Morton, C. (2014). Mathematical Content Knowledge For Teaching Elementary Mathematics: A Focus On Decimals. The Mathematics Enthusiast, 11(2), 311.

Katz, V. J., & Barton, B. (2007). Stages in the History Of Algebra With Implications For Teaching. Educational Studies in Mathematics, 66(2), 185-201.

Kementerian Pelajaran Malaysia. (2012). Kurikulum Standard Sekolah Rendah. Putrajaya: Kementerian Pelajaran Malaysia.

Khashan, K. H. (2014). Conceptual and Procedural Knowledge Of Rational Numbers For Riyadh Elementary School Teachers. Journal of Education and Human Development, 3(4), 181-197.

Lake, M. M. (2008). Examining the Effects Of A Community College Mathematics Teacher And Curriculum Reformation Program: An Application Of Action Research And Conceptual Change. ProQuest.

Lee, H. J. (2007). Developing an effective Professional Development Model To Enhance Teachers' Conceptual Understanding And Pedagogical Strategies In Mathematics. The Journal of Educational Thought (JET)/Revue de la Pensée Educative, 125-144.

Lim, H. L., Wun, T. Y., & Noraini Idris. (2011). Assessing a Hierarchy Of Pre-Service Secondary Mathematics Teachers' Algebraic Thinking. International Journal of Assessment and Evaluation in Education, 1, 38-51.

Lin, C.-Y., Becker, J., Ko, Y.-Y., & Byun, M.-R. (2013). Enhancing Pre-Service Teachers’ Fraction Knowledge Through Open Approach Instruction. The Journal of Mathematical Behavior, 32(3), 309-330.

Livy, S., Muir, T., & Maher, N. (2012). How Do They Measure Up? Primary Pre-Service Teachers' Mathematical Knowledge Of Area And Perimeter. Mathematics Teacher Education and Development, 14(2), 91-112.

Mahir, N. (2009). Conceptual and Procedural Performance Of Undergraduate Students In Integration. International Journal of Mathematical Education in Science and Technology, 40(2), 201-211.

Marchionda, H. (2006). Preservice Teachers' Procedural And Conceptual Understanding Of Fractions And The Effects Of Inquiry-Based Learning On This Understanding. (Doktor Falsafah), Clemson University.

Mason, J. (2008). Making Use Of Children’s Powers To Produce Algebraic Thinking. Algebra in the Early Grades, 57-94.

Masters, J. (2012). Eighth Grade In-Service Teachers’ Knowledge Of Proportional Reasoning And Functions: A Secondary Data Analysis. International Journal for Mathematics Teaching & Learning.

Mazlini Adnan, & Effandi Zakaria. (2012). Pengetahuan Konseptual Pecahan Dalam Kalangan Bakal Guru Matematik. Jurnal Pendidikan Sains dan Matematik Malaysia, 2(1), 12-22

Mazlini Adnan, Effandi Zakaria, & Siti Mistima Maat. (2012). Relationship Between Mathematics Beliefs, Conceptual Knowledge And Mathematical Experience Among Pre-Service Teachers. Procedia-Social and Behavioral Sciences, 46, 1714-1719.

Mazlini Adnan, Mohd Faizal Nizam Lee Abdullah, & Che Nidzam Che Ahmad. (2014). Aplikasi model Persamaan Berstruktur Dalam Menilai Kepercayaan Dan Pengetahuan Konseptual Guru Matematik Sekolah Rendah. Jurnal Pendidikan Matematik, 2(1), 32-50.

McCrory, R., Floden, R., Ferrini-Mundy, J., Reckase, M. D., & Senk, S. L. (2012). Knowledge of Algebra For Teaching: A Framework Of Knowledge And Practices. Journal For Research In Mathematics Education, 43(5), 584-615.

Miqdadi, R., & Al-Jamal, D. (2013). Difficulties in Content And Language Integrated Learning: The case of math. Jordan Journal of Educational Sciences, 9(4), 449-459.

Moses, R. P., & Cobb Jr, C. (2001). Organizing Algebra: The Need To Voice A Demand. Social Policy, 31(4), 4-4.

Nik Noralhuda Nik Mohamed. (2011). Pengetahuan Konseptual, Prosedural Dan Kesedaran Metokognitif Dalam Kelas Matematik Sekolah Menengah. (Sarjana Pendidikan), Universiti Kebangsaan Malaysia, Bangi.

Norliza Zaini, & Effandi Zakaria. (2007). Konsep dalam Matematik. In Effandi Zakaria, Norazah Mohd & Sabri Ahmad (Eds.), Trend Pengajaran dan Pembelajaran Matematik. Kuala Lumpur: Utusan Publications & Distributors Sdn. Bhd.

Olfos, R., Goldrine, T., & Estrella, S. (2014). Teachers' Pedagogical Content Knowledge And Its Relation With Students' Understanding. Revista Brasileira de Educação, 19(59), 913-944.

Rahmawati, F. D. (2014). Pengaruh Model Pembelajaran Conceptual Understanding Procedures (CUPS) Terhadap Hasil Belajar Pemahaman Konsep Dan Pemahaman Prosedur Matematika Kelas VII MTS Al Huda Bandung Tulungagung tahun ajaran 2013-2014. Fakultas Tarbiyah dan Ilmu Keguruan IAIN Tulungagung. Retrieved from http://repo.iain-tulungagung.ac.id/id/eprint/337 Date access: 17 Mei 2016

Rakes, C. R., Valentine, J. C., McGatha, M. B., & Ronau, R. N. (2010). Methods of Instructional Improvement In Algebra A Systematic Review And Meta-Analysis. Review of Educational Research, 80(3), 372-400.

Rohani Aziz, Mohamad Johari Yaakob, & Effandi Zakaria. (2007). Pemahaman Konseptual dan Prosedural dalam Matematik. In Effandi Zakaria, Norazah Mohd. Nordin & Sabri Ahmad (Eds.), Trend Pengajaran dan Pembelajaran Matematik, 80-94. Kuala Lumpur: Utusan Publications & Distributors Sdn. Bhd.

Schoenfeld, A. H. (2008). Early Algebra As Mathematical Sense Making. Algebra in the Early Grades, 479-510.

Selouly, A., & Saud, M. b. (2013). Conceptual Knowledge Questionnaire Regarding Differentiation Among Mathematics Teachers In Secondary Cycle. Pedagogical and Psychology Message - Saudi Arabia, 40, 41-57.

Sharp, J. M., & Hoiberg, K. B. (2005). Learning and Teaching K-8 Mathematics , 1. Boston: Allyn & Bacon.

Slaten, K. M. (2006). Effective Teaching And Uses Of Instructional Representations In Secondary Geometry: A Comparison Of A Novice And An Experience Mathematics Teacher. (Doktor Falsafah), North Carolina State University.

Star, J. R. (2007). Foregrounding Procedural Knowledge. Journal for research In Mathematics Education, 38(2), 132-135.

Star, J. R., Glasser, H., Lee, K., Gucler, B., Demir, M., & Chang, K. (2005). Investigating the Development Of Students’ Knowledge Of Standard Algorithms In Algebra. Retrieved June, 30, 2007.

Stein, M. K., Kaufman, J. H., Sherman, M., & Hillen, A. F. (2011). Algebra a Challenge At The Crossroads Of Policy And Practice. Review of Educational Research, 81(4), 453-492.

Stienstra, W. M. (2014). Developing understanding: Pre-Service Elementary Teachers' Changing Conceptions Of Mathematics. (Doctor of Philosophy), Lakehead University, Thunder Bay, Ontario.

Thaqi, X., Giménez, J., & Rosich, N. (2011, 9-13 Februari 2011). Geometrical transformations As Viewed By Prospective Teachers. Paper presented at the Seventh Congress of the European Society for Research in Mathematics Education, Rzeszów, Poland.

Turnuklu, E. B., & Yesildere, S. (2007). The Pedagogical Content Knowledge In Mathematics: Pre-Service Primary Mathematics Teachers' Perspectives In Turkey. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1.

Utomo, D. P. (2012). Pengetahuan Konseptual Dan Prosedural Dalam Pembelajaran Matematika. Jurnal Prosiding Matematika, 1(1), 21-31

Van Steenbrugge, H., Lesage, E., Valcke, M., & Desoete, A. (2014). Preservice Elementary School Teachers' Knowledge Of Fractions: A Mirror Of Students' Knowledge? Journal of Curriculum Studies, 46(1), 138-161.

Vergnaud, G. (1990). La théorie des champs conceptuels’ Recherches en Didactique desMathématiques 10 (2, 3), 133-170. Vergnaud213310Recherches en Didactique des Mathématiques1990.

Wetzel, D. (2008). Scientific Method And Problem-Based Learning. Teacher Tips/Training.

Yew, W. T., Lian, L. H., & Meng, C. C. (2014). Assessing Preservice Teachers’ Knowledge Of Area. Sains Humanika, 2(4), 225–229

Downloads

Published

2019-12-31

How to Cite

Abdullah, N. A. (2019). Mathematics Teachers’ Conceptual Knowledge of Algebra: A Literature Review/ Pengetahuan Konseptual Algebra Guru Matematik: Satu Kajian Literatur. Sains Humanika, 12(1). https://doi.org/10.11113/sh.v12n1.1048

Issue

Section

Articles