13May 2018

A MULTI-SITE CASE STUDY: ALGEBRAIC CONTENT AND PEDAGOGICAL KNOWLEDGE OF SIXTH GRADE MATHEMATICS TEACHERS.

  • Walden University, USA.
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Algebra is a fundamental topic in mathematics and lays the foundation for mathematical reasoning and complex problem-solving. A baseline study conducted in the Maldives showed that algebra test scores were the lowest compared to any other area of mathematics. Research shows that strengthening algebra instruction could improve student achievement. This concurrent mixed methods study examined the algebraic content and pedagogical knowledge of five sixth grade mathematics teachers who teach in five different schools across the Maldives. This study is guided by Shulman’s major categories of teacher knowledge and Ball, Thames, and Phelps’ domains of mathematical knowledge for teaching. The research questions examined the relationship between teachers’ perceptions of their mastery of algebraic content and pedagogical knowledge, and what teachers actually know about algebraic content and pedagogy. Purposive sampling was used to select the 5 participants. Quantitative data were collected using the Diagnostic Teacher Assessments of Mathematics and Science – Middle Mathematics Teacher Assessments and qualitative data were gathered through lesson observations, interviews, and analysis of teachers’ lesson plans and notes. All participants believed that they were proficient in both algebraic content and pedagogical knowledge. However, the results of this study showed that all participants lacked both algebraic content and pedagogical knowledge. Moreover, in-depth analysis of the textbooks and resource materials used by these teachers revealed that algebraic concepts were explained incorrectly in the prescribed textbooks, and resource materials.

  1. Adam, A. & Naseer, A. (2002). Mathematics for Maldivian Schools Six. Maldives: Educational Development Centre.
  2. Adam, A. & Naseer, A. (2002). Mathematics for Maldivian Schools Six Workbook. Maldives: Educational Development Centre.
  3. Adam, A. & Naseer, A. (2003). Mathematics for Maldivian Schools Six Teacher?s Resource Book. Maldives: Educational Development Centre.
  4. Baker, S. E., & Edwards, R. (2015). How many qualitative interviews is enough?: Expert voices and early career reflections on sampling and cases in qualitative research. United Kingdom: National Centre for Research Methods & Economic and Social Research Council. Retrieved from http://eprints.ncrm.ac.uk/2273/4/how_many_interviews.pdf
  5. Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers? mathematical knowledge. Handbook of Research on Teaching,4, 433-456.
  6. Ball, D. L., Thames, M. H., & Phelps, G. (2008) Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.
  7. Begle, E. G. (1979). Critical variables in mathematics education: Findings from a survey of the empirical literature. Washington, DC: Mathematical Association of America and National Council of Teachers of Mathematics.
  8. Brown, I. A., Davis, T. J., &Kulum, G. (2011). Pre-service teachers? knowledge for teaching algebra for equity in the middle grades: A preliminary report. Journal of Negro Education, 80(3), 266-283.
  9. Browning, C., Thanheiser, E., Edson, A. J., Kimani, P., Olanoff, D., Tobias, J., & Whitacre, I. (2014). Prospective Elementary Teacher Mathematics Content Knowledge: An Introduction. Mathematics Enthusiast,?11(2), 203-216.
  10. Buschang, R. E., Chung, G. K., Delacruz, G. C., & Baker, E. L. (2012). Validating measures of algebra teacher subject matter knowledge and pedagogical content knowledge.Educational Assessments,?17(1), 1-21.
  11. Caruth, G. D. (2013). Demystifying mixed methods research design: A review of the literature.Online Submission,?3(2), 112-122.
  12. Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. London, United Kingdom: SAGE Publications.
  13. Chick, H. L., Pham, T., & Baker, M. K. (2006). Probing teachers? pedagogical content knowledge: Lessons from the case of the subtraction algorithm. Identities, Cultures and Learning Spaces, 139-146.
  14. Cheng-Yao, L., Yi-Yin, K., & Yu-Chun, K. (2014). Changes in pre-service teachers' algebraic misconceptions by using computer-assisted instruction. International Journal for Technology in Mathematics Education,21(3), 21-30.
  15. Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (Laureate custom ed.). Boston, MA: Pearson Education.
  16. Darling-Hammond, L., & Sykes, G. (2003). Wanted, A national teacher supply policy for education: The right way to meet the" highly qualified teacher" challenge.Educational Policy Analysis Archives,?11(33).
  17. Diagnostic Teacher Assessments in Mathematics and Science - Middle Mathematics Teacher Assessments. (n.d.). Retrieved June 20, 2015, from http://louisville.edu/education/centers/crmstd/diag-math-assess-middle
  18. El Mouhayar, R. R., & Jurdak, M. E. (2013). Teachers? ability to identify and explain students? actions in near and far figural pattern generalization tasks. Educational Studies in Mathematics,82(3), 379-396.
  19. Fernandez, C. (2014). Knowledge base for teaching and pedagogical content knowledge (PCK): Some useful models and implications for teachers? training.Problems of Education in the 21st Century,?60, 79-100.
  20. Guest, G., Bunce, A., & Johnson, L. (2006). How many interviews are enough? An experiment with data saturation and variability.Field methods,?18(1), 59-82.
  21. Hauk, S., Toney, A., Jackson, B., Nair, R., & Tsay, J. J. (2014). Developing a model of pedagogical content knowledge for secondary and post-secondary mathematics instruction.Dialogic Pedagogy: An International Online Journal,?2.
  22. Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students.Journal for Research in Mathematics Education, 372-400.
  23. Jing-Jing, H. U. (2014). A critical review of Pedagogical Content Knowledge components: nature, principle and trend.International Journal of Education and Research,?2(4), 411-424.
  24. Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., ... & Baumert, J. (2015). Content knowledge and pedagogical content knowledge in Taiwanese and German mathematics teachers.Teaching and Teacher Education,?46, 115-126.
  25. Koency, G., & Swanson, J. (2000). The special case of mathematics: Insufficient content knowledge a major obstacle to reform.
  26. Lange, K., Kleickmann, T., & Moller, K. (2012). Elementary teachers? pedagogical content and student achievement in science education. In C. Bruguiere, A. Tiberghien & P. Clement (Eds.), Science Learning and Citizenship. Proceedings of the Ninth ESERA-Conference 2011. Lyon.
  27. Liu, S. (2010). Teachers' knowledge: Review from comparative perspective. New Horizons in Education,58(1), 148-158.
  28. Lopez-Fernandez, O., & Molina-Azorin, J. F. (2011). The use of mixed methods research in interdisciplinary educational journals.International Journal of Multiple Research Approaches,?5(2), 269-283.
  29. Ma, L. (1999).Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
  30. Marshall, B., Cardon, P., Poddar, A., & Fontenot, R. (2013). Does sample size matter in qualitative research?: A review of qualitative interviews in IS research.Journal of Computer Information Systems,?54(1), 11-22.
  31. Mason, M. (2010, August). Sample size and saturation in PhD studies using qualitative interviews. InForum Qualitative Sozialforschung/Forum: Qualitative Social Research?(Vol. 11, No. 3).
  32. Miles, M. B., & Huberman, A. M. (1994).Qualitative data analysis: An expanded sourcebook. London: Sage Publications.
  33. Naseer, M. S. (2015, September). Analysis of students? errors and misconceptions in pre-university mathematics courses. In M. N. Salleh, & N. F. Z. Abedin, (Eds.), Proceedings: First International Conference on Teaching & Learning 2015 (p. 34-39). Langkawi, Malaysia: MNNF Publisher. ISBN 978-967-13637-1-3.
  34. National Institute of Education. (2014). Mathematics in the National Curriculum Key Stage 2 (Grades 4, 5, & 6). Maldives: National Institute of Education.
  35. Ojose, B. (2014). Teaching Certain Mathematical Axioms: The Role Played by Conceptual Knowledge of Algebra Teachers.National Teacher Education Journal,?7(1).
  36. Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). London: Sage.
  37. Piccolo, D. (2008). Views of content and pedagogical knowledges for teaching mathematics.?School Science and Mathematics,?108(2), 46-48.
  38. Rittle-Johnson, B., Matthews, P. G., Taylor, R. S., & McEldoon, K. L. (2011). Assessing knowledge of mathematical equivalence: A construct-modeling approach.Journal of Educational Psychology,?103(1), 85-104.
  39. Ross, A., & Onwuegbuzie, A. J. (2012). Prevalence of mixed methods research in mathematics education.?The Mathematics Educator,?22(1), 84-113.
  40. Russell, M., O?Dwyer, L. M., & Miranda, H. (2009). Diagnosing students? misconceptions in algebra: Results from an experimental pilot study.Behavior research methods,?41(2), 414-424.
  41. Saderholm, J., Ronau, R., Brown, E. T., & Collins, G. (2010). Validation of the diagnostic teacher Assessments of mathematics and science (DTAMS) instrument.?School Science and Mathematics,?110(4), 180-192.
  42. Schnepper, L. C., & McCoy, L. P. (2013). Analysis of Misconceptions in High School Mathematics.Networks,?15(1).
  43. Shirvani, H. (2015). Pre-service Elementary Teachers' Mathematical content Knowledge: A Predictor of Sixth Graders' Mathematics Performance.?International Journal of Instruction,?8(1), 133-142.
  44. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. Retrieved from https://www.math.ksu.edu/~bennett/onlinehw/qcenter/shulmanpck86.pdf
  45. Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform.Harvard Educational Review,?57(1), 1-23.
  46. Stoddart, T., Connell, M., Stofflett, R., & Peck, D. (1993). Reconstructing elementary teacher candidates' understanding of mathematics and science content.Teaching and Teacher Education,?9(3), 229-241.
  47. Strand, K., & Mills, B. (2014). Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Algebra.The Mathematics Enthusiast, 11(2), 385-432.
  48. Tajudin, N. M. (2014). Exploring prospective mathematics teachers? mathematical knowledge for teaching algebraic problem-solving. Proceeding of the Social Sciences Research ICSSR 2014 (e-ISBN 978-967-11768-7-0). Malaysia: Kota Kinabalu, Sabah.
  49. Taton, J. A. (2015). Much more than it's cooked-up to be: Reflections on doing math and teachers' professional learning. Perspectives on Urban Education, 12(1).
  50. Tennant, G., & Colloff, K. (2014). Fruit salad algebra: Alive and kicking!.?Mathematics Teaching, (239), 40-43.
  51. Thanheiser, E., Browning, C., Edson, A., Lo, J. J., Whitacre, I., Olanoff, D., & Morton, C. (2014). Prospective elementary mathematics teacher content knowledge: What do we know, what do we not know, and where do we go?. The Mathematics Enthusiast,11(2), 433-448.
  52. United Nations Children?s Fund (UNICEF) & National Institute of Education (NIE). (2014). Longitudinal study on the impact of curriculum reforms 2012-2013. Maldives: UNICEF Maldives Country Office.
  53. Venkatesh, V., Brown, S. A., & Bala, H. (2013). Bridging the qualitative-quantitative divide: Guidelines for conducting mixed methods research in information systems.MIS quarterly,?37(1), 21-54.
  54. Welder, R. M. (2012). Improving algebra preparation: Implications from research on student misconceptions and difficulties. School Science and Mathematics, 112(4), 255-264.

[Mariyam Shahuneeza Naseer. (2018); A MULTI-SITE CASE STUDY: ALGEBRAIC CONTENT AND PEDAGOGICAL KNOWLEDGE OF SIXTH GRADE MATHEMATICS TEACHERS. Int. J. of Adv. Res. 6 (May). 178-193] (ISSN 2320-5407). www.journalijar.com

Dr. Mariyam Shahuneeza Naseer
Walden University, USA (Alumnus)

DOI:

Article DOI: 10.21474/IJAR01/7021      
DOI URL: http://dx.doi.org/10.21474/IJAR01/7021

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