Oral vs. written exams: What are we assessing in Mathematics?
Abstract
One of the most striking differences between the Canadian educational system and most European educational systems is the importance given to oral examinations, particularly in mathematics courses. In this paper, seven mathematics professors share their views on mathematics assessment, andtheir thoughts about the types of knowledge and understanding in mathematics that can be assessed on written and oral exams. Four out of seven professors were born and educated in Bosnia, Poland, Romania, and Ukraine, and they are currently teaching in Canada. The other three professors were born
and educated in Canada, the United States, and Germany, and they are all currently teaching in Germany. With the increased emphasis on closed book written examinations, the results in this study show that written exams alone are not sufficient to assess students’ conceptual knowledge and relational
understanding, and therefore, there is a critical need for implementing the oral assessments in mathematics courses.
References
[1] Boedigheimer, R., Ghrist, M., Peterson, D., and Kallemyn, B. (2015). Individual Oral Exams in Mathematics Courses: 10 Years of Experience at the Air Force Academy. PRIMUS, 25(2): 99-120.
[2] Ernest, P. (2016). Mathematics and values. In Mathematical Cultures (pp. 189-214). Springer International Publishing.
[3] Fan, L., and Yeo, S. M. (2007). Integrating oral presentation into mathematics teaching and learning: An exploratory study with Singapore secondary students. The Montana Mathematics Enthusiast, Monograph, 3, pp. 81-98.
[4] Gold, B. (1999). Assessment Practices in Undergraduate Mathematics. Washington DC: Mathematical Association of America, pp. 143–145.
[5] Hiebert, J., and Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Erlbaum.
[6] Hounsell, D., Falchikov, N., Hounsell, J., Klampfleitner, M., Huxham, M., Thompson, K., and Blair, S. (2007). Innovative Assessment Across the Disciplines: An Analytical Review of the
Literature. York: Higher Education Academy.
[7] Iannone, P., and Simpson, A. (2011). The summative assessment diet: how we assess in mathematics degrees. Teaching Mathematics and Its Applications, 30(4): 186–196.
[8] Iannone, P., and Simpson, A. (2012). “Oral Assessment in Mathematics: Implementation and Outcomes.” Teaching Mathematics and Its Applications, 31(4): 179–190.
[9] Iannone, P., and Simpson, A. (2014). Students´ views of oral performance assessment in mathematics: straddling the ‘assessment of’ and ‘assessment for’ learning divide. Assessment and Evaluation in Higher Education, 40(7): 971-987.
[10] Joughin, G. (1998). Dimensions of oral assessment. Assessment and Evaluation in Higher Education, 23(4): 367–378.
[11] Joughin, G. (2010). A Short Guide to Oral Assessment. Leeds: Leeds Met Press.
[12] Liljedahl, P. (2010). The four purposes of assessment. Vector, 2010(2): 4-12.
[13] Nelson, M. (2011). Oral assessments: improving retention, grades and understanding. PRIMUS, 21(1): 47–61.
[14] Nor, H. N. H. M., and Shahrill, M. (2014). Incorporating the use of poster and oral presentations as an alternative assessment in the teaching of secondary mathematics. In Proceedings of the 2nd International Conference on Social Sciences Research (pp. 369-378).
[15] Odafe, V. U. (2006). Oral examinations in college mathematics. PRIMUS, 15(3): 243–256.
[16] Skemp, R. (1976). Instrumental understanding and relational understanding. Mathematics Teaching, 77: 20-26.
[17] Stray, C. (2001). The shift from oral to written examination: Cambridge and Oxford 1700–1900. Assessment in Education: Principles, Policy & Practice, 8(1): 33-50.
[18] Wilson, S. and Cooney, T. (2002). Mathematics teacher change and development: The role of beliefs. In G.C. Leder, E. Pehkonen, & G. Törner (Eds.) Beliefs: A Hidden Variable in Mathematics Education? (pp. 127-147). Netherlands: Springer.
[2] Ernest, P. (2016). Mathematics and values. In Mathematical Cultures (pp. 189-214). Springer International Publishing.
[3] Fan, L., and Yeo, S. M. (2007). Integrating oral presentation into mathematics teaching and learning: An exploratory study with Singapore secondary students. The Montana Mathematics Enthusiast, Monograph, 3, pp. 81-98.
[4] Gold, B. (1999). Assessment Practices in Undergraduate Mathematics. Washington DC: Mathematical Association of America, pp. 143–145.
[5] Hiebert, J., and Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Erlbaum.
[6] Hounsell, D., Falchikov, N., Hounsell, J., Klampfleitner, M., Huxham, M., Thompson, K., and Blair, S. (2007). Innovative Assessment Across the Disciplines: An Analytical Review of the
Literature. York: Higher Education Academy.
[7] Iannone, P., and Simpson, A. (2011). The summative assessment diet: how we assess in mathematics degrees. Teaching Mathematics and Its Applications, 30(4): 186–196.
[8] Iannone, P., and Simpson, A. (2012). “Oral Assessment in Mathematics: Implementation and Outcomes.” Teaching Mathematics and Its Applications, 31(4): 179–190.
[9] Iannone, P., and Simpson, A. (2014). Students´ views of oral performance assessment in mathematics: straddling the ‘assessment of’ and ‘assessment for’ learning divide. Assessment and Evaluation in Higher Education, 40(7): 971-987.
[10] Joughin, G. (1998). Dimensions of oral assessment. Assessment and Evaluation in Higher Education, 23(4): 367–378.
[11] Joughin, G. (2010). A Short Guide to Oral Assessment. Leeds: Leeds Met Press.
[12] Liljedahl, P. (2010). The four purposes of assessment. Vector, 2010(2): 4-12.
[13] Nelson, M. (2011). Oral assessments: improving retention, grades and understanding. PRIMUS, 21(1): 47–61.
[14] Nor, H. N. H. M., and Shahrill, M. (2014). Incorporating the use of poster and oral presentations as an alternative assessment in the teaching of secondary mathematics. In Proceedings of the 2nd International Conference on Social Sciences Research (pp. 369-378).
[15] Odafe, V. U. (2006). Oral examinations in college mathematics. PRIMUS, 15(3): 243–256.
[16] Skemp, R. (1976). Instrumental understanding and relational understanding. Mathematics Teaching, 77: 20-26.
[17] Stray, C. (2001). The shift from oral to written examination: Cambridge and Oxford 1700–1900. Assessment in Education: Principles, Policy & Practice, 8(1): 33-50.
[18] Wilson, S. and Cooney, T. (2002). Mathematics teacher change and development: The role of beliefs. In G.C. Leder, E. Pehkonen, & G. Törner (Eds.) Beliefs: A Hidden Variable in Mathematics Education? (pp. 127-147). Netherlands: Springer.
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2017-02-17
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