pp. 777-798 | Article Number: iejme.2017.046
Published Online: November 27, 2017
Article Views: 799 | Article Download: 338
The lack of feedback in the student-teacher relationship creates an incomplete perspective about the learning process in Mathematics, as for example in Advanced Algebra. This research was conducted in Mexico using a theoretical framework for performance assessment, based on the competencies for Advanced Algebra learning at the high school level. The objective sought to explore students’ perceptions after a performance assessment process, using two groups of students who took Advanced Algebra for the second time because of low academic achievement. Mixed methods research was selected for understanding profoundly how performance assessment reports (PAR) could bring useful information to students for reaching expected performance levels. A performance rubric based on Marzano and Kendall’s New Taxonomy, as well as semi-structured interviews, were used for data collection purposes. The findings confirm that changing the assessment method from traditional grading to performance assessing can be a clearer approach for understanding students’ strengths and weakness as Advanced Algebra learners.
Keywords: Advanced Algebra, performance assessment, competencies, high school, feedback
Bahr, D. L. (2007). Creating Mathematics Performance Assessments that Address Multiple Student Levels. Australian Mathematics Teacher, 63(1), 33-40. Retrieved from: https://eric.ed.gov/?id=EJ769974
Bayazit, I. (2010). The influence of teaching on student learning: The notion of piecewise function. International Electronic Journal of Mathematics Education, 5(3), 146–164.
Bokhove, C., & Drijvers, P. (2012). Effects of feedback in an online algebra intervention. Technology, Knowledge and Learning, 17(1–2), 43–59. doi:https://doi.org/10.1007/s10758-012-9191-8
Carlson, M., Oehrtman, M., & Engelke, N. (2010). The precalculus concept assessment: A tool for assessing students’ reasoning abilities and understandings. Cognition and Instruction, 28(2), 113–145. http://dx.doi.org/10.1080/07370001003676587
Chi, M. T. H., Glasser, R., & Farr, M. J. (1988). The nature of expertise. Hillsdale, NJ.: Lawrence Erlbaum Associates, Inc., Publishers.
Creswell, J. W., & Clark, V. L. P. (2007). Designing and conducting mixed methods research. Thousand Oaks, CA: SAGE Publications.
Dupeyrat, C., Escribe, C., Huet, N., & Regner, I. (2011). Positive biases in self-assessment of mathematics competence, achievement goals, and mathematics performance. International Journal of Educational Research, 50(4), 241–250. Retrieved from http://0-search.proquest.com.millenium.itesm.mx/docview/964175861?accountid=41938
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. doi:https://doi.org/10.1007/s10649-006-0400-z
Frey, B. B., Schmitt, V. L., & Allen, J. P. (2012). Defining authentic classroom assessment. Practical Assessment, Research & Evaluation, 17(2). Available online: http://pareonline.net/getvn.asp?v=17&n=2
Gray, E., Pinto, M., Pitta, D., & Tall, D. (1999). Knowledge construction and diverging thinking in elementary & advanced mathematics. In D. Tirosh (Ed.), Forms of mathematical knowledge: Learning and teaching with understanding (pp. 111–133). Dordrecht, Netherlands: Springer Netherlands.
Godino, J. D., Castro, W. F., Aké, L. P., & Wilhelmi, M. R. (2012). Naturaleza del razonamiento algebraico elemental (The nature of elemetary algebraic reasoning). Boletim de Educação Matemática, 26(42B), 483–511.http://dx.doi.org/10.1590/S0103-636X2012000200005
Hancock, D. (2007). Effects of performance assessment on the achievement and motivation of graduate students. Active Learning in Higher Education, 8(3), 219-231. Retrieve from: http://alh.sagepub.com/content/8/3/219.short
Iannone, P., & Simpson, A. (2015). Students’ views of oral performance assessment in mathematics: straddling the ‘assessment of and assessment for learning divide. Assessment & Evaluation in Higher Education, 40(7), 971-987.
Jupri, A., Drijvers, P., & van den Heuvel-Panhuizen, M. (2014). Student difficulties in solving equations from an operational and a structural perspective. Mathematics Education, 9(1), 39–55.
Kartal, O., Dunya, B. A., Diefes-Dux, H. A., & Zawojewski, J. S. (2016). The relationship between students' performance on conventional standardized mathematics assessments and complex mathematical modeling problems. International Journal of Research in Education and Science, 2(1), 239–-252. Retrieved from http://0-search.proquest.com.millenium.itesm.mx/docview/1826538713?accountid=41938
Klein-Collins, R. (2013). Sharpening our focus on learning: The rise of competency-based approaches to degree completion. Occasional Paper, 20. Retrieved from: https://pdfs.semanticscholar.org/818d/803c2cac48a729a578f4497543d9eb7aad6d.pdf
Kop, P. M. G. M., Janssen, F. J. J. M., Drijvers, P. H. M., Veenman, M. V. J., & van Driel, J. H. (2015). Identifying a framework for graphing formulas from expert strategies. The Journal of Mathematical Behavior, 39, 121–134. https://doi.org/10.1016/j.jmathb.2015.06.002
Lesh, R., & Doerr, H. M. (2003). Foundations of a model and modeling perspective on mathematics teaching, learning, and problem solving. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching, (pp. 3–34). Mahwah, NJ: Lawrence Erlbaum Associates, Inc., Publishers.
Logan, T. (2015). The influence of test mode and visuospatial ability on mathematics assessment performance. Mathematics Education Research Journal, 27(4), 423–441. Retrieved from http://0-search.proquest.com.millenium.itesm.mx/docview/1773219202?accountid=41938
Marzano, R. J., & Kendall, J. S. (2007). The new taxonomy of educational objectives (2nd ed.). Thousand Oaks, CA: Corwin Press.
Mayfield, K. H., & Glenn, I. M. (2008). An evaluation of interventions to facilitate algebra problem solving. Journal of Behavioral Education, 17(3), 278–302. doi:https://doi.org/10.1007/s10864-008-9068-z
Oehrtman, M., Carlson, M., & Thompson, P. W. (2008). Foundational reasoning abilities that promote coherence in students’ function understanding. In M. P. Carlson & C, Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics education, (pp. 27–42). Washington, DC: Mathematical Association of America,
Oehrtman, M., Carlson, M., & Thompson, P. W. (2008). Foundational reasoning abilities that promote coherence in students’ function understanding. Making the connection: Research and teaching in undergraduate mathematics education, 27, 42.
OCDE (2016). PISA 2015 Mathematics Framwork. Retrieve from: http://edu.hioa.no/pdf/9816021ec005.pdf
Palm, T. (2008). Performance assessment and authentic assessment: A conceptual analysis of the literature. Practical assessment, research & evaluation, 13(4), 1-11. Retrieve from: http://pareonline.net/getvn.asp?v=13&n=4
Polya, G. (1957). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton, NJ: Princeton University Press.
Sadler, D. R. (1989). Formative assessment and the design of instructional systems. Instructional Science, 18(2), 119–144. doi:https://doi.org/10.1007/BF00117714
Schoenfeld, A. H. (2007). What is mathematical proficiency and how can it be assessed? In A. H. Schoenfeld (Ed.), Assessing mathematical proficiency (pp. 59–73).Cambridge, UK: Cambridge University Press.
Secretaría de Educación Pública (SEP). (2008, March 21). Acuerdo número 444 por el que se establecen las competencias que constituyen el marco curricular común del sistema nacional de bachillerato. Retrieved from: https://www.sep.gob.mx/work/models/sep1/Resource/7aa2c3ff-aab8-479f-ad93-db49d0a1108a/a444.pdf
Star, J. R., & Rittle-Johnson, B. (2009). Making algebra work: Instructional strategies that deepen student understanding, within and between representations. ERS Spectrum, 27(2), 11–18. https://nrs.harvard.edu/urn-3:HUL.InstRepos:4889486
Vega-Castro, D., Molina, M., & Castro, E. (2012). Sentido estructural de estudiantes de bachillerato en tareas de simplificación de fracciones algebraicas que involucran igualdades notables (High school students’ structural sense in the context of simplification of algebraic fractions that involve notable equations). Revista latinoamericana de investigación en matemática educativa, 15(2), 233–258.
Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293–305. http://dx.doi.org/10.1080/0020739830140305
Vollrath, H. J. (1984). Methodik des Begriffslehrens im Mathematikunterricht. Stuttgart, Germany: Klett,
Weigand, H. G. (2004). Sequences—Basic elements for discrete mathematics. ZDM, 36(3), 91–97. doi:https://doi.org/10.1007/BF02652776
Williams, L. M. (2000). Academic maturity: Qualifications to teach the nurse professionals of the future. Collegian, 7(4), 19–23. doi:https://doi.org/10.1016/S1322-7696(08)60386-8
Wiggins, G. (1998). Educative assessment. Designing assessments to inform and improve student performance. San Francisco, CA: Jossey-Bass Publishers,
Yachina, N. P., Gorev, P. M., & Nurgaliyeva, A. K. (2015). Open type tasks in mathematics as a tool for students’ meta-subject results assessment. Mathematics Education, 10(3), 211–220. doi: 10.12973/mathedu.2015.116a