RELATIONSHIP BETWEEN MATHEMATICAL LITERACY AND OPPORTUNITY TO LEARN WITH DIFFERENT TYPES OF MATHEMATICAL TASKS
Abstract
We investigated how the opportunity to learn (OTL) with different types of mathematics tasks are related to mathematical literacy and the role of perceived control in the relationship between OTL and mathematical literacy. The structural equation modeling was applied to the data of 1,649 Korean students from the PISA 2012 database. OTL with the four different types of tasks – algebraic word problems, procedural tasks, pure mathematics reasoning, and applied mathematics reasoning – were measured via student survey on how often they have encountered each type of task in their mathematics lessons and tests. The results showed that OTL with the procedural tasks was likely to increase mathematical literacy directly and indirectly through internal perceived control. Engaging in the applied reasoning tasks is positively related to external perceived control, but negatively to mathematical literacy.
Keywords
Full Text:
PDFReferences
Abedi, J., & Herman, J. (2010). Assessing English language learners’ opportunity to learn mathematics: Issues and limitations. Teachers College Record, 112(3), 723-746. https://www.ncaase.com/docs/Abedi_OTL_TRC_2010.pdf
Ajzen, I. (2002). Perceived behavioral control, self?efficacy, locus of control, and the theory of planned behavior 1. Journal of Applied Social Psychology, 32(4), 665–683. https://doi.org/10.1111/j.1559-1816.2002.tb00236.x
Asparouhov, T., & Muthen, B. (2006). Multilevel modelling of complex survey data. Paper presented at the Joint Statistical Meeting, ASA Section on Survey Research Methods, Seattle, WA.
Arbaugh, F., & Brown, C. A. (2005). Analyzing mathematical tasks: A catalyst for change? Journal of Mathematics Teacher Education, 8, 499–536. https://doi.org/10.1007/s10857-006-6585-3
Bailin, S., & Siegler, H. (2003). Critical thinking. In N. Blake, P. Smeyers, R. Smith, & P. Standish (Eds.), The Blackwell Guide to the Philosophy of Education (pp. 181–193). Malden, MA: Blackwell Publishing.
Barnard-Brak, L., Lan, W. Y., & Yang, Z. (2018). Differences in mathematics achievement according to opportunity to learn: A 4pL item response theory examination. Studies in Educational Evaluation, 56, 1–7. https://doi.org/10.1016/j.stueduc.2017.11.002
Berliner, D. C. (2002). Educational research: The hardest science of all. Educational Researcher, 31(8), 18–20. https://doi.org/10.3102/0013189X031008018
Bornemann, B., Foth, M., Horn, J., Ries, J., Warmuth, E., Wartenburger, I., & van der Meer, E. (2010). Mathematical cognition: Individual differences in resource allocation. ZDM, 42(6), 555–567. https://doi.org/10.1007/s11858-010-0253-x
Boston, M. D., & Smith, M. S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers’ classrooms. Journal for Research in Mathematics Education, 40(2), 119–156. https://doi.org/10.2307/40539329
Byrne, B. M. (1998). Structural equation modeling with LISREL, PRELIS, and SIMPLIS: Basic concepts, applications, and programming. Mahwah, NJ: Lawrence Erlbaum.
Carroll, J. B. (1963). A model for school learning. Teachers College Record, 64, 723–733. http://www.tcrecord.org/books/pdf.asp?ContentID=2839
Chaney, B., Jocelyn, L., Levine, D., Mule, T., Rizzo, L., Roey, S., . . . Williams, T. (2001). User’s guide for the Third International Mathematics and Science Study (TIMSS) (NCES 2001-065). Washington, DC: National Center for Education Statistics.
d'Ailly, H. (2003). Children's autonomy and perceived control in learning: A model of motivation and achievement in Taiwan. Journal of Educational Psychology, 95(1), 84-96. https://doi.org/10.1037/0022-0663.95.1.84
Elliott, S., & Bartlett, B. (2016). Opportunity to Learn. In P. Nathan (Ed.), Oxford Handbook of Education Online. New York: Oxford Press. https://doi.org/10.1093/oxfordhb/9780199935291.013.70
Foy, P., Brossman, B., & Galia, J. (Eds.). (2012). Scaling the TIMSS and PIRLS 2011 achievement data. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College and International Association for the Evaluation of Educational Achievement (IEA).
Jacobson, M. J., Levin, J. A., & Kapur, M. (2019). Education as a Complex System: Conceptual and Methodological Implications. Educational Researcher, 48(2), 112–119. https://doi.org/10.3102/0013189x19826958
Hammer, D. (2000). Student resources for learning introductory physics. American Journal of Physics, 68(S1), S52–S59. https://doi.org/10.1119/1.19520
Hanna, G., & Jahnke, H. N. (2007). Proving and modelling. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and Applications in Mathematics Education: The 14th ICMI Study (New ICMI Study Series ed., pp. 145–152). New York, NY: Springer.
Hayduk, L., & Littvay, L. (2012). Should researchers use single indicators, best indicators, or multiple indicators in structural equation models? BMC Medical Research Methodology, 12(159), 1-17. https://doi.org/10.1186/1471-2288-12-159
Henningsen, M., & 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, 28(5), 524-549. https://doi.org/10.5951/jresematheduc.28.5.0524
Hrbá?ková, K., Hladík, J., & Vávrová, S. (2012). The relationship between locus of control, metacognition, and academic success. Procedia - Social and Behavioral Sciences, 69, 1805-1811. https://doi.org/10.1016/j.sbspro.2012.12.130
Hwang, J., Choi, K. M., & Hand, B. (2020). Examining domain-general use of reasoning across science and mathematics through performance on standardized assessments. Canadian Journal of Science, Mathematics and Technology Education, 20, 521-537. https://doi.org/10.1007/s42330-020-00108-4
Jacobson, M. J., Levin, J. A., & Kapur, M. (2019). Education as a Complex System: Conceptual and Methodological Implications. Educational Researcher, 48(2), 112–119. https://doi.org/10.3102/0013189x19826958
Lane, S. (2004). Validity of high?stakes assessment: Are students engaged in complex thinking? Educational Measurement: Issues and Practice, 23(3), 6–14. https://doi.org/10.1111/j.1745-3992.2004.tb00160.x
Leland, S. C., & Schmidt, W. H. (2015).The concept of opportunity to learn (OTL) in international comparisons of education. In K. Stacey & R. Turner (Eds.), Assessing Mathematical Literacy (pp. 207-216). Springer. https://doi.org/10.1007/978-3-319-10121-7_1
Lipnevich, A. A., Preckel, F., & Krumm, S. (2016). Mathematics attitudes and their unique contribution to achievement: Going over and above cognitive ability and personality. Learning and Individual Differences, 47, 70–79. https://doi.org/10.1016/j.lindif.2015.12.027
Little, T. D., Lindenberger, U., & Nesselroade, J. R. (1999). On selecting indicators for multivariate measurment and modeling with latent variables: When “good” indicators are bad and “bad” indicators are good. Psychological Methods, 4(2), 192-211. https://doi.org/10.1037/1082-989X.4.2.192
Kline, R. B. (2011). Principles and practice of structural equation modeling (3rd ed.). New York, NY: The Guilford Press.
Martin, L., & Gourley-Delaney, P. (2014). Students' images of mathematics. Instructional Science, 42, 595–614. https://doi.org/10.1007/s11251-013-9293-2
Mcleod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grows (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York, NY: Macmillan.
McNabb, T. (2003). Motivational issues: Potential to performance. In N. Colangelo & G. Davis (Eds.), Handbook of gifted education (3rd ed., pp. 417–423). Boston, MA: Allyn & Bacon.
Muis, K. R., Psaradellis, C., Lajoie, S. P., Di Leo, I., & Chevrier, M. (2015). The role of epistemic emotions in mathematics problem solving. Contemporary Educational Psychology, 42, 172–185. https://doi.org/10.1016/j.cedpsych.2015.06.003
Mulnix, J. W. (2012). Thinking critically about critical thinking. Educational Philosophy and Theory, 44(5), 464–479. https://doi.org/10.1111/j.1469-5812.2010.00673.x
Murayama, K., Pekrun, R., Lichtenfeld, S., & vom Hofe, R. (2013). Predicting long-term growth in students’ mathematics achievement: The unique contributions of motivation and cognitive strategies. Child Development, 84(4), 1475–1490. https://doi.org/10.1111/cdev.12036
Obserski, D. (2016). lavaan.survey: Complex survey structural equation modeling (SEM). R package version 1.1.3.1
OECD. (2013). PISA 2012 assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. Paris, France: OECD Publishing.
OECD. (2014). PISA 2012 technical report. Paris, France: OECD Publishing.
OECD. (2017). PISA 2015 technical report. Paris, France: OECD Publishing.
OECD. (n.d.). OECD Programme for International Student Assessment 2012: Student questionnaire - form A. Retrieved from http://www.oecd.org/pisa/pisaproducts/PISA12_StQ_FORM_A_ENG.pdf
Ottmar, E. R., Decker, L. E., Cameron, C. E., Curby, T. W., & Rimm-Kaufman, S. E. (2014). Classroom instructional quality, exposure to mathematics instruction and mathematics achievement in fifth grade. Learning Environments Research, 17(2), 243-262. https://doi.org/10.1007/s10984-013-9146-6
Patrick, B. C., Skinner, E. A., & Connell, J. P. (1993). What motivates children's behavior and emotion? Joint effects of perceived control and autonomy in the academic domain. Journal of Personality and Social Psychology, 65(4), 781–791. https://doi.org/10.1037/0022-3514.65.4.781
Rotter, J. B. (1966). Generalized expectancies for internal versus external control of reinforcement. Psychological Monographs: General and Applied, 80(1), 1–28. https://doi.org/10.1037/h0092976
Rotter, J. B., & Mulry, R. C. (1965). Internal versus external control of reinforcement and decision time. Journal of Personality and Social Psychology, 2(4), 598–604. https://doi.org/10.1037/h0022473
Schmidt, W. H. (1992). The distribution of instructional time to mathematical content: One aspect of opportunity to learn. In L. Burstein (Ed.), The IEA study of mathematics III: Student growth and classroom processes (pp. 129–145). New York, NY: Pergamon.
Schmidt, W. H., Zoido, P., & Cogan, L. (2014). Schooling matters: Opportunity to learn in PISA 2012. Paris, France: OECD Publishing.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334–370). New York, NY: MacMillan.
Schoenfeld, A. H. (1994). Reflections on doing and teaching mathematics. In A. H. Schoenfeld (Ed.), Mathematical Thinking and Problem Solving (pp. 53–69). Hillsdale, NJ: Lawrence Erlbaum Associates.
Schreiber, J. B., Nora, A., Stage, F. K., Barlow, E. A., & King, J. (2006). Reporting structural equation modeling and confirmatory factor analysis results: A review. Journal of Educational Research, 99(6), 323–338. https://doi.org/10.3200/JOER.99.6.323-338
Schunk, D. H. (1984). Self?efficacy perspective on achievement behavior. Educational Psychologist, 19(1), 48–58. https://doi.org/10.1080/00461528409529281
Skinner, E. A., Wellborn, J. G., & Connell, J. P. (1990). What it takes to do well in school and whether I've got it: A process model of perceived control and children's engagement and achievement in school. Journal of Educational Psychology, 82(1), 22–32. https://doi.org/10.1037/0022-0663.82.1.22
Skinner, E. A., Zimmer-Gembeck, M. J., Connell, J. P., Eccles, J. S., & Wellborn, J. G. (1998). Individual differences and the development of perceived control. Monographs of the Society for Research in Child Development, 63(2/3), 1–231. https://doi.org/10.2307/1166220
Son, J. W. (2012). A cross-national comparison of reform curricula in Korea and the US in terms of cognitive complexity: the case of fraction addition and subtraction. ZDM, 44(2), 161-174. https://doi.org/10.1007/s11858-012-0386-1
Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488. https://doi.org/10.3102/00028312033002455
Stevens, F. I., & Grymes, J. (1993). Opportunity to learn: Issues of equity for poor and minority students. Washington, DC: National Center for Education Statistics.
Stevens, F. (1996, April). The need to expand the opportunity to learn conceptual framework: Should students, parents and school resources be included? Paper presented at the annual meeting of the American Educational Research Association. New York, NY.
Tabachnick, B. G., & Fidell, L. S. (2012). Using Multivariate Statistics. New York, NY: Pearson.
Törnroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation, 31(4), 315–327. https://doi.org/10.1016/j.stueduc.2005.11.005
von Davier, M., Gonzalez, E., & Mislevy, R. J. (2009). What are plausible values and why are they useful? IERI Monograph Series. Issues and Methodologies in Large-Scale Assessments, 2, 9–36.
Watson, A. (2003). Opportunities to learn mathematics. Mathematics education research: Innovation, networking, opportunity, 29–38.
Yeo, J. B. W. (2007). Mathematical tasks: Clarification, classification and choice of suitable tasks for different types of learning and assessment. Technical Report Me 2007-01. National Institute of Education, Nanyang Technological University, Singapore.
DOI: https://doi.org/10.22342/jme.12.2.13625.199-222
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Kampus FKIP Bukit Besar
Jl. Srijaya Negara, Bukit Besar
Palembang - 30139
p-ISSN: 2087-8885 | e-ISSN: 2407-0610
Journal on Mathematics Education (JME) is licensed under a Creative Commons Attribution 4.0 International License.
View My Stats