Bayesian Assessment of Undergraduate Students About the Real Function Mathematical Concept

Flor Monserrat Rodríguez-Vásquez; Francisco J. Ariza-Hernandez

doi:10.29333/ejmste/10776

Full Text (PDF)

Flor Monserrat Rodríguez-Vásquez ¹, Francisco J. Ariza-Hernandez ¹ ^*

More Detail

¹ Facultad de Matemáticas, Universidad Autónoma de Guerrero, MEXICO
^* Corresponding Author

Abstract

The evaluation of learning in mathematics is a worldwide problem, therefore, new methods are required to assess the understanding of mathematical concepts. In this paper, we propose to use the Item Response Theory to analyze the understanding level of undergraduate students about the real function mathematical concept. The Bayesian approach was used to make inferences about the parameters of interest. We designed a test containing twelve items, to which a reliability analysis and validation test were applied. The experiment consisted in administer our test to 48 undergraduate students (18-20 years old) who are in a math career. We concluded that 25% of the students reached a high level of understanding, 39.6% a medium level of understanding and, 35.4% a low level of understanding. Furthermore, that students obtained low levels of understanding for tasks with high cognitive demand, and they obtained high levels of understanding for tasks with low cognitive demand.

Keywords

understanding
assessment
mathematics education
IRT model
validation test

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

https://doi.org/10.29333/ejmste/10776

EURASIA J Math Sci Tech Ed, 2021 - Volume 17 Issue 3, Article No: em1949

Publication date: 17 Mar 2021

Article Views: 1211

Article Downloads: 389

Open Access References How to cite this article

References

Afriyani, D., Sa’dijah, C., Subanji., & Muksar, M. (2018). Characteristics of Students’ Mathematical Understanding in Solving Multiple Representation Task based on Solo Taxonomy. International Electronic Journal of Mathematics Education, 13(3). 281-287. https://doi.org/10.12973/iejme/3920
Albert, L., & Kim, R. (2015). Applying CCSSM’s definition of understanding to assess students’ mathematical learning. In C. Suurtamm & A. Roth (Eds.), Assessment to Enhance Teaching and Learning (pp. 233-246). Reston, VA: The National Council of Teachers of Mathematics, Inc.
Baker, F. B., & Kim, S. H. (2004). Item response theory: parameter estimation techniques. New York, NY: Marcel Dekker, Inc. https://doi.org/10.1201/9781482276725
Brunker, N., Spandagou, I., & Grice, C. (2019). Assessment for Learning while Learning to Assess: Assessment in Initial Teacher Education Through the Eyes of Pre-Service Teachers and Teacher Educators. Australian Journal of Teacher Education, 44(9), 89-109. https://doi.org/10.14221/ajte.2019v44n9.6
Casella, G., & George, E.I. (1992). Explaining the Gibbs sampler. The American Statistician, 46(3), 167-174. https://doi.org/10.1080/00031305.1992.10475878
Chib, S., & Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. The American Statistician, 49, 327-335. https://doi.org/10.1080/00031305.1995.10476177
Doruk, M. (2019). Examination of freshmen’s conceptual knowledge on function in the context of multiple representations. International Journal of Research in Education and Science (IJRES), 5(2), 587-599.
Elton, L., & Laurillard, D. (1979). Trends in Research on Student Learning. Studies in Higher Education, 4, 87-102. https://doi.org/10.1080/03075077912331377131
Fox, J. P. (2010). Bayesian item response modeling. Theory and applications. New York, NY: Springer. https://doi.org/10.1007/978-1-4419-0742-4
Haylock, D., & Cockburn, A. (2013). Understanding mathematics for young children. SAGE.
Hiebert, J., & Carpenter, T. P. (1992). Learning and Teaching with Understanding. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning: A project of the National Council of Teachers of Mathematics (pp. 65-97). New York, N.Y: Macmillan Publishing Co, Inc.
Hiebert, J., & 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: Lawrence Erlbaum Associates.
Jinfa, C., & Meixia, D. (2017). On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers. Journal of Mathematics Teacher Education, 20(1), 5-29. https://doi.org/10.1007/s10857-015-9325-8
Kastberg, S. E. (2002). Understanding Mathematical Concepts: The Case of The Logarithmic Function (Doctoral dissertation). University of Georgia.
Lord, F. M. (1952). A theory of test scores [Psychometric Monograph No. 7]. Richmond, VA: Psychometric Corporation. Retrieved from https://www.psychometricsociety.org/sites/default/files/pdf/MN07.pdf
Lord, F. M. (1980). Applications of item response theory to practical testing problems. New York, NY: Routledge Taylor and Francis Group.
Malatjie, F., & Machaba, F. (2019). Exploring Mathematics Learners’ Conceptual Understanding of Coordinates and Transformation Geometry through Concept Mapping. Eurasia Journal of Mathematics, Science and Technology Education, 15(12), em1818. https://doi.org/10.29333/ejmste/110784
Mejía, J., Fuller, E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79, 3-18. https://doi.org/10.1007/s10649-011-9349-7
Mellor, K., Clark, R., & Essien, A. (2018). Affordances for learning linear functions: A comparative study of two textbooks from South Africa and Germany. Pythagoras, 39(1), 378. https://doi.org/10.4102/pythagoras.v39i1.378
Michener, E. R. (1978). Understanding understanding Mathematics. Cognitive Science, 2, 361-383. https://doi.org/10.1207/s15516709cog0204_3
National Governors Association for Best Practices and Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, D.C: NGA Center and CCSSO.
Nickerson, R. S. (1985). Understanding Understanding. American Journal of Education, 93(2), 201-239. https://doi.org/10.1086/443791
Pecharromán, C. (2014). El aprendizaje y la comprensión de los objetos matemáticos desde una perspectiva ontológica [Learning and understanding mathematical objects from an ontological perspective]. Educación Matemática, 26(2), 111-133.
Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it?. Educational Studies in Mathematics, 26, 165-190. https://doi.org/10.1007/BF01273662
Plummer, M. (2012). JAGS version 3.3.0 user manual. Retrieved from http://people.math.aau.dk/~kkb/Undervisning/Bayes14/sorenh/docs/jags_user_manual.pdf
R Core Team (2016). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
Rakkapao, S., Prasitpong, S., & Arayathanitkul, K. (2016). Analysis test of understanding of vectors with three-parameter logistic model of item response theory and item response curve technique. Physical Review Physics Education Research, 12, 020135. https://doi.org/10.1103/PhysRevPhysEducRes.12.020135
Sierpinska, A. (1990). Some remarks on understanding in mathematics. For the learning of mathematics, 10(3), 24-34.
Sierpinska, A. (1992). Theoretical perspectives for development of the function concept. On understanding the notion of function. In E. Dubinsky & G. Harel (Eds.), The Concept of Function Aspects of Epistemology and Pedagogy (pp. 25-58). Washington, DC: Mathematical Association of America.
Sierpinska, A. (1994). Understanding in Mathematics. Washington, DC: The Falmer Press.
Sierpinska, A. (2000). On Some Aspects of Students’ Thinking in Linear Algebra. In J. L. Dorier (Ed.), On the Teaching of Linear Algebra (p. 209-246). Dordrecht: Springer. https://doi.org/10.1007/0-306-47224-4_8
Skemp, R. (1976). Relational Understanding and Instrumental Understanding. Mathematics Teaching, 77, 20-26.
van der Linden, W. J., & Hambleton, R. K. (Eds.). (1997). Handbook of Modern Item Response Theory. New York, NY: Springer. https://doi.org/10.1007/978-1-4757-2691-6
Wilkerson-Jerde, M. H & Wilensky, U. J. (2011). How do mathematicians learn math?: resources and acts for constructing and understanding mathematic. Educational Studies in Mathematics, 78, 21-43. https://doi.org/10.1007/s10649-011-9306-5

How to cite this article

APA

Rodríguez-Vásquez, F. M., & Ariza-Hernandez, F. J. (2021). Bayesian Assessment of Undergraduate Students About the Real Function Mathematical Concept. Eurasia Journal of Mathematics, Science and Technology Education, 17(3), em1949. https://doi.org/10.29333/ejmste/10776

Vancouver

Rodríguez-Vásquez FM, Ariza-Hernandez FJ. Bayesian Assessment of Undergraduate Students About the Real Function Mathematical Concept. EURASIA J Math Sci Tech Ed. 2021;17(3):em1949. https://doi.org/10.29333/ejmste/10776

AMA

Rodríguez-Vásquez FM, Ariza-Hernandez FJ. Bayesian Assessment of Undergraduate Students About the Real Function Mathematical Concept. EURASIA J Math Sci Tech Ed. 2021;17(3), em1949. https://doi.org/10.29333/ejmste/10776

Chicago

Rodríguez-Vásquez, Flor Monserrat, and Francisco J. Ariza-Hernandez. "Bayesian Assessment of Undergraduate Students About the Real Function Mathematical Concept". Eurasia Journal of Mathematics, Science and Technology Education 2021 17 no. 3 (2021): em1949. https://doi.org/10.29333/ejmste/10776

Harvard

Rodríguez-Vásquez, F. M., and Ariza-Hernandez, F. J. (2021). Bayesian Assessment of Undergraduate Students About the Real Function Mathematical Concept. Eurasia Journal of Mathematics, Science and Technology Education, 17(3), em1949. https://doi.org/10.29333/ejmste/10776

MLA

Rodríguez-Vásquez, Flor Monserrat et al. "Bayesian Assessment of Undergraduate Students About the Real Function Mathematical Concept". Eurasia Journal of Mathematics, Science and Technology Education, vol. 17, no. 3, 2021, em1949. https://doi.org/10.29333/ejmste/10776