Fractions: teachers' knowledge and their contribution to the teaching of fourth grade students in Chilean schools.
DOI:
https://doi.org/10.22458/ie.v25i38.4549Keywords:
Primary school teachers, math teaching, learning, education, mathematicsAbstract
Fractions are a complex mathematical subject, difficult to learn and to teach. Previous studies suggest that student learning may be limited by teachers' understanding of fractions. The objective of this study is to examine the extent to which teachers' knowledge in association with socioeconomic status, students' prior knowledge, and the level of mathematics knowledge obtained in schools contributes to students' learning achievement in fractions. Using a quantitative methodology, the study instruments were structured tests with closed questions applied to 714 fourth grade students and 23 teachers from 23 Chilean schools. The data are analyzed using multilevel models. The results show that of the variability observed in the conceptualization of fractions, 76% could be attributed to student level variables, while the remaining 24% could be attributed to school level variables. The variance between schools could be explained 26% by teacher knowledge and 8% by socioeconomic level. This means that teacher knowledge, alone or in combination with other factors, explains about 6% of the total variability in student progress, with a significance of 5%. The level of mathematical knowledge observed in the schools is not significant. In conclusion, the present study reports that teacher knowledge contributes to student learning achievement in addition to the effect of socioeconomic level.
References
Álvarez, A. y Martínez, G. (2016). El Informe Coleman a Debate en su Cincuenta Aniversario. International Journal of Sociology of Education, 5(2), 87-106. http://dx.doi.org/10.17583/rise.2016.2104
Avcu, R. (2019). Turkish pre-service middle level mathematics teachers’ knowledge for teaching fractions. Research in Middle Level Education Online, 42(9), 1-20. https://doi.org/10.1080/19404476.2019.1681624
Azid, N., Hasan, R., Nazarudin, N. F. M. y Md-Ali, R. (2020). Embracing Industrial Revolution 4.0: The Effect of Using Web 2.0 Tools on Primary Schools Students’ Mathematics Achievement (Fraction). International Journal of Instruction, 13(3), 711-728. https://doi.org/10.29333/iji.2020.13348a
Ball, D., Thames, M. y Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
Barbieri, C. A., Young, L. K., Newton, K. J. y Booth, J. L. (2021). Predicting Middle School Profiles of Algebra Performance Using Fraction Knowledge. Child Development, 92(5), 1984-2005. https://doi.org/10.1111/cdev.13568
Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M. y Tsai, Y. M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133-180. https://doi.org/10.3102/0002831209345157
Behr, M. J., Lesh, R., Post, T. R. y Silver, E. A. (1983). Rational numbers concepts. En R. Lesh y M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 91-125). Academic Press. https://bit.ly/3ukOpQH
Braithwaite, D. W. y Siegler, R. S. (2021). Putting fractions together. Journal of Educational Psychology, 113(3), 556-571. https://doi.org/10.1037/edu0000477
Charalambous, C. Y. y Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293-316. https://doi.org/10.1007/s10649-006-9036-2
Coleman, J. S., Campbell, E., Hobson, C., McPartland, J., Mood, A., Weinfeld, F. y York, R. (1966). Equality of educational opportunity. https://eric.ed.gov/?q=ED012275&id=ED012275
Copur-Gencturk, Y. (2021). Teachers’ conceptual understanding of fraction operations: results from a national sample of elementary school teachers. Educational Studies in Mathematics, 107, 525-545. https://doi.org/10.1007/s10649-021-10033-4
Cueto, S., León, J., Sorto, M. A. y Miranda, A. (2017). Teachers’ pedagogical content knowledge and mathematics achievement of students in Peru. Educational Studies in Mathematics, 94(3), 329-345. https://doi.org/10.1007/s10649-016-9735-2
Deringöl, Y. (2019). Misconceptions of primary school students about the subject of fractions: views of primary teachers and primary pre-service teachers. International Journal of Evaluation and Research in Education, 8(1), 29-38. http://doi.org/10.11591/ijere.v8i1.16290
Heyneman, S. P. y Loxley, W. A. (1982). Influences on academic achievement across high and low income countries: a Re-Analysis of IEA data. Sociology of education, 55(1), 13-21. https://www.jstor.org/stable/2112607
Hill, H. C., Ball, D. L. y Schilling, S. G. (2008). Unpacking Pedagogical Content Knowledge: Conceptualizing and measuring teachers´ topic-specific Knowledge of Students. Journal for Research in Mathematics Education, 39(4), 372-400. https://www.jstor.org/stable/40539304
Hill, H. C., Rowan, B. y Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American educational research journal, 42(2), 371-406. https://doi.org/10.3102/00028312042002371
Jiang, Z., Mok, I. A. C. y Li, J. (2020). Chinese students’ hierarchical understanding of part-whole and measure subconstructs. International Journal of Science and Mathematics Education, 19(7), 1441-1461. https://doi.org/10.1007/s10763-020-10118-1
Kelcey, B., Hill, H. C. y Chin, M. J. (2019). Teacher mathematical knowledge, instructional quality, and student outcomes: a multilevel quantile mediation analysis. School Effectiveness and School Improvement, 30(4), 398-431. https://doi.org/10.1080/09243453.2019.1570944
Kieren, T. E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. En R. Lesh (Ed.), Number and measurement: Papers from a research workshop (pp. 101-144). ERIC/SMEAC. https://eric.ed.gov/?id=ED120027
Lenz, K., Dreher, A., Holzäpfel, L. y Wittmann, G. (2019). Are conceptual knowledge and procedural knowledge empirically separable? The case of fractions. British Journal of Educational Psychology, 90(3), 809-829. https://doi.org/10.1111/bjep.12333
Ma, L. (2010). Conocimiento y enseñanza de las matemáticas elementales. La comprensión de las matemáticas fundamentales que tienen los profesores en China y los EE.UU. Academia Chilena de Ciencias. https://hdl.handle.net/20.500.12365/17686
Maas, C. y Hox, J. (2005). Sufficient sample sizes for multilevel modeling. Methodology. European Journal of Research Methods for the Behavioral and Social Sciences, 1(3), 86-92. https://doi.org/10.1027/1614-2241.1.3.86
Ministerio de Educación. (2013). Matemática: Programa de Estudio Cuarto Año Básico. https://hdl.handle.net/20.500.12365/644
Pardo, A., Ruiz, M. A. y San Martín, R. (2007). Cómo ajustar e interpretar modelos multinivel con SPSS. Psicothema, 19(2), 308-321. https://www.psicothema.com/pii?pii=3365
Ramadı̇antı̇, W., Prı̇atna, N. y Kusnandı̇, K. (2019). Misconception analysis of junior high school student in interpreting fraction. Journal for the Education of Gifted Young Scientists, 7(4), 1159-1173. http://dx.doi.org/10.17478/jegys.631567
Reeder, S. y Utley, J. (2017). What is a fraction? Developing fraction understanding in prospective elementary teachers. School Science and Mathematics, 117(7-8), 307-316. https://doi.org/10.1111/ssm.12248
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.2307/1175860
Siegler, R. S. y Lortie-Forgues, H. (2017). Hard lessons: Why rational number arithmetic is so difficult for so many people. Current Directions in Psychological Science, 26(4), 346-351. https://doi.org/10.1177/0963721417700129
Soni, M. y Okamoto, Y. (2020). Improving children’s fraction understanding through the use of number lines. Mathematical Thinking and Learning, 22(3), 233-243. https://doi.org/10.1080/10986065.2020.1709254
Stelzer, F., Richard’s, M. M., Andrés, M. L., Vernucci, S. y Introzzi, I. (2021). Cognitive and maths-specific predictors of fraction conceptual knowledge. Educational Psychology, 41(2), 172-190. https://doi.org/10.1080/01443410.2019.1693508
Tchoshanov, M., Cruz, M. D., Huereca, K., Shakirova, K., Shakirova, L. y Ibragimova, E. N. (2017). Examination of lower secondary mathematics teachers’ content knowledge and its connection to students’ performance. International Journal of Science and Mathematics Education, 15(4), 683-702. https://doi.org/10.1007/s10763-015-9703-9
Van Steenbrugge, H., Lesage, E., Valcke, M. y Desoete, A. (2014). Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge? Journal of Curriculum Studies, 46(1), 138-161. https://doi.org/10.1080/00220272.2013.839003
Varas, M., Lacourly, N., López, A. y Giaconi, V. (2013). Evaluación del conocimiento pedagógico del contenido para enseñar matemáticas elementales. Enseñanza de las Ciencias, 31(1), 171-187. https://doi.org/10.5565/rev/ec/v31n1.857
Wijaya, A. (2017). The Relationships between Indonesian Fourth Graders’ Difficulties in Fractions and the Opportunity to Learn Fractions: A Snapshot of TIMSS Results. International Journal of Instruction, 10(4), 221-236. https://doi.org/10.12973/iji.2017.10413a
Xu, C., Li, H., Burr, S. D. L., Si, J., LeFevre, J. A. y Huang, B. (2022). Divide and conquer: Relations among arithmetic operations and emerging knowledge of fraction notation for Chinese students in grade 4. Journal of Experimental Child Psychology, 217(105371). https://doi.org/10.1016/j.jecp.2021.105371
Yang, X., Kaiser, G., König, J. y Blömeke, S. (2020). Relationship between pre-service mathematics teachers’ knowledge, beliefs and instructional practices in China. ZDM Mathematics Education, 52(3), 281-294. https://doi.org/10.1007/s11858-020-01145-x
Zhang, S., Yu, S., Xiao, J., Liu, Y. y Jiang, T. (2021). The Effects of Concrete-Representational-Abstract Sequence Instruction on Fractions for Chinese Elementary Students with Mathematics Learning Disabilities. International Journal of Science and Mathematics Education, 1-18. https://doi.org/10.1007/s10763-021-10215-9
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Innovaciones Educativas
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.