Student-Teacher Level of Statistical Reasoning Ability Reviewed by Apos Theory (Action, Process, Object, Schema)
DOI:
https://doi.org/10.35194/jp.v12i2.3139Keywords:
APOS theory, mathematics education, statistical reasoningAbstract
In learning statistics, there is the term statistical reasoning. Statistical reasoning arises because of the opinion that learning statistics using a traditional approach does not lead students to have statistical reasoning abilities or to think statistically. There are four statistical reasoning levels: idiosyncratic, transitional, quantitative, and analytical. Student-teachers must understand fundamental statistical concepts more deeply to develop statistical reasoning abilities. The mental construction of a statistical concept can be analyzed using APOS (Action, Process, Object, Schema) theory. Through the APOS theory, researchers can determine individual understanding of statistical concepts that cause individuals to reason or draw reasonable conclusions based on the statistical information obtained. This study aims to analyze the interrelationships and make conjectures regarding the level of statistical reasoning ability based on the APOS theory. The research subjects are. 19 informants. The research results obtained four conjectures, namely. Students at the idiosyncratic level are in the action stage; students at the transitional stage are in the action, process, or object stage; students at the quantitative stage are in the process or object stage; lastly, students at the analytical are in the schema stage.References
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, R. S., Trigueros, M., & Weller, K. (2014). APOS Theory A Framework for Research and Curriculum Development in Mathematics Education. Springer. https://doi.org/10.1007/978-1-4614-7966-6
Ben-Zvi, D., & Garfield, J. (2004). The Challenge Of Developing Statistical Literacy, Reasoning And Thinking. Kluwer Academic.
Burrill, G., & Ben-Zvi, D. (2019). Topics and Trends in Current Statistics Education Research. Springer. http://www.springer.com/series/15585
Corbin, J., & Strauss, A. (2008). Basic of Qualitative Research: Techniques and Procedures for Developing Grounded Theory (3rd ed.). Sage.
Dubinsky, E., Weller, K., McDonald, M. A., & Brown, A. (2005). Some historical issues and paradoxes regarding the concept of infinity: An APOS-based analysis: Part 1. Educational Studies in Mathematics, 58(3), 335–359. https://doi.org/10.1007/s10649-005-2531-z
Garfield, J., & Gal, I. (1999). Teaching and Assessing Statistical
Reasoning. Developing Mathematical Reasoning in Grades K-12: National Council Teachers of Mathematics 1999 Year, 207–219.
Idris, K. (2018). Teaching and learning statistics in college: How learning materials should be designed. Journal of Physics: Conference Series, 1088. https://doi.org/10.1088/1742-6596/1088/1/012032
Jones, G. A., Langrall, C. W., Mooney, E. S., & Thornton, C. A. (2004). Models Of Development In Statistical Reasoning.
Jones, G. A., Langrall, C. W., Thornton, C. A., Mooney, E. S., Wares, A., Jones, M. R., Perry, B., Putt, I. J., & Nisbet, S. (2001). Using students’ statistical thinking to inform instruction. Journal of Mathematical Behavior, 20, 109–144.
Jones, G. A., Thornton, C. A., Langrall, C. W., Mooney, E. S., Perry, B., & Putt, I. J. (2000). A Framework for Characterizing Children’s Statistical Thinking. Mathematical Thinking and Learning, 2(4), 269–307. https://doi.org/10.1207/s15327833mtl0204_3
Lavigne, N. C., & Lajoie, S. P. (2007). Statistical reasoning of middle school children engaged in survey inquiry. Contemporary Educational Psychology, 32(4), 630–666. https://doi.org/10.1016/j.cedpsych.2006.09.001
Lee, S., & Kim, G. (2019). How middle-school mathematics textbooks of Korea and the US support to develop students’ statistical reasoning. The Mathematical Education, 58(1), 139–160. https://doi.org/10.7468/mathedu.2019.58.1.139
Mooney, E. S. (2002). A Framework for Characterizing Middle School Students’ Statistical Thinking. Mathematical Thinking and Learning, 4(1), 23–63. https://doi.org/10.1207/s15327833mtl0401_2
Oktay, J. S. (2012). Grounded Theory. Oxford University Press.
Olani, A., Hoekstra, R., Harskamp, E., & Van Der Werf, G. (2011). Statistical Reasoning Ability, Self-Efficacy, and Value Beliefs in a Reform Based University Statistics Course. Electronic Journal of Research in Educational Psychology, 9(1), 1696–2095.
Onwuegbuzie, A. J., & Wilson, V. A. (2003). Statistics Anxiety: Nature, etiology, antecedents, effects, and treatments--a comprehensive review of the literature. Teaching in Higher Education, 8(2), 195–209. https://doi.org/10.1080/1356251032000052447
Rohana, R., & Ningsih, Y. L. (2020). Students’ Statistical Reasoning In Statistics Method Course. Jurnal Pendidikan Matematika, 14(1), 81–90. https://doi.org/10.22342/jpm.14.1.6732.81-90
Rosidah, Ketut Budayasa, I., & Juniati, D. (2018). An Analysis of Statistical Reasoning Process of High School Students in Solving the Statistical Problem. Journal of Physics: Conference Series, 1028(1). https://doi.org/10.1088/1742-6596/1028/1/012125
Ben-Zvi, D., & Garfield, J. (2004). The Challenge Of Developing Statistical Literacy, Reasoning And Thinking. Kluwer Academic.
Burrill, G., & Ben-Zvi, D. (2019). Topics and Trends in Current Statistics Education Research. Springer. http://www.springer.com/series/15585
Corbin, J., & Strauss, A. (2008). Basic of Qualitative Research: Techniques and Procedures for Developing Grounded Theory (3rd ed.). Sage.
Dubinsky, E., Weller, K., McDonald, M. A., & Brown, A. (2005). Some historical issues and paradoxes regarding the concept of infinity: An APOS-based analysis: Part 1. Educational Studies in Mathematics, 58(3), 335–359. https://doi.org/10.1007/s10649-005-2531-z
Garfield, J., & Gal, I. (1999). Teaching and Assessing Statistical
Reasoning. Developing Mathematical Reasoning in Grades K-12: National Council Teachers of Mathematics 1999 Year, 207–219.
Idris, K. (2018). Teaching and learning statistics in college: How learning materials should be designed. Journal of Physics: Conference Series, 1088. https://doi.org/10.1088/1742-6596/1088/1/012032
Jones, G. A., Langrall, C. W., Mooney, E. S., & Thornton, C. A. (2004). Models Of Development In Statistical Reasoning.
Jones, G. A., Langrall, C. W., Thornton, C. A., Mooney, E. S., Wares, A., Jones, M. R., Perry, B., Putt, I. J., & Nisbet, S. (2001). Using students’ statistical thinking to inform instruction. Journal of Mathematical Behavior, 20, 109–144.
Jones, G. A., Thornton, C. A., Langrall, C. W., Mooney, E. S., Perry, B., & Putt, I. J. (2000). A Framework for Characterizing Children’s Statistical Thinking. Mathematical Thinking and Learning, 2(4), 269–307. https://doi.org/10.1207/s15327833mtl0204_3
Lavigne, N. C., & Lajoie, S. P. (2007). Statistical reasoning of middle school children engaged in survey inquiry. Contemporary Educational Psychology, 32(4), 630–666. https://doi.org/10.1016/j.cedpsych.2006.09.001
Lee, S., & Kim, G. (2019). How middle-school mathematics textbooks of Korea and the US support to develop students’ statistical reasoning. The Mathematical Education, 58(1), 139–160. https://doi.org/10.7468/mathedu.2019.58.1.139
Mooney, E. S. (2002). A Framework for Characterizing Middle School Students’ Statistical Thinking. Mathematical Thinking and Learning, 4(1), 23–63. https://doi.org/10.1207/s15327833mtl0401_2
Oktay, J. S. (2012). Grounded Theory. Oxford University Press.
Olani, A., Hoekstra, R., Harskamp, E., & Van Der Werf, G. (2011). Statistical Reasoning Ability, Self-Efficacy, and Value Beliefs in a Reform Based University Statistics Course. Electronic Journal of Research in Educational Psychology, 9(1), 1696–2095.
Onwuegbuzie, A. J., & Wilson, V. A. (2003). Statistics Anxiety: Nature, etiology, antecedents, effects, and treatments--a comprehensive review of the literature. Teaching in Higher Education, 8(2), 195–209. https://doi.org/10.1080/1356251032000052447
Rohana, R., & Ningsih, Y. L. (2020). Students’ Statistical Reasoning In Statistics Method Course. Jurnal Pendidikan Matematika, 14(1), 81–90. https://doi.org/10.22342/jpm.14.1.6732.81-90
Rosidah, Ketut Budayasa, I., & Juniati, D. (2018). An Analysis of Statistical Reasoning Process of High School Students in Solving the Statistical Problem. Journal of Physics: Conference Series, 1028(1). https://doi.org/10.1088/1742-6596/1028/1/012125
Downloads
Published
2023-12-20
Issue
Section
Articles
License
As a journal Author, you have rights for a large range of uses of your article, including use by your employing institute or company. These Author rights can be exercised without the need to obtain specific permission.
Authors and readers can copy and redistribute the material in any medium or format, as well as remix, transform, and build upon the material for any purpose, even commercially, but they must give appropriate credit (cite to the article or content), provide a link to the license, and indicate if changes were made. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
The Authors submitting a manuscript do so on the understanding that if accepted for publication, copyright of the article shall be assigned to PRISMA as publisher of the journal.
PRISMA by UNIVERSITAS SURYAKANCANA is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://jurnal.unsur.ac.id/prisma.
