TEACHING STATISTICS WITH POSITIVE ORIENTATIONS BUT LITTLE KNOWLEDGE? TEACHERS' PROFESSIONAL COMPETENCE IN STATISTICS
DOI:
https://doi.org/10.52041/serj.v23i1.610Keywords:
Statistics education research, Professional competence, Motivational and emotional orientations, Content knowledge, In-service teachers, Teacher educationAbstract
Research suggests teachers have positive motivational and emotional orientations regarding statistics but little statistical knowledge. How does this fit together? Since teachers’ professional competence in statistics has not been well explored, we asked 88 in-service mathematics teachers about their orientations regarding teaching statistics and tested their statistical content knowledge. First, we investigated how “positive” their orientations were by comparing them to their orientations regarding teaching fractions. Then, we analyzed relationships between teachers’ orientations and content knowledge in statistics using mixed-effects logistic regression models. The results showed that teachers’ orientations regarding teaching statistics were: (1) poorer than those regarding teaching fractions and (2) related to their statistical knowledge. Teachers with high self-efficacy showed higher knowledge than teachers with low self-efficacy, and anxious female teachers had higher knowledge than less anxious female teachers. We also found that knowledge decreased with increasing age of the teachers. The findings underscore the need to strengthen statistics in teacher education, including both content knowledge and the development of positive orientations.
References
Bartón, K. (2020). MuMIn: Multi-model inference. https://CRAN.R-project.org/package=MuMIn
Batanero, C. (2011). Teachers’ beliefs, attitudes and knowledge. In C. Batanero, G. Burrill & C. Reading (Eds.), Teaching statistics in school mathematics—Challenges for teaching and teacher education. A joint ICMI/IASE study: The 18th ICMI study (pp. 147–150). Springer.
Batanero, C., Burrill, G. & Reading, C. (Eds.). (2011). Teaching statistics in school mathematics— Challenges for teaching and teacher education. A joint ICMI/IASE study: The 18th ICMI study. Springer. https://doi.org/10.1007/978-94-007-1131-0
Bates, A. B., Latham, N., & Kim, J. (2011). Linking preservice teachers’ mathematics self-efficacy and mathematics teaching efficacy to their mathematical performance. School Science and Mathematics, 111(7), 325–333. https://doi.org/10.1111/j.1949-8594.2011.00095.x
Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48. https://doi.org/10.18637/jss.v067.i01
Baumert, J., & Kunter, M. (2013). The COACTIV model of teachers’ professional competence. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers: Results from the COACTIV project (pp. 25–48). Springer. https://doi.org/10.1007/978-1-4614-5149-5_2
Baumert, J., Kunter, M., Blum, W., Klusmann, U., Krauss, S., & Neubrand, M. (2013). Professional competence of teachers, cognitively activating instruction, and the development of students’ mathematical literacy (COACTIV): A research program. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers: Results from the COACTIV project (pp. 1–21). Springer. https://doi.org/10.1007/978-1-4614-5149-5_1
Ben-Zvi, D., & Makar, K. (2016). International perspectives on the teaching and learning of statistics. In D. Ben-Zvi & K. Makar (Eds.), The teaching and learning of statistics (pp. 1–10). Springer. https://doi.org/10.1007/978-3-319-23470-0_1
Bortz, J., & Schuster, C. (2010). Statistik für Human- und Sozialwissenschaftler [Statistics for human and social scientists]. (7th ed.). Springer.
Brauer, M., & Curtin, J. J. (2018). Linear mixed-effects models and the analysis of nonindependent data: A unified framework to analyze categorical and continuous independent variables that vary within-subjects and/or within-items. Psychological Methods, 23(3), 389–411. https://doi.org/10.1037/met0000159
Buscemi, S., & Plaia, A. (2020). Model selection in linear mixed-effect models. AStA Advances in Statistical Analysis, 104(4), 529–575. https://doi.org/10.1007/s10182-019-00359-z
Callingham, R., Carmichael, C., & Watson, J. M. (2016). Explaining student achievement: the influence of teachers’ pedagogical content knowledge in statistics. International Journal of Science and Mathematics Education, 14(7), 1339–1357. https://doi.org/10.1007/s10763-015-9653-2
Campbell, P. F., Nishio, M., Smith, T. M., Clark, L. M., Conant, D. L., Rust, A. H., Neumayer DePiper, J., Frank, T. J., Griffin, M. J., & Choi, Y. (2014). The relationship between teachers’ mathematical content and pedagogical knowledge, teachers’ perceptions, and student achievement. Journal for Research in Mathematics Education, 45(4), 419–459. https://doi.org/10.5951/jresematheduc.45.4.0419
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge. https://doi.org/10.4324/9780203771587
de Vetten, A., Schoonenboom, J., Keijzer, R., & van Oers, B. (2019). Pre-service primary school teachers’ knowledge of informal statistical inference. Journal of Mathematics Teacher Education, 22(6), 639–661. https://doi.org/10.1007/s10857-018-9403-9
delMas, R., Garfield, J., Ooms, A., & Chance, B. (2007). Assessing students’ conceptual understanding after a first course in statistics. Statistics Education Research Journal, 6(2), 28–58. http://www.stat.auckland.ac.nz/~iase/serj/serj6(2)_delmas.pdf
Eichler, A., & Erens, R. (2015). Domain-specific belief systems of secondary mathematics teachers. In B. Pepin & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education (pp. 179–200). Springer. https://doi.org/10.1007/978-3-319-06808-4_9
Eichler, A., & Zapata-Cardona, L. (2016). Empirical research in statistics education. ICME-13 Topical Surveys. Springer. https://doi.org/10.1007/978-3-319-38968-4
Emmons, R. A. (2020). Joy: An introduction to this special issue. The Journal of Positive Psychology, 15(1), 1–4. https://doi.org/10.1080/17439760.2019.1685580
Estrada, A., & Batanero, C. (2008). Explaining teachers’ attitudes towards statistics. In C. Batanero, G. Burrill, C. Reading & A. Rossman (Eds.), Teaching statistics in school mathematics—Challenges for teaching and teacher education. Proceedings of the 18th ICMI study and 2008 IASE round table conference. https://iase-web.org/documents/papers/rt2008/T2P4_Estrada.pdf
Estrada, A., Batanero, C., & Díaz, C. (2018). Exploring teachers’ attitudes towards probability and its teaching. In C. Batanero & E. J. Chernoff (Eds.), Teaching and learning stochastics: Advances in probability education research (pp. 313–332). Springer. https://doi.org/10.1007/978-3-319-72871-1_18
Estrada, A., Batanero, C., & Lancaster, S. (2011). Teachers’ attitudes towards statistics. In C. Batanero, G. Burrill & C. Reading (Eds.), Teaching statistics in school mathematics—Challenges for teaching and teacher education. A joint ICMI/IASE study: The 18th ICMI study (pp. 147–150). Springer. https://doi.org/10.1007/978-94-007-1131-0_18
Fagerland, M. W. (2012). T-tests, non-parametric tests, and large studies: A paradox of statistical practice? BMC Medical Research Methodology, 12, Article 78. https://doi.org/10.1186/1471-2288-12-78
Fives, H. (April, 2003). What is teacher efficacy and how does it relate to teachers’ knowledge? A theoretical review. Paper presented at the American Educational Research Association Annual Conference, Chicago.
https://msuweb.montclair.edu/~fivesh/Research_files/Fives_AERA_2003.pdf
Frenzel, A. C. (2014). Teacher emotions. In R. Pekrun & L. Linnenbrink-García (Eds.), International handbook of emotions in education (pp. 494–518). Routledge.
Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In G. C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 39–57). Springer. https://doi.org/10.1007/0-306-47958-3_3
Garfield, J. (2003). Assessing statistical reasoning. Statistics Education Research Journal, 2(1), 22–38. https://doi.org/10.52041/serj.v2i1.557
Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Springer. https://doi.org/10.1007/978-1-4020-8383-9
Gleason, J. (2007). Relationships between pre-service elementary teachers’ mathematics anxiety and content knowledge for teaching. Journal of Mathematical Sciences & Mathematics Education, 3(1), 39–47. http://ww.msme.us/2008-1-6.pdf
Groth, R., & Meletiou-Mavrotheris, M. (2018). Research on statistics teachers’ cognitive and affective characteristics. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 327–355). Springer. https://doi.org/10.1007/978-3-319-66195-7_10
Han, J., & Yin, H. (2016). Teacher motivation: Definition, research development and implications for teachers. Cogent Education, 3(1), 1217819. https://doi.org/10.1080/2331186X.2016.1217819
Hannigan, A., Gill, O., & Leavy, A. M. (2013). An investigation of prospective secondary mathematics teachers’ conceptual knowledge of and attitudes towards statistics. Journal of Mathematics Teacher Education, 16(6), 427–449. https://doi.org/10.1007/s10857-013-9246-3
Hannula, M. S. (2011). The structure and dynamics of affect in mathematical thinking and learning. In M. Pytlak, T. Rowland & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 34–60). http://erme.site/wp-content/uploads/2021/06/CERME7.pdf
Hannula, M. S. (2019). Young learners’ mathematics-related affect: a commentary on concepts, methods, and developmental trends. Educational Studies in Mathematics, 100(3), 309–316. https://doi.org/10.1007/s10649-018-9865-9
Haroun, R. F., Ng, D., Abdelfattah, F. A., & AlSalouli, M. S. (2016). Gender difference in teachers’ mathematical knowledge for teaching in the context of single-sex classrooms. International Journal of Science and Mathematics Education, 14(S2), 383–396. https://doi.org/10.1007/s10763-015-9631-8
Harradine, A., Batanero, C., & Rossman, A. (2011). Students and teachers’ knowledge of sampling and inference. In C. Batanero, G. Burrill & C. Reading (Eds.), Teaching statistics in school mathematics—Challenges for teaching and teacher education: A joint ICMI/IASE study: The 18th ICMI study (pp. 235–246). Springer. https://doi.org/10.1007/978-94-007-1131-0_24
Harrell-Williams, L. M., Lovett, J. N., Lee, H. S., Pierce, R. L., Lesser, L. M., & Sorto, M. A. (2019). Validation of scores from the high school version of the self-efficacy to teach statistics instrument using preservice mathematics teachers. Journal of Psychoeducational Assessment, 37(2), 194–208. https://doi.org/10.1177/0734282917735151
Harrell-Williams, L. M., Sorto, M. A., Pierce, R. L., Lesser, L. M., & Murphy, T. J. (2014). Validation of scores from a new measure of preservice teachers’ self-efficacy to teach statistics in the middle grades. Journal of Psychoeducational Assessment, 32(1), 40–50. https://doi.org/10.1177/0734282913486256
Harrell-Williams, L. M., Sorto, M. A., Pierce, R. L., Lesser, L. M., & Murphy, T. J. (2015). Identifying statistical concepts associated with high and low levels of self-efficacy to teach statistics in middle grades. Journal of Statistics Education, 23(1). https://doi.org/10.1080/10691898.2015.11889724
Hascher, T., & Krapp, A. (2014). Forschung zu Emotionen von Lehrerinnen und Lehrern [Research on teachers’ emotions]. In E. Terhart, H. Bennewitz & M. Rothland (Eds.), Handbuch der Forschung zum Lehrerberuf [Handbook of research on the teaching profession] (2. überarbeitete und erweiterte Auflage [revised and expanded edition], pp. 679–697). Waxmann.
Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.
Hill, H. C., Rowan, B., & 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
Johnson, T., Kulesa, P., Cho, Y. I., & Shavitt, S. (2005). The relation between culture and response styles. Journal of Cross-cultural Psychology, 36(2), 264–277. https://doi.org/10.1177/0022022104272905
Judd, C. M., Westfall, J., & Kenny, D. A. (2012). Treating stimuli as a random factor in social psychology: A new and comprehensive solution to a pervasive but largely ignored problem. Journal of Personality and Social Psychology, 103(1), 54–69. https://doi.org/10.1037/a0028347
Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., & Baumert, J. (2013). Teachers’ content knowledge and pedagogical content knowledge. Journal of Teacher Education, 64(1), 90–106. https://doi.org/10.1177/0022487112460398
Kunter, M. (2014). Forschung zur Lehrermotivation [Research on teacher motivation]. In E. Terhart, H. Bennewitz & M. Rothland (Eds.), Handbuch der Forschung zum Lehrerberuf [Handbook of research on the teaching profession] (2. überarbeitete und erweiterte Auflage [revised and expanded edition], pp. 698–711). Waxmann.
Kunter, M., & Holzberger, D. (2014). Loving teaching. In P. W. Richardson, S. A. Karabenick & H. M. G. Watt (Eds.), Teacher motivation: Theory and practice (pp. 83–99). Routledge. https://doi.org/10.4324/9780203119273-6
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