TEACHERS’ CONCEPTIONS AND PROFESSIONAL KNOWLEDGE OF VARIABILITY FROM THEIR INTERPRETATION OF HISTOGRAMS: THE CASE OF VENEZUELAN IN-SERVICE SECONDARY MATHEMATICS TEACHERS
DOI:
https://doi.org/10.52041/serj.v20i2.412Keywords:
Statistics education research, Statistical literacy, Specialized content knowledge, Teachers’ professional competencies, VariabilityAbstract
Many studies have reported on the influence of teachers’ conceptions of variability on different aspects of their professional knowledge for teaching statistics and their classroom practices. However, research on these kind of conceptions is still scarce, particularly in Latin American countries like Venezuela. In an effort to help fill this gap, a qualitative study was conducted that aimed to characterize the different ways in which Venezuelan in-service secondary school mathematics teachers conceptualize variability. For that purpose, a survey instrument was developed and administered to 27 teachers working at the metropolitan area of Caracas. This paper focuses on the participants’ answers to two items in which interpretation of histograms was necessary. It was found that about a third of the participants exhibited a sophisticated recognition of variability (e.g., gave answers connecting both middles and extremes), whereas about half of them exhibited misconceptions of variability, such as acknowledging variability from the viewpoint of idiosyncratic ideas, or the degree of symmetry (or lack thereof) of a histogram. Moreover, it was also found that about two-thirds of the participants were unable to correctly match real-life contexts to their corresponding histograms, while about two-fifths were unable to correctly determine the accuracy or inaccuracy of descriptions of the variability in a histogram. The author discusses possible reasons for the obtained results, in order to identify relevant implictions for teacher education in the area of statistics.
Abstract: Spanish
Diversos estudios han reportado que las concepciones de los docentes sobre variabilidad influencian tanto su conocimiento profesional para la enseñanza de la estadística, como sus prácticas en el aula. Sin embargo, investigaciones sobre este tipo de concepciones son aún escasas, particularmente en países latinoamericanos como Venezuela. Intentando satisfacer esta necesidad, se condujo un estudio cualitativo para identificar y caracterizar las diferentes maneras en que maestros venezolanos de matemáticas a nivel de secundaria conceptualizan la variabilidad. Con tal propósito, un cuestionario fue desarrollado y administrado a 27 docentes en el área metropolitana de Caracas. Este artículo se centra en las respuestas dadas por los participantes a dos ítems del cuestionario, en los que era necesaria la interpretación de histogramas. Se descubrió que aproximadamente un quinto de los participantes demostró un reconocimiento sofisticado de la variabilidad (e.g., considerar simultáneamente valores centrales y extremos de un histograma), mientras que alreadedor de la mitad exhibió concepciones erróneas, tales como el reconocimiento de la variabilidad a partir de ideas idiosincrásicas, o del grado de simetría de un histograma. Además, unos cuatro quintos de los participantes fueron incapaces de establecer una correspondencia entre contextos de la vida real y sus respectivos histogramas, mientras que unos dos quintos fueron incapaces de determinar si descripciones de la variabilidad en un histograma eran o no correctas. El autor discute las posibles razones de los resultados obtenidos, con el fin de identificar implicaciones relevantes para la formación docente en el área de la estadística.
References
Ball, D. L., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
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.
Biehler, R., Frischemeier, D., Reading, C., & Shaughnessy, J. M. (2018). Reasoning about data. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 139–192). Springer.
Blömeke, S., & Delaney, S. (2012). Assessment of teacher knowledge across countries: A review of the state of research. ZDM, 44(3), 223–247.
Bruno, A., & Espinel, M. C. (2009). Construction and evaluation of histograms in teacher training. International Journal of Mathematical Education in Science and Technology, 40(4), 473–493.
Centro Nacional para el Mejoramiento de la Enseñanza de la Ciencia y la Matemática. (1990). Programa de articulación: Contenidos de matemática para la educación media, diversificada y profesional. Primer y segundo año (Ciencias). [Articulation program: Mathematics content for secondary, diversified and vocational education. First and second year (Science)] CENAMEC.
Döhrmann, M., Kaiser, G., & Blömeke, S. (2012). The conceptualisation of mathematics competencies in the international teacher education study TEDS-M. ZDM, 44(3), 325–340.
Gal, I. (2004). Statistical literacy. Meanings, components, responsibilities. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 47–78). Kluwer.
González, O. (2014a). Examining Venezuelan secondary school mathematics teachers’ statistical knowledge for teaching: Focusing on the instruction of variability-related concepts [Doctoral dissertation]. Hiroshima University.
González, O. (2014b). Survey on secondary school teachers’ statistical knowledge for teaching: The need of developing Venezuelan teachers’ competence to teach statistics. International Journal of Curriculum Development and Practice, 16(1), 27–44.
González, O. (2014c). Secondary mathematics teachers’ professional competencies for effective teaching of variability-related ideas: A Japanese case study. Statistique et Enseignement, 5(1), 31–51.
Isoda, M., Chitmun, S., & González, O. (2018). Japanese and Thai senior high school mathematics teachers’ knowledge of variability. Statistics Education Research Journal, 17(2), 196–215. https://doi.org/10.52041/serj.v17i2.166
Kuntze, S., & Friesen, M. (2018). The role of mathematics teachers’ views for their competence of analysing classroom situations. In B. Rott, G. Törner, J. Peters-Dasdemir, A. Möller, & Safrudiannur (Eds.), Views and beliefs in mathematics education: The role of beliefs in the classroom (pp. 183–194). Springer.
León, N. (2011). Explorando el conocimiento probabilístico informal en niños de edad temprana. [Exploring informal probabilistic knowledge in young children] Paper presented at the XIII Interamerican Conference on Mathematics Education (IACME), Universidade Federal de Pernambuco, Recife, Brazil, June 26–30.
Makar, K. M., & Confrey, J. (2004). Secondary teachers’ reasoning about comparing two groups. In D. Ben-Zvi & J. Garfield (Eds.), The challenges of developing statistical literacy, reasoning, and thinking (pp. 327–352). Kluwer.
Meletiou, M., & Lee, C. (2003). Studying the evolution of students’ conceptions of variation using the transformative and conjecture-driven research design. In C. Lee (Ed.), Reasoning about variability (pp. 1–39). Central Michigan University.
Merriam, S. B., & Tisdell, E. J. (2016). Qualitative research: A guide to design and implementation (4th ed.). Jossey-Bass.
Ministerio de Educación. (ME) (1997). Programas de Estudio de 7° a 9° Grado de Educación Básica. [Study Programs from 7th to 9th grade of Basic Education]. ME.
Peters, S. A. (2009). Developing an understanding of dispersion: AP statistics teachers’ perceptions and recollections of critical moments. [Doctoral dissertation, Pennsylvania State University].
Pfannkuch, M. (2018). Reimagining curriculum approaches. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 387–413). Springer.
Pratt, D. D. (1992). Conceptions of teaching. Adult Education Quarterly, 42(4), 203–220.
Salcedo, A. (2006). Statistics education in Venezuela: The case of elementary and middle school. In A. Rossman & B. Chance (Eds.), Working cooperatively in statistics education. Proceedings of the Seventh International Conference on Teaching Statistics (ICOTS-7), Salvador, Brazil, July 2–7. IASE. https://iase-web.org/documents/papers/icots7/C125.pdf?1402524966
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36.
Shaughnessy, J. M. (2007). Research on statistics’ reasoning and learning. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957–1009). Information Age Publications & NCTM.
Sivunen, M., & Pehkonen, E. (2009). Finnish elementary teachers’ conceptions on problem solving in mathematics education. In J. Maass & W. Schlöglmann (Eds.), Beliefs and attitudes in mathematics education (pp. 75–86). Sense Publishers.
Tapia, J. M. (2011). Propuesta didáctica para la enseñanza de la estadística basada en R Commander. [Didactic proposal for the teaching of statistics based on R Commander] Paper presented at the XIII Interamerican Conference on Mathematics Education (IACME), Universidade Federal de Pernambuco, Recife, Brazil, June 26–30.
Tatto, M. T., Schwille, J., Senk, S., Ingvarsson, L., Rowley, G., Peck, R., & Reckase, M. (2012). Policy, practice and readiness to teach primary and secondary mathematics in 17 countries. IAE.
