Lexical ambiguities in statistics declared by in training and in-service teachers

Francisco Rodríguez-Alveal; Ana C. Maldonado-Fuentes; Danilo Díaz-Levicoy

doi:10.29333/ejmste/14359

Full Text (PDF)

Francisco Rodríguez-Alveal ¹ ^* , Ana C. Maldonado-Fuentes ¹ , Danilo Díaz-Levicoy ²

More Detail

¹ Universidad del Bío-Bío, Chillán, CHILE² Universidad Católica del Maule, Talca, CHILE^* Corresponding Author

Abstract

This article aims to evaluate how teachers, in training and in-service, define the concepts of randomness, probability, chance and variability, fundamental terms in the teaching of statistics. To this end, a printed recording protocol of natural semantic networks was applied to 16 teachers in training and 58 in-service teachers, selected through non-probabilistic sampling. The results provide evidence that the concept with the lowest conceptual density in both groups is variability. Likewise, a greater presence of similar words was observed between randomness, chance and probability, despite being different concepts. Another finding is the association of the inducing concepts to words that are used within the basic lexicon in Chilean Spanish, whose dictionary is not specialized in statistics. It is concluded about the scarce use of technical language by the participants, which would eventually affect the teaching of statistics.

Keywords

terminology
statistical literacy
lexical ambiguities
natural semantic networks
teachers in training
in-service teachers

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

EURASIA J Math Sci Tech Ed, Volume 20, Issue 4, April 2024, Article No: em2422

https://doi.org/10.29333/ejmste/14359

Publication date: 01 Apr 2024

Online publication date: 14 Mar 2024

Article Views: 764

Article Downloads: 460

Open Access References How to cite this article

References

Ancer, L., Muñiz, M. G., Sánchez, M. P., Garza, A. D. L., & Barrón, V. M. (2013). Redes semánticas naturales sobre la práctica del psicólogo en escuelas públicas federales [Natural semantic networks on psychologist practice in federal public schools]. Spenta University Mexico.
Ata, A. (2014). Öğretmen adaylarının olasılık konusuna ilişkin kavramsal ve işlemsel bilgi düzeylerinin incelenmesi [Examining the conceptual and procedural knowledge levels of teacher candidates regarding the subject of probability] [Unpublished master’s thesis]. Eskisehir Osmangazi University.
Ayer, A. J. (1974). El azar [Chance]. In M. Kline (Ed.), Matemáticas en el mundo moderno [Mathematics in the modern world] (pp. 172-181). Blume.
Batanero, C. (2005). Significados de la probabilidad en la educación secundaria [Meanings of probability in secondary education]. Revista Latinoamericana de Investigación en Matemática Educativa [Latin American Journal of Research in Educational Mathematics], 8(3), 247-263.
Batanero, C., & Serrano, L. (1995). La aleatoriedad, sus significados e implicancias educativas [Randomness, its meanings and educational implications]. Revista UNO [UNO Magazine], 5(15), 15-28.
Ben-Zvi, D., & Garfield, J. (2004). Statistical literacy, reasoning, and thinking: Goals, definitions, and challenges. In D. Ben-Zvi, & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 3-15). Kluwer. https://doi.org/10.1007/1-4020-2278-6_1
Canavos, G. (1988). Probabilidad y estadística aplicaciones y métodos [Probability and statistics applications and methods]. McGraw-Hill.
Cantú-Martínez, P. (2023). Explorando la construcción social del cambio climático a través de redes semánticas naturales: Un estudio sobre las perspectivas de los estudiantes universitarios [Exploring the social construction of climate change through natural semantic networks: A study of university students’ perspectives]. Educación [Education], 32(62), 33-51. https://doi.org/10.18800/educacion.202301.009
Castillo, M. (2021). Léxico básico del Español de Chile [Basic lexicon of Chilean Spanish]. Liberalia.
Chance, B. L. (2002). Components of statistical thinking and implications for instruction and assessment. Journal of Statistics Education, 10(3). https://doi.org/10.1080/10691898.2002.11910677
Crossley, S., Liu, R., & McNamara, D. (2017). Predicting math performance using natural language processing tools. In M. Hatala (Ed.), Proceedings of the 7^th International Conference on Learning Analytics and Knowledge (pp. 339-347). ACM. https://doi.org/10.1145/3027385.3027399
Devore, J. (2008). Probabilidad y estadística para ingeniería y ciencias [Probability and statistics for engineering and science]. CENGASE Learning.
Dunn, P., Carey, M., Richardson, A., & McDonald, C. (2016). Learning the language of statistics: Challenges and teaching approaches. Statistics Education Research Journal, 15(1), 8-27. https://doi.org/10.52041/serj.v15i1.255
Durkin, K., & Shire, B. (1991). Primary school children’s interpretations of lexical ambiguity in mathematical descriptions. Journal of Research in Reading, 14(1), 46-55. https://doi.org/10.1111/j.1467-9817.1991.tb00005.x
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
Estrella, S., Olfos, R., & Mena-Lorca, A. (2015). El conocimiento pedagógico del contenido de estadística en profesores de primaria [Pedagogical knowledge of statistics content in primary school teachers].Educação E Pesquisa [Education and Research], 41(2), 477-493. https://doi.org/10.1590/S1517-97022015041858
Ferreira, A., Salcedo, P., & del Valle, M. (2014). Estudio de disponibilidad léxica en el ámbito de las matemáticas [Study of lexical availability in the field of mathematics]. Estudios Filológicos [Philological Studies], 54, 69-84. https://doi.org/10.4067/S0071-17132014000200004
Franklin, C., Kader, G., Mewborn, D. S., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2005). A curriculum framework for K-12 statistics education. GAISE report. American Statistical Association.
GAISE. (2016). Guidelines for assessment and instruction in statistics education (GAISE) college report 2016. American Statistical Association.
Garfield, J. (2002). The challenge of developing statistical reasoning. Journal of Statistics Education, 10(3). https://doi.org/10.1080/10691898.2002.11910676
Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Springer.
Groth, R. E. (2007). Research commentary: Toward a conceptualization of statistical knowledge for teaching. Journal for Research in Mathematics Education, 38(5), 427-437.
Guven, B., Baki, A., Uzun, N., Ozmen, Z. M., & Arslan, Z. (2021). Evaluating the statistics courses in terms of the statistical literacy: didactic pathways of pre-service mathematics teachers. International Electronic Journal of Mathematics Education, 16(2), em0627. https://doi.org/10.29333/iejme/9769
Hinojosa, G. (2008). El tratamiento estadístico de las redes semánticas naturales [The statistical treatment of natural semantic networks]. Revista Sociotam [Sociotam Magazine], 18(1), 133-154.
Huerta, P. (2020). Hipótesis y conjeturas en el desarrollo del pensamiento estocástico: Retos para su enseñanza y en la formación de profesores [Hypotheses and conjectures in the development of stochastic thinking: Challenges for teaching and teacher training]. Revista Latinoamericana de Investigación en Matemática Educativa [Latin American Journal of Research in Educational Mathematics], 23(1), 79-102. https://doi.org/10.12802/relime.20.2313
Kaplan, J., Fisher, D. G., & Rogness, N. T. (2010). Lexical ambiguity in statistics: How students use and define the words: Association, average, confidence, random and spread. Journal of Statistics Education, 18(2). https://doi.org/10.1080/10691898.2010.11889491
Kaplan, J., Fisher, D.G., & Rogness, N.T. (2009). Lexical ambiguity in statistics: What do students know about the words association, average, confidence, random and spread? Journal of Statistics Education, 17(3). https://doi.org/10.1080/10691898.2009.11889535
Konold, C. (1995). Issues in assessing conceptual understanding in probability and statistics. Journal of Statistics Education, 3(1). https://doi.org/10.1080/10691898.1995.11910479
Kurt-Birel, G. (2017). The investigation of pre-service elementary mathematics teachers’ subject matter knowledge about probability. Mersin Üniversitesi Eğitim Fakültesi Dergisi [Mersin University Faculty of Education Journal], 13(1), 348-362. https://doi.org/10.17860/mersinefd.306023
Lavy, I., & Mashiach-Eizenberg, M. (2009). The interplay between spoken language and informal definitions of statistical concepts. Journal of Statistics Education, 17(1). https://doi.org/10.1080/10691898.2009.11889502
Leung, C. (2005). Convivial communication: Recontextualizing communicative competence. International Journal of Applied Linguistics, 15(2), 119-144. https://doi.org/10.1111/j.1473-4192.2005.00084.x
López-Cortés, N., & Horno-Chéliz, C. (2021). La naturaleza de la ambigüedad léxica. Un estudio sobre los sustantivos en Español [The nature of lexical ambiguity. A study on nouns in Spanish] [PhD thesis, Universidad de Zaragoza].
Maldonado-Fuentes, A.C., Tapia-Ladino, M., & Arancibia-Gutiérrez, B. (2019). ¿Qué significa evaluar? [What does it mean to evaluate?] Perfiles Educativos, 42(167), 138-157. https://doi.org/10.22201/iisue.24486167e.2019.167.59208
McMillan, J., & Schumacher, S. (2011). Investigación educativa [Educational investigation]. Pearson-Adisson Wesley.
Merino, R., Muñoz, V., Pérez, B., & Rupin, P. (2016). Texto del estudiante matemática, 7° básico [Math student text, 7^th grade]. SM.
Meyer, P. (1973). Probabilidad y aplicaciones estadística [Probability and statistical applications]. Reverte.
MINEDUC. (2012). Bases curriculares primero a sexto básico [Curriculum bases first to sixth grade]. Unidad de Currículum y Evaluación [Curriculum and Assessment Unit].
Moore, D. (1997). New pedagogy and new content: The case of statistics. International Statistical Review, 65(2), 123-165. https://doi.org/10.2307/1403333
Moore, D. (2007). The basic practice of statistics. Freeman and Company.
Nacarato, A., & Grando, R. (2014). The role of language in building probabilistic thinking. Statistics Education Research Journal, 13(2), 93-103. https://doi.org/10.52041/serj.v13i2.283
O’Halloran, K.L. (2000). Classroom discourse in mathematics: A multi-semiotic analysis. Linguistics and Education, 10(3), 359-388. https://doi.org/10.1016/S0898-5898(99)00013-3
Oliveira, A.P., Aparecida, F., & da Silva, L.R. (2023). Ambiguidade lexical em probabilidade: conhecimento de alunos do ensino fundamental sobre acaso, aleatório e incerteza [Lexical ambiguity in probability: elementary school students’ knowledge about chance, randomness and uncertainty]. Areté, Revista Digital del Doctorado en Educación de la Universidad Central de Venezuela [Areté, Digital Magazine of the Doctorate in Education of the Central University of Venezuela], 9(17), 99-126. https://doi.org/10.55560/arete.2023.17.9.5
Ortiz, J. J., Batanero, C., & Serrano, L. (2001). El lenguaje probabilístico en los libros de texto [Probabilistic language in textbooks]. Suma [Addition], 38, 5-14.
Pérez-Pascual, J. I. (2012). El léxico de especialidad [The specialty lexicon]. In L. Luque, J. F. Medina, & R. Luque (Eds.), Léxico Español actual III [Current Spanish lexicon III] (pp. 189-219). Università Ca’Foscari di Venezia [Ca’Foscari University of Venice].
RAE. (2014). Diccionario de la lengua Española [Dictionary of the Spanish language]. Real Academia Española.
Ramírez, G., & Batalha, A. (2019). Aprendizaje de la aleatoriedad y conceptos asociados: Un estudio en secundaria con apoyo de GeoGebra [Learning randomness and associated concepts: A study in secondary school with the support of GeoGebra]. Revista Digital: Matemática, Educación e Internet [Digital Magazine: Mathematics, Education and Internet], 20(1). https://doi.org/10.18845/rdmei.v20i1.4591
Rangecroft, M. (2002). The language of statistics. Teaching Statistics, 24(2), 34-37. https://doi.org/10.1111/1467-9639.00080
Reading, C., & Shaughnessy, J. M. (2004). Reasoning about variation. In J. Garfield, & D. Ben-Zvi (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 201-226). Kluwer. https://doi.org/10.1007/1-4020-2278-6_9
Reyes, L. I. (1993). Las redes semánticas naturales, su conceptualización y su utilización en la construcción de instrumentos [Natural semantic networks, their conceptualization and their use in the construction of instruments]. Revista de Psicología Social y Personalidad [Journal of Social Psychology and Personality], 9(1), 81-97.
Rodríguez-Alveal, F., & Maldonado-Fuentes, A. C. (2023). Tipología de las preguntas sobre variabilidad en los textos escolares y su relación con la alfabetización y pensamiento estadístico [Typology of questions about variability in school textbooks and their relationship with literacy and statistical thinking]. Uniciencia, 37(1), 65-83. https://doi.org/10.15359/ru.37-1.4
Rodríguez-Alveal, F., Aguerrea, M., & Díaz-Levicoy, D. (2022). El concepto aleatoriedad en los libros de texto chilenos de educación primeria [The concept of randomness in Chilean primary education textbooks]. Acta Scientiae, 24(7), 1-27. https://doi.org/10.17648/acta.scientiae.6974
Rodríguez-Alveal, F., Díaz-Levicoy, D., & Vásquez, C. (2018). Evaluación de la alfabetización probabilística del profesorado en formación y en activo [Assessment of probabilistic literacy of teachers in training and in service]. Estudios pedagógicos (Valdivia), 44(1), 135-156. https://doi.org/10.4067/S071807052018000100135
Rodríguez-Alveal, F., Díaz-Levicoy, D., & Vásquez, C. (2021). Análisis de las actividades sobre variabilidad estadística en los libros de texto de educación secundaria: Una mirada desde las propuestas internacionales [Analysis of activities on statistical variability in secondary education textbooks: A look from international proposals]. Uniciencia, 35(1), 108-123. https://doi.org/10.15359/ru.35-1.7
Sánchez, E., da Silva, C. B., & Coutinho, C. (2011a). Teachers’ understanding of variation. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education (pp. 211-221). Springer. https://doi.org/10.1007/978-94-007-1131-0_22
Sánchez, M., de la Garza, G., & López, R. (2011b). Redes semánticas naturales del tema de medio ambiente en dos grupos de contraste [Natural semantic networks of the environmental topic in two contrast groups]. Revista Mexicana de Investigación en Psicología [Mexican Journal of Research in Psychology], 3(1), 60-71. https://doi.org/10.32870/rmip.v3i1.495
Sánchez, M., de la Garza, G., & López, R. (2013). Simulaciones computacionales sobre cuestiones ambientales en dos grupos de contraste [Computer simulations on environmental issues in two contrast groups]. Liberabit, 19(2), 223-233.
Schleppegrell, M. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading and Writing Quarterly, 23(2), 139-159. https://doi.org/10.1080/10573560601158461
Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 465-494). Macmillan Publishing Co.
Stohl, H. (2005). Probability in teacher education and development. In J. Graham (Eds.), Exploring probability in school: Challenges for teaching and learning (pp. 345-366). Springer. https://doi.org/10.1007/0-387-24530-8_15
Thibaut, C., Medrano, D., & Jiménez, A. (2018). Evaluación en aula de textos escolares: ¿Una estrategia posible? [Classroom evaluation of school texts: A possible strategy?] Estudios Pedagógicos (Valdivia) [Pedagogical Studies (Valdivia)], 38(2), 243-257. https://doi.org/10.4067/S0718-07052012000200015
Triola, M. (2009). Estadística [Statistics]. Pearson.
Vásquez, C., & Alsina, Á. (2015). Un modelo para el análisis de objetos matemáticos en libros de texto chilenos: Situaciones problemáticas, lenguaje y conceptos sobre probabilidad [A model for the analysis of mathematical objects in Chilean textbooks: Problematic situations, language and concepts about probability]. Profesorado, Revista de Currículum y Formación del Profesorado [Teachers, Journal of Curriculum and Teacher Training], 19(2), 441-462.
Vera-Noriega, J. A., Pimentel, C. E., & Batista, F. J. (2005). Redes semánticas: Aspectos teóricos, técnicos, metodológicos y analíticos [Semantic networks: Theoretical, technical, methodological and analytical aspects]. Ra Ximhai, 1(3), 439-451. https://doi.org/10.35197/rx.01.03.2005.01.jv
Watson, J., Kelly, B., Callingham, R., & Shaughnessy, M. (2003). The measurement of school students ́ understanding of statistical variation. International Journal of Mathematical Education in Science and Technology, 34(1), 1-29. https://doi.org/10.1080/0020739021000018791
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-265. https://doi.org/10.2307/1403699
Zisimos B., & Tasos P. (2021). Understanding 15-year-old students’ conceptions of randomness through their ‘potential worlds’: A qualitative analysis. International Journal of Mathematical Education in Science and Technology, 52(2), 237-258. https://doi.org/10.1080/0020739X.2019.1676928

How to cite this article

APA

Rodríguez-Alveal, F., Maldonado-Fuentes, A. C., & Díaz-Levicoy, D. (2024). Lexical ambiguities in statistics declared by in training and in-service teachers. Eurasia Journal of Mathematics, Science and Technology Education, 20(4), em2422. https://doi.org/10.29333/ejmste/14359

Vancouver

Rodríguez-Alveal F, Maldonado-Fuentes AC, Díaz-Levicoy D. Lexical ambiguities in statistics declared by in training and in-service teachers. EURASIA J Math Sci Tech Ed. 2024;20(4):em2422. https://doi.org/10.29333/ejmste/14359

AMA

Rodríguez-Alveal F, Maldonado-Fuentes AC, Díaz-Levicoy D. Lexical ambiguities in statistics declared by in training and in-service teachers. EURASIA J Math Sci Tech Ed. 2024;20(4), em2422. https://doi.org/10.29333/ejmste/14359

Chicago

Rodríguez-Alveal, Francisco, Ana C. Maldonado-Fuentes, and Danilo Díaz-Levicoy. "Lexical ambiguities in statistics declared by in training and in-service teachers". Eurasia Journal of Mathematics, Science and Technology Education 2024 20 no. 4 (2024): em2422. https://doi.org/10.29333/ejmste/14359

Harvard

Rodríguez-Alveal, F., Maldonado-Fuentes, A. C., and Díaz-Levicoy, D. (2024). Lexical ambiguities in statistics declared by in training and in-service teachers. Eurasia Journal of Mathematics, Science and Technology Education, 20(4), em2422. https://doi.org/10.29333/ejmste/14359

MLA

Rodríguez-Alveal, Francisco et al. "Lexical ambiguities in statistics declared by in training and in-service teachers". Eurasia Journal of Mathematics, Science and Technology Education, vol. 20, no. 4, 2024, em2422. https://doi.org/10.29333/ejmste/14359