Archives
Current issue
About
About us
Aims and Scope
Abstracting and Indexing
Editorial Office
Open Access Policy
Publication Ethics
Journal History
Publisher
Follow us: Twitter
Contact
For Authors
Editorial Policy
Peer Review Policy
Manuscript Preparation Guidelines
Copyright & Licencing
Publication Fees
Fee Waiver Policy for Doctoral Students
EJMSTE Language Editing Service
More
Statistics
Special Issues
Special Issue Announcements
Published Special Issues
RESEARCH PAPER
An approach to inferential reasoning levels on the Chi-square statistic
1
Universidad de Los Lagos, Osorno, CHILE
Publication date: 2024-01-16
EURASIA J. Math., Sci Tech. Ed 2024;20(1):em2388
KEYWORDS
ABSTRACT
This paper presents an approach of progressive levels of inferential reasoning on the Chi-square
statistic, going from informal to formal reasoning. The proposal is based on epistemic criteria
retrieved from a historical-epistemological study of such statistic and the contributions of
statistics education literature on inferential reasoning. In this regard, some theoretical and
methodological notions from the onto-semiotic approach were used to identify meanings
attributed to the Chi-square statistic throughout its evolution and development. The
mathematical characteristics of those meanings are closely linked to the indicators of the levels
proposed. The nature of the four levels on the Chi-square statistic allowed us to develop an initial
approach to levels of inferential reasoning, which could be applied to other statistics such as z,
student’s t and F.
REFERENCES (74)
1.
Aké, L. P. (2013). Evaluación y desarrollo del razonamiento algebraico elemental en maestros en formación [Evaluation and development of elementary algebraic reasoning in training teachers] [Doctoral dissertation, Universidad de Granada].
2.
Bakker, A., & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13(1-2), 5-26. https://doi.org/10.1080/109860....
3.
Bakker, A., & Gravemeijer, K. (2004). Learning to reason about distribution. In D. Ben-Zvi, & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 147-168). Springer. https://doi.org/10.1007/1-4020....
4.
Bakker, A., Ben-Zvi, D., & Makar, K. (2017). An inferentialist perspective on the coordination of actions and reasons involved in making a statistical inference. Mathematics Education Research Journal, 29(4), 455-470. https://doi.org/10.1007/s13394....
5.
Batanero, C. (2013). Del análisis de datos a la inferencia: Reflexiones sobre la formación del razonamiento estadístico [From data analysis to inference: Reflections on the formation of statistical reasoning]. Cuadernos de Investigación y Formación en Educación Matemática [Research and Training Notebooks in Mathematics Education], 11, 277-291.
6.
Batanero, C., Vera, O. D., & Díaz, C. (2012). Dificultades de estudiantes de psicología en la comprensión del contraste de hipótesis [Difficulties of psychology students in understanding the contrast of hypotheses]. Números. Revista de Didáctica de las Matemáticas [Numbers. Mathematics Didactics Magazine], 80, 91-101.
7.
Ben-Zvi, D., & Aridor-Berger, K. (2016). Children’s wonder how to wander between data and context. In D. Ben-Zvi, & K. Makar (Eds.), The teaching and learning of statistics: International perspectives (pp. 25–36). Springer. https://doi.org/10.1007/978-3-....
8.
Ben-Zvi, D., & Garfield, J. B. (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). Springer. https://doi.org/10.1007/1-4020....
9.
Biehler, R., Frischemeier, D., & Podworny, S. (2015). Preservice teachers reasoning about uncertainty in the context of randomization tests. In A. Zieffler, & E. Fry (Eds.), Reasoning about uncertainty: Learning and teaching informal inferential reasoning (pp. 129-162). Catalyst Press.
10.
Cañadas, G., Batanero, C., Díaz, C., & Gea, M. M. (2012). Comprensión del test Chi-cuadrado por estudiantes de psicología [Understanding of the Chi-square test by students of psychology]. In A. Estepa, Á. Contreras, J. Deulofeu, M. C. Penalva, F. J. García, & L. Ordóñez (Eds.), Investigación en educación matemática XVI [Research in mathematics education XVI] (pp. 153 - 163). SEIEM.
11.
Cohen, J. (1994). The earth is round (p<. 05). American Psychologist, 49(12), 997-1003. https://doi.org/10.1037/0003-0....
12.
Dierdorp, A., Bakker, A., Eijkelhof, H., & van Maanen, J. (2011). Authentic practices as contexts for learning to draw inferences beyond correlated data. Mathematical Thinking and Learning, 13(1-2), 132-151. https://doi.org/10.1080/109860....
13.
Dinov, I. D., Palanimalai, S., Khare, A., & Christou, N. (2018). Randomization-based statistical inference: A resampling and simulation infrastructure. Teaching Statistics, 40(2), 64-73. https://doi.org/10.1111/test.1....
14.
Doerr, H. M., delMas, R. & Makar, K. (2017). A modeling approach to the development of students’ informal inferential reasoning. Statistics Education Research Journal, 16(2), 86-115. https://doi.org/10.52041/serj.....
15.
Dolor, J., & Noll, J. (2015). Using guided reinvention to develop teachers’ understanding of hypothesis testing concepts. Statistics Education Research Journal, 14(1), 60-89. https://doi.org/10.52041/serj.....
16.
English, L. D., & Watson, J. (2018). Modelling with authentic data in sixth grade. ZDM-International Journal on Mathematics Education, 50(1-2), 103-115. https://doi.org/10.1007/s11858....
17.
Estrella, S., Méndez-Reina, M., Salinas, R., & Rojas, T. (2023). The mystery of the black box: An experience of informal inferential reasoning. In G. F. Burrill, L. de Oliveria Souza, & E. Reston (Eds.), Research on reasoning with data and statistical thinking: International perspectives (pp. 191-210). Springer. https://doi.org/10.1007/978-3-....
19.
Font, V., & Rubio, N. V. (2017). Procesos matemáticos en el enfoque onto-semiótico [Mathematical processes in the onto-semiotic approach]. In J. M. Contreras, P. Arteaga, G. R. Cañadas, M. M. Gea, B. Giacomone, & M. M. López-Martín (Eds.), Actas del Segundo Congreso International Virtual sobre el Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemáticos [Proceedings of the 2nd International Virtual Congress on the Ontosemiotic Approach to Mathematical Knowledge and Instruction]. Universidad de Granada.
20.
Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82(1), 97-124. https://doi.org/10.1007/s10649....
21.
Galton, F. (1875). IV. Statistics by intercomparison, with remarks on the law of frequency of error. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Series 4, 49(322), 33-46. https://doi.org/10.1080/147864....
22.
Galton, F. (1885). The application of a graphic method to fallible measures. Journal of the Statistical Society of London, 262-271.
23.
Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Springer. https://doi.org/10.1007/978-1-....
24.
Gil, E., & Ben-Zvi, D. (2011). Explanations and context in the emergence of students’ informal inferential reasoning. Mathematical Thinking and Learning, 13(1-2), 87-108. https://doi.org/10.1080/109860....
25.
Godino, J. D. (2022). Emergencia, estado actual y perspectivas del enfoque ontosemiótico en educación matemática [Emergence, current state and perspectives of the onto-semiotic approach in mathematics education]. Revista Venezolana de Investigación en Educación Matemática [Venezuelan Journal of Research in Mathematics Education], 2(2), e202201. https://doi.org/10.54541/revie....
26.
Godino, J. D. Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM Mathematics Education, 39(1-2), 127-135. https://doi.org/10.1007/s11858....
27.
Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos [Institutional and personal meaning of mathematical objects]. Recherches en Didactique des Mathématiques [Research in Mathematics Didactics], 14(3), 325-355.
28.
Godino, J. D., Batanero, C., & Font, V. (2019). The onto-semiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39(1), 37- 42.
29.
Godino, J. D., Font, V., Wilhelmi, M. R. & Lurduy, O. (2011). Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects. Educational Studies in Mathematics, 77(2), 247-265. https://doi.org/10.1007/s10649....
30.
Godino, J. D., Neto, T., Wilhelmi, M., Aké, L., Etchegaray, S., & Lasa, A. (2015). Algebraic reasoning levels in primary and secondary education. In K. Krainer, & N. Vondrová, (Eds.) Proceedings of 9th Congress of the European Society for Research in Mathematics Education (pp. 426-432). ERME.
31.
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 (pp. 235-246). Springer. https://doi.org/10.1007/978-94....
32.
Jacob, B. L., & Doerr, H. M. (2014). Statistical reasoning with the sampling distribution. In K. Makar, B. de Sousa, & R. Gould (Eds.), Proceedings of the 9th International Conference on Teaching Statistics. IASE.
33.
López-Martín, M. D. M., Batanero, C., & Gea, M. M. (2019). ¿Conocen los futuros profesores los errores de sus estudiantes en la inferencia estadística? [Do prospective teachers know their students’ errors in statistical inference?] Bolema: Boletim de Educação Matemática [Bulletin: Mathematics Education Bulletin], 33(64), 672-693. https://doi.org/10.1590/1980-4....
34.
Lugo-Armenta, J. G., Pino-Fan, L. R., & Ruiz, B. (2021). Meanings of the Chi-square statistic: A historical-epistemological overview. Revemop - Revista de Educação Matemática de Ouro Preto, 3, 1-33. https://doi.org/10.33532/revem....
35.
Lugo-Armenta, J. G., & Pino-Fan, L. R. (2021a). Inferential reasoning of high school mathematics teachers about chi-squared statistic. Mathematics, 9(19), 2416. https://doi.org/10.3390/math91....
36.
Lugo-Armenta, J. G., & Pino-Fan, L. R. (2021b). Niveles de razonamiento inferencial para el estadístico t-student [Levels of inferential reasoning for the t-student statistician]. Bolema: Boletim de Educação Matemática, 35, 1776-1802. https://doi.org/ 10.1590/1980-4415v35n71a25.
37.
Lugo-Armenta, J. G., & Pino-Fan, L. R. (2022). Razonamiento inferencial de profesores de matemáticas de enseñanza media sobre el estadístico t-student [Inferential reasoning of high school mathematics teachers on the t-student statistic]. Uniciencia, 36(1), 1-29. https://doi.org/10.15359/ru.36....
38.
Makar, K. (2016). Developing young children’s emergent inferential practices in statistics. Mathematical Thinking and Learning, 18(1), 1-24. https://doi.org/10.1080/109860....
39.
Makar, K., & Ben-Zvi, D. (2011). The role of context in developing reasoning about informal statistical inference. Mathematical Thinking and Learning, 13(1-2), 1-4. https://doi.org/10.1080/109860....
40.
Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82-105. https://doi.org/10.52041/serj.....
41.
Makar, K., & Rubin, A. (2018). Learning about statistical inference. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 261-294). Springer. https://doi.org/10.1007/978-3-....
42.
Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1-2), 152-173. https://doi.org/10.1080/109860....
43.
Matis, T., Riley, L., & Matis, J. (2004). Integrating technologically-based laboratory modules into the stochastic processes curriculum. In G. Burrill, & M. Camden (Eds.), Curriculum development in statistics education: International association for statistics education (pp. 93-103). International Statistical Institute. https://doi.org/10.52041/SRAP.....
44.
Medrano, I., & Pino-Fan, L. R. (2016). Estadios de comprensión de la noción matemática de límite finito desde el punto de vista histórico [Stages of understanding the mathematical notion of finite limit from a historical point of view]. REDIMAT, Journal of Research in Mathematics Education, 5(3), 287 - 323. https://doi.org/10.17583/redim....
45.
Mineduc. (2019). Bases curriculares 3º y 4º medio [Curriculum bases 3rd and 4th year]. Unidad de Currículum y Evaluación. Ministerio de Educación de Chile [Curriculum and Evaluation Unit. Ministry of Education of Chile].
46.
Molina, O. J. (2019). Sistema de normas que influyen en procesos de argumentación: Un curso de geometría del espacio como escenario de investigación [System of norms that influence on argumentation processes: A space geometry course as research scenario] [Doctoral dissertation, Universidad de Los Lagos].
47.
Ortiz, C. V., & Alsina, Á. (2019). Intuitive ideas about chance and probability in children from 4 to 6 years old. Acta Scientiae [Journal of Science], 21(3), 131-154. https://doi.org/10.17648/acta.....
48.
Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 50(302), 157-175. https://doi.org/10.1080/147864....
49.
Pearson, K. (1904). On the theory of contingency and its relation to association and normal correlation. Draper’s Company Research Memoirs Biometric Series I.
50.
Peirce, C. S. (1958). Collected papers of Charles Sanders Peirce. 1931-1935. Harvard UP.
51.
Pfannkuch, M. (2007). Year 11 students’ informal inferential reasoning: A case study about the interpretation of box plots. International Electronic Journal of Mathematical Education, 2(3), 149-167. https://doi.org/10.29333/iejme....
52.
Pfannkuch, M., Arnold, P., & Wild, C. J. (2015). What I see is not quite the way it really is: Students’ emergent reasoning about sampling variability. Educational Studies in Mathematics, 88(3), 343-360. https://doi.org/10.1007/s10649....
53.
Pfannkuch, M., Budgett, S., Fewster, R., Fitch, M., Pattenwise, S., Wild, C., & Ziedins, I. (2016). Probability modeling and thinking: What can we learn from practice? Statistics Education Research Journal, 15(2). https://doi.org/10.52041/serj.....
54.
Pino-Fan, L. R., Font, V., Gordillo, W., Larios, V., & Breda, A. (2017). Analysis of the meanings of the antiderivative used by students of the first engineering courses. International Journal of Science and Mathematics Education, 16, 1091-1113. https://doi.org/10.1007/s10763....
55.
Pino-Fan, L. R., Godino, J. D., & Font, V. (2011). Faceta epistémica del conocimiento didáctico-matemático sobre la derivada [Epistemic facet of didactic-mathematical knowledge about the derivative]. Educação Matemática Pesquisa, 13(1), 141-178.
56.
Pino-Fan, L. R., Godino, J. D., & Font, V. (2018). Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: the case of the derivative. Journal of Mathematics Teacher Education, 21(1), 63-94. https://doi.org/10.1007/s10857....
57.
Pino-Fan, L. R., Guzmán, I., Font, V., & Duval, R. (2017). Analysis of the underlying cognitive activity in the resolution of a task on derivability of the absolute-value function: Two theoretical perspectives. PNA, 11(2), 97-124. https://doi.org/10.30827/pna.v.... 6076.
58.
Presmeg, N. (2014) Semiotics in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education. Springer. https://doi.org/10.1007/978-3-....
59.
Reading, C., & Reid, J. (2006). An emerging hierarchy of reasoning about distribution: From a variation perspective. Statistics Education Research Journal, 5(2), 46-68. https://doi.org/10.52041/serj.....
60.
Rossman, A. J. (2008). Reasoning about informal statistical inference: One statistician’s view. Statistics Education Research Journal, 7(2), 5-19. https://doi.org/10.52041/serj.....
61.
Rossman, A. J., & Chance, B. L. (2014). Using simulation-based inference for learning introductory statistics. Wiley Interdisciplinary Reviews: Computational Statistics, 6(4), 211-221. https://doi.org/10.1002/wics.1....
62.
Sánchez Acevedo, N., & Ruiz Hernández, B. (2022). Análisis de las actividades que proponen dos libros de texto de educación primaria. Un acercamiento comparativo desde la perspectiva de la inferencia informal [An analysis of the activities proposed by two primary education textbooks. A comparative approach from the perspective of informal inference]. Revista de Estudios y Experiencias en Educación [Magazine of Studies and Experiences in Education], 21(46), 76-101. https://doi.org/10.21703/0718-....
63.
Sotos, A. E. C., Vanhoof, S., Van den Noortgate, W., & Onghena, P. (2007). Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education. Educational Research Review, 2(2), 98-113. https://doi.org/10.1016/j.edur....
64.
Stohl Lee, H., Angotti, R. L., & Tarr, J. E. (2010). Making comparisons between observed data and expected outcomes: Students’ informal hypothesis testing with probability simulation tools. Statistics Education Research Journal, 9(1), 68-96. https://doi.org/10.52041/serj.....
65.
Trumpower, D. L. (2013). Formative use of intuitive analysis of variance. Mathematical Thinking and Learning, 15(4), 291-313. https://doi.org/10.1080/109860....
66.
Trumpower, D. L. (2015). Aspects of first year statistics students’ reasoning when performing intuitive analysis of variance: Effects of within-and between-group variability. Educational Studies in Mathematics, 88(1), 115-136. https://doi.org/10.1007/s10649....
67.
Vallecillos, A (1994). Estudio teórico experimental de errores y concepciones sobre el contraste de hipótesis en estudiantes universitarios [Theoretical experimental study of errors and conceptions on the contrast of hypotheses in university students] [Doctoral dissertation, Universidad de Granada].
68.
Vera, O. D., & Díaz, C. (2013). Dificultades de estudiantes de psicología en relación al contraste de hipótesis [Difficulties of psychology students in relation to hypothesis testing]. In J. M. Contreras, G. R. Cañadas, M. M. Gea, & P. Arteaga (Eds.), Actas de las Jornadas Virtuales en Didáctica de la Estadística, Probabilidad y Combinatoria [Minutes of the Virtual Conference on Didactics of Statistics, Probability and Combinatorics] (pp. 197-203). Universidad de Granada.
69.
Vera, O. D., Díaz, C., & Batenero, C. (2011). Dificultades en la formulación de hipótesis estadísticas por estudiantes de psicología [Difficulties in the formulation of statistical hypotheses by students of psychology]. UNIÓN. Revista Iberoamericana de Educación Matemática [UNION. Ibero-American Journal of Mathematics Education], 27, 41-61.
70.
Vidal-Szabó, P., Kuzniak, A., Estrella, S., & Montoya, E. (2020). Análisis cualitativo de un aprendizaje estadístico temprano con la mirada de los espacios de trabajo matemático orientado por el ciclo investigativo [Qualitative analysis of early statistical learning with a view to mathematical workspaces guided by the research cycle]. Educación Matemática [Mathematics Education], 32(2), 217-246. https://doi.org/10.24844/EM320....
71.
Weinberg, A., Wiesner, E., & Pfaff, T. J. (2010). Using informal inferential reasoning to develop formal concepts: Analyzing an activity. Journal of Statistics Education, 18(2). https://doi.org/10.1080/106918....
72.
Wild, C. J., Utts, J. M., & Horton, N. J. (2018). What is statistics? In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 5-36). Springer. https://doi.org/10.1007/978-3-....
74.
Zieffler, A., Garfield, J., delMas, R., & Reading, C. (2008). A framework to support research on informal inferential reasoning. Statistics Education Research Journal, 7(2), 40-58. https://doi.org/10.52041/serj.....
Share
RELATED ARTICLE
| eISSN: | 1305-8223 |
| ISSN: | 1305-8215 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
