Ann Kiefer & Khoi Mai Huy

These days, it is essential to understand the issues at stake in debates on education, society, politics, the environment and health. To do this, it is essential to master the interpretation of statistical data and make informed judgements about the validity of the results. Statistics are ubiquitous in modern society, and understanding them is an essential part of making informed decisions.

Many authors stress that current and future citizens must be able to understand and interpret statistics to make informed decisions, especially given the abundance of data in the media (Cobb, 1999; Lajoie, Jacob and Lavigne, 1995). There is a risk that the general public will readily accept this data without critically evaluating its validity. Moreover, data are frequently selected or presented in ways intended to influence public opinion or behavior – whether by political leaders, the media, or advertising aimed at the general public. To counter these dangers of statistical manipulation by the media and politicians, Huff (1954), in his book How to lie with statistics, was already emphasising the need for a statistical language at the time of the Cold War, because otherwise all citizens run the risk of statistical ignorance, which means that they will be more susceptible to manipulation. More recently, Brest (2012) re-emphasises this omnipresent danger in his famous book Damned lies and Statistics. In it, the author presents and discusses the best examples from recent political debates that illustrate the challenges of improving statistical literacy.

Teaching statistics at school is crucial to creating informed citizens capable of analysing quantitative information. Historically, statistics education has focused on computational skills and statistical calculation procedures. However, more recent approaches to teaching and learning statistics, starting at primary level in some Western countries such as Canada (Ministère de l’éducation du Québec, 2001), place greater emphasis on the development of statistical thinking, understanding of concepts and the ability to interpret results. In Luxembourg, these skills are included in the mathematics curricula for the lower cycles of general and lower secondary education¹ . One of the areas of competence in the Reference Guide for Media Literacy² also concerns information and data.

A number of studies have highlighted the importance of thinking critically about statistical data (Shaughnessy, 2007; Shaughnessy, Garfield and Greer, 1996). Several authors (Cobb, 1999; Gattuso, 2011; Lajoie, Jacob and Lavigne, 1995; McClain, Cobb and Gravemeijer, 2000; McNab et al., 2006; Whitin, 2006) argue that the process of thinking with and about statistical data must be carried out with critical thinking in mind, i.e. the person in question must have the skills and posture to approach these quantitative situations. In addition, many other authors state that it is important for young people to understand meaning rather than learning solutions in order to be able to think independently, reflectively and critically about mathematics and science (Daniel, Lafortune, Pallascio and Sykes, 1996; Daniel, 2005). It is precisely critical thinking that enables pupils to organise, select and analyse data in order to draw relevant conclusions or predictions. In addition, pupils are able, at least in part, to judge and predict the importance and scope of their conclusions and communications in quantitative situations (Daniel, 2005).

Critical thinking, a flagship element of the 4Cs model, was identified in Guiding Principles for Learning in the Twenty-first Century, by Hughes and Acedo (2017) as a key educational issue.

Critical thinking is essential for pupils to become autonomous, independent and open-minded individuals.

It is essential in everyday life for making informed and considered decisions. It is also essential for evaluating statistical data rigorously. In maths lessons, pupils should therefore learn to ask questions, question statistical models and consider potential biases.

This is why, in this module, pupils analyse real data, have to solve concrete problems and justify their statistical choices. The idea, of course, is not to develop general critical thinking through a single statistics module, but rather to help their pupils develop a ‘critical perspective’ in relation to the notion of ‘justice’ through the processing of data. In this way, a ‘critical perspective’ would be a metacognitive tool for pupils to take a critical look at and question their mathematical models to arrive at a final model that they feel is fairer, more appropriate and better argued.

A second fundamental idea of this module is to show that in statistics there is no single correct answer. Several different approaches can be justified. We can even go one step further and show pupils that different perspectives on the same theme can lead to different statistical models and different conclusions.

It should also be noted that several studies highlight the importance of thinking critically about statistical data (Shaughnessy, 2007; Shaughnessy, Garfield and Greer, 1996). However, this research does not address the question of how to think critically about statistics and understand their implications for decision making in a school context. In general, there is a lack of explicit and systematic links between critical thinking and learning statistics.

1 https://ssl.education.lu/eSchoolBooks/Web/ES
2 https://edumedia.lu/wp-content/uploads/2024/12/Medienkompass_FR_web.pdf

Références

1. Best, J. (2012). Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists (1st ed.). University of California Press.
2. Cobb, P. (1999). Individual and Collective Mathematical Development: The Case of Statistical Data Analysis. Mathematical Thinking and Learning, 1(1), 5-43.
3. Daniel, M.-F. (2005). Pour l’apprentissage d’une pensée critique au primaire. Québec : Les Presses de l’Université du Québec.
4. Daniel, M.-F., Lafortune, L., Pallascio, R., et Sykes, P. (1996a ; rééditions 1999, 2004). Philosopher sur les mathématiques et les sciences. Québec : Le Loup de Gouttière.
5. Gattuso, L. (2011). L’enseignement de la statistique : où, quand, comment, pourquoi pas ? Statistique et Enseignement, 2(1), 5-30 http://publications-sfds.fr/index.php/StatEns/article/view/71 
6. Huff, D. (1954). How to lie with statistics. New York: W. W. Norton.
7. Hughes, C. et Acedo, C. (2017). Guiding principles for learning in the twenty-first century. Educational practices series, 28. https://unesdoc.unesco.org/ark:/48223/pf0000262678
8. Lajoie, S., Jacobs, V. et Lavigne, N. (1995). Empowering Children in the Use of Statistics. Journal of Mathematical Behavior, 14, 401-425.
9. McClain, K., Cobb, P. et Gravemeijer, K. (2000). Supporting Students’ Ways of Reasoning about Data. In M. J. Burke et R. F. Curcio (Eds.) Learning Mathematics for a New Century, 2000 Yearbook (p. 174-187). Reston: National Council of Teachers of Mathematics.
10. McNab, S., Moss, J., Woodruff, E. et Nason, R. (2006). « We were nicer, but we weren’t fairer! » Mathematical modeling exploring « fairness » in data management. Thinking and Reasoning with Data and Chance: 68th NCTM Yearbook (p. 171-184). Reston: National Council of Teachers of Mathematics.
11. Ministère de l’éducation du Québec (2001). Programme de formation de l’école québécoise. Éducation préscolaire et enseignement primaire. Québec, QC: Gouvernement du Québec.
12. Shaughnessy, J. M. (2007). Research on statistics learning and reasoning. In F. Lester (dir.) Second handbook of research on mathematics teaching and learning: National Council of Teachers of Mathematics, (p. 957-1009). Reston, VA: National Council of Teachers of Mathematics.
13. Shaughnessy, J. M., Garfield, J., et Greer, B. (1996). Data handling. In A. Bishop et al. (dir.), International handbook of mathematics education (v.1, p. 205-237). Dordrecht, Netherlands: Kluwer.
14. Whitin, D. J. (2006). Learning to talk back to a statistic. In Thinking and Reasoning with Data and Chance: 68th NCTM Yearbook (p. 31-40). Reston: National Council of Teachers of Mathematics.