Raimundo Elicer, a Chilean researcher at the Danish School of Education at Aarhus University, made his intellectual concerns and questions about mathematics his field of research. After a career as a researcher and teacher in public secondary schools in Chile, he decided to question the understanding of mathematics as a neutral element when making personal and collective decisions.
Cloudy days, cold, rain, little sunlight. These words can describe the weather of a city in Denmark as well as the weather of a city located in southern Chile. These two landscapes have been home to Raimundo Elicer, a young Chilean researcher now based in Denmark. Elicer is currently (2022) working at the Danish School of Education at Aarhus University after completing his PhD at Roskilde University.
His research focuses on mathematical education, critical theory and computational thinking. His interest in these topics began after graduating as a mathematical engineer from the Catholic University of Chile and working for a couple of years as a mathematics teacher in a high school in Chile.
“During my years as a mathematics teacher, I realized that the curriculum in Chilean schools does not imply that students learn to make decisions strategically, which is a very important skill. That was my initial motivation to do my research. Specifically, I wanted to investigate whether decision-making scenarios had pedagogical value for students and if they learn probability and statistics along the way,” says Raimundo.
After working for a couple of years in a school in Lanco, a small city located in the southern part of Chile, he decided to carry out his doctoral research in Denmark to delve into this question. Once in Denmark, his doctoral research incorporated a critical mathematical research line. “I learned about this idea that challenges the statement that mathematics is neutral,” explains the researcher. “So, I decided to focus my doctoral research along these two lines: the impact of probability and statistics on the learning of mathematics and the cultural place that the latter occupies in Chilean society. Mathematics is not intrinsically good or bad, but it is not neutral. So, when it comes to teaching it, you have to take a certain stance. This is especially important when we talk about decision making”, he claims.
Making decisions with a critical perspective
Within the framework of understanding that mathematics is not a neutral tool, the researcher established that decision-making is a very important element in society as it has an impact beyond our private lives. “Government and policymakers make important decisions through probability and statistics,” he states. In his research, Raimundo was concerned with the challenges of designing and implementing a teaching practice that aims to be coherent with the critical perspective on probability and statistics education.
To prove this point, during his doctoral research, he developed four didactic experiments in collaboration with teachers from different public secondary schools in Chile.
“The first was in a school in Quintero and Puchuncaví in Chile, an area where there are environmental conflicts between thermoelectric companies and communities due to air pollution. We worked on making decisions in contexts of risk. The students, very aware of the environmental crisis, worked on a fictional scenario where a new thermoelectric plant would be installed in addition to environmental risk indicators.”
In this experiment, students analyzed the advantages and disadvantages of this likely scenario through statistics and probability. “The important thing was that they could reflect on questions such as: Do numbers matter when we talk about environmental risk? If the calculations and the measured environmental risk is low, would students change their opinion?”
In his second experiment, Raimundo and a teacher from a school in Santiago made students estimate the number of people who attended a protest through photos. In this estimation task, students experienced the construction and sampling of data, the use of statistical estimation, and the role of context knowledge.
“In 2018, several student strikes took place and a lot of the students who participated in the experiment participated in the strikes,” explains Raimundo. “This put them at a kind of crossroads. They knew and were very honest in saying that of course they would like the number of people that attended the rally to be as large as possible. But despite their political opinion, the students were very objective with their answers”, he recounts.
“The third experiment was about understanding how the scores of the selection test for entering university in Chile are calculated”. The students explored the calculation of higher education admission tests, illustrating their background through percentiles, social statistics in a fabricated normality, and political arithmetic in graphs. “Our goal was that the students reflected on how statistics are used. They took the data, understood how the scores were calculated, and then reflected on it”.
The last experiment, named “Guilty or innocent?”, was based on a real wrongful conviction case. Students worked with data and probabilistic evidence, and discussed the problematic use of probability in matters of the law.
The exercises made by the students were transferred to Elicer’s own research. Based on the analyses and the teacher’s input, he presented four main issues which the students reflected upon through mathematics. First, the assumption of independence can validate the collection of data and shape their perceptions of risk. Second, when applied to the social world, statistical investigations and their variables can produce discourses of political division and exclusion of certain kinds of people. Third, probability and statistics not only shape perceptions, but inform automated and deliberate action. Their use has consequences. Fourth, probabilistic calculations play a role in transmitting the sense that an idea or belief can be objective.
On a personal level, he reflected on the power that mathematics has, and, in particular, the role that probabilities and statistics play in understanding political and public policy processes in society.
“Beyond whether a mathematical analysis is correct or incorrect, I was looking for ways to discern how a number, a result, a mathematical model, can influence our opinion or can change the future of a society”, he adds.
According to Raimundo, Chile is a society that is highly influenced by technical knowledge and, particularly, by mathematical models, but it must be clear to policy makers, public opinion and citizens that these models have assumptions and political intentions behind them and they will have consequences. “For example: During the social crisis in 2019 in Chile, the biggest protest in the history of the country took place on October 25, 2019. The estimated number of people that attended this rally were more than a million people. The huge number of people who attended that day gave legitimacy to the protest and politicians started the political process of the new constitution to solve the political outburst. Months later, during the International Women’s Day rally (March 8, 2020), there was a dissonance between the estimated people who attended the march. The police estimated that 125,000 people were gathered while the organizers stated that 1 million people attended. In this context, the number of people who went to this rally is very political because the more people attend the protest, the bigger the legitimacy of political demands becomes for this rally.”
“Many political decisions are made based on statistical evidence. Using certain mathematical models can illuminate and illustrate certain problems, but it can also hide them. For example, when, with the students of Quintero and Puchuncaví, we focus on analyzing the probability of an environmental disaster, we are at the same time reducing other important elements to make decisions.”
“It is important to acknowledge that probability and statistics are a model or a metaphor that reduce many variables. For example, in probability you can repeat an experiment many times, and this would be considered a successful result. But this interpretation is not useful in the case of the installation of a thermoelectric plant, as we saw in the experiment with the students, because we are not going to install thousands of thermoelectric plants based on their possibility of success”.
In the new curriculum: Computer Science
It should be noted that one of the Chilean researcher’s first publications was in the Nordic Journal of Mathematics Education, where he established a comparison between the Chilean and Danish curricula of secondary schools.
“I investigated the differences. From the point of view of the curriculum, and also my experience as a teacher, in both countries the “decision making in the face of uncertainty” exercise is a justification tool for teaching probability and statistics. However, in Chile the trend is that mathematics, especially statistics and probabilities, is focused on teaching how to make personal decisions such as what to buy? Do I get involved in a loan? In Denmark, the tendency is more on teaching these tools by exemplifying social and political decisions”.
After his doctoral research, Raimundo continued to be linked to research in mathematics education in Denmark. He started his postdoctoral research at the Danish School of Education, Aarhus University. Currently, Raimundo’s postdoctoral research focuses on the interrelationships between programming, computational thinking, and digital mathematical skills. “The background of this work is that in several European countries, elements of computational thinking are entering the educational curriculum of the subject of mathematics. Particularly in Europe this is becoming a big trend, and, given the history of certain epistemological considerations as well, there are clear connections between computer science as a discipline and mathematics as a discipline”.
“In this context, math teachers are taking on the burden of teaching computational thinking strategies, including programming, which means something new to learn. We are studying the pros and cons”, he concludes.
Marta Apablaza Riquelme is a freelance science journalist based in Santiago, Chile