On the teaching and learning of probability and statistics in the perspective of Critical Mathematics Education

In this thesis, I define and address research questions about the justification, possibility and implementation problem fields of mathematics education, anchored in Chilean upper secondary school context; to explore the coherence along a problématique of teaching and learning probability and statistics through the lens of Critical Mathematics Education.

In a comparative study, I first investigate the role of decision making in Chilean and Danish probability and statistics upper secondary school curricula. The main finding is that, though it is acknowledged that scenarios of uncertainty and statistical information have societal relevance, the connection to probability and statistics as school subjects is unclear beyond the personal psychological scope.

Concerning the design, I delineate three design principles, namely exemplarity, inquiry approach and pragmatism. They account for the quality of the chosen examples, the structure of the learning environments, and practical considerations of the teaching context. As a result of four classroom experiences, some general tensions and re-definitions are made. I draw on Skovsmose's notion of reflective knowing to analyse the ability of the learning environments to provoke critical reflections on the formatting power of mathematics in the classroom.

As for the domain-specific character of students' reflective knowing, five overarching probabilistic and statistical constructs play a significant role in those reflections and are approachable in upper secondary school: the conflicting meanings of probability, the assumption of independence, the asymmetry and meanings of conditional probabilities, the use of distributions to make sense of phenomena, and statistical inference as an inductive tool to make generalisations about a population.