Articulating combinatorics and probability

modeling the curriculum of middle school

Abstract

This work presents an excerpt from a doctoral thesis study that addressed the following research question: How are Combinatorics and Probability approached in different curricular instances for Middle School, and what can be done to articulate these topics? In this regard and based on the Theory of Conceptual Fields and classifications of different combinatorial and probabilistic situations, the research aimed to investigate Combinatorics, Probability, and their articulations within both prescribed and presented curricula of Middle School. To this end, official curriculum documents and textbooks were analyzed. Based on the findings from these stages of the research, a teacher-oriented resource was developed. This paper presents this material, which consists of eight sets of tasks adapted from problems found in the textbooks analyzed – materials already accessible to teachers and their students. The proposed adaptations aim to expand the contexts addressed, allowing for the exploration of different cognitive demands of Probability through combinatorial problems. Moreover, the questions also cover a range of difficulty levels, related to the number of possibilities involved and the symbolic representations presented or required from the students. It is important to emphasize that this material, like any other educational resource a teacher may use, should not be viewed as definitive or complete. Rather, it is intended as a starting point: one that can and should be adapted by teachers to suit the specific needs and goals of their classrooms.