Combinatorial reasoning and its assessment

In this chapter we provide some answers to the following questions: (1) What is combinatorics and what role does it play in teaching and learning probability?, (2) What components of combinatorial reasoning should we develop and assess in our students?, (3) Are there any task variables that influence students' reasoning and provoke mistakes when solving combinatorial problems?, and (4) What are the most common difficulties in the problem-solving process? How should we consider these variables in the teaching and assessment of the subject? We illustrate these points by presenting some examples and test items taken from different research work about combinatorial reasoning and samples of students' responses to these tasks.