What do I mean by combinatorial thinking?

As mathematics teachers and researchers, we speculated around a claim that learning combinatorial concepts require a special way of thinking, and reviewing the related literature showed that some researchers acknowledged this speculation and have called it combinatorial thinking. To design the study, we used the first author's class as a useful setting and the data were collected via a counting task. We categorized the four levels of understanding combinatorial thinking as investigating some cases, how am I sure that I have counted all the cases, systematically generating all cases, changing the problem into another combinatorial problem and understanding combinatorial reasoning. © 2010 Published by Elsevier Ltd. Selection and pee r-review under responsibility of Masterprof team