We are investigating how collaboration leads to deeper understanding. We targeted sixth-grade math-classes. In the lesson, the teacher asked "What's the number of games of a round-robin football tournament?" In the first half, the children solved problem in groups, and in the second half, they reported their solutions and then the teacher explained the correct answer. We analyzed the protocol-data of two groups. One group discussed how to solve problems while sharing and comparing multiple levels of abstraction: conceptual, calculative, diagram, or concrete. The other group discussed only the concrete abstraction. At the end, both groups' children checked "I understand" on the self-evaluation sheet. One month later the teacher gave the retrospective test to children. The results were that one group could describe how to solve problems and the other group's ideas in detail, while the other group could provide only the answer and explain the other group members’ name.