Sandwiches: Problem Solving on Combinatorics in Early Mathematics Education

This paper presents a study on the ways Swedish 6-year-old students depict combinations when solving a combinatorics problem-solving task. The task posed to the students was: How many different sandwiches with one slice of bread and one topping can you make with two types of bread and three types of toppings? The empirical material analyzed in the paper consists of documentation from 155 students from four different schools. The results show that students drew sandwiches or drew lines between pictures of the bread and toppings to depict the different combinations. Duplicates did not occur often, and when they did occur, students detected these and did not include them in their final answers. Six-year-old students used systematic strategies, often leading to a result that was in line with the problem, and thus, they found all the solutions.