Using various representations in the process of solving mathematical problems

Mathematics uses a wide range of representations, but the mathematical symbol is not the only way to code information. Different ways of representing mathematical concepts and relationships are used, especially in the early stages of learning. Generally, the teacher decides on the choice of representational forms to use. But in the process of solving mathematical problems, it is the pupils – not the teacher – who are engaged in the problem-solving, and the coding used should support their cognitive work. This paper analyses how different representations can influence the results of work on an untypical mathematical problem. The task was solved by a group of 7–8 year-old pupils participating in a mathematics club. The examples selected for analysis indicate a strong relationship between the choice of representations and the final result of the pupils’ work.

http://www.edukacja.ibe.edu.pl/images/numery/2017/5-5-swoboda-using-various-representations.pdf