An Empirical Study on the Use and Transitions of Representations in Primary Math Lessons

The goal of mathematics education is no longer the fast production of correct computations that technology can do more precisely and quicker than a human. An important goal today is to develop the ability to see the use of mathematical concepts as problem-solving tools. To be able to use mathematical ideas creatively one must first understand them. To foster conceptual understanding of mathematics one needs to make connections among concepts. For that, instructional content should incorporate diverse representations of mathematical ideas, and students should be given opportunities to link these representations together. This study aims to explore the use of representations and the connections between them in elementary math classrooms. Participants were 11 teachers from Latvia, Sweden and Norway. The data gathering was self-reflective. Teachers recorded the representations and transitions they used in their mathematics lessons. Beforehand, a consensus on the understanding of five representations (visual, math symbols, language, real-world and manipulatives) was gained via workshops and discussions. Closer understanding of transitions was achieved by collectively watching and analyzing a lesson video recording and agreeing on the transitions seen. The results show that manipulative and real-world situations are the least used in the lessons and the most used transitions were from visual to math symbols and from language to math symbols. While the importance of representation use is generally acknowledged in elementary math education, our study reveals a noticeable gap in the integration of concrete objects and real-life situations in everyday lessons. This raises a question about bridging the gap between research insights and actual teacher practices. Identifying strategies to enhance the incorporation of manipulatives and real-world scenarios in classrooms becomes imperative for fostering a deeper conceptual understanding of mathematics among students.