First year university students` use of words, symbols and images to convey mathematical ideas: A case of definitions

Abstract

This qualitative case study analyzed how first year university mathematics students used words, images, and symbols to convey the same mathematical ideas. The study was located within the interpretivist paradigm and took naturalistic methodology. Twenty-six first year students were purposefully selected to participate in the study. Data was collected through analyzing students’ assignments scripts followed by semi-structured interviews. The study sought to answer the questions: How did the first-year university students` use of words, symbols and images to convey mathematical ideas. The data were analyzed using Lave and Wenger`s situated learning and Seo ` mathematical communication theories. Data analysis focused on the structure and usage of symbols, images, and words to communicate mathematical ideas. The result of the study shows that the students experienced difficulties in using words, images, and symbols to communicate the same mathematical idea. There were contradicting meanings between images, words, and symbols usage in attempt to define same concept. It is recommended that encouraging students to wave between words, symbols, and images to communicate mathematical ideas will improve understanding of mathematical concepts. First year university mathematics teachers are encouraged to not only use one method of mathematical communication when defining concepts. Moreover, it is recommended that formal mathematics definition be used after students grasped the meaning of concepts using everyday day words and images. The abstractness should only follow the definitions are understood intuitively and can be represented diagrammatically or with natural language.