Discussion Student talk in explaining and questioning is often hesitant. We hypothesise this is because students are thinking and explaining alternately. In the examples we have given, the thinking involves searching for deep features of geometric objects or images, and it seems to be just this focus of attention that inhibits speech at that moment. We have found no evidence for this in the psychological literature. Evidence from mathematically advanced students of varying levels of attainment shows that such difficulties occur in practice and are probably common.
Students have difficulty in speaking fluently as they examine deep features of objects or images.
To us, it indicates that such fluent verbal descriptions do not involve inspection or perception of deep features of images or objects. In other words, fluency of verbal description is generally incompatible with concurrent deep perception or imagery. Someone who describes such deep features fluently may have previously examined them deeply. However, they are not examining deep features at the same time as they talk fluently. If we, as teachers, explain mathematics in a clear, fluent manner, the chances are we are not thinking about deep visual features of the mathematics at the same time.