A comparison of a visual-spatial approach and a verbal approach to teaching mathematics

Abstract

Pamela WoolnerSchool of Education, Communication and Language Sciences University of Newcastle Upon Tyne Newcastle Upon Tyne NE1 7RU UKDespite mathematicians valuing the ability to visualize a problem and psychologists finding positive correlations of visual-spatial ability with success in mathematics, many educationists remain unconvinced about the benefits of visualization for mathematical understanding. This paper describes research that compared a ‘visual’ to a ‘verbal’ teaching approach through teaching a range of early secondary school mathematics topics to two classes using one or other approach. The two classes were compared through a post-intervention test of mathematical competency, on which the verbally taught class scored significantly higher. No interactions were found between teaching style and the learner’s preferred style although the pupils identified as ‘visualizers’ did tend to perform more poorly. INTRODUCTIONUnderstanding mathematics, visually and verbally Educators would tend to agree that a major aim of teaching mathematics is for students to develop understanding, even if it can be difficult to conceptualize this understanding fully (Sfard, 1994: Sierpinska, 1994). Taking a broadly constructivist view of knowledge, as teachers are inclined to (Sfard, 1994), suggests the importance of individually constructed understanding. Yet this interpretation still leaves the problem of how teachers interact with learners’ constructions and facilitate their building. The challenge of communication can lead beyond a concern with issues of vocabulary and clarity to a tendency to think that verbal descriptions constitute knowledge (Davis, 1984) and that mathematical abstraction is essentially verbal (Anghileri, 1999). However, the history of the development of mathematical concepts points to the importance within the subject of its visual side (Sfard, 1991). Furthermore, it has been argued that students should be encouraged to develop this aspect within their own understanding (Davis, 1984). It seems necessary to see how a broadly visual approach compares in the classroom to a more verbal approach.