Student teachers’ concept definitions of area and their understanding about two-dimensionality of area

ABSTRACT

We examine what kind of concept definitions of area a group of Finnish primary and lower secondary student teachers (N = 82) use, and how the quality of the definitions is associated with the participants’ success in seven exercises involving area. We are especially interested in how the understanding of the two-dimensionality of area appears in the participants’ responses. Only six student teachers were able to give a mathematically precise and correct definition of area. Altogether 26 participants defined it as ‘the size of a figure’ and 20 respondents required that a figure must be bounded. Further, 22 of them associated area with a formula or an example and eight respondents gave an incorrect or nonsensical definition. On average, student teachers master rather well the area formulae of a circle and a rectangle but already the relationship between the surface area of a cube and its volume is less commonly perceived. Most student teachers associate the area of an irregular domain with the method of exhaustion but clearly fewer of them acknowledge the difference between the area and an approximation of it. Surprisingly, there is only a weak Spearman correlation between the participants’ scores in the test exercises and the qualitatively ordered categories of concept definitions.

KEYWORDS:

• Area
• concept definition
• concept image
• primary and lower secondary student teacher

Acknowledgment

We warmly thank Fr Vladimir (William P. Lysak) for proofreading the language of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.