1 Issues with learning about area and perimeter

Pause for thought Think about your life outside the mathematics classroom. Where else do you need to work with the concepts of area and perimeter? Note down some examples. Do you think your students might have similar experiences? What knowledge and misunderstandings might your students bring into the mathematics lesson from their lives outside?

Although the concepts of area and perimeter are widely used in everyday life, it is often considered a confusing topic when it comes to studying these concepts as part of the mathematics curriculum in school (Watson et al., 2013). Some of the issues students have about learning about area and perimeter are listed here.

• They may see area, and also sometimes perimeter, as purely an application of formulae without understanding what area and perimeter actually are.
• They sometimes mix up the concepts of area and perimeter.
• They have difficulty developing an understanding of dimension. Often they do not understand that perimeter is a length, which is one-dimensional and measured in units of length such as metres, centimetres or inches, while area is measured in squares with bases of a certain length and hence is expressed in two-dimensional units such as m² (metres squared, or square metres).
• They might not have the experience of measuring in other unconventional units of measurement such as hands, twigs, etc. and therefore do not know why it is better to use standard units of measurement – for example using metres instead of hand-spans, which vary between individuals.
• They may not link their everyday experiences and intuitive understanding of area and perimeter to what they learn in the mathematics classroom.

In the activities in this unit you will use teaching approaches that address these issues.

Pause for thought Think back to when you taught area and perimeter on a previous occasion. Do you remember your students having any of the difficulties described above? Think about some specific students in your class who you think might have experienced some of these difficulties. Can you think of an explicit example that suggests they struggled with these? Thinking of a particular student might help you in future to spot similar issues more easily with other students.