One of the most common questions children ask in relation to mathematics is ‘When will I ever use this?’ Often they don’t realise that we use mathematics in almost every aspect of our lives, from the minute we wake up each morning and estimate whether we should push the snooze button, to working out how many minutes or hours there are until we get to finish school or work for the day. The perception that mathematics has little or no relevance to their lives beyond the classroom is one of the reasons children begin to disengage from mathematics during the primary years. In order to bridge the gap between children’s lives and the mathematics classroom I firmly believe that all mathematics teachers should take every opportunity to make mathematics meaningful by using the real world where appropriate, whether through the use of objects, photographs or physically taking children into the world beyond the classroom and engaging them in rich, worthwhile activities. This blog post was originally posted in 2015 and I thought the messages here would be a timely reminder, given that I have continue to receive invitations to assist teachers and schools in engaging their students with mathematics.
So how can you make mathematics more meaningful? If you are new to teaching with contextual mathematics, I would suggest that you begin by designing a mathematics trail at your school or somewhere out in the community – it could even take place at the local shopping centre. Find points of interest that have mathematical potential, photograph them and then plan a set of activities. For example, if you have a giant chessboard in the school playground, you might pose the following questions:
- Estimate the following and explain your thinking: The area of the chessboard, the perimeter of the chessboard, and the area of each tile
- Use words to describe the position of the chessboard without coordinates and in relation to its surroundings.
- Locate the chessboard on a map of the school grounds. What are the coordinates?
- Investigate the total number of squares (of any size) in the chessboard.
- Design a new maths game that can be played on the chessboard and write a set of instructions for another group to follow.
You will notice that the questions above are quite open-ended. This will allow for all students to achieve some success and provides an important opportunity for children to show what they can or cannot do. Open-ended questions are more engaging for students and often require them to think harder and more creatively about the mathematics they are engaging in.
Another idea for contextualising mathematics is to use objects or photographs of real life objects, items or events. It could be something as simple as a school lunchbox, with questions such as the following:
- Explore the ways sandwiches are cut. What different shapes can you see? Can you draw them?
- Before recess, compare the mass of your lunchbox with five other lunchboxes. Can you order the lunchboxes from lightest to heaviest?
- List the types of food in the lunch boxes today. Can you sort them into different categories? What categories do you have? Is there another way to sort them?
- Conduct a survey to find out the most popular recess or lunch food in your class. Do you think this is a healthy food?
- How many Unifix cubes do you think would fit in your empty lunchbox? Write down your estimate and then test it out. Was your estimate close? Find someone with a different size or shape lunch box and repeat the activity.
- Use a special bin to collect rubbish from your lunch boxes. How much rubbish did you collect?
- Sort out the lunch box rubbish and organise it into a graph. What information does your graph give you?
Another idea is to collect interesting photographs from around the world. I took the photograph above recently in Oslo, Norway. What sorts of questions could you ask students to explore relating to the interesting shapes you see in the bridge and the building? Here’s another interesting photograph from Morocco.
There are several interesting mathematical questions you could pose relating to the phtograph:
- Can you work out the number of hats in the photograph without actually counting them one by one? How? Is there another way?
- The hats at the top of the photograph are called a ‘fez’ or ‘tarboosh’. Investigate their history and construct a timeline.
- If each fez cost 80 Moroccan Dirham, how much would each one cost in Australian currency? Would the entire contents of the shop be worth more than $200?
A great free resource (and one of my favourites) that often has fantastic mathematical potential is the website, Daily Overview (http://www.dailyoverview.nyc/). Each day Daily Overview post a different aerial photograph from somewhere in the world. The photograph is accompanied by background information that could also be explored within a mathematics lesson.
There are many ways to bridge the gap between school mathematics and children’s lives. If we can promote the relevance of mathematics to children while at primary school, then we have a much better chance of sustaining their engagement through the secondary years, when mathematics becomes more abstract. We want children to continue the study of mathematics beyond the compulsory years and this is more likely to happen when they no longer ask ‘When am I every going to use this?’.