Ever wonder why young people struggle with mathematics? Some say it's too abstract. But very practical users of maths like accountants and store clerks would probably disagree. Others say it's too disconnected from real life, but most tradesmen would point out you cant build a house, lay bricks or make furniture without it. Some think its because we teach maths as technique. But architects, engineers and physicists rely on routines to make numerous calculations simple.
Another view is that unless your teacher knows their mathematics, neither will you. But as any teacher will tell you, neophyte teachers often learn more about a subject by teaching it. That's how I learned to love maths.
The biggest problem maths teachers face - especially in secondary schools - is the poor foundations on which they are having to lay more complex concepts in algebra and geometry. It's like trying to stand a skyscraper on tree stumps.
The problem begins in primary school. If you can't understand numbers, fractions and decimals and the four basic functions - add, sutract, multiply and divide - you are not in the race. Or if you can't tell the difference between a circle and an ellipse, or a square and a rectangle, or comprehend angles, you are also in trouble.
Most primary teachers have very little confidence is their own maths ability and even less in their ability to help young people learn the basics. The last time most primary students in the UK studied maths was towards the end of secondary school. Now the UK government is spending million of pounds to hire 13,000 maths specialists to coach students and teachers. The USA has similar problems. Just 27 per cent of 600 Massachusetts teachers who took a teaching licensing exam passed the maths part of the test, although most of those who failed, went on to become teachers.
But simply knowing your maths may not be enough. How you learn maths could be much more than important, such as learning to discuss mathematical ideas, in addition to knowing how to use mathematical techniques/operations.
I have had the pleasure of working with some gifted mathematics teachers such as Ian from Middlesborough in the north of England. They are gifted because they inspire young people to fall in love with mathematics. It's not only because they know their mathematics but because they know how to engage young people in exploring the patterns and the mysteries.
Middlesborough Ian helps "feral" secondary students become capable mathematicians in less than 12 months. He uses an approach which is more akin to the "change management" tactics employed in big corporations. Very few of the techniques are specific to mathematics. But every primary school teacher would recognize the teaching techniques he applies as the fundamental principles of "co-operative learning".
The students practise working/learning in groups. They give leadership to their peers, helping each other achieve their goals, resolving conflicts and communicating ideas. They value their own opinions and the opinions of others. Along the way, they play with mathematical ideas and begin to think, act and and feel like a community of mathematicians. They could be just as easily be learning to think and act like geographers, scientists or writers.
The class is organised into three groups. A demonstration team guides other groups through whole-of-class learning activities using a team learning system. A resource team searches the internet for images, videos, simulations and sounds that can be used with questions and question sequences used to explore mathematical topics. Activity builder teams, which includes everyone in the class, design and create the questions and methods and decide which to trial.
Most class activities begin with a ten minutes-long engaging, fun activity that reflects on previous learning, not necessarily about mathematics, but often about general student literacy or a mental oral activity.
Six months into the school year, the culture of the class begins to change. The teacher is no longer "the enemy" but is valued as a mentor and challenger. The students begin to see themselves as "risk takers", willing to explore any new ideas to which they are exposed. They take full ownership of their activities and the bad behaviour evaporates.
There is a good explanation for this change, and it is provided by Complexity Theory, which predicts how systems change state, like the shift from ice to liquid water. A group of students is just another system. New order emerges in the group "auto-catalytically" when the discussion cross-fertiilizes other discussion. This occurs when the ideas provoke so many new ideas, that the process becomes, self-sustaining.
Like a contagious disease!
Here's an example of a workshop designed to help students create their own learning activities:
1. Search the internet for an image, simulation or website that would help you learn about the names of the parts of a circle, and how to calculate the diameter and circumference. Make a list of the sites, images etc.you have discovered and what each explains.
2. Design an activity/sequence of questions to a) describe all the parts of a circle and b) how they relate or connect to each other.
3. Describe a technique for calculating the circumference of a circle if you know the radius. Give an example
4. If you know the diameter, how could you go about calculating the circumferene of the circle. What's a really simple trick/technique to remember?
5. Describe a technique for measuring the area of a circle if you know the radius? If you know the diameter?
6. Explain the number Pi to a five year old.
Fitzgerald, R.N., & Findlay, J. (2006). Transforming a mathematics classroom with new roles, rules and tools. Presentation at Transformational Tools for 21st Century Minds conference, Rockhampton, October 25-27, Queensland. Download this article.
