In the clip below, Dan Walton (Teacher of the Year) is teaching his class Pythagoras. My memories of pythagoras at school mainly involve textbooks, much like most other maths topics in high school. We were taught the rule and how to apply it (instrumental understanding) and given textbook work to consolidate our knowledge. However, Dan’s approach to teaching this topic is very different.
Pythagoras is the rule that the squares of the shorter two sides with equal the square of the shortest side – a²+b²=c². Rather than simply teaching this rule to his class, he has them find out the answer. Some of the children simply draw the triangle to scale, giving them the correct answer, others must work out the rule using numbers. This is giving the children multiple ways to solve the problem and they then realise that the formula is more efficient than drawing triangles every time. By having the children investigate this rule for themselves, Dan instantly has the children engaged in the lesson.
By using a real life example (golf hole), Dan is showing the children the context of this learning in the world outside of the classroom. He gives them the option to solve the problem any way they want, allowing them to choose between the two methods they have explored. All of the children opted for the formula method, showing their ability to select an appropriate method for solving a problem.
When Dan then moves on to working out the length of a shorter side, he has a small piece of paper showing the rules of pythagoras, but does not tell the children anything about what they have to do. This investigation and discovery really has the children engaged and involved in the lesson in a way that a textbook cannot do. The children are working out what they must do – they are taking control of their own learning. By giving the children the opportunity to do this, Dan is helping them with long term problem solving skills. The children learn that the answer is not going to be given to them, they must work it out themselves.
The climax of the lesson, drawing on all the pythagoras they have learned, is a murder mystery 
problem. There are multiple pythagoras questions which they must solve in order to find out who the murderer is etc. This is an incredible way to find out if the children have taken in all that has been taught. If the children can find out the answer, then they understand the rules of pythagoras that they have been taught. Dan even hides some of the questions around the school to bring some energy and movement to the lesson. There is no doubt that this is substantially more rewarding for children than sitting at a desk with a textbook.
While pythagoras may be a more advanced topic than those of primary mathematics, I believe that many lessons can be learned from Dan’s lesson. Children should be encouraged to explore numbers and mathematics, rather than being told a rule and applying it. If they can work the rules out for themselves, not only are they much more likely to remember it, but they are more likely to enjoy this learning. While we cannot allow primary children to run around the school looking for questions, it is important that we allow them to have active maths, even taking them outside as a class into the playground to solve some problems will be much more engaging and exciting than a normal maths lesson. Dan also does not share the learning intention with the children at the start of the lesson, again, promoting discovery and exploration. I believe that this is even more important in a primary classroom as allowing children to find out what they are learning themselves shows that they have actually understood what is being taught.
In my future maths lessons, I want to incorporate some of these techniques, especially taking learning outdoors. Maths does not need to be sitting in front of a textbook. Maths should be a wonderful, exciting discovery of the whys and hows of numbers – an idea all too often overlooked in the primary classroom.
