Mathematics teaching

Editor's Notes

• #3: Welcome – thank you for completing the pre session evaluation on the w/b – We would be grateful if you could complete another after this session. If you have any comments over the course of the evening, please jot them on the post its and put them on the w/b outside. Now it is a maths evening so I thought we would get ourselves warmed up with a maths activity! Would anyone like to share? The main aims of the new national curriculum in maths are Fluency Reasoning Problem solving Because of the outstanding achievements of pupils in maths, in countries like Singapore, many schools across the UK are incorporating their teaching methods. The aims of our national curriculum are such that they are suitable to be taught through the Singapore methods. We will look at these approaches tonight. Teaching approaches in Singapore have been shown to develop all children’s understanding of maths aims, and are based on the expectation that all children can achieve highly in maths. We are 1 of 3 schools in Cambs that are lucky enough to be trialling maths textbooks and workbooks designed specifically to teach the currciulum using these methods. Our teachers have received specialist training to support their teaching using these resources and we regular have visits from other schools wanting to gain a deeper understnindg . A typical Singapore maths philosophy is that it is better to have 5 ways of answering one question than one way of answering 5 questions. This links directly to their flexibility and their ability to look at the numbers and decide what is the most appropriate method. Previousl, children have been taught procedures whereas now the emphasis is on understanding and application.
• #4: There are 3 recognised levels of learning: Shallow / deep and deeper. The second 2 are the levels of learning we aim to teach through our mastery approach and we shall have a look a bit later at some tasks that demonstrate these 3 levels. So what is mastery?
• #6: These are some of the Singapore teaching approaches that we will discuss tonight. Firstly, understanding the term mastery. Then, we will look at what this might look like in the class through the use of practical resources. This links to the concrete, pictorial and abstract approach. After, we will look at the bar model, which is a specific teaching method to support children’s understanding in many areas of maths, in particular problem solving. You will then hear from the teachers across all year groups about the resources and activities that place in class. Finally, it is your opportunity to have a go at different tasks, across all year groups and ask any questions.
• #7: The essential idea behind the mastery teaching approach is that all pupils gain a deep understanding of the mathematics. This ensures that: future mathematical learning is built on solid foundations which do not need to be re-taught (less breadth but greater depth) Increasingly, there will be less need for separate catch-up programmes due to some children falling behind; pupils who, under other teaching approaches, can often fall a long way behind, are better able to keep up with their peers, so that gaps in attainment are narrowed whilst the attainment of all is raised.
• #16: The concrete, pictorial, abstract approach is a progressive teaching strategy to ensure that children’s learning and understanding is deep. Therefore, they can apply this to different contexts and situations. Concrete refers to the physical resources and objects which children may use to investigate with, identify patters with and reason with others, to reach possible answers / solutions. Once children are secure with using concrete material to understand an idea they progress to representing the model through pictures and diagrams. The final stage of children’s understanding is for them to represent the model using numbers and symbols. This is the abstract part of this approach. In the example above, children are investigating addition of two digits. They begin using multilink cubes, where the two digits are represented by different colours. They explore what the digit looks like using the resources and the meaning of addition. They then progress to the pictorial representations. Here you can see two models. The first is a part part whole model and the second is the bar model (which we will come to later). Finally, the children are able to use numbers to represent their investigation. Through this deep understanding, children will be able to investigate the inverse and explore the subtraction.
• #19: In order to make sense of the bus stop method, used for division, we begin by representing our numbers using physical resources as show, such as dienes and place value counters. Using specific language such as ‘how many sets of 3 can we make’ the children gain a deep understanding of where the numbers come from.
• #20: Intro-We use the Bar Model when working out fractions of amounts. A typical question children in Year 3 and 4 will face is to find 1/5 of 10. We can use the bar and concrete resources such as numicon, to help us calculate this. Find the orange bar on your table. This represents the whole amount that we have, which is 10 for this question. Now we would ask the children to find the pieces of numicon that would fit into the whole exactly 5 times and emphasise that these pieces must all be equal in size. On your table, these are the red pieces. All 5 red pieces represent the same amount as the whole orange bar. So to find what each red piece represents we need to split 10 into 5 equal groups. This draws on the children’s understanding of division –and leads to them using the abstract notation: 10 divided by 5 = 2, so each red piece represents 2.
• #26: Bar model can be both a concrete and pictorial representation of a problem. We use numicon rods for the concrete representations (you will hear about an example using this resource soon) In the model shown ‘a’ represents any number which is the whole amount. Therefore ‘b’ and ‘c’ represent numbers / the parts that together are the same amount as ‘a’.
• #28: Talk about websites – Now we are going to hear about tasks used by different year groups which ensure all children to investigate and deepen their understanding in maths.