After the input about Intriguing maths I decided to consider the theory behind teaching of math. During the input, we explored Boalers research into the teaching of mathematics within two different settings.
Within the first setting the children were taught with the traditional set methods and procedures much like that of the 5-14 curriculum where the children were taught specific topics and were taught certain methods to solve problems. They found within this setting the children understood the rules and procedures for solving problems but Boaler found after time the children in this setting lost this information.
The second setting provided different math opportunities involving some degree of choice. The children were not provided with the answers or correct way of completing a calculation but were encouraged to find their own methods to finding answers and be able to give reason to their thinking. The setting did less textbook work which focused on specific topics. In this case Boaler found the children to have flexible thinking, can adapt their knowledge of one subject into another and adapt to new challenges.
Two psychologists that could give reasoning to the difference of these two settings and what the children got from their leaning. Piaget views cognitive development as a result of maturation and environmental experiences meaning the children’s original abilities in addition to the experiences they have been provided with have affected the way in which they process information provided. Therefore, the experience of the second setting would be an explanation for the different thinking processes when faced with a problem.
Vygotsky’s social development theory places more emphasis on cultural and social influences than Piaget. Vygotsky views social interaction as a vital part of development of thinking which can be seen within the second setting with teachers asking children to explain their thinking and discuss answers.
Therefore when teaching maths we should be looking into the best possible methods to ensure the children become effective learners and problem solvers.

Liping Ma defines the Key principles of mathematics as:
• Interconnectedness
• Multiple perspectives
• Basic ideas
• Longitudinal coherence

The principle I will be focusing on in this post is the idea of multiple perspectives in mathematics. Looking into this topic I found a talk by Roger Antonsen who believes mathematics is made up of patterns which he addresses as being connections which you need to find in order to understand. He explains this idea of finding patterns everywhere by considering the different methods of tying a tie and shoe laces.
He begins looking into different perspectives by looking into a simple equation x+x= 2x. The equals sign in this equation shows the break of the two different perspectives. This can be seen through all mathematical equations as something equals something else meaning you are looking at the same thing from two different perspectives.
To strengthen his idea of perspectives and understanding of mathematics giving a greater understanding of the world by looking into the number 4/3. He began looking at the number from the perspective of a decimal then changes the base system to show different perspectives. He then uses lines going around circles at 4/3 and uses then to draw the ‘image of 3/4’.
He then looked at the number from a musical perspective creating the sound of 4/3 then the beat of 4/3. He then looks at the shape created by 4/3 which is an octahedron. He shows how changing perspectives of a shape and taking it apart and reconstructing you learn more about the object.
This talk helped me to understand the importance of perspectives in mathematics as you can never fully understand until you are willing to explore different avenues. If someone is telling a story from one perspective you aren’t getting the full story with all the information which is why it is necessary to have different angles from different people. Therefore, I have grown to understand the importance of perspectives not only in mathematics but in the world around us.