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:
• 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.
The main issue in both the Suzanne Zeedyke and John Carnochan videos is that the early stages of brain development within babies is crucial and the main thing that can promote or hinder the development is the child’s environment and their interactions with other humans. The connected baby was very focused on the biological effects of different environments for children and how they create different chemical pathways within the brain from pre-birth to three. She explained how a child from a domestic violence background could have a high level of stress hormone within the brain which could restrict the level of concentration they have and limit their development. This is important to understand within our profession as we are teachers we would need to understand that not all children will come into the classroom with the same levels of ability. In addition, they will all have very different life experiences which may mean that some children react differently in situations than others and as teachers we would need to find ways to benefit each child’s capacity to focus and learn. There was also mention that the brain continues to develop until the age of 20, therefore as teachers we have the ability to still make a change within an individual’s life by being a positive role model within their life. The John Carnochan video explained the need for focus to switch to early years as changes in early years could be early intervention for some children which he believes could change their pathway in life. He believed that interactions as a baby could mean the difference between important social and physical skills being developed within a child. This is important to think about in practice as it shows the interactions with the children within any particular setting and forming positive relationships with these children could make a change within their lives.
My own experience of dance is very limited. A years’ experience of dance class, Scottish country dancing throughout high school and dancing to the radio in the kitchen is as far as it goes. Before the dance input I was apprehensive as I only ever dance in front of family and close friends purely to make them giggle. However, the thought of dancing and making a fool out of myself in front of people I barely knew was not something I welcomed with open arms. Leaving the dance session, I still felt a little embarrassed but a lot less apprehensive over teaching dance within the primary setting as I learned that to teach dance you didn’t need to be a professional but instead have the ability to facilitate the children to be able to enjoy dance. The challenges I feel I may face when teaching dance would be to be able to push myself out of my comfort zone of my kitchen to actually joining in with the children and experiencing the lesson with them. This I feel would display to the children that there is nothing to be embarrassed about during a dance lesson. In addition, I feel getting the older children within a setting to get involved with dance would be difficult as from my own experience of being apprehensive within those lessons that it could be difficult to get children who feel the same as I do/did to be able to give as much as they can to the class to get out a lot from the sessions. I feel a way to work round this would be having quick fire warm ups to get the children into the swing of things and to feel less self-conscious before beginning the main bulk of the lesson. My professional goal for the next four years in particular is to be less self-aware when participating in these kinds of workshops or even when delivering them to a class.
I originally had the idea that I wanted to be involved in teaching after my first work experience in my third year of high school. My placement was in a nursery but I was fascinated how over the space of a few weeks children can develop their understanding of different topics as well as widen their vocabulary and further develop their social skills. I was able to be part of meeting in which the practitioners planned activities and the possible outcomes and it opened my eyes to the world of learning through play and planning around the child.
It was however my second placement within a school working with a Primary two class that cemented my decision I wanted to be a teacher. I was able to observe the curriculum being used in many ways by the teacher in order to ensure that each child developed their understanding of the topic that was being focused on.
Thinking back to my own teachers at primary school I do feel that some of the activities that were organised; including school trips, debates, talks, group work and plays all helped me to become a more confident and sociable person whilst still developing my knowledge of different subjects. This has inspired me to also be able to develop my own methods of teaching in the future and pursue my career and gain more knowledge and understanding of children and teaching through this course.