# Teaching mathematics progressively!

In the “School maths or intriguing maths?” workshop, I experienced mathematics being taught in an maths in an intriguing, creative and progressive way. I saw how teaching maths in a progressive way gives more depth to children’s learning which is one of the principles in Curriculum for Excellence (The Scottish Government, 2008, p.30) which furthermore, suggests using acting learning to do so in order to deepen understanding.

In the workshop we were learning how to teach the fundamental basics or principles of volume and capacity using active learning. To do so, we made a cube using squared paper. Once we drew out out cube, (which we choose to be 3 x 3 x 3)  then folded the cube up, sellotaping the sides together. In order to find out the volume of this cube, we filled our cube with 1cm^3 cubes. This was a much more creative way of learning about volume than rote learning a formula by a procedure. By doing this experiment, we were surrounded in mathematical language and had more questions whilst exploring volume.

I found that learning through experience is much more beneficial than just sitting in class writing on paper. It is much more memorable and exciting! An idea that I hope to take forward in teaching! For example, in class an idea was given that if there is a question about money for example, use real money. If it’s about buying and selling, I could get the pupils to set up a pretend shop or they could go to the secretary office for an exchange of money and before the practical, pupils could make a hypothesis, then observe what happened and can reflect on their learning.

There are various ways or perspectives from which maths can be taught, linking to advice given by Ma (2010, p. 104) which is to solve a problems by looking at things from multiple perspectives. However, Eastaway (2010, p. 33) states that even though using for example, the fun finger method for multiplying which is learning multiplications using a different way, it still might be better to memorise the times tables and he claims that memorising them may be the “…best method” for some. So, from this I am aware that even though there may be more fun ways to learn maths and they are fantastic, for some people, learning maths by just using paper may be the best way for them.

Alternatively, Mason, J. Burton,L. and Stacey, K (2010, p. 134) suggest making maths more creative and relevant which it was through making the cube and by finding the volume of the elephants. This was as Ma (2010, p. 104) states, building upon basic ideas and foundations which creates questions and developes understanding  throughout the experiences since we had to think of how to find the volume of the elephants which were not square. This also demonstrates how to view the problem from another perspective to aid understanding (Ma, 2010, p. 104). I never would have thought of teaching how to find the volume of an elephant in such a creative and interesting way which encourages a pupil to think (Mason, Burton and Stacey (2010, p.138). Maths can be fun when you use creative, active learning to teach it.

In addition to the workshop, I read how to teach children to think mathematically and to approach a maths question or problem without panicking about it. Mason, Burton and Stacey (2010, p.135) suggests firstly looking at what they know, what they want to know and how they can check. This approach, increases pupil confidence, as they can check whether their answer is correct without having to ask the teacher as they can prove themselves that their answer is correct.

Pupils can develop a positive mindset when approaching a question and they can think of what they do know when looking at it instead of looking at what they don’t know. If stress or panic is the first result then that can block your thinking. (Mason, Burton and Stacey (2010, pp.135-136). This is advice for pupils that I would like to take forward when teaching children maths to help both them and myself develop a fundamental understanding of mathematics.

However, what I found interesting was that Mason, Burton and Stacey (2010, p.139) state that reflecting on successes increases confidence. Yes, I do believe it can but at the same time I think there can be a potential for future stress in order to keep up with previous success and self-confidence in the subject could decrease if the next time you are not successful. Therefore, as a teacher successes are to be celebrated but failures should be supported too and this is why having a positive mindset is important!

In conclusion, teaching maths can be fun! Pupils can learn maths with a positive mindset, through a progressive way, that is creative and interesting, that stirs up questions from children and deepens their understanding through active learning. Maths doesn’t have to be just on paper, it is all around us!

References:

• Eastaway, R. (2010) How many sock make a pair?. London: JR Books.
• Ma, L., (2010) Knowing and teaching elementary mathematics (Anniversary Ed.)New York: Routledge.
• Mason, J., Burton, L. and Stacey, K. (2010). Thinking Mathematically. 2nd edn. Harlow: Pearson Education Ltd.
• The Scottish Government (2008) curriculum for excellence building the curriculum 3. Available at: http://www.gov.scot/resource/doc/226155/0061245.pdf (Accessed: 25 September 2017).

# More than memorising!

Can I really link everything back to basic mathematics?  This is what I am keen to explore and learn about through the Discovering Mathematics module.  In this blog post I am going to discuss how connecting mathematical errors made in other areas of maths can be linked back to basic, fundamental mathematical principles.

In the first workshop of discovering mathematics, we discussed how many things around us can be linked back to basic principles and concepts in mathematics. Some basic principles and concepts of maths are weight, quantity, addition, subtraction and division. It is interesting how there are some things that we have just accepted when we are taught mathematics. A word to describe this is, axiomatic. (English Oxford Living Dictionaries, no date).  For example, one add one is two however, what is the number one? It is universally agreed that one is one.  One is a number that represents or symbolises for example, one pen, a quantity of something. Quantity being a basic concept in maths.

However, the number one is something that I just seem to accept, one is one.  It’s universally accepted. This can’t be the same for all things to do with maths. Pupils need to understand why things just are, why they are accepted

More complex maths or maths errors that children or even some adults might make can be linked back to fundamental basics. Ma (2010, pp.24-25) looks at errors in pupils’ long multiplication answers. Children when doing long multiplication where not lining up numbers into the correct positions. Teachers had different opinions as to why this was a problem. Some teachers said that it was because pupils just did not line the numbers up correctly whilst others argued that the the errors are because the pupils do not understand the reason or relevance of what they are doing in their algorithms. Therefore, an argument between algorithms being  just a process that children need to memorise and the need to understand why they were doing something.

I agree with the latter argument, that the mistakes were due to a basic principle and concept not having been  understood. This being, place value. For me personally, I know that when I was taught how to do long multiplication I was taught a process, a procedure that I had to memorise. I was not told why I was doing the procedure and some pupils may not have understood the basic principle that connects to the solution that is necessary in order to solve the maths question.  The children in this example given by Ma, is that the pupils did not understand the value of the the numbers.

Therefore, since this mistake can be connected to a basic mathematical principle not being understood then maybe other mistakes can be too! This is why when teaching in the future, I should analyse the mistakes made by pupils since once basics are understood then they can be applied to other mathematical concepts and teach children to further their own understanding of fundamental mathematics by being able to work back to the basic concepts to see where they may have made an error.

In chapter 5, Ma (2010, p. 104) gives advice that I want to take on board in my teaching practice such as, making connections between the current topic or concept of maths to other concepts in maths, to show pupils more than one way to solve a problem so that they can take various approaches to solve a problem thereby, looking at things from multiple perspectives, to focus on the basic ideas and to build upon these foundations.

In conclusion, to aid my understanding of mathematics and the reason behind pupils errors, I will demonstrate the rationale behind the maths that pupils are doing and the connection that it has to other concepts so that it’s not just a memorised procedure that is accepted. Therefore, pupils can understand why they are doing what they are doing, the logic behind it and how it connects to fundamental mathematical concepts that they need to understand first. Pupils can therefore see how the maths that they are doing makes sense.

References:

• English Oxford Living Dictionaries, (no date) Definition of axiom in English. Available at: https://en.oxforddictionaries.com/definition/axiom (Accessed on: 20th September 2017).
• Ma, L., (2010) Knowing and teaching elementary mathematics (Anniversary Ed.)New York: Routledge.