Reflection | A Time for Reflection

As Semester one draws to its conclusion, I can’t help but feel a bit sentimental on my time in the ‘Discovering Mathematics’ elective. It has been a very enjoyable experience for me and I would encourage anyone who is going into second year to pick it as your elective. It is not about learning complex quadratic equations or even recapping on trigonometry, it actually is more useful that any of those concepts will ever be. I have mentioned in previous blogs that I was not the biggest fan of mathematics due to my stubbornness and having bad experiences at high school level. However, this elective has totally changed my ideology and it will definitely help me gain confidence as I go into my third year placement. I thought since the elective is over that I talk about my ideas and give my ideology and interpretation of what a profound understanding of mathematics is.

At the very beginning of this elective, the idea of fundamental mathematics was introduced. We were given some input on what it meant, but in all honesty I found it hard to understand. This was the case until I came across the work of Liping Ma. Ma conducted research in china and America to identify why the U.S was falling behind in terms of the world rankings and test results. She concluded that teachers in the U.S did not posses a deep understanding of elementary mathematics. Ma (2010) hypothesised that initial teacher training and that during this teachers should become familiar with basic mathematics (fundamental mathematics) much like her teachers in china. In hind sight, Ma (2010) came up with four characteristics which would allow a teacher to have a profound understanding of fundamental mathematics:

connectedness – this factor is about teachers emphasising how maths connects to other procedures that the pupils are learning.
multiple perspectives – moving away from the idea that there is only one way to get an answer
basic ideas (principles) – that teachers should bring ideas back to basics to encourage good attitudes in mathematics to promote understanding and a love for the subject
longitudinal coherence – progression: the teacher needs to be able to see where the child is and how to further their progress in mathematics.

When you break these four principles of fundamental mathematics down, it is clear to see why maths is so important for everyone. When we think about connectedness, we need to look to our Curriculum for Excellence where cross curricular learning has to be incorporated. This is so important because maths is in everything that we see and do and it is also very important to see the links between maths and our world. Secondly, there is a huge maths myth that has been around for decades – ‘there is only one way to find an answer’… no there is not. There are multiple ways in which problems can be solved – its just about teaching maths in different ways. Thirdly, basic ideas is fundamental to fundamental mathematics because fundamental actually means ‘basic’. We as practitioners need to take maths back to its roots in order for children to progress and love maths at face value. In addition, basic does not mean that it can’t be challenging or fun (I will get to this). Finally, when we think about longitudinal coherence, we think of progression. Teachers need to know where each of their children are at in their learning and the teacher needs to take the steps necessary in order for our children to progress.

It is all very well talking about the theory of fundamental mathematics, but what have I learned about it? Well for starters, I can say that maths is absolutely everywhere… in the outdoors, in the weather – you name it and its there (links to connectedness). I believe that it is absolutely vital to make the connections that mathematics allows us to see. We need to make our children aware of this in order to heighten their love and interest for mathematics. I am aware that maths needs to be an active subject for children to really get their teeth into and enjoy. My blog post ‘active learning in mathematics’ covers this – it highlights that basic principles of mathematics can be taught in fun and interesting ways in which your children will understand. Furthermore, there is no better feeling in the world than seeing the children in your class engaged, learning and having fun. Maths allows us as practitioners to experiment and play with certain theories in order to evoke fun and enjoyment. For example, the lesson on demand planning was absolutely fantastic!! Moreover, enthusiasm counts for a lot in teaching. I mean why do you think I had such a negative view on mathematics? Its probably because my teachers in the past have never shown a passion for it. Our lecturers for this module have been the most enthusiastic people I have ever seen. It has made me become enthusiastic and, of course, if your enthusiastic as a teacher, your children will also become enthusiastic.

Therefore, I believe that fundamental mathematics for a practitioner to be confident and have a profound knowledge of basic maths in order for our children to understand and develop a love for mathematics. In addition, the practitioner needs to be able to encourage and motivate their children through meaningful and engaging activities that incorporates active learning. Furthermore, practitioners need to also make connections with mathematics in the real world and encourage their children to make these connections as well. Finally, and I can’t emphasise this enough, we must be able to paint a picture of each child’s progress and be able to plan the steps in order for them to succeed and develop in mathematics.

reference

Ma, L. (2010). Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. 2^nd ed. New York: Routledge. P1-50.

During the Discovering Mathematics elective, I have been amazed by some of the maths that I have encountered, particularly when linking maths to play and stories. I, beforehand, had a very narrow-minded view of what maths was as my school experience was not a good or successful one. I remember mostly being stuck and it made me think of myself as a failure. In addition, I vaguely remember my teacher(s) writing mathematical equations for on the board for us to copy and learn. Was it interesting? Most definitely not. I was disengaged most of the time which probably lead to me having bad memories about mathematics. However, this elective (along with my college experience) has opened my eyes to mathematics on a wide scale – especially through play and stories.

Lets go back in time to my second year of college. This is where my mind-set began to change on the whole concept of maths. As part of our early years placement, we had to make our own story sack which had to include many subjects from the CFE – one of them being maths. To say the least, I was pretty petrified. All that was going through my head was ‘how can I incorporate mathematics from a story?” And yes, the maths anxiety began to set in. However, after researching many different books to use for my story sack, I began to see the links between maths and stories. I chose the Wizard of Oz as my book and managed to include maths from ideologies like character order to the shape of the yellow brick road. Ultimately it opened my eyes and laid a basis for my love of maths to grow from.

Today in the primary school, children still have this maths anxiety. I thoroughly believe that it stems down from older generations. This is because learning and teaching has transformed in the modern day classroom from the mid 20th century. Older generations of people may see maths as copying down sums off the board in a kind of rote learning manner. This left these people with maths anxiety to have very bad memories of mathematics and generations of adults who don’t see the need to learn mathematical theories. Ultimately, our responsibility is to teach young learners that mathematics is relevant to every day life like money, time, fractions and so on. Ultimately, because our older generations do not have the greatest view of mathematics, it gets passed on to our children and they become “scared” of maths (Furner and Duffy, 2002). I believe this statement is true because our attitudes need to convey a love of maths in order for it to pass on to our children. Not only must we as teachers be enthusiastic and encouraging, we also need to introduce maths in fun and interactive ways so it will be memorable for our children (see my last blog post on active learning in mathematics for further information).

Parents as Teachers
I found this concept to be rather interesting and intriguing because parent are children’s first point of contact in education. Parents are the child’s pioneer of education and it could be argued that parents are children’s first teachers. Within the context of maths, this should be no different. However, when it comes to children needing help with their maths homework, parents might try to avoid the matter. According to Pound (2003), parents of young children have a narrow minded view of mathematics and may not prioritise it within the home. I am not suggesting that this is the case for every child, but maths is a hard and abstract concept for children to understand and they probably will need help with their homework. This is why it is important for parents to get involved and convey a love for mathematics so their children can have a love for mathematics.

With regards to cognitive development, mathematical concepts allow children to think, reason, understand and learn. According to Piaget’s 4 staged theory, he believed that schemas are the way in which we organise information and for children to understand mathematics the should repeat their actions (sums and questions) in order to learn. In addition to this, Margaret Donaldson agreed with Piaget on some aspect but believed that if children think of abstract situations then they will fail. I do not believe that children will fail due to abstract concepts. I understand that maths is an abstract concept but with the right help and support, children will thrive. Maths is so beneficial for a child’s cognitive development due to the problem solving aspect of it and, without the children realising it, maths allows them to think articulately.

Fundamentally, we should see children as independent learners and should give them the space to work on an individual basis, This can be achieved through immersing the children in mathematical events before school (for example, ‘how many cows can you see in the field?’). As time progresses, children’s skills will develop, but it is important for parents to not give them direct instructions. Children naturally absorb the patterns and regularities that exist in the day to day natural and cultural world (Ginsburg, Cannon, Eisband, and Pappas, 2006). Effectively, routines are mathematical concepts and children pick up the patters very quickly. Of course, we as teachers need to be able to explain the maths correctly to the children in order for them to learn it (Henlock, 2003). In addition, this can be done through a number of strategies:

Open ended questions
Using mathematical language
Written communication through mark making

Effectively, these strategies should be used by teacher in order to develop their ideas and understanding of mathematical concepts. A good way to achieve this is through play. Play is important because it allows children to be a team players, communicate effectively, learn through interaction and ultimately allows children to express themselves in different ways. Furthermore, play is innate and allows children to make connections, be creative and use flexible thinking. Moreover, it refines and rehearses their skills and encourages perseverance. So where does this link into mathematics? Well mathematics allow children to make decisions through imagination, reasoning, predicting, planning, experimenting with strategies and learning through rhymes and songs.

In conclusion, I never realised that maths and play go hand in hand with one another. It is a fascinating thought that has allowed me to realise that there is more to maths than copying sums off the blackboard. Maths should be fun and inviting and I will definitely try to incorporate this into my lessons while on future placements and when I am a qualified teacher. However, parent play a huge role within mathematics. Parents should encourage a love for mathematics and view maths as a positive thing in order for our children to absorb a love for mathematics – lead our children forward!!

The end is near… My Profound Understanding of Fundamental Mathematics

Maths, Play and Stories