Category Archives: 3.1 Teaching & Learning

What is mathematics?

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What is mathematics?

Though this question is impossible to summarise in a few words, these were my responses to this question from today’s input:math-wordle

“mathematics is solving problems with numbers”

“mathematics is universal”

“mathematics is everywhere” (This was proven to us by being tasked to highlight in a newspaper wherever we saw maths. The yellow highlight strewn across the front page was evidence enough).

Maths anxiety is not something I believe I have, however, being informed in our lecture that in order to be numerate, you must not only understand the mathematics you are doing, you must be able to explain your thinking. If I was confident in my own ability to do a maths problem and was put on the spot to show how I did it, I think I would feel immense pressure and embarrassment in case I was wrong. Showing me there can always be doubt and fear.

Before my first year school placement I felt confident about teaching mathematics and felt I had an understanding of the basics at least. Maths is a subject I enjoyed and was good at, at school until Higher level – but that’s a different story and I won’t go there now. However, during my placement, I taught an extensive amount of mathematics. During one lesson I won’t forget, I had a really tough time helping a small group understand the lesson objective. Repeatedly breaking down the success criteria for the children but this group just weren’t getting it. I thought the way I was explaining it was simple enough however saying it over and over again did not work. I realised the problem lay with me and my inability to explain it in a different way. Therefore, my confidence in my own ability plummeted.

maths-frustration

The example above is why I am glad I chose this elective module as I need to better understand mathematical concepts, to improve not only my competence but re-build my confidence in a subject that I enjoy.

Our lecture on “what is maths? Why teach it?” was really interesting and dare I say fun! The task to work out how many snaps to break up a bar chocolate with 64 squares brought about many things which are so important to exploring maths: discussion, conversation, sharing language and most importantly, play. We were able to visualise and draw connections from this task to help us and we had help with props too.

I think we have got off to a great start in not only understanding but actually doing what mathematicians do. In the lecture we did all of the following without even realising it:

  • solve problems
  • investigate
  • explore
  • discover
  • use symbols, tables and diagrams
  • collaborate

Another task was to discuss which way we would calculate this problem:

“In a warehouse you can obtain 15% discount but you must pay 20% VAT. Which way would you prefer your final bill to be calculated: with discount first or with VAT first?”

I first dove in with working out the answer doing 15% off first then 20% VAT and vice versa and was not surprised to find that both answers were the same. It was interesting to hear other people’s ideas that the reasoning behind perhaps adding the VAT first was that so there was a greater number therefore when it came to the 15% discount there would be more money off. This was a great task to see how other people’s mind worked as, as I said I just dove straight in, however, others had more logical thinking, albeit the answers were the same, it shows that no two minds think alike.

Not so scary Maths

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When asked to rate ourselves on a scale of 1-10 for enjoyment and confidence of maths I rated 8 and 4 respectively. Maths is a subject that I enjoyed at school but the thought of teaching maths is frightening. It’s been while – almost 2 years since I’ve studied mathsimages and prior to that 5 years since school – so I am nervous children may know more than I do!

In Tara’s input we discussed maths myths and anxieties:

  • It’s not needed for everyday life
  • You are better at maths or language and not both
  • My mum wasn’t good at maths so I won’t be either
  • Some people just can’t do maths

Genuinely, I’d never heard of maths anxiety until I started University but it is something I need to understand. Maths is not something I was ever frightened of. That’s not to say I’m an expert but I did and still do enjoy using numbers. I feel I do have a positive attitude to maths and but must admit I did/do agree one of the myths that you are stronger in either maths or language as I felt exactly that, that maths was my stronger subject compared to language. (Something I need to get out of the habit of thinking).

It is paramount that teachers show a positive attitude and confidence to maths. As soon as you show weakness with any subject but particularly in maths you give reason for children to doubt their own abilities. Mistakes can be made but not being indexembarrassed and using them as learning opportunities is important as a teacher to show children it’s ok. Equally saying something like “I wasn’t very good at maths” or “I was better at language” sets doubt and leads to a self-fulfilling prophecy.

My thoughts were that I may have confidence in my own ability but not teaching maths and as long as I show enthusiasm then I’ll be ok. However, Tara then showed us a quote:

“Teaching enthusiasm cannot be maintained where a teacher is unsure of the material… consequences of unsound subject knowledge is hesitancy in teaching, lack of direction to the lesson and lack of clarity in explanation”. Banks and Mayes, 2001, p25.

This then scared me.  I have only engaged with the Online Literacy Assessment a few times (okay only once) and my score was embarrassingly low.  I really need to get my knowledge up to scratch and there is little time left until placement.  We are not required to teach hard mathematics but unless there is understanding (apparently) then doubt will be cast over my teaching of the subject. Better get to it…

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Not just a warm up…

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I was really excited for our P.E. input as anyone who knows me knows I enjoy exercising and playing sports. I think we were all a bit nervous as we weren’t sure what was going to be involved in terms of efforts of exertion however I think wilovepee knew Will wouldn’t have us running laps for the whole hour. I was surprised the find out the aims of a warm up that I had not considered before in a P.E class. For our warm up Will gave us a series of simple instructions to follow. He asked us what the intention of this and most of our answers were as you would expect such as increase heart rate and preparing the body. Will then explained his intentions were not only of that mentioned but to also identify areas such as:

  • Physical ability
  • Ability following instructions
  • Potential bullying
  • Competitiveness
  • Motivation

The simple instruction that were given for us to follow were also allowing Will to assess who is or isn’t physically able to do some movement. If a child cannot bend touch toesdown to touch their toes or they aren’t co-ordinated they may need further help in certain areas. Another of the instructions was to stop jogging and sprint in the opposite direction – this was so assess spacial awareness.

 

The next part of our warm up was to jog round the hall and when will shouted “freeze”, he would show the number of fingers of how many people to get in to groups. What he was doing here was to see if we could follow non-verbal instruction but also identifying possibilities of bullying e.g. do the same people always go in a group and are some people always left out. By doing this when it comes to grouping for further drills or activities the teacher can work out ways to put people in different groups. I am guilty of saying in school we did try to outsmart our teachers by not all lining up in a row to try to be grouped together.

Next in partners we took turns to dribble a ball, however there were only one or two full sized basketballs. What Will was showing us here is that the resources available to us may not match up with our lesson plans so we should checking to see what is available before planning.

I did come across some interesting information while researching for this blog post and came across this report. sportscotland and Education Scotland invested £5.8m to support local authorities in providing two hours for primary and two period for secondary school of quality physical education per week. This report details how some local authorities spent this money including buying resources, sports equipment and inclusion training for teachers to fully include children with additional support needs. From this hopefully the schools we work in will have benefited from this investment and resources won’t be an issue.

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Most importantly from this input I learned that P.E isn’t about doing a gym class for two hours per week and that’s it. It provides learners with the opportunity to build and improve physical fitness but also build upon interpersonal skills from working in groups. It allows for children to take on leadership roles and demonstrate fair play.

Improvement without reflection?

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Reflection, in its simplest form, is recalling what you have done and is an essential part of learning. There are different levels of reflection that can take many forms. A reflective model I am encouraged to use in my social work module is Stephen Brookfield’s Four Lenses: autobiographical, peer (student), that of or fellow professionals and theoretical. The lens titles have been adapted slightly to suit the module but ultimately have the same meaning. By looking at ourselves through an autobiographical lens we identify our own assumptions in order to reveal pedagogy that may need reinforced. A peer (student) lens focuses on observations, evaluations and group work. Fellow professionals can provide support and feedback to enhance learning and teaching. A theoretical lens offers a view to support, understand and consider teaching or learning.

Reflection correlates with one of the most important professional values of being a teacher in my opinion: integrity. The SPR description of integrity is “critically examining the connections between personal and professional attitudes and beliefs, values and practices to effect improvement and, when appropriate, bring about transformative change in practice”. We must reflect on what we do in order to improve ourselves; it is imperative to recognise strengths and weaknesses. Without reflection there can be no improvement or change and without reflection, we are doing, not only ourselves, but our students a disservice.

Reflective writing is an opportunity to critically analysis what you have or haven’t done and include suggestions of your intentions to improve and develop yourself. I am really enjoying using the ePortfolio to reflect on my university life so far. Previously my writing may only have been conveying information but my ePortfolio is helping not only identify where I am, but what I need to, to help shape me to be the best practitioner that I can.