Mathematics? Oh so fearful of it…are you? Or… look… there’s a sum! And… the answer? Let me spend time sourcing it. Right now. Some people leave education with this desire to crawl under the table when 5,6,7 and all the other numbers approach them. Others, well others, carry maths in their head – and would prefer to speak in digits if possible. The myth (according to the results of a 2013 research study) of ‘I’m right brained so call me a problem solver’ vs. ‘I’m the more rational leftie’ means that children should no longer be brought up to consider themselves as naturally mathematical or a born linguistic. Indeed: we have talents, we have strengths, we have preferences. But – of course, there’s a ‘but’ – mathinking is vital if we are to efficiently carry out everyday tasks. From recipe reading to saving our red squirrels ‘in the animal superhero cape,’ the digits that surround us must be of comfort. And, most certainly not, be treated as those spheres in bubble wrap. Our toddlers, our children, our adolescents ought to grow up ready to fail. Then succeed. Then… realise… that mathinking is about the effort and determination and less about the green-tick solution. That’s confidence-fuelled mathinking… in my head.

Recently (in fact only a matter of less than 72 hours ago) MA2 – that’s moi included – received their final STEM input. Nope… not how to arrange flowers for Valentine’s Day  or for the Chelsea Flower Show. However, we did receive a Happy Valentine’s on the top of our sign-in sheet from a lecturer with the last name of Valentine! And, that was topped off by creating our own game involving mathematical concepts. (Smiley face!) Lots of discussions were held on how to take maths out of the textbook and away from standardised assessments. A connectionist-belief approach involving open conversations was found to be the most effective way: and well, a recent starter-activity on consecutive numbers confirmed that. Sometimes, our inputs involve being the children – or attempting what the primary students have to do but with a university student’s mind on. Once (a very long time ago… not really, but I like to pretend I’m a storyteller sometimes) we had to figure out a word-problem involving consecutive numbers. At first, we all panicked. By the end, however, it was ‘Happy Ever After’ and everyone was wearing fairy-tale gowns. How lovely. Let me tell the story without imaging that a bunch of five-year olds were sitting beside my seat – here it goes:

Many of us stared. We realised there was no prince-charming. We put our hand up.#

The teacher (very friendly) told us to keep persevering through the rubber hail and rain.

We succeeded in writing down an answer.

And that’s the ending for you.

The latter may be more like reality, if we are setting the picture straight and not at an 89 degrees angle! At first, many of us in the lecture room were not at all sure about how to attempt the problem-solving question. Deliberately, purposefully and cleverly was the question slide jammed packed with information – and the only picture remained to be a table of consecutive numbers in blue and white. For me, lots of writing was the ‘tying the shoes tight enough’ hurdle. But, for others… the fear of making a mistake prevented them from taking the leap of faith. What reminisced with me was the impact sides, pictures, diagrams (and all the visual jazz) can have on a student’s learning. During my first year placement, my teacher advised me to keep it simple! Yes.. nothing like the Mona Lisa or a Magic Eye picture… from Miss Smith. And almost a year later, the same point was made again. Kids prefer simplicity when learning (although I personally believe that the occasional rainbow cannot go a miss). That pot of gold still does exist… Somewhere Over the Rainbow! Jokes aside, it’s easy enough to alter the layout of questions for our students however… calming a raging maths anxiety monster in them may take more than a few kind words (or a ROY G. BIV smiley – acronym lovers… you’ll know what I mean!)

The past few lessons, lecturers (or whatever name they should be termed) have taught me something more than ‘cut away’ all that text. As a future educator, I really do hope that my pupils will be like mathematical bees. Buzz, buzz, buzz… isn’t that algorithm so full of pollen? Understandably, some children will have a dislike for certain areas of maths (like me and symmetry and learning R and L) but overall, the wonder of maths must be ignited in them. A fire (with infinite logs) for problem solving does not always come from the pupil. Nope. Instead, as Ofsted writes, it is about the maths spirit adopted in the classroom:

“[Teachers] made conscious efforts to FOSTER A SPIRIT OF ENQUIRY [deliberate capitalization from your blog-post author], developing pupils’ reasoning skills through approaches that saw problem-solving and investigation as integral to learning mathematics. They checked that everyone was challenged to think hard and they adapted how they were teaching to achieve this. As a result, their classrooms were vibrant places of learning.” (Ofsted, 2008, p.12).

Spirit of enquiry. That is it. How do we develop that? Well, there would be many theories including Askew et al 1997’s research which deems that teachers tend to lean towards a particular set of believes (either connectionist, discovery or transmission). Most effective practice flourishes from the first mentioned belief-set, in which the most effective teaching happens when students can appreciate that all areas in maths are, in some way, related to each other. For instance: fraction word-problems are sometimes better solved by involving decimal conversion. It’s that simple thing like… why buy fresh bread when you already have some in the freezer? Enabling students to use the skills they already have is also of priority in the teaching of maths. Connectionist-orientated teachers set aside time (maybe in a circular fashion if Early Years students melt their hearts) to talk. Just openly talk.

#Why do we solve it this way? Is there another mathematical route that we can take to reach our destination? What about a storyboard?

That leads me on another path to bringing up storyboards but before… I’ll let you know that I want to be a connectionist teacher. That’s a seed already sown – thanks Dundee University. (That phrase was most certainly not sarcastic bee the way).

Storyboards (in the past – okay!) reminded me of ‘how to stretch’ and satisfy the students whose brains make them wish to reach for the nearest paint pot and brush. They were a time-waster. Just show some grit and keep moving forward with the sum. Write the working out, Claire. (That what previously motivated me in maths). But, well, you live’n’learn and realise that 1 + 1 doesn’t always make a two. Sometimes, a window is the result!!! After hearing about the various strategies and understanding the purpose of drawing out the number sentences, storyboards are on my Pinterest. (Sorry, I’m one of THOSE teachers.) Uh-huh, daydreaming about my classroom (maths) displays can occasionally happen with moi. Back to the point now, it is important not to overlook resources that you didn’t enjoy as a child yourself. There’s no excuse for not using something in your classroom because it was futile to you as a learner. Open-mind please. Keep considering all the options, Miss Smith.

Maths, I’m admitting, has a soft-spot in my heart. Whenever I was stressed out about an essay, me would run to do maths. Yes, on occasions, scuttering down the stairs to the kitchen for my textbook… but well I loved when you just got the answer after trying hard. There was a tick or cross – and you knew the result. Maybe it was a sense of control in the subject? After all, sciences were my thing until long reports became involved. I have always been torn between the arts and maths, yet teachers need to be enthusiastic for them all. There is something good, something interesting, something positive in every subject: my own maths students who enter with a dislike for maths need to feel that way. Mathinking… thinking abstractly… can be done by everyone – not just males too. Hemree (1990) found that maths anxiety stems from previous failure in maths examinations and is more common among female students than male students. The gender gap in STEM subject is already evident and it is common knowledge that our generation is trying to remove the female electric fence that surrounds females in careers such as engineering. A survey (conducted for the United Kingdom WISE Campaign) highlighted that 89% of engineers were male in the workplace – and so carrying out a subtraction leaves us realising that only 11% were female. Only 11. As I see it, that is a gap that an elephant would struggle to sort out. It really is.

To finish off, it is clear that the style of teaching is all-important. As mentioned above, discussions are vital to student’s success in maths. However, we ought to consider our own underlying nervous system when we approach numbers? Do we shake? Our hands: do they turn red when seen by a thermal camera? Are we still (like I was) centred on achieving those ticks? Or… the process… do we strive when something makes us want to scribble or shred the paper into as many miniscule pieces as possible. According to Finlayson (2014) our own experiences can make us teach with a straight ‘yes’ or ‘no’ style or be flexible. Bee like a ballerina who is trying to bee a flower. Don’t get me wrong… I’ve failed many times in maths (and still use the trick to remember my left and rights)… but well it’s amusing to buzz around afterwards. That’s what I want my students to do so I ought to love a struggle myself. That’s what teaching is really: setting a true example. But, someone please, is there a faster way to stop mixing up left and rights? Maybe my students could teach me that. I’m up for a role reversal every so often!

References:

Finlayson, M. (2014) ‘Addressing math anxiety in the classroom’, Improving Schools, 17(1), pp. 99-115. Available at: https://journals.sagepub.com/doi/abs/10.1177/1365480214521457(Accessed: 18 February 2019).

Hemree, R. (1990) ‘The Nature, Effects, and Relief of Mathematics Anxiety’, Journal for Research in Mathematics Education, 22(1), pp.33-46.

Nielson, J. (2013) ‘An Evaluation of the Left-Brain vs. Right-Brain Hypothesis with Resting State Functional Connectivity Magnetic Resonance Imaging’, PLoS ONE, 8(8). Available at: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0071275

2 thoughts on “Let’s think about (ma)thinking, okay?”

1. Linda Lapere says:

Claire, what a wonderful blog post on your thoughts about your learning over the last few weeks and reflecting upon your years of maths experiences! I am delighted that your MA2 inputs have resulted in such deep thinking and reflection.
Your post also sums up brilliantly how our feelings about maths can spill over into the classroom and why the beliefs we hold about mathematics and learning can have such an impact on our learners through the sometimes subconscious choices we make about our teaching and learning.
If you are interested, I’d suggest looking at the work of Richard Skemp in conceptual understanding vs procedural knowledge and the work of Sian Beilock and colleagues regarding female teachers’ maths anxiety on girls’ achievements in maths.

1. Claire Smith says:

Aw thank you Linda for your help and advice! I forgot to add that I now use ‘algorithm’ instead of chimney sums whenever teaching….! Before I used to draw a house when teaching the sum but place value makes more logical sense!!! Thanks also for the suggestions 🙂