Category Archives: 1.3 Trust & Respect

The Daily Mile-matics

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Throughout this module, we have often been asked to reflect on our own experiences of learning mathematics at school and my memories are almost exclusively textbooks in the classroom and being excited that you had filled all of the squared paper in your jotter.  Fast forward 15 years or so to ‘Miss Duncan’ teaching mathematics on placement, I tried to include a lot of stimulating concrete material to introduce concepts and always asked the children how we might use the mathematics outside of school but didn’t actually use the mathematics outside of the classroom with them.  In this blog, I want to look further into some of the benefits of planning outdoor mathematics lessons as well as the challenges and give an example of how I might incorporate fundamental principles of mathematics in future lessons.

A benefit of any outdoor learning session is that it allows for a slightly different relationship between teacher and learner away from the, sometimes stressful, classroom.  This is supported in Maynard and Waters’ (2007, p.260) discussion about outdoor learning which states ”while the teachers indicated that they were unsure whether or not they should change their pedagogical approach when working outside, several indicated that they felt more relaxed outdoors.”  In the outdoor lessons I took part in during my recent placement, I witnessed a lot more teamwork and peer support among children who would normally be at opposite ends of the classroom in their normal maths groups.  So, outdoor learning may provide more opportunity for children to build important transferable skills and even improve relationships with peers and teachers than the more constrained nature of the classroom.

Much like morning break and lunchtime, an outdoor lesson is a chance to get some fresh air and expel some energy before returning to the classroom with more focus. This is echoed in the reasoning for introducing ‘The Daily Mile’ which encourages teachers and children to walk, run or jog for around 15 minutes each day to improve health and wellbeing.

NB: not the last mention of The Daily Mile… stay tuned.

However, as a student teacher, I can certainly say that outdoor lessons were a bit daunting. Fear of the unknown, or something like that.  It seems I’m not alone as Dillon et al (2006, p.107) cited teachers’ lack of confidence and limited time and resources as barriers to outdoor learning in our schools today.  Understandable, right?  Well, the good news is that these fears are already being somewhat alleviated by more exposure to outdoor learning early in teacher education.  The General Teaching Council for Scotland’s (2012) updated standards for provisional registration now state that students must demonstrate that they can use a variety of teaching approaches and resources before qualifying as a teacher – outdoor learning, for example.

So, how can we incorporate more outdoor learning in mathematics?

Back to ‘The Daily Mile’.  The class are already outside for at least 15 mins – it would be a good start to firstly make the most of this time for the children to start to develop a profound understanding of fundamental mathematics (PUFM).  However, as Bilton (2010, p.4) states ”merely taking indoor equipment outside does not constitute quality provision.”  Not to worry – the best part is that the resources are already there waiting for us.

In our ”Maths & The Great Outdoors” input, we were able to estimate the height of a tree by measuring the same distance on the ground.  We modified the method somewhat by (gracefully) looking at the tree upside-down and creating the 45° angle by continuing on from where we could only just see the top of the tree to the grass.  For those of you who didn’t have the pleasure of seeing this first-hand, the start of this video shows how a question like ”how tall do you think that tree is?” leads to discussions and problem-solving opportunities using basic ideas such as the properties of the triangle and how concepts such as estimation and finding an average help us answer the question (inter-connectedness).  This is just one example of many new ideas I have for future lessons, thanks to my participation in this module.

In conclusion, it is clear that outdoor learning has benefits and I don’t think anyone really disagrees with that.  Instead, what holds us back is the fear of trying something new.  New = good!  We know that teachers and children benefit hugely from learning in a ‘new’ environment, even if that environment is the school grounds they walk across every day,  We have discovered so far in Discovering Maths and as cliché as it sounds, maths really is everywhere.  It is simply not enough to ask the children where they might use their new-found knowledge, we must support them in using it so that they truly understand what it is they are learning about and why it is so important.

References

Bilton, H. (2010), Outdoor learning in the early years. 1st ed. New York: Routledge.

Dillon, J., Rickinson, M., Teamey, K., Morris, M., Choi, M.Y., Sanders, D. and Benefield, P., (2006) The value of outdoor learning: evidence from research in the UK and elsewhere. School science review, 87(320)

GTCS (2012) Standards for Registration Available at: http://www.gtcs.org.uk/web/FILES/the-standards/standards-for-registration-1212.pdf

Maynard, T,  Waters, J. (2007) Learning in the outdoor environment: a missed opportunity?. Available at: https://www.tandfonline.com/doi/abs/10.1080/09575140701594400#aHR0cHM6Ly93d3cudGFuZGZvbmxpbmUuY29tL2RvaS9wZGYvMTAuMTA4MC8wOTU3NTE0MDcwMTU5NDQwMD9uZWVkQWNjZXNzPXRydWVAQEAw 

 

After learning about the cognitive and affective domains with regards to learning in an input in my Discovering Maths module, I have been thinking about how maths groups based on ability and their seemingly neutral names may be affecting the way children feel about mathematics.

Do ability groups still have a place in a modern classroom? Are there other options?

We should have ability groups because…

It is almost guaranteed that in a typical class, there will be children from very varied backgrounds – some nurtured and encouraged to learn but also some children who have extremely difficult home lives with little to no encouragement and support,  This is reflected in a child’s attainment through their learning journey and unfortunately, there is a significant ”attainment gap” between those living in the least deprived areas and the most.  (Scottish Government, 2018)

So, because there is an attainment gap between children in most classes, surely we need to group children by ability in order to provide enough support and to differentiate within lessons?

We shouldn’t have ability groups because…

The children know what they really mean.  Whether their group is named ”The Triangles” or ”The Circles”, there is evidence to show that children see right through these seemingly harmless and neutral names – right through to ”top” or ”bottom” group.

An article published on independent news website The Conversation delved into how children feel about ability groups and quoted one child as saying “I’ve always been last in every maths group … I’ll just be low now in my next school, too.” (The Conversation, 2016)

Reading this article made my heart sink a bit, to be honest.

This relates directly to our learning about the relationship between a child’s cognitive and affective domains. (Hiebert, J., & Grouws, D. A. (2007)

In other words, content knowledge and feelings respectively.

As shown in this diagram, a child’s development has affective and cognitive domains which both need to be nurtured in order for them to thrive academically and socially.

The quote above tells us this might be a child who’s affective domain has been attacked by feelings of negativity and inadequacy in mathematics which, unfortunately, might hinder his academic progress as he moves into secondary school.

Surely, as educators, we wouldn’t want any child to have such negative feelings towards their ability in a subject?

So, are there other options?

Drum roll please…

YES.  Plenty, in fact.  Across the world, schools have come to different conclusions about how to create the best learning environment for their children.

Maths Mastery resonated most with me as I could easily link it to Liping Ma’s 4 fundamental principles of mathematics (2010);

  1. Inter-connectedness (understanding how concepts are related)
  2. Multiple perspectives (ability to adapt and use alternative methods)
  3. Basic ideas (foundational knowledge)
  4. Longitudinal coherence (developing understanding through time)

The following link explains Maths Mastery in more detail but in a nutshell, it has the whole class working together on a particular concept until everyone is confident, albeit with some mistakes along the way.

https://www.tes.com/news/maths-mastery-makes-setting-according-ability-irrelevant

Although I haven’t seen this approach in action, I can almost picture a bustling classroom filled with children helping each other and sharing their own ways of working which would undoubtedly support their affective development more than just accepting that they are destined to be in the ”bottom” maths group.

Perhaps there are aspects of both approaches that will be useful in my future classrooms.

I’m looking forward to finding out.

References

Dweck, C., Walton, G. M., Cohen, G. L., Paunesku, D. and Yeager, D. (2011) Academic tenacity: Mindset and skills that promote long-term learning. Gates Foundation. Seattle, WA: Bill & Melinda Gates Foundation. Available online at: http://www.scribd.com/doc/118972490/Academic-Tenacity-Mindsets-and-Skills-that-Promote-Long-Term-Learning Accessed 24/09/18

”Children put in the bottom maths group at primary believe they’ll never be any good”, The Conversation.  Available at http://theconversation.com/children-put-in-the-bottom-maths-group-at-primary-believe-theyll-never-be-any-good-54502 (accessed 22/09/18)

Ma, L., (2010) Knowing and teaching elementary mathematics (Anniversary Ed.) New York: Routledge. (Chapter 5, page 122)

Scottish Government (2018) Scottish Attainment Challenge. Available at https://education.gov.scot/improvement/learning-resources/Scottish%20Attainment%20Challenge (accessed 22/09/18)