Monday, 7 September 2015

Applying the Learning Pyramid to maths learning

The Learning Pyramid

We began by discussing what sort of activities we felt helped us learn best and to remember new skills or information.

The empty learning pyramid was shown. I explained how educators and psychologists had researched this extensively over many years and we are going to find out what they discovered.

Partners were given 7 different types of learning activities to learn about Roman numerals and needed to sort in order from which they felt would be the most helpful to learn / remember to least helpful.

You watch a youtube about how Roman numerals work.
Group Discussion

As a whole class or in a small group, you discuss how Roman numerals work.  
People ask each other questions and share their understandings.
Teach Others

You teach your parents, friends or classmates what you have learnt about 
how Roman numerals work.

Mr Anshaw shows you how Roman numerals work perhaps with the 
whiteboard and some display cards or some blocks etc.

Mr Anshaw stands in front of our class and explains how Roman numerals 
work only using his words.
Practise By Doing

You practise writing and converting Roman numerals to our Hindu-Arabic 
numerals and maybe add or subtract Roman numerals to learn how they work.

You read a book or a website that explains how Roman numerals work.

They placed these against their own copy of the pyramid. It was really interesting listening in to students drawing upon their own learning experiences to support their theories. 

Partners then buddied up with other partners and shared their theories. After sharing the new group of 4 needed to come up with a consensus as a group.  

The groups then displayed their theories and as a whole class we analysed commonalities the groups had.

Eventually as a class we were able to create the learning pyramid just like the research had shown:

Looking at this research, I asked what should we be doing the most of and the least of in our classroom to learn effectively.  We all agreed that I shouldn't be lecturing much and that they should have opportunities to be discussing, practising to do and to peer teach as much as possible.

To reflect on what we had just learnt, we had a few minutes to write down on a post it note what we found surprising or still wondered or had thought was interesting about this research and shared these with the class. 

To apply this to our maths learning as an example, we continued with our enquiries into our base 10 number system we have been exploring.

Last week, we had found out how and why we can multiply by 10, 100, 1 000 etc easily.

I showed on the screen what we had done:

(Incidentally, this is one of the more effective ways of differentiating number skills I use in my class. Students select a column of questions to try to do in 4 or so minutes. This helps them to self-assess where their understandings are at. I always explain beforehand that it doesn't matter whether we feel we should try the easier or the more challenging columns as we are all learners. Using this strategy to practise number skills can cater to all the varying levels in the class whilst also giving the children ownership of their learning)

We looked at the key concept question:

 FUNCTION: How does multiplying numbers by 10, 100 1 000 etc work?


Using mini whiteboards, partner A taught partner B the strategy, but more importantly why that strategy works by using their own question examples:

This peer-teaching approach helped all students regardless of their level of understanding. Those with stronger understandings gave more complex decimal examples and those new to this concept were given an opportunity to also process their own thinking at a level they were comfortable at comprehending by teaching their partner. The partners often asked each other for clarification which made the learning more meaningful.

Then after a minute, the partners swapped teaching roles.

We discussed whether we felt 'teaching others' was or wasn't a useful way to best learn and remember.

Most of us agreed that it was really useful as we need to really think about it so we can explain it in a clear manner.

A few of us felt though, it was the 'practising by doing' as we showed examples to our partners that was the more effective part of the learning process.  We respected their thoughts on that and wondered if they could be right.

We then looked at ways we could prove that multiplying by 10, 100 etc really does work.  Several ideas were shared in the discussion.  One student suggested we could split the numbers (partitioning). Multiply each and then add them.  We were really curious about this so we created our own questions and tried it out. 

Before starting though, we looked at the learning pyramid and thought about which activity type we were about to start. We agreed we were 'practising by doing' which according to the research is the second best thing we can do to deepen our learning.

Students created their own questions as complex or as simple as they felt their understanding was at:

We discussed how we felt about 'practising by doing'.  Everyone felt this was an effective way to learn in a meaningful and memorable way. 


We then 'taught' our partner what we had had. Not just explaining the strategy, but to also be mindful in explaining why this strategy can be used and how we are changing the place values of the digits. 

We then repeated the whole process with dividing numbers by 10, 100 1 000 etc

Thinking back to the two approaches of learning we had just experimented with, we felt as a whole that teaching others was indeed a very powerful way for us to learn and that we should try to do this in all our activities including maths as much as possible this year.   

To help serve this as a reminder to the children, but also to me, we have our learning pyramid with reflections displayed at the front of our room. We will refer to it often as a way of developing an understanding of metacognition and for when they are given opportunities to enquire into maths or other subject areas to decide what they should do.  I'm hopeful they will start suggesting we should be peer teaching and thus develop a stronger ownership of our learning.

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