It’s that time of the year again.. it’s time to teach the wonderful fractions.  Many of your children may have an idea of what is going on, depending on the year group you’re teaching; however, if you’re lucky, your children will have very similar preconceptions (hopefully correct – makes your job a bit easier).  You have everything set up perfectly, you have explained what they are expected to have achieved by the end of the lesson; we’ll take the example of adding two fractions BUT with different denominators.  You can already guess the misconception…adding the denominators!

What is happening in their brain?

Imagine there is a battle going on in the gladiator ring.  There are two people, imagine one being called the ‘current understanding’ (their misconception) and the ‘accepted understanding’ (the right one!).  You, the teacher, are supporting and cheering on the ‘accepted understanding’ (you need to have common denominators before adding them!), you are giving your best lesson, you have visuals and concrete materials – everything your teacher training has taught you to do!  However, you are battling something a child has previously understood and is trying so hard to make it easy for themselves so they are not learning a new method.  This battle of gladiators, the neuroscientists and psychologists call it cognitive conflict.  Of course, you want the ‘accepted understanding’ gladiator to win!

Where does it take place in the brain?

Mareschal (2016) discusses how, a wonderfully fancy name in the brain, the anterior cingulate cortex (I’ll refer to it as the ACC) and multiple regions of the prefrontal cortex (the picture shows where they are highlighted below) play a crucial role in the child’s change of conception.  This is done by identifying their ‘misconception’ (current understanding) and modifying it to the actual right method and answer (accepted understanding).  So we know where it lives in the brain – this horrible confusion feeling – but how do they actually overcome this misconception?

Mareschal (2016) picks this apart further by suggesting an element of cognitive control is needed – i.e., being able to adequately maintain this overwhelming sense of confusion (cognitive conflict – the battle of thoughts!).  One aspect that Mareschal (2016) suggests can overcome this, is a sensori-motor factor – basically, something physical, bringing the abstract into a physical and concrete form.  He then goes on to say that the child needs to inhibit irrelevant information whilst activating the relevant information.  Sounds simple enough?  Stop thinking about what is wrong and start thinking about what is right and use that to help.  To me, that just sounds like ‘you’re a teacher…fix it’.

How does this help in the classroom?

To those teaching the older age bracket of children, there is good news, Mareschal (2016) discusses literature that suggest inhibitory control (able to stop thinking about irrelevant information) is developed, leading to a reduced cognitive load (lots of things and thoughts piling on top of each other).  That doesn’t bring in choice: if someone does not want to accept a difference, they will make sure they do not – this could be why it is so hard to challenge so many preconceptions of adults (they have lots of evidence supporting their current conception so they have a choice to use their evidence or yours).  Moving back to children, a wide range of research cited by Mareschal (2016) evidence the importance of inhibitory skills in both maths and science learning.  So how can you apply this abstract inhibitory control based on a child’s cognitive conflict when adding fractions with different denominators?

• Pose the question.
• Investigate their method of reaching what they believe the answer is.
• Give children time to go through this cognitive conflict.
• Use concrete and physical materials to show how your version is correct and logical.

Then you can start explaining the reasoning behind it, using concrete materials (remember how sensori-motor experiences can develop inhibitory control from earlier?) and then have a conversation about it.   Then repeat, allowing the children to explore themselves with their new investigative knowledge.  This can develop their embedding skills, so the ‘accepted understanding’ gladiator can win – it can even become stronger when it can be applied to different problems!

Note about the journal article

Mareschal’s (2016) paper discussed many other parts of the brain and their importance; however, the parts that have been focused on, does not detract from the ‘essence’ of the paper nor its message but to ensure the relevant parts for you as the practical teacher are found.

Article reviewed: Mareschal, D. (2016). The neuroscience of conceptual learning in science and mathematics, Current Opinion in Behavioral Sciences, 10, 114-118. https://eprints.bbk.ac.uk/15634/1/15634.pdf

Further reading:

You could have a look at different papers below relating to Mareschal’s (2016) publication to develop a more in-depth understanding:

Brookman-Byrne, A., Mareschal, D., Tolmie, A.K., & Dumontheil, I. (2018). Inhibitory control and counterintutive science and maths reasoning in adolescence. PloS one, 13(6). 10.1371/journal.pone.0198973

Thomas, M.S., Ansari, D., & Knowland, V.C. (2019). Annual research review: educational neuroscience: progress and prospects, Journal of Child Psychology and Psychiatry, 60(4). https://doi.org/10.1111/jcpp.12973