How very manipulative

This lecture was all about how/when & why to use manipulatives in maths.

The article by Laksi et al. (2015) was really interesting. I had never thought about not using manipulatives in lessons but their argument was compelling. It wasn't so much not to use them, it is more about how to use them well so that they benefit the children. Using the the same equipment for a long time so that the children are really familiar with it seem like a great idea. The advise to not use items which look like everyday items is really valuable as I can imagine the children just playing with them and regarding them as toys, rather than maths equipment. The toy and the maths manipulatives need to be distinct. So it's about planning the manipulatives well so that the are a tool for the learning. It was also good to think about when to stop using the manipulatives. They should be there to help the children grasp a concept and to see the structure of the maths. Once they have done that, the manipulatives are a crutch, rather than a tool. By Year 3, they should not really be using them, unless they are being introduced to a new concept (i.e. Algebra in Year 6).

Using the right manipulatives for the learning:

Addition - Bead strings and numicon are good

Subtraction: Dienes are good for this as you can show the exchanging which has to happen.

I gravitated towards the Cuisinere as they reminded me of the equipment I had as a child. However they are not good to use for place value and are much better to use for fractions or to show the bar model.

Looking at the Moscardini article, the results seemed reasonably mixed and my main take away from it was:

it is more useful for teachers to think about the way in which learners' mathematical thinking is developed by using particular tools (Hiebert et al, 1997)

In layman's terms - you need the dog to shake the bone, and not the other way around. It also seems to be reliant on the teacher making the appropriate aids accessible to the children and ensuring that the problems they are giving the children are appropriate for the level of conceptual understanding the child has at that time.

I read through the chapter on manipulatives in Enriching Mathematics in the Primary Curriculum by S. Pope & P. Mayorga. It is a very clear layout of lots of different manipulatives and their uses and a great resource to refer back to when I'm teaching maths so that I choose the most appropriate aid to use. They make a good point here:

Learners do not learn mathematical knowledge through being told facts that they have to memorize.

This made me think of the KIRFs the children learn at Orleans and how pointless this might be then?