The first point in introducing ANY new concepts or topics is to find out what the children already know.
If this is a completely new area that has not been covered or touched upon previously in school then of course we are trying to find out what the children may have picked up about this subject or topic based on their out of school experiences.
However for maths things are slightly different as the subject builds on itself as it unfolds and develops across the year groups.
Maths can be broadly divided into 2 spheres
- Maths Number
- Maths Topic
Whereas the Maths number work is progressive and interlinked, the maths topic areas (..examples would be measurement, geometry, money, time etc ) do not overlap with each other…however having said that they do closely rely on the elements of number within their calculation and understanding.
So lets take a look at the scenario of introducing a new unit area within what we are broadly going to call maths number.
Before we launch into specifics let me draw an analogy here – there are occasions when we receive a new pupil…transferred from another school. In most circumstances these pupils will come accompanied by all their records but there are instances where, for whatever reasons, the child appears with little or no records.
This of course means that some forms of assessment must take place in order to get some ideas of just where on the achievement scale this pupil is positioned.
Lets take the simple example of finding a reading level / book. The easiest way of doing this is to send the child out with a T.A and a few books of differing levels. The T.A basically says “read this” (but in a nicer and much kinder way!) and we go up the scale of books until we find the failure point.
This approach is identical to how we should be introducing any new maths unit…but especially in the area of maths number.
It is simply not possible to assume that the class you have in front of you are equipped (in a maths sense) and ready to immediately tackle what is stipulated in your year group section of the National Curriculum!
Go back to go forward
The approach we have to take is to go back to go forward.
In other words we have to establish just how competent the pupils in your class are on the building blocks of whatever you are about to teach before you can actually teach it!….Does that make sense – I hope so…try reading it again a little slower and understand the logic of what we are saying.
It does not matter whatsoever what the National curriculum is asking you to do if the FAILURE POINT for your children is prior to what you want to achieve. If this is the case then you can teach it all you like but you may as well not bother because non of it will stick!
How far do I go back?
You can go back as far as you like really – if you go back to simple stuff then you will find that (hopefully) all the children are competent at this level and you can very quickly move through to higher stages. It does not do any harm to have quick fire questions that start very simply and progressively get more difficult.
Basically you know the starting point to work from and you know the level they hopefully will be at following the previous year groups teaching – rattle through things and watch for the failure points!
Remember the reading tests for the pupil with no school records – the T.A simply said “read this – ok – now read this – ok…now this” until the failure point was noted.
It’s the same here except that you will have various failure points and misconceptions that appear.
Having done this what do I do?
You now have to make the judgement as to where the class are achieving. Is it possible for them to move onto the new unit based on a sound knowledge of what has been taught before; or will you have to reteach or correct any misconceptions BEFORE you can move forward. You will have also found any pupils who will need support in this unit. Let me be honest with you – in most cases you will have to re-teach or correct some aspects before you can introduce the new unit…so don’t be surprised if and when this happens!
Of course when you have chosen where to start and in which areas to go over there will always be children in your class for whom this is not necessary. Don’t try to extend their learning or move them onto other things – there are benefits in doing this for everyone.
- Correcting misconceptions
- Further explanation and understanding
- Revision of key facts and knowledge
- Consolidation of approach and method
There are however some maths units (mostly in the “maths topic” side of things) that are not particularly progressive. In other words you will be introducing them cold! …right from the start.
Many children will have absolutely no concepts or understanding of what you are about to teach them and your initial questioning to “find out what they know” will reveal – “they know absolutely nothing!”
On such occasions you are starting from the lowest level you can think of…literally start at base camp and explain and talk as a class about every aspect of the unit focus. Here are some things to consider.
- Make sure the children write the basics in their books….definitions, explanations, how, what where and why….even down to how to spell key words (these should also appear on your working wall and possibly even for homework)
- Demonstrate how things are done from the front and if needed write a list of how to approach things so that children can move from step 1 to step 2 etc when doing either calculations or practical work for themselves
- Have practical work wherever possible…it converts theory in practice and really cements the learning
- Keep it fun but keep it relevant and useful
You will be surprised just how simple you need to make things when starting a totally unknown unit…but its fun to do but don’t assume the children know anything!
I have actually had the children draw round the edge of their rulers and then put on the markings to show where we start measuring from….not the edge but the 0 !
In conclusion – The core understanding of maths concepts underpins every aspect of mathematics irrespective of the focus. In order to move your pupils on to a higher understanding these progressively built concepts need to be mastered.
It is vitally important therefore that when introducing new units of mathematics you review and act upon the current levels of pupil understanding before using this as a springboard to move things forward from that point.