I am presenting a practical hands-on session at a convention in a few weeks about maths strategies (www.learningdifferenceconvention.com) and have a restricted time limit (one hour) – how on earth will I condense this topic?
Well, I begin by not condensing anything – my first draft of anything is always incredibly long, but the initial brain dump is the best way for me to then shape a final product. And, as a complete aside for any students reading this – I am a creature of habit and complete this initial plan early in the piece so I can have a few days break before revisiting it to start the cull, this extra thinking time allows the overall shape of my presentation or written piece to really form.
So, I am going to present a single slide with this title, “Why is maths so hard?” with a few dot points.
Knowledge
There is much to “know” in maths – there is simply no way around this, mathematics relies on an enormous bank of symbols and words that must be remembered and recalled at the appropriate time (working memory issues make this so difficult for some children). You can’t be expected to add 4 and 3 unless you know that 4 is 4 and means 4 objects, that 3 is 3 and means 3 objects, that the cross symbol + is add and means combining, and finally the equal sign = is where the answer is written!
A list you ask? Here are but a few examples:
- Numbers 0-9, 10-19, 20-99, 100-999, 1000 à (then upon reaching high school the curtain is unveiled and all of these numbers have a matching mirror with the negative symbol – in front of them)
- Symbols + – x -:- = > < …
- Shapes (2D, 3D)
- Words (add subtract multiply divide equal)
Procedural
The wonderful thing about maths is that there are no exceptions to the steps that guide the procedures, once you have learnt and mastered these you can always rely on them. The horrendous thing about maths is that there are so many steps to remember …
Procedural learning is about mastery, completing these steps many times under supervision and in as errorless as possible, before progressing to independent practise until mastered. These steps are both cognitive and kinaesthetic (remembering that long multiplication involves drawing 4 lines under the question and placing the 0 in the middle row becomes a kinaesthetic memory for students). They take time, but without this they are incredibly effortful (and often error filled!)
Applications
Maths involves numbers, right? Unfortunately, not all the time!
The introduction of a very specific language related to mathematics is a factor compounding its complexity. There are some clear cut words – “add” and “subtract”, but “difference” can mean subtract or qualitative distinctions between shapes. The word “rose” doesn’t mean the sweet smelling flower in my garden and depending on the wording of the question may actually mean addition or subtraction. Strategies can be taught to approach a worded problem and some commonalities can be established, but in these questions each one must be considered in its own context.
So, “Why is maths so hard?”
Because even after a great deal of time is spent recognising and recalling numbers, symbols and maths words and then procedures are rehearsed and mastered, the question will then be hidden in a worded problem that requires unique comprehension!
I haven’t even mentioned maths anxiety, both inherited (parents and siblings who regularly publically comment on their poor maths) or the result of failed experiences (a percentage written in red can be soul destroying). Maths anxiety is a complication that weaves its way throughout the complexity of mathematics as a subject and can hinder or facilitate success.
Hi Samantha,
I liked the doco you were in ages ago and like your website. However, you mention Maths but only talk about Arithmetic. Arithmetic is a relatively unimportant branch of Maths, there are other branches of maths that dyscalculics can excel in that do not require Arithmetic. For example Einstein is thought to have had dyscalculia.
Counting is the basis of Arithmetic, if you can’t count you can’t do Arithmetic. If you build on this an understanding of the four rules and their relationships the procedures logically flow.
Thank you for speaking about dyscalculia at the convention. Anything that can be done to increase awareness of dyscalculia has to be a good thing.
Cheers,
Ann
Thanks for your feedback Ann – this is the first of a few posts I’ll put up regarding maths. When working with students struggling with maths I find they roughly fall into two camps – number-based issues or language-based issues. In these initial posts I will be chatting about the numerical aspect, you are totally correct if you can’t count nothing happens from there. Students struggling with maths (whether we call this dyscalculia or something else!) need so much support in this area.
Hi Samantha,
Thank you for your prompt response.
I think it is not generally well known, within the community, that all the SLDs are co-morbid. For example about 50% of dyslexics also have dyscalculia. So when a parent says to me something like ‘Of course I was also useless at Maths because of my dyslexia’, it makes me think it could be that she has un-identified dyscalculia.
Inevitably, if a child has a number of SLDs the most obvious or well known will get identified first and possibly the others can get overlooked.
If dyscalculia is not identified the child is not likely to get the appropriate help or be taught using appropriate strategies.
Hi Ann
Your point is absolutely correct and I saw this all the time in my work. I completely believe in the importance of reading and that reading assessment and instruction should be prioritised. But, more and more I see children kit with further challenges down the road with their maths because it hasn’t been addressed alongside the reading support. Many of the underlying contributors to difficulties in reading (memory, processing speed) also impact maths.
This is really prompting the current postings in this area.
Hi Samantha,
There are also the issues of self esteem and Maths anxiety. Maths is the only academic subject with its own REAL psychological condition. There is no research , that I know of, which correlates dyscalculia and Maths anxiety but I think it would be high. (A good research question?)
Hi Ann
I agree, my own research for my PhD dissertation was in the area of reading difficulties, but my interest has always been more for maths – there is a real lack of research in this area. I too haven’t seen research linking dyscalculia with maths anxiety, but I suspect that possibly one of the contributors to that is the relative infancy of the term.
I would tend to err on the side of caution in this area and all of my teaching programs include an element of self-concept feedback to assist.
Hi S,
I agree, also self efficacy and resilience help.
Hi Samantha,
I hope your presentation at the LD convention went well yesterday.
Cheers,
Ann