Dr Lucy Cragg from the University of Nottingham comes to SciBar at the Vat and Fiddle to tell us about the range of factors that can contribute to being successful in mathematics.
21% of children leave primary school without passing maths tests at the level expected of them. This continues into adulthood where a fifth of adults have skills below the basic level needed for everyday situations.
There are a number of different skills that you need to be successful in mathematics. Some of these are maths specific skills such as counting skills, understanding of quantity and symbol knowledge. However, some are more general skills such as executive function, spatial skills, language ability and IQ.
Lucy’s work looks at three main areas as the components for mathematical skills: factual knowledge, procedural skills and conceptual understanding. Difficulties in one of these areas may lead to overall problems at a later date.
With regard to basic number representations, we’ve all seen the newspaper stories claiming that, “even babies can do maths”. Well, even animals can deal with quantity information. It is this quantity information that gives numbers meaning. Children and adults who do well in basic number representation tasks have been found to have higher levels of maths achievement. Dyscalculia stems from problems with this magnitude system.
Rather than looking at specific maths skills, most of Lucy’s research is looking at general thinking skills. More specifically she is looking at executive function (which controls our attitudes and behaviours), working memory and inhibition.
We have a short term memory which is used for storing information. We also have this working memory which we use to manipulate that information. For example this is what we would use when performing mental arithmetic, working through recipes or following directions. Lucy then takes the audience through an example which shows that while remembering a string of numbers is quite straightforward, repeating them back in reverse order is a lot harder. The average adult can remember about 6 numbers and recite them in order when they have to reverse them this drops to around 4 (just as a comparator, on average children can only remember around 2 numbers even if they don’t have to reverse them)
Those who do well in working memory tasks have higher levels of maths achievement. Similarly, it’s been shown that mathematicians have better spatial skills. However, we still don’t know which came first, the mathematical ability or the spatial skills. People who are born pre-term (less than 32 weeks) also tend to be worse at maths, have poor working memory and poor spatial skills.
Inhibition is how good you are at ignoring distracting information or supressing unwanted responses. For example how good you are at the Stroop Paradigm where you have the name of a colour printed in a different colour and you have to name the colour of the word rather than the word itself. Inhibition can stop you rushing in to try and solve problems, it can help overcome confusion from number facts and it can help you to ignore irrelevant information.
In the Q and A session following the talk, we learn that most of Lucy’s research has been into arithmetic rather than other areas of maths and that there is actually very little difference in ability levels in terms of gender. It also seems that there could be a genetic component to maths ability. Lucy’s main interest though is how can we improve people’s working memory.
So, poor performance in mathematics could be due to maths specific skills or due to poor general thinking skills. Looking at it holistically, your ability in maths is driven by a combination of your factual knowledge, your procedural skills, your conceptual understanding, your working memory, how well you can ignore distractions and how flexible your thinking is.
Talk from 30/09/2015 at The Vat & Fiddle – Dr Lucy Cragg: Barriers To Success In Mathematics