Why do some students struggle with maths? And what can be done to help them?
Definitive answers to these questions could certainly change the world and maybe even win a Nobel Prize. Sadly, no one seems to be putting their hand up just yet.
Conducting high quality research in education is expensive and time-consuming, so often the research that is published needs to be treated cautiously – applying to a particular age group, gender, ethnicity and school system, for example. Unfortunately, with little hard data, education theory can often devolve into ideological battles over control of the academic sandpit.
However, there are clues to draw upon.
In the classroom
First, let’s take a step back to look at the processes behind learning maths. When students are introduced to multiplication, they are striving to come to terms with its meaning, and how it relates to earlier concepts like addition. Solving even a simple multiplication question is a conceptual struggle. With repetition over time, the simpler multiplication questions (and their answers) become familiar, and the concept starts to become embedded. Answering the questions moves from being a calculation process to a recall process. At the same time, students can now apply the concept of multiplication to more difficult questions. With repetition of the recall process, speed improves which leads to fluency and ultimately, to automaticity.
With modern scanning techniques, it is now possible to observe this happening in the brain – learning a new concept is associated with the establishment of a new neural connection. Consolidation leads to additional neurons strengthening this connection.
Automaticity means for the student that recall is fast and effortless. This is an advantage but the critical benefit flows from the fact that working memory is no longer required. As a result, working memory is then available to grasp the next level concept. By contrast, working memory is quickly overwhelmed by a new concept if automaticity has not been attained.
Fluency and automaticity can only be achieved with time. No child learns about multiplication and masters the times tables without putting in the time – even Einstein was no standout in school. Achieving automaticity is a consequence of many maths lessons and revision activities. For example, a lesson in long multiplication can act as a reinforcement of prior learning in times tables. However, the effectiveness of either the new learning or the reinforcement (or both) can be reduced for individual students if they haven’t already reached sufficient fluency.
Understandably, teachers would not list automaticity as a learning outcome in their lesson plan for any particular session or learning module. In fact, automaticity is unlikely to ever be directly measured in the classroom, and may not even be considered in many contexts; yet arguably it is critical to a student’s long term maths learning trajectory.
Where students struggle
Now, back to the issue of helping students who struggle with maths. The logical consequence of our knowledge about automaticity would be that students at danger of falling behind in their current work would gain most benefit from additional consolidation of earlier work. That would apply even if there are no particular holes in their prior knowledge, but especially if there are indeed gaps. But is any of this supported by research? Yes.
One study set out to forensically examine gender differences in maths performance at major assessments (Royer et al 1999). They found that eliminating all sources of bias almost entirely removed systematic gender differences in maths. Critically, they found that in the limited situations where gender differences appeared to be real, those differences were explained by proficiency in math fact retrieval – up to and including our old friend automaticity. So a proven intervention targeted at maths fact fluency is an obvious strategy.
A second study looked at the math performance of both learning-disabled and attention-disordered individuals compared to average students (Zentall 1990). Again, the differences between these groups were traced directly to fact-retrieval automaticity, leading to the conclusion that the best way to help these groups was through strategies boosting recall fluency and automaticity.
These two disparate pieces of sound research have both pin-pointed boosting automaticity as the single most effective intervention. It is reasonable to project that this would also be a big factor for various other cohorts of struggling maths students.
Recent research confirms that lifting fluency and automaticity makes a big difference
Maths Invaders from EdAlive has a proven track record of lifting fluency and automaticity across diverse student groups. Research shows an average recall speed improvement of 1.1 seconds or 26% for a range of question topics, concurrent with an impressive 12-month improvement in maths age. The flexible workload associated with these gains was far from onerous – the equivalent of 10 half-hour sessions, which could easily be completed in one school term even in addition to normal maths lessons.
The vital ingredient is EdAlive’s automated Adaptive Learning which individualises material for each student – the perfect balance of challenge and reinforcement. In combination with the mixed-content format and the engaging game Space Rescue, Maths Invaders is a winning formula for ensuring maths success in your classroom.
It can all too easily happen that students who struggle with maths reach the early conclusion that “I’m just not good at maths” which can slide to an ingrained attitude affecting their whole approach to school and learning. By contrast, there is widespread anecdotal evidence that confidence in maths will often spread to other subjects, transforming school from a chore to an adventure and unlocking the joy of learning.
The game-changing technology behind the full range of EdAlive’s websites
EdAlive’s other online learning websites feature equivalent technology – Typing Tournament, Words Rock, Baggin’ the Dragon Maths and Volcanic Panic Reading Success. Research indicates that students using these websites are also making remarkable learning progress.
Cholmsky, P. (2011). From acquisition to automaticity: The Reflex solution for math fact mastery. http://harringtonmath.com/wp-content/uploads/2012/01/Reflex_White_Paper.pdf.
Royer, J. M., Tronsky, L. N., Chan, Y., Jackson, S. J., & Merchant, H. (1999). “Math fact retrieval as the cognitive mechanism underlying gender differences in math test performance.” Contemporary Educational Psychology, 24, 181-266.
Zentall, S. S. (1990). “Fact-retrieval automatization and math problem-solving: Learning disabled, attention disordered, and normal adolescents.” Journal of Educational Psychology, 82, 856- 865.