
Question: I was wondering if people know of good studies supporting either side in the 'math' wars ? My suspicion is that skils learning makes ypu good at precisely that, and rote learning likewise just makes you good at that. But is there much evidence to suggest which approach has more merit generally ?
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Lucy commented on :
I asked some colleagues who are experts in maths cognition about this. Matthew Inglis suggested this article (www.math.cornell.edu/~henderson/courses/EdMathF04/MathWars.pdf) which reviews the math wars. It concludes that both approaches are needed and includes a really nice analogy with reading: “Consider the phonicsversus
wholelanguage controversy, for example. Of course children need to learn to sound out words – a healthy dose of phonics at the right time is salutary. Of course children need to make sense of what they’re reading – learning to use context is an essential skill, and motivational as well. Any sensible person would realize that children need both phonics and reading for understanding. Either of the two perspectives, taken to extremes, is nonsensical…..The same is the case in mathematics. An exclusive focus on basics leaves students without the understandings that enable them to use mathematics effectively. A focus on “process” without attention to skills deprives students of the tools they need for fluid, competent performance. The extremes are untenable.”
Matthew also recommended this study (www.ncbi.nlm.nih.gov/pmc/articles/PMC3779611/) which compares the effect of speeded and nonspeeded practice (both alongside number knowledge tutoring) in first grade. It suggests that rote learning and skills learning may interact. Nonspeeded practice was designed to reinforce relations and principles addressed in the number knowledge tutoring, while speeded practice aimed to promote quick responding and the use of efficient counting procedures to generate many correct responses. Speeded practice was more effective than nonspeeded practice in promoting complex calculation and simple arithmetic. The authors suggest that the additional speeded practice may have helped the students to “compensate for the demands on reasoning ability, which an instructional focus on number knowledge creates.”
Rod commented on :
Like all wars, the math wars generate more heat than light, and resurface every few years. Like most wars it’s the extremists you have to watch for, those who appear to think they have the absolute truth on their side. And have most to gain from the publicity generated. My comment strongly supports Lucy’s earlier one, but may add some useful theory.
There are various versions over the years. One is for early school maths where the protagonists line up on the ‘rote learning first’ to ‘rote learning in an abomination’ divide. The other is for algebralevel maths where one version is ‘principles first, applications second’ and the other is ‘examples first, principles second’.
The underlying issue really is ‘how do we get the learner to get the answers right and also to understand the underlying principles?’ My own view, as a learning specialist is that one needs a bit of both, but most of all one needs consistent successes. Otherwise the learner gets discouraged and switches off.
So, lots of examples, that the learner gets right. These allow the inbuilt ‘statistical learning’ capabilities to kick in, slowly extracting the more general principles (but in an implicit, notaccessibletoconsciousness fashion, much like the way we have an intuitive feel for our own language we can tell whether a sentence is syntactically correct or not, but not why). Then one needs to seed in a few ‘declarative’ questions, that get the learner to consider what the underlying principles might be, again with a high success ratio. Then, with any luck one has got over the hurdle of implicit to explicit knowledge, and the relevant principles and facts can build consistently.
For arithmetic learning such as number bonds, there aren’t really any principles to be learned, so it’s a question of how best to learn isolated facts. Here the rote learning capabilities – chanting, succeeding, little and often – are actually very powerful. It’s by the far the best to have relatively errorless learning, so that the learner remains confident. If a child has lost confidence and is confused, then strategies to add meaning – mnemonic strategies that allow an answer to be worked out so that success occurs and the “I can’t do it” context is avoided – are often the best way forward.
Much the same applies to the ‘reading wars’ where one side lined up on phonics only, and the other on ‘real books’ only, and after 50 years of intensive research, the conclusion is that a combination of approaches, applied systematically so that all skills (phonics, vocabulary, fluency, enjoyment) develop in step rather than in isolation.
I should perhaps mention here the ‘dark side’. If a child fails with maths (or reading) this leads to anxiety, so that the next time, the situation triggers the anxiety, and this in itself reduces the effective learning ability (generating a ‘fight, flight or freeze’ state) which leads to further failure, increases the anxiety, and so on, essentially leading to a learned helplessness approach. This has been shown by brain imaging studies of children with ‘math anxiety’, where the predominant pattern of brain activity when imagining doing a maths test, is pretty much a fear response.
In short, each method is inadequate in isolation, and each needs to be used in conjunction. But the key to learning is consistent success. And indeed, frequent repetition. But above all, success.