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Suppose you isolate a class of undergraduate mathematics majors who are about to enroll in a semester of real analysis (rigorous, proof-based calculus) and split them into two groups. Then, you schedule the first group to study n hours of real analysis every week and the other group to study (n-m) hours of real analysis every week and perform m hours of n-back training (assume that n and m are reasonably well tuned; m is probably much smaller than n).

Also assume that the second group does not take shortcuts in doing the training (where certain patterns are exploited).

  • Which group do you conjecture to perform better in the analysis course and why?
  • To what degree will one group perform better and why?

  • Does having a wider short-term memory horizon of numbers (which I assume n-back produces) result in being able to keep track of more variables and rigorous proof steps in a sharper way (working memory) and in faster comprehension of mathematical concepts (fluid intelligence)?

  • Does the training result in a larger attention span and therefore to better grades?

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2 Answers 2

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I assume that the group that spends 100% of their time studying real analysis and 0% of their time doing n-back training will do best in any subsequent real analysis course.

Cognitive skill acquisition does not generalise all that much (for a review see VanLehn, 1996). Transfer is often limited. I'm sceptical of any claims that short term training can lead to far reaching cognitive change as implied by n-back training.

The demands on working memory of problems in a domain get less as the knowledge and rules implied by a domain get better acquired. Over time students will start to recognise patterns, and will learn to apply rules specific to the domain. Domain specific practice is probably the best way to acquire that knowledge. And in general, the more time that is spent on learning that knowledge, the more knowledge that will be acquired.

Of course, much could be said about creating an optimal learning environment for real analysis. For example, consolidation of prerequisite knowledge, providing practice at the right level of difficulty, providing feedback to the learner, providing a good mix of presentation of content with problem exercises, distributing practice over time, and so on are all important components of an effective learning environment. However, these have nothing to do with n-back, and everything to do with good pedagogy. In particular, if you want to teach something other than real analysis, but your aim is effective performance in real analysis, then you should examine what are the relevant skills and prerequisites for effective performance in real analysis. And combine this with an examination of student difficulties and knowledge gaps.

Empirical Evaluations

@Ofri Raviv pointed out two references (Shipstead et al, 2012; Melby-Lervag et al, 2013) that provide reviews of working memory training and are generally critical of its utility.

Melby-Lervag and Hulme (2013) did a meta-analysis of working memory training studies:

To be included in the review, studies had to be randomized controlled trials or quasi-experiments without randomization, have a treatment, and have either a treated group or an untreated control group. Twenty-three studies with 30 group comparisons met the criteria for inclusion. The studies included involved clinical samples and samples of typically developing children and adults. Meta-analyses indicated that the programs produced reliable short-term improvements in working memory skills. For verbal working memory, these near-transfer effects were not sustained at follow-up, whereas for visuospatial working memory, limited evidence suggested that such effects might be maintained. More importantly, there was no convincing evidence of the generalization of working memory training to other skills (nonverbal and verbal ability, inhibitory processes in attention, word decoding, and arithmetic). The authors conclude that memory training programs appear to produce short-term, specific training effects that do not generalize.

References

  • VanLehn, K. (1996). Cognitive skill acquisition. Annual review of psychology, 47(1), 513-539.
  • Shipstead, Zach; Redick, Thomas S.; Engle, Randall W. Psychological Bulletin, Vol 138(4), Jul 2012, 628-654. doi: 10.1037/a0027473 2
  • Melby-Lervag, M., & Hulme, C. (2013). Is working memory training in children effective? A meta-analytic review. Developmental Psychology, 49, 270-291. PDF
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Another, more recent review, claiming that we currently have no good evidence of working memory improvement due to practice, and certainly not of transfer to other areas: Shipstead, Zach; Redick, Thomas S.; Engle, Randall W. Psychological Bulletin, Vol 138(4), Jul 2012, 628-654. doi: 10.1037/a0027473 –  Ofri Raviv Aug 12 '13 at 18:32
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And another one: Melby-Lervag, M., & Hulme, C. (2012). Is working memory training in children effective? A meta-analytic review. Developmental Psychology. –  Ofri Raviv Aug 12 '13 at 18:37
    
@Ofri perhaps you could add those references as a spearate answer; or if you'd prefer I could just add the refs to my answer. My answer is quite light on the references regarding working memory training, although my general reading of the literature has led me to be very sceptical. –  Jeromy Anglim Aug 13 '13 at 2:04
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I don't think we need another answer saying the same thing. Feel free to add the refs to your answer. I would maybe only add that even the improvement of working memory capacity due to practice is doubted (and not just the transfer). –  Ofri Raviv Aug 13 '13 at 6:26
    
Okay. I've added the refs and a quote from one of them. –  Jeromy Anglim Aug 13 '13 at 6:34

I'm only be able to answer part of your question in specific ways.

Does having a wider short-term memory horizon of numbers (which I assume n-back produces) result in being able to keep track of more variables and rigorous proof steps in a sharper way (working memory) and in faster comprehension of mathematical concepts (fluid intelligence)?

*Answer*$\rightarrow$ dual-n-back in my experience was more like a booster to help me achieve my peak on working memory for several minutes and deduct while time goes by. The effect usually last for half a day. Since it is like a booster, it can't help me to maintain the peak high performance. The training gives "intuition" only; it helps me to verify logical fallacies most, and it does make me speak much more logically with only a sufficient number of words. (I did learn concrete some knowledge about different kind of fallacies.) Eliminating logical mistakes made me draw rational decisions. But it is only a booster, and in fact I did maintain some of the "recalling ability". It is most likely possible to maintain the fruits, since I've given up some time to calm down after training, and it takes me long hours. If you can't do this with the proof of actually knowing how exactly it affects you, don't train. It has side effect while you're over-trained.

Does the training result in a larger attention span and therefore to better grades?

*Answer*$\rightarrow$ I'm not sure about what you mean by attention span. But I can tell you that it helps to read effectively by eliminating crap.

And most IMPORTANT, the gameplay of "brainworkshop" is not the best; time interval shouldn't be fixed while training and it varies for different people. This setting is the worst in that it could make your answers out of control. E.g., you can't recall the letter or the position without having 1 more second, and the task remaining will be ruined.

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