My view on the paper "Learning to 'See' Less Than Nothing"

30 Jun 2016 / Leonardo Barichello

Sometime ago, I fount the paper Learning to “See” Less Than Nothing: Putting Perceptual Skills to Work for Learning Numerical Structure by Jessica M. Tsang, Kristen P. Blair, Laura Bofferding & Daniel L. Schwartz. The paper is not directly related to my research, but I think it is one of the best papers in Mathematics Education I have ever read. Below, I will comment a bit about it.

This is the starting point of the paper:

“Our proposal [...] is that people recruit the distinct perceptuo-motor system of symmetry to make meaning of and to work with integer structure. If true, how can we use this knowledge to help children learn?” (pp. 157).

To answer that question, the authors utilized an experimental design: three groups, each learning integers with a different approach (two common in American textbooks and one emphasizing symmetry). They took a series of measures to ensure the basic premisses of experimental designs (something that is not common in educational research), but what I think makes this paper particularly good is how they defined the null hypothesis. Instead of only comparing the results in a pre and post-test, they used two measures: regular pre and post-tests + a post-test composed of generative questions.

If the results in the regular post-test showed differences between the groups, it would not mean that one of the approaches was better or worst than the others, but it would mean that the quality of the instruction received by the groups varied and this would be a problem in terms of their research question. Therefore, they were expecting similar results in the regular post-test and better performance in the generative questions by the group taught using symmetry.

This was the first time I saw a research using this approach. I think this is very distinctive and improves greatly the quality of the results because it neutralizes the interference of unexpected changes in engagement, excitement, expectations and instruction quality due to simply "being involved in a research project" due to the requirement of similar results in the regular post-test.

Every time I read a paper of a researcher or teacher trying two different approaches in a classroom and simply comparing pre and post-test results, I think: how can I know if the teacher was equally engaged in the lessons? I wouldn't! It is natural to expect that the involvement of the teacher in the research would affect his expectations and performance in the classroom. That is why I think the requirement of similar results in the regular post-test and a second measure to indicate the success of the intervention (generative questions, for instance) sounds very appropriate.

In fact, there are some issues related to the validity of the generative questions, but it is already a step towards more convincing experimental approaches in educational researches directly connected to classrooms.

PS: the paper has other merits beyond what was discussed here. It really worth reading.


Tsang, J. M., Blair, K. P., Bofferding, L., & Schwartz, D. L. (2015). Learning to “See” Less Than Nothing: Putting Perceptual Skills to Work for Learning Numerical Structure. Cognition and Instruction, 33(2), 154–197.

Drury: brilliant coffees in the UK

22 May 2016 / Leonardo Barichello

You may have noticed that I love coffee. Since I arrived in the UK, I started to try several different brands and styles of grounded coffee for my espresso machine (one of those non-especial domestic espresso machines). I tried Costa, Nero, Tesco, Sainsbury, Waitrose and M&S. The only one I considered acceptable was Tesco Finest Espresso. The solution was to buy Illy (I prefer the dark roast version), but it is quite expensive and sometimes unavailable in grocery stores (even when you buy online!).

But one day, walking in the Covent Garden region in London, my girlfriend noticed a good-looking coffee and tea store. We gave it a shot and voi la: we found Drury.
drury logo
After I describe my preferences for coffee, the seller recommended the Moka D'or blend. We tried. Several times. We also tried other blends and beans. Some of them are good, but Moka D'or is, by far, my favourite. The taste is amazing: toasted and zero acidity. And it goes perfectly in my espresso machine: fine enough to release the flavour but not too much to get bitter.

I never found a restaurant serving their coffee (only their tea, but I am not a big fan), but it is possible to buy online a big range of coffees for a very reasonable prices. If you don't know, please, give it a try!

The best stroopwafels in Amsterdam

20 Apr 2016 / Leonardo Barichello

I am a big fan of stroopwafel, specially accompanied by a very strong espresso. Try to place the stroopwafel over the cup for a minute after serving the coffee, it gets a little humid and then you eat it. Just brilliant!

I am such a fan of it, that even the commercial ones use to make me happy.
However, the last time I visited Amsterdam, I decided to look for a proper stroopwafel and I did find it! This is the place: Yes, their website is only in Dutch and they don't really care about attracting more clients, but I assure you that they worth the visit.

stroopwafel from Lanskroon

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