The aim of this page is to organize the posts in the blog about my research (Ph.D. - School of Education, University of Nottingham).

My general interest is on tasks about fractions emphasizing visual representations for low achieving students, thus most posts will be about these issues.

I do not have the intention of being systematic here, I only want to post particularly interesting papers and ideas that occurred to me during the research process as a way to help myself to make sense of it.

Papers and presentations about my research

Possible parallels between visual representations and informal knowledge is the first paper I published (informal proceedings) related to my PhD research. It is based on a piece of data collected in a sort of pilot study in the same school I am carrying out my actual data collection. The paper shows a student reasoning about fraction addition and, I would argue, based on the visual representation that were being used in his instruction. This is paper is related to this post about the work of Nancy Mack.

A teacher changing her practice: a tentative explanation for the reasons behind it is a paper by Rita Santos Guimaraes, whose research is focused on the same teachers that are taking part in my research. In fact, she is investigating the impact of all the process of discussing and enacting the lessons I am proposing in their practice in general.

On March 2017 I presented some theoretical arguments that are emerging from my data collection at the BSRLM Conference. It is working-in-progress, but here is the presentation and here is the informal proceedings paper for those who may be interested.

The lessons

A second version of all the lessons I used during my data collection are available here. If you are a teacher and want to try to teach fraction addition and subtraction using visual representations, you are more than welcome to try the lessons.

Other relevant/interesting references

The papers published by Nancy Mack about fraction operations and informal knowledge were quite inspiring for me.

Mayer (1997) is a fundamental paper for my research because it justifies why use a visual approach to teach mathematics to low-achieving students.

Ramani and Siegler (2008) analysed the relation between playing linear number board games, numerical knowledge and socio-economic status.

I quite like the way Martyn Hammersley discusses methodological issues. Particularly, his view of what is a case study helped me a lot.

Post in Portuguese about ability setting as it is done in England inpired by the paper "Exploring the relative lack of impact of research on ‘ability grouping’ in England: a discourse analytic account" (Francis et al, 2016). This post is aimed at Brazilians that want to know a bit more about this practice.

The paper Social class and the visual in mathematics (Gates, 2015) puts together arguments from different areas, such as sociology and cognitive sciences, in favour of more emphasis on visual representations in the teaching of mathematics, specially when it comes to socially disadvantaged students.

Tool case

If you have to transcribe audio (from interviews), I recommend the web app oTranscribe. Read more about it here.

During my data collection, I collect almost 2000 worksheets. Or course I do not want to analyse all of them, but I knew from the beginning that I would need a good organizational system that included to possibility of applying tags (or codes) to the worksheets. Because I could not find a good open software for the job, I started to develop my own: OpenQDA. Although it is still not fully featured, it is available online for anyone to use.

The scripts developed by Jonathan Schultz to export qualitative projects from Nvivo to a friendly and flexible format are very useful for those who used Nvivo but need something beyond they weird set of tools. More info about the scripts here.


Some links

My Flickr:

Repositório de recursos educacionais:

Centre for Research in Mathematics Education (University of Nottingham):

TED-Ed: The last banana:

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