Posts Tagged ‘History’

The article gives a history of the mathematics landscape in the UK since 1837. Algebra has been part of this throughout.

We see algebra as a key tool to help solve problems now, but historically “problem solving was seen as a specialized skill, only for mathematicians in opening up new fields.”

Key points:

  • “A problem solver needs a rich, connected understanding of mathematics and the abilty to see patterns of similarity and association, as well as the skills to carry out the planned attack, and to check that the results make sense in the context of the problem.”
  • “A Royal Commision, reporting on the state of mathematics teaching in nine leading Public (i.e., private) Schools in 1837, noted that the typical two weekly hours of mathematics consisted of Arithmetic, a little manipulative Algebra, and “Euclid“, learned by rote.”


  • Burkhardt, H., Bell, A. (2007) ‘Problem solving in the United Kingdom’ ZDM, Vol. 39, no. 5, pp. 395-403

This reading discusses how an average student can benefit from a structured and ordered approach to the teaching of fractions. It could probably be applied to any mathematics topic.

The approach taken was one of understanding the needs of the child first and having an in depth idea of where her weaknesses were. There was a strong focus on the language of fractions – this relates to some of the findings I wrote about yesterday. Fractions are a relative part of maths and their outcome depends entirely on whatever the whole is.

However, we initially observed Audrey having problems in comparing the equivalent fractions 1/3 and 2/6. We therefore used the fraction-lift to clarify equivalent fractions, by making them fractions living at the same floor of the fraction-building and by introducing the metaphor of “roommates” for fractions at the same position on the number line. We now observed how Audrey used the strategy of doubling both the numerator and the denominator to generate equivalent fractions, for example by replacing 2/3 by 4/6 to compare the latter fraction with 5/6.

This gives Audrey a hook to hang her ideas on, something concrete that she can build her learning on. I’m convinced that children need to have the basics of any topic before moving on. I also think that the current approach we have to teaching in this country, based on the current Mathematics Framework, is far too fleeting and jumpy. As practitioners, I feel we need to consider the needs of our children – group parts of topics together so that they have more time to practise and consolidate their learning.

Link (the full article): Ronald Keijzer and Jan Terwel: Audrey’s Acquisition Of Fractions: A Case Study Into The Learning Of Formal Mathematics.

Spent tonight altering the links listed here. They are all either maths or school related. Hopefully some of them will come in handy! If anyone knows any other pertinent links, feel free to comment and let me know.

March 2018
« Oct    
Blog Catalog