Thursday, September 29, 2011

Context or Con: How might we better represent real-world in the classroom?

Ward-Penny, R. (2010). Context or con: how might we better represent real-world in the classroom. Mathematics in School, 29(1), 10-12.

First, this article makes an important distinction about the strength of a real-world connection. There are many problems disguising themselves as real-world that, in fact, are rather useless in our everyday lives. Take, for example, the following problem:

"A piece of wood measures 40cm by 104m. Work out the area of the wood in square metres."

"This question is a pseudo-context - the real-world elements have no bearing on or relevance to the problem. The wood could quite happily have been replaced by a piece of card, or a strip of turf; furthermore, the answer itself has no use that is made obvious to or could be imagined by the pupil. In terms of the pupils' understanding and development, there is no difference between this question and a simple 'work out the area of this rectangle' question." (10)

Second, the author identifies the importance of meaningful context and offers the reader a framework for identifying it. Context, he argues, must fit in one of the following categories: consolidation, motivation, or exploration. " A context consolidates if it gets the pupil to practice a previously learnt skill or technique. It motivates if it encourages the pupil to see the relevance and usefulness of the topic. If it requires pupils to problem solve or link a skill to other areas of maths, it can be said to involve exploration. These three areas are not mutually exclusive. In fact, we can say that a context is 'weak' if it only invokes one of these three headings, whereas a 'strong' context involves two or more areas." (11)

Lastly, the author gives examples of how to increase the 'strength' of a context through the use of various problems. Mostly, this seems to involve investing students in the problem by including them in its formation (i.e. pick an item from a catalogue and calculate the manufacturer's purchase price) or by using a more realistic context (i.e. using actual items and sales tax figures versus made up ones).


There were no citations in this article and no mention of research done in the field. The tone would indicate that the author has personal experience and success in working with this model but there is no data or explicit mention of that.


I was really intrigued by the main ideas in the first half of this article. I have heard of the term 'pseudo-context' before and I love that people are exploring the authenticity of real-world connection in mathematics. I was also intrigued by his trio of context strengths: consolidation, motivation, and exploration. He included all three in a sort of venn diagram. I would be interested in exploring this idea more. It seems to me that motivation does not belong here. I suspect that the strength of the context is what increases motivation and not the other way around, as the author suggests. I am also curious if consolidation and exploration are exclusively beneficial in increasing the strength of a context or if it is their overlap (imagine venn diagram) that increases the strength of the context and, therefore, the motivation of the student.

1 comment:

Kali Frederick said...

The notion of authentic context is a challenge for all subjects. I can relate to the intro problem of the piece of wood because I feel like we all try to make some long shot connection even when we ourselves cannot find the connection, the students just need to know it. Which makes me question the importance of the information if we struggle to find the context (unless it's just a super interesting concept or fact). What kind of evidence or data would you have liked provided? Why do you think motivation does not belong in the "trio of context"?

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