While it is possible to argue that language is a part of every piece of learning, as we think, talk and read the language all the time, it is also possible to consider the role of mathematics across many aspects of learning too. This latter point needs to be teased out a little.
I’d always want to use talk for maths, like talk for writing, with a broad range of appropriate different concrete apparatus. This would allow the learners to develop visual images from which to develop mental structures. I’d allow learners to draw processes throughout their learning, if that enables them to visualise more effectively.
One, to, three, four, five… Once I caught a fish alive
Ten green bottles; one man went to mow; There were ten in the bed..
There is a rich language of number in song and nursery rhyme.
Simply asking how many, or how much embeds a mathematical concept, number or amount, involving perhaps some estimation before more accurate matching, or 1:1 counting. It is possible therefore to utilise mathematical language across the majority of subjects in school and outside, if teachers, parents and children seek out opportunities. It may be an area where parents need some additional support if they are to become partners in progress in maths, either through information booklets or parent evenings, but possibly with carefully structured talking maths homework.
On the 8th November, the #ukedchat was a special on mathematics. An enjoyable hour spent discussing issues surrounding the learning of maths. It was interesting to hear so many teachers saying that they found this more difficult to incorporate in lessons. The whole chat can be viewed here: http://ukedchat.com/2013/11/08/session-176-maths-subject-special/
My own take on this was captured in a series of tweets, which the archive and the infografic allowed me to access for reference.
Teachers should be looking for real life situations within which to explore the maths- emphasise reality of maths.
I have a firm belief that maths is all around us and we carry with us the tools to explore the world mathematically all the time. Everything can be counted; how many cars, lampposts, trees, can you see? Measures can also be counted; how many paces between lampposts? “Which of these leaves is larger?” takes us into comparison, which can be extended by putting a series of items into order by estimated size or weight. The use of body parts, hand spans and thumb widths for example, allows the estimation of size through non-standard measures. Knowing that my hand span is approximately 22cm (9inches) has allowed me to estimate items with more accuracy in the absence of a measure.
A collection of leaves, drawn onto squared paper, allows the number of whole squares to be counted, greater than half to be counted as a whole, if the less than halves are not counted, so giving a close estimate of the area.
Measuring spaces around the school links to counting; for example, how many metres long is the playground? Representation onto squared paper allows discussion of scale.
Even in English, maths can play a part. A prime example would be the excellent 100 word challenge, where learners have to write within a 100 word limit. Haiku work within a specific number of syllables per line. It is possible to explore text to find the most common letters or how frequently some words occur in a text, creating tally charts then using the data for bar charts.
Music has beats in a bar to be counted.
Art has perspective, seeking to show distance, but also uses shape in different ways.
Practical, link to pictorial representation then to more formal diagrammatic then to abstract.
In my opinion based on a long career, learners are too quickly removed from the concrete apparatus which underpins much of their early experience, which has a particular bearing on their understanding as numbers get bigger. A child who can manipulate multilink blocks, bridging through ten to twenty, does not yet have a firm grasp of number sufficient to explore place value. Multibase especially base ten materials, were developed, by Dienes, to illustrate place value concepts through manipulation within functions.
Handling the material, keeping drawn records of actions taken, then introducing diagrammatic forms to simplify allows the teacher insights into the child’s thinking before moving on.
The move to abstract too quickly is the bigger problem, can undermine the teacher’s room to differentiate effectively.
Mathematics becomes “fuzzy” for young learners, and for some adults, when the numbers involved are greater than their mental comfort, or are doing something that they do not understand and cannot picture. The ability to utilise skills from an earlier stage, whether to use concrete materials or to draw should be an active part of all mathematics teaching. This supports thinking.
A quantity surveyor will work from diagrams and architect drawings in order to estimate the quantity of material that will be needed for a particular job. Estimation and working out quantities are essential life skills, with a mathematical base.