TEACHING INCORRECT MATHEMATICAL META-LANGUAGE
Among the many awesome and accurate maths resources, there are some that makes us say ‘nooo!!!’, and teaching students incorrect mathematical metalanguage is one of them!
One that is oft repeated is calling three-dimensional objects, ‘shapes’. A shape by definition has 2 dimensions.
The 3 dimensions are left to right, front to back, up and down.
Another that we’ve come across is calling one of the vertices on a pyramid, an apex. An apex is simply the highest point on an object. If the pyramid is not standing on its base, it no longer has an apex.
The point where sides meet are vertices (singular = vertex), regardless of the number of sides that meet there.
In an interesting exchange, a provider of maths resources defended the two mathematical inaccuracies, saying that, in many Maths books the language is widely-used and highly acceptable.
We argue that widely-used and highly acceptable does not equal correct! Indeed many maths textbooks are just plain wrong.
Why teach students correct grammatical terms (nouns, verbs, adjectives), then teach the same students incorrect mathematical terms? Is it because we were also not taught correct mathematical terms, and so think they are somehow too difficult for a student to develop as metalanguage?
On posters available on some pay resource sites, we’ve seen shapes described as having ‘straight sides’.
Again, sides, by definition are straight! If a line on a shape is not straight, it is just a curved line!
Unfortunately, these are just a few examples.
Current learning research emphasises the importance of using correct mathematical metalanguage to explain understanding. As William L Schaaf observed, ‘Maths is a linguistic activity; its ultimate area is preciseness of communication’.
With number talks currently experiencing great popularity, it is vital that teachers and students alike, ensure they are using mathematical language precisely.