CHAPTER 7
LOCATION, SHAPE AND COMPARISON
ESOL learners will need to know about prepositions, or what I call locating words or positional language, if they are going to pass a Maths assessment even at the lowest Entry 1 level. Unfortunately, whilst prepositions are vital in English, they are not universally used. Those short and insignificant-looking words like in, by, with, next to, under, on and near, to name but a few, may make the difference between pass and fail in the exam, understanding or confusion in real life. As a Maths teacher coming into ESOL teaching I was totally unprepared for the necessity and importance of understanding these small words for my learners. I had never had to do more than visit this vocabulary with native English speakers, to check that we were using the same definitions.
All levels of ESOL learners will also need to work on comparatives and superlatives in their maths lessons, as they are used so often in our work, and crop up from Entry 1 on the exam papers. English is not consistent in its use of these, for instance I can say ‘big, bigger, biggest’, but I do not say ‘good, gooder, goodest’. Still, that probably won’t have come as a surprise by this time!
We also have rules which are a bit more than guidance about the word order for descriptions in sentences, which is size, shape, then colour, as in the small, round, blue ball. Native English speakers will know these rules and apply them implicitly; ESOL learners will not unless they have the same rule in their first language. Bear in mind that you cannot ask an ESOL learner, as you would a native speaker, if something sounds right, or which of two options sounds better, because it is unlikely they will know.
Common mistakes include using ‘more’ or ‘less’ instead of comparatives, such as ‘this car is more big than this one’, especially for lower level language students. Maths classes provide opportunities for consolidating work on the simple present tense, and the difference between singular and plural nouns.
Matching activities and missing words out of sentences are both great ways to get learners going with comparatives and superlatives. I find the best way to start is with kinaesthetic activities including the learners themselves- who is the tallest, who is the shortest, the oldest, the youngest? Then you can put someone in the middle and you have tall, taller, tallest etc. Of course we do not always use the same words for objects as we do for people, so we talk of the height of a mountain or a cupboard, the depth of a swimming pool or the sea, and the length of animals that walk on four or more feet.
The same principles and activities apply when teaching the names of 2D (two dimensional, flat, have length and width) and 3D (three dimensional; have length, width and depth or height) shapes. Again this is a topic that, in most native speakers’ classes, you could move swiftly through as a recap session, as they will be very bored if you do not. However for ESOL learners some words may be the same, such as ‘oval’, which is the same in Bulgarian as it is in English, but most will be new to them, and it will need a full session and visiting the vocabulary in a number of different ways to help consolidate the new words. If you revisit the topic some months later you may be surprised at how much they have forgotten; I always am!
It will be necessary to teach how the words change depending on the context, for instance, long goes to length, wide goes to width, high changes to height and deep changes to depth.
In my classes I use the same resources for perimeter, area and volume as I would for native English speakers, and the same types of activities, such as measure up the room for carpet and tracking rod, but I deal with new vocabulary first on the board and that will have to include tracking rod along with Maths concepts such as perimeter.
In Functional Skills exams at Level 1 and 2 there are many drawing activities, including scale drawings. Redesigning the class room after installing new carpet is a great way to do this. It will be even more like the FS exam if you can bring in a selection of prices for carpets from two suppliers, with different fitting costs, and they have to work out the better option, which is likely to be cheaper. Sometimes the width of the carpet is also a factor. In Functional Skills tests, as in real life, there may not be one correct answer and, providing learners can justify their choice, marks for correct follow through are given.
Symmetry, reflection and tessellation are in the Adult Core Curriculum, but do not seem to be appearing in exams yet. These topics are very important for the GCSE however, so you may want to cover them anyway so learners who are progressing are better prepared.
JMS 2013/14