Chapter 4 Number Operations

CHAPTER 4

NUMBER OPERATIONS

By number operations I mean what we can do with numbers in terms of adding, subtracting, multiplying and dividing. You might think that these simple processes are the same the world over, but, guess what? They are not!

In English we have many alternative words for the number operations (Resource: Number Operations-Words). In the case of subtraction and division there are also a number of ways of phrasing the questions, so the numbers are not in a fixed order in the sentence, and learners need to understand the sentence to ensure their answer is correct. For instance ‘Deduct 7 from 19’ is the same sum as ‘What is 19 take away 7?’, but the numbers are reversed in order, which is very confusing for ESOL learners. You might find ‘take away’ causes a few issues too. These sums where numbers cannot be swapped round means the operation is ‘non-commutative’, as opposed to the ‘commutative’ operations, add and multiply, where it does not matter which way round you put the numbers, the outcome or answer will be the same.

In other languages there may only be one way to say a number operation, such as subtract in Italian which translates literally as ‘remove’. Sadly, we don’t use ‘remove’, which is odd when you think about it, as we seem to use everything else. Also in some countries in Asia the word 'into' tells people to multiply, whereas in English it is used for division, so the answer to '5 into 20' for some learners will be 100 and others will be four.

In addition, in the UK we have a number of different methods ourselves, some of which learners may have seen, some not. Currently in UK primary schools there is a belief that being able to use a range of methods depending on circumstances is desirable, so those ESOL learners who have young people coming home from school with homework, and who want to be able to help, or who are hoping to help out in school, will need to see all the options. For instance, if we want to add 2 numbers in our head we might use the partition method, or we might round then add or subtract to get the answer spot on. If we are multiplying we might use a traditional method, or a grid method, or a lattice method. The latter is often very successful for learners who are on the dyslexia spectrum, and can help those learners to succeed where other methods have failed them.

I have found that most ESOL learners use a traditional method that looks the same as ours, but the exception to this is division, which looks different. As a general rule if the method the learner has works, by which I mean the answer is correct, I will not alter it, however bizarre it looks. If the learner wants to work with others then they will need to know the methods used in the UK. If the learner's method is not working then either you need to know what is going wrong, and another learner with the same first language could help here, if both learners are happy with that, or you need to offer alternatives that the learner feels happy with.

Thankfully, with Functional Skills learners can use a calculator in the exam, but if they hope to progress with their maths, say onto a GCSE course, a calculator is not always allowed, so they will still need a working method they can remember and apply.

There are worksheets covering all these options at the back in the appropriate section. The matching activity with the words and symbols for the number operations will usually generate much discussion, and I often start with this, leading into practice with work sheets of examples of the types of sentences learners could come across in real life and the exams. Learners could then practise in pairs with one asking the other the questions, and the second person giving the answer, either in a full sentence, or just the number, depending on their English level. They could then swap over.

Repetition is vital when learning new vocabulary, and using these resources in more than one way in your lessons will save you time and effort that can then be focused on the learners, making sure answers are correct, misconceptions are eradicated and that pronunciation is improving. Learners will have used reading, writing, speaking and listening skills, in line with ESOL Core Curriculum guidelines. This is an example of how much an ESOL maths session will differ from a maths session for native English speakers, and an indication of how important a language perspective is for the teacher.

Rounding and Estimating

Rounding and estimating are both concepts that cause ESOL learners problems. Firstly, round means a shape like a circle, doesn't it? So what is this rounding rule? To estimate an answer we always need to round first, and then work out a rough or approximate answer. Working it out exactly, then rounding the answer will NOT be marked as right! Or should I say correct? These concepts do not appear in all other nations’ maths classes, and many learners are used to the idea that the exact answer is the only one that counts, so rounding and estimating answers can take some practice and are best put into practical scenarios. Shopping is ideal, as most of us will roughly add up the cost of items in a shopping basket whilst waiting in the queue.

Topic based work

Topic based work also exposes the ESOL learners to a potentially unfamiliar culture and language in a covert rather than an overt way, as we might find in an ESOL or a Citizenship class. Allowing learners to use dictionaries is highly recommended, and I will come back to this later, but not everyone will have a bilingual dictionary, and even if they do, where there is more than one definition for a word can lead to much confusion for learners. I have spent some time drawing pictures on the board to explain ‘shelf’, as in what we place objects on (that‘s ok, there is one in the room and I can point to it) versus a flat piece of land under the sea just away from the shoreline. The first definition in a Chinese- English dictionary was the later.

JMS 2013/14