Numeracy – Adult Learners
When writing materials for numeracy teaching there are additional concerns to keep in mind.
Numeracy has mathematics as its core. NALA defines numeracy as a lifeskill that gives adults ‘the confidence to manage the mathematical demands of real-life situations’.
The challenge is to identify ’contexts’ that have meaning to the individual student and to identify the mathematics an individual might use in his or her everyday life. The everyday mathematical needs of the majority of the adult population are covered through the following mathematical strands:
- Quantity and number
- Space and shape
- Data handling and chance
- Problem solving
- Patterns and relationships
Remember, as with all areas of learning, numeracy is not value free. Therefore the context of the worksheet or learning material needs to be culturally appropriate and inclusive.
Numeracy: Posing real world problems
The way we pose a particular problem will influence the way that students respond.
Consider these two examples, where the same situation is put in two different ways.
Example 1: Consider how adult learners might respond to the following problem:
‘You have gone out for pizza with two of your friends and you are going to share the cost. Let’s say the pizza cost €18.20. How would you and your friends pay for it?’
There are many real life or ‘real world’ answers to this question. Some people might do an approximate calculation. Some might work it out precisely. Some might make a rough estimate to a convenient current note and get one person to pay the extra. One might say that they would take their turn to pay the full bill, because that is the custom within the group.
The benefit of this way of posing the problem is that it allows students to solve relevant problems in a range of ways available to them in their everyday lives.
Example 2: The question could also be posed in the following way:
‘Three friends went out for a pizza and shared the cost equally. The total cost of the pizza was €18.20. How much did each person pay?’
This question is not a real life problem but a mathematical problem. Adults often recognise these problems as ‘school mathematics’ and respond accordingly, by providing an exact answer. Some adult learners are interested in this mathematics and want to master it. Others will want to avoid ‘school mathematics’ altogether and focus on the ‘real world’ mathematics such as that in Example 1 above. Tutors need to develop materials to suit both types of learner.
Be clear about the focus of the numeracy worksheet
Tutors also need to be clear about what they are asking the students to do and what the focus and learning objective of the worksheet is.
For example, a worksheet might ask the student to do the following:
3 + 4 =
In this activity you are asking the student to add 3 and 4. The focus is on giving practice in the skill of addition (not on how well the learner can write the numbers, for example). So it might help if the worksheet included the numbers 0 – 9. That will help the student to form the shape of the number – in this case, 7. They will still have to do the calculation and select the correct answer, but are freed from the pressure of remembering how they should write the number 7.
Remember that the way addition, subtraction or multiplication problems are written does not necessarily have to follow the ‘school’ approach. Use a variety of ways of asking these problems and encourage learners to format the problem in a way that they prefer. For example, there are different ways to format, or lay out, the following calculation:
“A cup of coffee costs me €2. I buy a cup of coffee 4 times a week. How much do I spend every week on coffee?”
We could format this as: 2 + 2 + 2 + 2 = 8
Or we could format it as: 2 x 4 = 8
Design materials that use a range of formats and help students to become familiar with them.
Visuals and graphics in numeracy materials
Using graphics and visuals is an excellent way of building numeracy skills, especially number sense. The use of photographs, for example, could be a starting point for students talking about and building such skills. Questions such as “how big is the building?” or “how many people are in the photograph?” encourage learners to use their own strategies for working out an answer. Simple pictures – for instance, tomatoes on a vine or children in a playground – can be used as a starting point for developing number skills. Visuals are not value free; they need to be inclusive and culturally appropriate.
Conventions for writing numeracy materials
Group individual digits in three’s from the right.
Insert a comma to separate each group.
Four Digit numbers 2,345
Four or more digits 20,999
Units and Symbols
When a symbol is being used for the first time include it in brackets after the full word. For example, “The road was 10 metres (m) long”. After that, use just the symbol.
Glossary of mathematical symbols
square metres: m2
cubic metres: m3
The correct spelling for metre is ‘metre’ (not meter)
The correct spelling for gram is ‘gram’ (not gramme)
Numeracy and ESOL
It’s important to ensure there is a shared understanding of the meaning of words and symbols used in numeracy.
Mathematical concepts are common to many languages and cultures, but they are learned and expressed through particular languages. For example, whereas ‘3 + 3 = 6’ may be widely understood, the English expression ‘three plus three equals six’ is not. Many words used in maths are borrowed from everyday language. These words tend to be ambiguous: they have one meaning in mathematics and another meaning in everyday language. Examples include the words ‘mean’, ‘natural’, ‘power’, ‘difference’ and ‘take away’.
- Different countries have different conventions for writing mathematics. There are conventions around the way we use symbols. For example, in Ireland the sum ‘seven multiplied by four’ is symbolised as 7 x 4. In other countries the same sum would be written as 7.4.
- The same or similar words may have different meanings in different countries. For example, the American ‘ton’ weight is a different unit of measurement to the European ‘metric tonne’.
- Languages also differ in how they write numbers greater than a thousand and in how they write decimals. The number ‘twenty thousand five hundred and sixty’ would be written as 20,560 in Ireland but as 20.560 in most non-English speaking countries.
- Although in Ireland ‘nine point four’ is written as 9.4, in many countries the decimal point is replaced by a comma: 9,4.
- Another common difference is the method of writing long division. For example, if 14 people are sharing a restaurant bill of €62.60 equally there are a number of ways to write the division: