Numeracy skills

What is numeracy?

Numeracy is essential to an individual’s ability to learn and to engage productively in society. Numeracy doesn’t necessarily mean complex skills, like different calculations or algebra, it rather means to be confident enough to use basic math/numeracy in daily life situations. Numeracy and literacy go hand in hand, and both are equally important for coping in an increasingly complex society.

Why is numeracy important?

Andreas Schleicher is Director for Education and Skills, and Special Advisor on Education Policy to the Secretary-General at the Organisation for Economic Co-operation and Development (OECD) in Paris. He formulates the importance of numeracy as below:

“A high level of numeracy is the best protection against unemployment, low wages and poor health.”

We use math and numeracy in many different areas in daily situations. When you go shopping you need to know how much to pay, receive exchange, discounts, special offers like “take three and only pay two” etc. Public transport requires that you can read a timetable. How many minutes are left before the bus leaves? It also entails that you know the digital time. If you are sick you need to measure medicine doses and maybe manage diet or nutrition. Furthermore, understanding statistics and graphs when you watch the news and comprehending information about government spending are important too. When it comes to manage our finances, it is crucial to understand how to define and maintain a budget. How does interest work when you borrow many from the bank or handle your savings? In the kitchen we use numeracy when making dinner or baking cakes from a recipe. How much is 1 deciliter, a teaspoon, 100 grams?

Basic skills in numeracy contribute to our ability to make sense of the world around us and to be able to act in it and influence it, and they therefore form part of what we can call a person’s democratic competence. 

PIAAC – Survey of Adult Skills

In this context, the Survey of Adult Skills (PIAAC) assesses the knowledge of adults from the age of 16 to 65 years in literacy, numeracy and problem-solving in technology-rich environments. Skills that are relevant and important to adults in their daily lives and everyday situations and essential for full integration and participation in the society. 

The table below shows the mean proficiency score of 16–65-year-olds regarding numeracy and literacy results of the PIAAC survey:

OECD countries and economies

Legend

Not significantly different from the average
Significantly above the average
Significantly below the average
Australia 280 268
Austria 269 275
Canada 273 265
Chile 220 206
Czech Republic 274 276
Denmark 271 278
England (UK) 273 262
Estonia 276 273
Finland 288 282
Flanders (Belgium) 275 280
France 262 254
Germany 270 272
Greece 254 252
Hungary 264 272
Ireland 267 256
Israel 255 251
Italy 250 247
Japan 296 288
Korea 273 263
Lithuania 267 267
OECD Average 266 262
Mexico 222 210
Netherlands 284 280
New Zealand 281 271
Northern Ireland (UK) 269 259
Norway 278 278
Poland 267 260
Slovak Republic 274 276
Slovenia 256 258
Spain 252 246
Sweden 279 279
Turkey 227 219
United States 2012/2014 272 257
United States 2017 271 255
Cyprus¹ 269 265
Ecuador 196 185
Kazakhstan 249 247
Peru 196 178
Russian Federation² 275 270
Singapore 258 257

A couple of observations on the PIAAC survey results:

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In many countries native born adults tend to score higher than adults born in another country.

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Immigrants who have lived in their new country longer than 5 years score better than recent immigrants.

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The level of knowledge is closely related to labor market outcomes (employment, wages).

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The survey has been conducted in the language of each participating country, which means that good knowledge of that language will be crucial to pass the exercises and it may no be fair to compare the results of the immigrants with native speakers.

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Some low scores among migrants indicate linguistic problems rather than a lack of knowledge of numeracy.

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The lower the level of education, the lower the score.

Numeracy in relation to culture and language

Mathematics is often seen as a science that is not influenced by culture or language; one which only has to do with numbers and formulas. In the Ethnomatic mathematical perspective, the focus is on making use of the individual’s own frame of reference and experience. In this context, mathematics is not seen as a universal science, but as a cultural product. Different cultures have developed different tools to handle the activities that fall within mathematics and numeracy, such as different kinds of measurement systems, different number systems, different ways of performing calculations and developing a terminology that is consistent with words and expressions in someone’s culture. Critiques regarding this approach refer to individuals in risk of being marginalized, hence not being put in the conditions to develop mathematical knowledge needed today and for further studies. Others believe that cultural mathematics / numeracy and the informal skills of individuals are a good basis to better understand mathematical concepts and apply and formulate them with more ease.

Different languages have unique ways of expressing mathematical terms. The difficulty for individuals may lie in the fact that, even though they recognize different terms regarding numeracy/mathematics in their own language, it is not certain that they will understand them in a new language. There are words and concepts that create difficulties when they are translated into a new language and therefore it is better to focus on the mathematical properties of a concept instead of focusing on the name of the concept. The focus should not be put onto specific names of concepts, which might confuse non-native speakers. Instead, the focus should be on the properties of an object, e.g., a square, which has four corners, four sides, angles etcetera[1]

[1] https://www.skolverket.se/publikationsserier/ovrigt-material/2021/nyanlanda-vuxnas-numeracitet

 

Example of how to work with numeracy with adult learners

 

Adult learners might lack basic knowledge in numeracy, for example regarding quantity, number, parts of or half of etcetera. By working with practical elements individuals can develop an understanding and get a sense of what different concepts mean. It is important to relate to everyday situations where the individual recognizes themselves and can relate to the subject. By making numeracy more practical, individuals’ perceptions of how useful mathematics are increases. However, it is also important to highlight the need for calculations and modeling that presupposes knowledge in mathematics.[1]

The pictures below show how we can easily work with everyday things and visualize to increase the understanding of numeracy:

[1] https://www.skolverket.se/publikationsserier/ovrigt-material/2021/nyanlanda-vuxnas-numeracitet

 

 

Measuring tape

Dice

Liter measure

Yarn

Money

DL-measure

Button

Teaspoon

Pot/Casserole

House

Thermometer

Example of how to use the items:

Dl-measure, liter-measure, pot

  • Let the individuals translate a recipe, discuss how they used to bake/cook in their own countries. What kind of measurements did they use?
  • How much is a deciliter? How many deciliters fill in a liter measure? How many liters fill in a pot?
  • If the recipe says two eggs, how many eggs do you need if you double or cut the recipe in half?
  • How much is a teaspoon? How many teaspoons fit in a deciliter?

Dice

  • How many sides has some dice?
  • What shape does the dice have? (Discuss different geometric figures)
  • What is the total sum of all the numbers on the dice?
  • Having a sheet with numbers in front of them, each individual rolls the dice, says the name of the number and points to the correct number on the sheet.
  • Summarize different sides of the dice

House

  • How many rooms does your accommodation have and how many people live there?
  • What shape do the rooms have?
  • If half the people move, how many will stay?
  • How many windows does your home have and what shape do they have?
  • In this moment it is also possible to include everyday finances. How much do you pay in rent, monthly costs for water, insurance and electricity etcetera.?

Yarn and measuring tape

  • Use the yarn to measure the length of a person. Cut the yarn and measure with the measuring tape.
  • How many centimeters is the yarn? How many centimeters does it take in one meter?
  • Compare the length of different individuals? Who is the tallest? Shortest? How much is the difference?
  • Cut the yarn in half and discuss the meaning of whole and half.

Buttons

  • Working with buttons provides opportunities to discuss and visualize quantity.
  • It also provides opportunities to sort and categorize objects.
  • Give the individuals a set of buttons and ask them to categorize by colour and then by the number of holes in the buttons.
  • How many buttons of each colour do they have? How many with two holes? How many together?
  • Put all the buttons together. How many are there now? Divide the number of buttons into two equal piles. How many are in each?

Money

  • Working with money provides unlimited opportunities. It is possible to make different kinds of role-plays where the individual can practice handling money. Calculate how much he / she should pay or give back.
  • How much money is it?
  • What is the name of the currency in your country?

Thermometer

  • Practice important concepts such as plus and minus
  • What is the difference between plus and minus degrees?
  • How many degrees does it differ a hot and a cold day?

Working with practical examples for numeric tasks offers endless possibilities. It is only the imagination that sets the limits. Individuals who have no previous knowledge of numeracy can be helped by practical elements that lay the foundation for developing more complex knowledge in numeracy/mathematics. It is important to take advantage of the individual’s previous experiences of numeracy and connect to real situations to increase interest and make them understand the importance of knowledge in numeracy to cope with their everyday life in their new country.

Best practise example – Basic mathematics with language helpers

Why language helpers?

This example is taken from the National Agency for Education in Sweden, which refers to a project with language helpers that has been implemented with great success in Norway (Kompetanse Norge, 2018).

Adult migrants with a short school background bring with them experiences and knowledge from their home culture. Despite our differences, we can find common denominators such as counting, locating, that measuring, designing, playing, and explaining. A language helper in basic mathematics/numeracy can contribute to gaining insight into the participants’ mathematical/numeracy resources in these areas. This can thus contribute to building bridges between mathematics in different cultures. Knowledge and experience that the adult migrant carries with them are closely linked to the mother tongue. If the individual is given the opportunity to use their mother tongue, it makes it easier to be able to absorb new knowledge in the second language. If you have learned what a concept means in the first language, it may be easier to learn the concept that has the same or similar meaning in the second language. A language helper can point out similarities and differences between the languages, which will give an increased awareness and improved development of second language skills.

Who can be a language helper?

Individuals who have:

  • The same mother tongue as the current participants,
  • Come further in second language development,
  • A longer school background or
  • Slightly higher mathematical/numeracy competence than the current participants.

Other important criteria and elements are:

  • that they are motivated to be a language helper,
  • that they have proven to be a diligent participant with low absenteeism,
  • that the helper in exchange will of opportunities to increase their competence in both the second language and mathematics as well,
  • that they are culturally accepted by the relevant participants,
  • that they, whenever possible, have a variety of words to explain in participants’ native language.

The language helper must receive information about:

  • The reasons why they are language helpers as well as
  • What the language helpers’ role is about.

The language helpers must also receive teaching and guidance before each session with the other participants. It is very important that the language helper is aware of their role. They will assist

participants in the group, encourage them and act as a bridge and an interpreter where it is necessary, but they should not “take over” the work and do the tasks themselves so that the others participants become passive and hindered in their learning and development.

The guidance sessions can begin with conversations about experiences from the previous session of basic mathematic/numeracy. The language helpers can talk about situations that arose and respond to them stating what worked well or less for the participants. They can also provide important information about the participants’ cultural experiences and knowledge within a given theme, which can be a starting point for further teaching.

The following points are examples of what could be discussed at the guidance meetings with the language helpers:

  • Experiences from the last session with the participants,
  • Introduction of the next session’s theme,
  • Conversations about the language helpers’ experiences and knowledge in relation to the theme, from the home country and the new country.,
  • Additional teaching in the subject if needed,
  • Prepare and practice activities and tasks to be done together with the participants in the basic mathematics/numeracy group, and make the language helper aware of their role,
  • Specify what the language helper should practice before the next session with the large group.

The learning objectives for the project was taken from Forsøkslæreplan for språklige minoriteter – grunnmodul for forberedende voksenopplæring (FVO), kap. 4.2.4. Förståelse av tal och matematiska begrepp (Kompetanse Norge, 2017).

The learning objectives for the participants are to be able to:

  • count and use some mathematical concepts in the mother tongue and in the second language,
  • talk about different ways of counting that the participants are experienced in,
  • easily tell about your own experiences of using mathematic/numeracy in everyday life,
  • use the mathematical concepts greater than / less than, before / after, first / last, before / behind, most/least, equal to as well as plus and minus,
  • understand and show the connection between number symbol and quantity,
  • write, understand and count from zero to hundred,
  • show that you understand the oneties
  • master addition and subtraction up to ten
  • read and understand simple tables – paper-based and digital,
  • be able to use the units’ kilograms, grams, meters, centimetres, litres and decilitres in practical situations,
  • name the geometric shapes rectangle, triangle and circle,
  • use calendar, date, ordinal number and clock in everyday chores,
  • use and check that amounts are correct when buying and selling as well as
  • tell about income, expenses and consumption in a very simple way.

At the beginning of the first session, following questions can be helpful to give a picture of the participants relationship and thoughts about numeracy:

  • What is mathematics/numeracy? What can we use mathematics/numeracy for?
  • Is mathematics/numeracy important? Why? Why not?
  • In what situations did you use mathematics/numeracy in your home country? (Conversation about experiences from home, school and professional life).
  • Have you had math in school?
  • Do you need math/numeracy in your new country? For what?
  • Do you need/want to learn math/numeracy? Why? Why not?

Overview of project outcomes

The professionals experienced that using language helpers in the teaching was a unique opportunity to gain insight into the participants’ cultural experience and knowledge related to numeracy. The teaching became relevant and understandable for the participants. The language helpers were able to counteract misunderstandings, intercept the participants input and help them increase their motivation to learn and become more active.

The language helpers in this project contributed to understanding and learning by acting as a connecting link between the mother tongue and Norwegian, a bridge between the resources the participants bring with them in the form of knowledge and experience and the new knowledge to be acquired and adapted for everyday life in the Norwegian society. They further experienced that they had been a good support to the participants and had motivated them to be more active. Furthermore, they felt that the participants had become much happier and that they wanted to have more sessions and subjects with them. Finally, they also developed their own skills in the second language as well as their skills in numeracy.[1]

[1]https://www.skolverket.se/download/18.2f324c2517825909a162851/1629098214695/Basmatematik-med-sprakhjalpare-200630-2.pdf