Numeracy Related Activities

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Number, Measures, Shape and Space, Handling Data

Language of Maths and enabling strategies

Description of Numeracy Related Activities

Numeracy covers the ability to:

understand and use mathematical information;
calculate and manipulate mathematical information;
interpret results and communicate mathematical information.

Numeracy is a proficiency which is developed mainly in mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data is gathered by counting and measuring, and presented in graphs, diagrams, charts and tables.

Skills required for numeracy:

Problem solving;
Observation;
Attention to detail.

Numeracy and Vocational Education and Training (VET)

It is recognised that good numeracy skills are critical, not just to the achievement of vocational and academic qualifications, but also to efficient performance in the workplace and in personal and social life.

Examples of numeracy within VET:

Understanding of proportion: for example, when mixing hair dye or cement;
Cash handling;
Following technical drawings.

Skills required for Numeracy

Numeracy involves a wide range of specific abilities, any of which may prove difficult for particular learners and can affect their acquisition of skills. Some of the underlying knowledge and skills involved include the following:

giving digits/numbers meaning;
understanding number concepts and relationship between numbers;
interpreting mathematical information;
short-term memory and ability to memorise;
visual perceptual skills;
ability to perceive and predict patterns;
spatial and measurement skills;
ability to sequence and organise;
ability to reason and think logically;
ability to calculate;
ability to perceive and remember direction;
language skills;
handwriting/motor skills;
ability to decode an algorithm or numerical task from a complex problem;
ability to relate/choose actions appropriate to purpose (problem solving);
ability to abstract from the concrete;
ability to categorise and hence identify relationship.

Numeracy can be subdivided into related categories based on size, shape, space and quantity. Learners' difficulties might be limited to a specific area of knowledge or skill.

Number, Measures, Shape and Space, Handling Data

The adult numeracy core curriculum in the UK follows a model based on the National Curriculum for mathematics:

number includes numbers and the number system, and calculations;
measures, shape and space includes common measures of money, time, temperature, distance, length, weight, capacity, perimeter, area and volume, and shape and position;
handling data includes data and statistical measures, and probability.

Learners need to develop skills, knowledge and understanding in each of these areas of mathematics. An understanding of numbers and the relationships between them, and an ability to manipulate numbers efficiently and confidently, is critical for success in other areas of the curriculum. For example, a learner might be able to understand the concept of area and how it is calculated, but success in solving area problems also requires the ability to multiply numbers efficiently; similarly, the ability to solve problems with money and metric measures requires the ability to manipulate decimal numbers. However, this does not mean that skills must be taught sequentially. Learners' previous knowledge and experience can be drawn upon to develop new skills and understanding; for example, familiarity with money written in decimal notation can form the basis for understanding decimal numbers, which can then be applied in other areas of the curriculum.

Language of maths

Many learners will have problems with the language of maths rather than with mathematical processes. There are many words for each operation in numeracy. These are often everyday words that are used much more precisely in maths, e.g. difference, share, product.

The use of several words for one operation may also affect the order of the calculation, for instance '15 take away 2' is the same as '2 from 15'. These can cause problems for learners with sequencing or directional difficulties, as well as those with difficulties manipulating language or dealing with multiple meanings.

When doing a word problem, learners may become confused because of the vocabulary, sentence structure or sequence in which the problem is presented. It is important to identify whether learners are having difficulty with the maths or the language, and to make issues in the language of maths explicit to learners.

Many learners are likely to need constant repetition and revision of past learning. This is particularly important in terms of language and mental operations. The language of mathematics and the ability to calculate mentally are fundamental. Learners with only basic skills often lack, or have inadequate, language and mental strategies which have contributed to their 'failure' with formal, standard methods of representing calculations. These difficulties are increased for learners with learning difficulties and disabilities.

Concrete materials are important for all learners but doubly so for learners experiencing difficulties. Mathematics involves concepts; these cannot be assimilated without actual experience.

Enabling Strategies

Learners need practice and help to acquire basic concepts before being able to transfer learning to new situations.
Learners will have to be shown how to interpret the language of maths, which often appears ambiguous and confusing.
Compensation strategies have to be implemented to help memorise and recall basic facts. Number squares, number lines and calculators may prove useful to compensate. The use of pencil and paper is also helpful.
Use squared paper to help organisation and place value accuracy.
Discuss the whole context/situation of a problem, so that learners can make sense of it over and above the number crunching required. Wherever possible, use real, relevant and familiar contexts.
Show different ways of doing operations or solving problems - allow learners to choose the method they prefer.
Develop and use a range of memory aids and ready references (e.g. a ruler is a good number sequence aid; a personal maths chart can be used to keep track of alternative words for operations, maths facts, etc).
Explain terms, symbols and operations each time they are used and encourage learners to explain to themselves, for example, by subvocalising the steps of adding a two-digit number. This will help learners to hold information in memory and also help with the diagnosis of errors and misconceptions.
Use concrete examples to illustrate the variety of ways in which number operations can be written and what they mean in each case (e.g. 6 + 4 is the same as 4 + 6, but 7 - 2 is not the same as 2 - 7).
Make as much use as possible of colour, objects, sound and rhythm, movement and large maths props and illustrations (flipchart paper rather than A4), to engage all the senses in maths learning.

Assessment

Remember that people with the same impairments may need different adjustments to practice to enable them to engage with the assessment process and demonstrate their learning.

When assessing your learners, be very clear about exactly what it is you are testing. For example, in asking learners to write an essay in an exam, are you testing the learners’ knowledge and understanding of the topic, or the ability to write clearly and precisely? Decide what you are assessing and how many marks are apportioned for each element (knowledge or good writing, memory or understanding)

Consider why you are assessing in a particular way, and whether another method may be more inclusive. In some cases, the exact format of the assessment is critical to the demonstration of the intended learning outcome. For example a course in hairdressing would require a practical demonstration of competence; but, where possible, allow your learners to have a choice about how they demonstrate their knowledge and skills; in other words allow them to demonstrate their knowledge and skill in a variety of formats.

There may be occasions where you have provided the disabled learner with an alternative assessment (e.g. a blind learner may need to give their answers orally rather than in writing). In such cases, you should ensure the integrity of the alternative and make sure that the disabled learner is judged on their ability to meet the criteria – providing neither a disadvantage nor advantage over other learners.

Adaptations for Assessment

Some students may rely on equipment to meet the needs of the assessment, whether in a formal examination environment, or the less formal setting in which assignments are prepared for continuous assessment.
Consider how much time will be needed for completing assignments.
Some disabled learners will need extra time to complete their assessments.
Some disabled learners who are working in a group may need extra time to complete the assignment.
Can work be dictated onto tape or can the student give an oral presentation instead?
Will the learner require an assistant or a scribe?
Students with visual difficulties may require examination papers in formats such as Braille, tape or enlarged print.
The questions and/or titles of the assignment may need to be provided on disk.
A tape recorder, computer, scribe or assistant, may be needed to enable a a disabled learner to complete their assignment.
Be clear about the role and involvement of equipment or an assistant; ensure that the student maintains control and is fully responsible for producing their assignments.

Click here for Adjustments for Assessments taken under Examination Conditions

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