The Language of Maths

Stuart de Boer

Teacher

Dyslexia Action

Interrelated Areas in the Learning of Maths

Maths or Literacy ?

You go into a shop with £1. You buy two bags of crisps at 25p each and a bar of chocolate at 35p.

How much change will you get ?

Why does the Dyslexic Student Under-Achieve in

Maths ?Numeracy problems (tables and four operations)Memory (rote learning does not work)Speed (dyslexic student slower)Concentration (usually poorer than peers)Mis-match of learning/teaching styleUndeveloped skills (held back by poor numeracy

skills)Anxiety and self esteem (big problem)Literacy problems

- failure to read and understand the language of maths

Aspects of Maths Language

• READING The ability to read a question correctly (three/there)

• JARGON The ability to understand the specific vocabulary of maths

• SYMBOLS The ability to understand the signs and symbols in maths (with a bit of algebra thrown in for good measure)

The Language of MathsREADING

symmetricalparallelogramperpendicularsphericalconsecutivemillimetremillilitrecongruentquadrilateral

equationcylindricaldenominatorintegerapproximatelyevaluatepercentagecircumferenceisosceles

The JARGON of Maths

angles and angels

multiples LCMfactors HCFthirdeven/oddtimessumsevaluate

differenceirregularaxes (chop chop)originleft angles ?primeplace valuesecond hand (on a

clock)

The Jargon of Addition

• 3 add 4 (or 4 add 3)• 3 + 4 ( or 4 + 3)• What is 4 more than 3? (or 3 more than 4)• What is the total of 3 and 4? (or 4 and 3)• What are 3 and 4 altogether? (or 4 and 3)• What is the sum of 3 and 4? (or 4 and 3)• What is 3 plus 4? (or 4 plus 3)• Increase 3 by 4 (or 4 by 3)

Hidden Addition LanguageI have 4 CDs and buy 3 more how many do I have

now?

There are 6 students in the room and another 2 come in, how many are there now ?

I have 50p and find 10p how much have I got now ?

A plant is 7cm tall and grows 2 cm. How tall is it now ?

In the first leg of a football tie the score was 4 – 3 and in the second leg, 1 – 2. What was the aggregate score ?

The Jargon of Subtraction

• 7 take away 3• What is left if I take 3 from 7 ?• 7 - 3 • What is the difference between 3 and

7 ? (or 7 and 3)• What is 3 less than 7 ?• What is 7 less 3 ?• 7 subtract 3• 7 minus 3 • Decrease 7 by 3

The Jargon of Multiplication

• 5 times 2 (and 2 times 5)• 5 x 2 ( and 2 x 5)• What is the product of 2 and 5 (or 5

and 2)• 2 of 5 (or 5 of 2)• 2 lots of 5 (or 5 lots of 2)• 5 2s (or five twos)• 5 groups of 2 (or 2 groups of 5)

Hidden Multiplication Language

• How much for 30 litres of petrol at 85p per litre ?

• How many bottles in a crate of 12 rows by 8 rows

• How many days in 3 weeks

The Jargon of Division

12 divided by 33 divided into 12How many 3’s in 12How many groups of 3 in 12Split 12 into 3Share 12 by 3Share 3 into 12Group 12 into 3’sHow many times can you subtract 3 from

12

Hidden Division Language• If two pizzas are eaten by eight people,

how much does each person get ?• A box of contains 24 chocolates. How

many each between 3 ?• How many will be in each team if there

are three teams and 18 students ? • How many quarter hour sessions in 3

hours ?• Four friends go for a meal. The total cost

of the meal is £120 – how much each ?

The Language of Maths

• leaves

The Language of Maths

The Language of Maths

The Language of Maths

•

The Language of Maths

The Language of Maths

The Language of Maths

3 4

The Language of Maths

O

The Language of Maths

The Language of Maths

346,000,000

Winston Churchill

Tony Blair

Albert Einstein

Help for Jargon

• Recognition – that there may be a problem

• Card families – to link clue words to meanings/symbols

• Highlight clue words and symbols – to focus mind in right direction

• Question analysis techniques - what operations are required and in what

order • Pictures of Questions – makes multisensory

• Mnemonics – student generated

• Apply Common Sense – is answer sensible ?

Maths Symbols

•

More Maths Symbols

Help for Symbols

• Recognition – that there may be a problem

• Card families – to link symbol to meaning

• Practice at writing – so are clear and distinct from

others

• Mnemonics – preferably student generated

• Personalised dictionary – useful reference and revision aid

Numbers and Words

Illogical order

four

fourteen

twenty four

Logical order

4

14

24

Associated Problems

Associated Problems

1979

3456

448

• MCMLXXIX

• MMMCDLVI

• CDXLVIII

Place Value Appreciation

Associated Problems

Orientation and Direction

6 and 9• + and x• Start at left or right ?• Brackets priority (cf. literacy)• 4 + 5 = b !!!!!

The Language of MathsAlgebra

x + 3 = 7

[ ] + 3 = 7

3x + 5

Three times plus five

2(x + 4) = 14 cf 2x + 4 = 14

Help with Algebrax + 3 = 7

Help with Algebra2x + 4 = 14

Help with Algebra2(x + 4) = 14

Help with Algebra

Squares X2

Help with AlgebraCubes X3

Help Summary• Recognition of reading, jargon, symbols

problems• Need for specific literacy help ?• Reader for exams• Card families

• Question analysis techniques

• Mnemonics

• Apply common sense to answers

• Symbol (and number) writing practice

• Personalised dictionary

• Some concrete assistance

And Lastly ………

Just how badly can maths be misunderstood ?

If you are of a nervous disposition please look away now …..

Thank you

for listening

The Language of Measurement - Time

How long ?When ?What time is it ?Seconds (and

sub-divisions)MinutesHours

DaysWeeks (+ fortnights)MonthsYearsDecadesCenturiesMillennia

Intuitive Time• Just a minute• Just a moment, half a sec, two ticks• Half a sec• Half an hour• Eastenders• Typical film• Weeks, months, years

The Language of Measurement - Length

• How long• How far• How big• Length• Distance• Height• Along• Width• Span (of hand or bridge)• End to end

Millimetres (mm)Centimetres (cm)Metres (m)Kilometres (km)Miles (m)

Intuitive Length

• Foot• Stride• Sports distances e.g. 100metres• Football pitch• Distances to familiar places

The Language of Measurement - Capacity

• Volume• How

much• Amount

of Space

Millilitres (ml)Cubic Centimetres

(cc or cm3)Centilitres (cl)Litres (l)PintsGallons

Intuitive Capacity

• Drinks cans/bottles• Cup/mug/beer mug/wine glass• Bottles of wine• Petrol tank• Car engines (note cc/ml confusion)

The Language of Measurement - Time

How long ?When ?What time is it ?Seconds (and

sub-divisions)MinutesHours

DaysWeeks (+ fortnights)MonthsYearsDecadesCenturiesMillennia

The Language of Measurement - Weight

• How heavy• Mass• Load

Grams (g or gm)Kilogrammes (kg)Tonnes (t)

Ounces (oz)Pounds (lb)Stones

Intuitive Weight

• Yourself• Feathers/lead• Postage• Cooking/food• Gymnasium• Brick

Other Measurements

Area

Pressure

Temperature

Humidity

Just number e.g shoe sizes