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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