The Language of Maths Stuart de Boer Teacher Dyslexia Action.
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Transcript of The Language of Maths Stuart de Boer Teacher Dyslexia Action.
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