The Language of Maths Stuart de Boer Teacher

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 25 p each and a bar of chocolate at 35 p. 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 style Undeveloped 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 Maths READING equation cylindrical denominator integer approximately evaluate percentage circumference isosceles symmetrical parallelogram perpendicular spherical consecutive millimetre millilitre congruent quadrilateral

The JARGON of Maths difference irregular axes (chop) origin left angles ? prime place value second hand (on a clock) angles and angels multiples LCM factors HCF third even/odd times sums evaluate

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 Language I 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 50 p and find 10 p how much have I got now ? A plant is 7 cm 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 2 s (or five twos) • 5 groups of 2 (or 2 groups of 5)

Hidden Multiplication Language • How much for 30 litres of petrol at 85 p 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 3 3 divided into 12 How many 3’s in 12 How many groups of 3 in 12 Split 12 into 3 Share 12 by 3 Share 3 into 12 Group 12 into 3’s How 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

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The Language of Maths

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The Language of Maths

The Language of Maths 346, 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

Associated Problems Numbers and Words Logical order 4 Illogical order four 14 fourteen 24 twenty four

Associated Problems Place Value Appreciation • MCMLXXIX 1979 • MMMCDLVI 3456 • CDXLVIII 448

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 Maths Algebra x+3=7 [ ]+3=7 3 x + 5 Three times plus five 2(x + 4) = 14 cf 2 x + 4 = 14

Help with Algebra x+3=7

Help with Algebra 2 x + 4 = 14

Help with Algebra 2(x + 4) = 14

Help with Algebra Squares X 2

Help with Algebra Cubes X 3

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) Minutes Hours Days Weeks (+ fortnights) Months Years Decades Centuries Millennia

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 Millimetres (mm) How far Centimetres (cm) How big Metres (m) Length Kilometres (km) Distance Miles (m) Height Along Width Span (of hand or bridge) End to end

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

The Language of Measurement - Capacity • Volume • How much • Amount of Space Millilitres (ml) Cubic Centimetres (cc or cm 3) Centilitres (cl) Litres (l) Pints Gallons

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) Minutes Hours Days Weeks (+ fortnights) Months Years Decades Centuries Millennia

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