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Mathematics and Special Educational Needs. Seán Delaney, Coláiste Mhuire, Marino [email protected] Menu. Problem Tables Games Commutative Property Modes of Representation Language Place Value Assessment and IEPs Reading List. Problem!.

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Presentation Transcript
slide2
Menu
  • Problem
  • Tables
  • Games
  • Commutative Property
  • Modes of Representation
  • Language
  • Place Value
  • Assessment and IEPs
  • Reading List

Seán Delaney, July 5th 2003

problem
Problem!
  • A Census-taker stopped at a house and wanted to find out how many children she had. The lady of the house wanted to see if the Census-taker was good at mathematics.
  • Census-taker to lady: How many children do you have?
  • Lady: Three.
  • Census-taker: How old are they?
  • Lady: the product of their ages is 36 and, coincidentally, all their birthdays occur today.
  • Census-taker: Well, that's just not enough information.
  • Lady: The sum of their ages is our house number.
  • Census-taker looks at the house number thinking this would give it away, but says: Still not enough information!.
  • Lady: My oldest child plays football.
  • Census-taker: OK. Now I know their ages. Thank you!
  • How did the census-taker figure out their ages?

SolutionBack to Menu

Seán Delaney, July 5th 2003

solution
Solution

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Seán Delaney, July 5th 2003

problem back up
Problem (Back-up)
  • Place the numbers 1-8 in the squares on the left so that no two consecutive numbers are next to each other, either vertically, horizontally or diagonally?

Solution

Seán Delaney, July 5th 2003

problem solution back up
Problem Solution (Back up)

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Seán Delaney, July 5th 2003

tables number facts 1
Tables/Number Facts (1)

Learn off the following:

Charlie David lives on George Avenue

Charlie George lives on Albert Zoe Avenue

George Ernie lives on Albert Bruno Avenue

Charlie David works on Albert Bruno Avenue

Charlie George works on Bruno Albert Avenue

George Ernie works on Charlie Ernie Avenue

From Dehaene, Stanislas (1999)

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Seán Delaney, July 5th 2003

tables number facts 2
Tables/Number Facts (2)

3 4 + 7 =

Charlie David lives on George Avenue

3 7 + 1 0 =

Charlie George lives on Albert Zoe Avenue

7 5 + 1 2 =

George Ernie lives on Albert Bruno Avenue

From Dehaene, Stanislas (1999)

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Seán Delaney, July 5th 2003

tables number facts 3
Tables/Number Facts (3)

3 4 x 1 2 =

Charlie David works on Albert Bruno Avenue

3 7 x 2 1 =

Charlie George works on Bruno Albert Avenue

7 5 x 3 5 =

George Ernie works on Charlie Ernie Avenue

From Dehaene, Stanislas (1999)

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Seán Delaney, July 5th 2003

tables numer facts 4
Tables/Numer Facts (4)

Why are tables so difficult to learn?

Because our memories are associative.

E.g. Lunch last Friday

Tables: 7+6 doesn’t help with 7x6

7x6 doesn’t help with 7x5

7x8= 56, 63, 48, 54 never 55, 51 etc.

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Seán Delaney, July 5th 2003

tables number facts 5
Tables/Number Facts (5)

Addition number facts

Relate them to the traditional tables layout or to the addition square

Show children all the facts that they need to learn.

When children learn facts they can delete them.

Begin by teaching the commutative property

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Seán Delaney, July 5th 2003

tables number facts 6
Tables/Number Facts (6)

Continue with other number facts:

  • +0
  • +1
  • +2
  • +10
  • Doubles
  • Near doubles
  • Numbers that make 10
  • Numbers that make 9
  • +5
  • Through 10 facts

Illustration on Addition SquareBack to Menu

Seán Delaney, July 5th 2003

tables number facts 7
Tables/Number Facts (7)

Multiplication Number Facts

  • Commutative Facts
  • x0 (How many coins in 1 empty pocket, 2 empty pockets etc)
  • x1
  • x10
  • x2 (note even number answers)
  • x5 (clock)
  • x4 (twice two)
  • x3 (2 groups + 1 group), x7 (5 groups + 2 groups), x9 (10 groups -1 group; fingers)
  • x3, x6 (5 groups + 1 group)

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Seán Delaney, July 5th 2003

commutative property 1 addition
Commutative Property (1) Addition

3 + 4 = 4 + 3

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3 + 4

4 + 3

Seán Delaney, July 5th 2003

commutative property 2 multiplication
Commutative Property (2) Multiplication

Introduce terms:

  • rows (horizontal)
  • columns (vertical)

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Seán Delaney, July 5th 2003

commutative property 3 multiplication
Commutative Property (3) Multiplication
  • 3 x 6 = 6 x 3

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Back to Tables

Seán Delaney, July 5th 2003

modes of representation
Modes of Representation

Real World Situation

Models

Concrete Pictorial

Mental Language

Mathematical World

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Based on Cathcart et al 2000

Seán Delaney, July 5th 2003

language difficulties
Language Difficulties
  • Specific Vocabulary (denominator, fraction, equivalent)
  • Multiple meanings of symbols (e.g. = means is the same as, equals, makes) and similar symbols (x, x)
  • Words in maths have a specific meaning

(e.g. net, sum, record, prime, line, ‘whole’ number, round a decimal, odd, even, order numbers,)

  • Words that sound similar (e.g. hundreds, hundredths; sixteen, sixty)

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Seán Delaney, July 5th 2003

mathematical games 1 kamii
Mathematical Games (1) - Kamii
  • “Attentiveness during practice is as crucial as time spent.” (Kate Garnett)
  • It is good for the teacher to play the games with the children, without ‘being in charge.’ It allows the teacher to assess the children’s knowledge.
  • Questions to children, can help promote children’s knowledge and give an insight into their development.
  • It is also good for the teacher to circulate and observe the games.

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Seán Delaney, July 5th 2003

mathematical games 2 kamii
Mathematical Games (2)- Kamii
  • Write summary rules on game boxes
  • Modify rules and allow pupils to modify rules
  • Discuss with children why games are used
  • Allow pupils to choose the game and the partner. Keep a log and this rule may need to be modified.
  • Practise:Multiplication Salute and O’NO 99

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Seán Delaney, July 5th 2003

place value 1
Place Value (1)
  • Grouping
  • Equivalent representations
  • Multiplicative and additive principles
  • 0 as a placeholder
  • Number name difficulties (teens: irregular, order and pronunciation)

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Seán Delaney, July 5th 2003

place value 2 10 x 10 array
Place Value (2) 10 x 10 array

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Seán Delaney, July 5th 2003

place value 3 ross s 1999 stages a
Place Value (3) Ross’s (1999) Stages-a
  • Pupils can identify the positional names but do not necessarily know what each digit represents. For example, in 54 a child may say that there are 4 tens and 5 ones.
  • The child knows that digits in a two-digit numeral represent a partitioning of the whole quantity into tens and units and that the number represented is a sum of the parts.
  • Pupils can identify the face value of digits in a numeral such as in 34, the 3 means '3 tens' and the 4 means '4 units'. They might not know that 3 tens means thirty.
  • Pupils associate two digit numerals with the quantity they represent. E.g. 28 means the whole amount.
  • Transitional stage

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Seán Delaney, July 5th 2003

place value 4 ross s 1999 stages b
Place Value (4) Ross’s (1999) Stages-b

2.Pupils can identify the positional names but do not necessarily know what each digit represents. For example, in 54 a child may say that there are 4 tens and 5 ones.

5.The child knows that digits in a two-digit numeral represent a partitioning of the whole quantity into tens and units and that the number represented is a sum of the parts.

3.Pupils can identify the face value of digits in a numeral such as in 34, the 3 means '3 tens' and the 4 means '4 units'. They might not know that 3 tens means thirty.

1.Pupils associate two digit numerals with the quantity they represent. E.g. 28 means the whole amount.

4.Transitional stage

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Seán Delaney, July 5th 2003

assessment and ieps
Assessment and IEPs
  • Standardised tests
  • Read the psychologist’s report on Jane Smyth
  • Identify some of her difficulties relating to mathematics
  • Suggest some possible supports for her
  • Examine the accompanying IEP and suggest improvements

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Seán Delaney, July 5th 2003

further reading
Further Reading
  • Cathcart, George W., Pothier, Yvonne, M., Vance, James H. & Bezuk, Nadine S. (2000) Learning Mathematics in Elem. and Middle Schools NJ: Prentice Hall
  • Chinn, Stephen and Ashcroft, Richard (1999) Mathematics for Dyslexics: A Teaching Handbook London: Whurr Publishers
  • Dehaene, Stanislas (1999) The Number Sense: How the Mind Creates Mathematics London: Penguin
  • NCCA (2003) Mathematics Draft Guidelines for Teachers of Students with Mild General Learning Disabilities (Primary)
  • O'Brien, Harry and Purcell, Greg (1998) The Primary Mathematics Handbook St. Australia: Horwitz Publications Pty Ltd.
  • Vaughn, Sharon, Bos, Candace S. & Schumm, Jeanne Shay Schumm Teaching Exceptional, Diverse, and At-Risk Students in the General Education Classroom (Ch. 14) Boston:Pearson Education
  • http://people.clarityconnect.com/webpages/terri/terri.html
  • http://falcon.jmu.edu/~ramseyil/math.htm#A

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Seán Delaney, July 5th 2003

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