1. Mathematics and Special Educational Needs Seán Delaney, Coláiste Mhuire, Marino Sean.Delaney@mie.ie

2. Seán Delaney, July 5th 2003 Menu  Problem Problem  Tables Tables  Games Games  Commutative Property Commutative Property  Modes of Representation Modes of Representation  Language Language  Place Value Place Value  Assessment and IEPs Assessment and IEPs  Reading List Reading List

3. Seán Delaney, July 5th 2003 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? SolutionSolution Back to MenuBack to Menu

4. Seán Delaney, July 5th 2003 Solution 6, 6, 1 4, 9, 1 2, 18, 1 3, 12, 1 6, 2, 3 4, 3, 3 2, 9, 2 Back to Menu

5. Seán Delaney, July 5th 2003 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

6. Seán Delaney, July 5th 2003 Problem Solution (Back up) Back to Menu

7. Seán Delaney, July 5th 2003 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) Back to Menu

8. Seán Delaney, July 5th 2003 Tables/Number Facts (2) 34+7=34+7= Charlie David lives on George Avenue 37+1 0 = Charlie George lives on Albert Zoe Avenue 75 +1 2 = George Ernie lives on Albert Bruno Avenue From Dehaene, Stanislas (1999) Back to Menu

9. Seán Delaney, July 5th 2003 Tables/Number Facts (3) 34x 1 2 = Charlie David works on Albert Bruno Avenue 37x 2 1 = Charlie George works on Bruno Albert Avenue 75x 3 5 = George Ernie works on Charlie Ernie Avenue From Dehaene, Stanislas (1999) Back to Menu

10. Seán Delaney, July 5th 2003 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. Back to Menu

11. Seán Delaney, July 5th 2003 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 propertycommutative property Back to Menu

12. Seán Delaney, July 5th 2003 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

13. Seán Delaney, July 5th 2003 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) Back to Menu

14. Seán Delaney, July 5th 2003 Commutative Property (1) Addition 3 + 4 = 4 + 3 Back to Menu 3+43+4 4+34+3

15. Seán Delaney, July 5th 2003 Commutative Property (2) Multiplication Introduce terms: rows (horizontal) columns (vertical) Back to Menu

16. Seán Delaney, July 5th 2003 Commutative Property (3) Multiplication  3 x 6 = 6 x 3 Back to Menu Back to Tables

17. Seán Delaney, July 5th 2003 Modes of Representation Real World Situation Mathematical World Models Concrete Pictorial MentalLanguage Back to Menu Based on Cathcart et al 2000

18. Seán Delaney, July 5th 2003 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) Back to Menu

19. Seán Delaney, July 5th 2003 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. Back to Menu

20. Seán Delaney, July 5th 2003 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 Back to Menu

21. Seán Delaney, July 5th 2003 Place Value (1)  Grouping  Equivalent representations  Multiplicative and additive principles  0 as a placeholder  Number name difficulties (teens: irregular, order and pronunciation) Back to Menu

22. Seán Delaney, July 5th 2003 Place Value (2) 10 x 10 array Back to Menu

23. Seán Delaney, July 5th 2003 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 Back to Menu

24. Seán Delaney, July 5th 2003 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 Back to Menu

25. Seán Delaney, July 5th 2003 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 Back to Menu

26. Seán Delaney, July 5th 2003 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://people.clarityconnect.com/webpages/terri/terri.html  http://falcon.jmu.edu/~ramseyil/math.htm#A http://falcon.jmu.edu/~ramseyil/math.htm#A Back to Menu