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Mathematics and Special Educational Needs

Mathematics and Special Educational Needs. Seán Delaney, Coláiste Mhuire, Marino Sean.Delaney@mie.ie. Menu. Problem Tables Games Commutative Property Modes of Representation Language Place Value Assessment and IEPs Reading List. Problem!.

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Mathematics and Special Educational Needs

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

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

  3. 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

  4. Solution Back to Menu Seán Delaney, July 5th 2003

  5. 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

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

  7. 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 Seán Delaney, July 5th 2003

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

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

  10. 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 Seán Delaney, July 5th 2003

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

  12. 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

  13. 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 Seán Delaney, July 5th 2003

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

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

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

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

  18. 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 Seán Delaney, July 5th 2003

  19. 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 Seán Delaney, July 5th 2003

  20. 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 Seán Delaney, July 5th 2003

  21. 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 Seán Delaney, July 5th 2003

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

  23. 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 Seán Delaney, July 5th 2003

  24. 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 Seán Delaney, July 5th 2003

  25. 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 Seán Delaney, July 5th 2003

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

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