3.  What forms of instruction are most effective? cont.

Every remedial/instructional session should have the following components:

• Developing the prerequisite and support skills.
  
  
• Learning arithmetic facts orally.
  
  
• Visualizing problems and information.
  
  
• Verbalizing and recording procedures and estimation.
  
  
• Helping the child form problems relating to the given concept.
  
  
• Counting forward beginning with a given number e.g. begin with 53 and count forward by two's, by three's, etc.
  
  
• Counting backwards beginning with a given number, e.g., begin with 97 and count backward, by 1's, 2's, 5's, and 10's.
  
  
• Showing patterns of number facts, e.g., 4 + 4 = 8, then 4 + 5 = 9; 8 + 10 = 18, then 18 + 10 = 28, 78 + 10 = 88, etc.

The three components of a mathematical idea: linguistic, conceptual and procedural should be carefully included in all mathematical instruction. Therefore, before the student performs any arithmetic operations he should be asked about the language, procedure, and the conceptual model of the problem first. When the student has completed the problem, they should be asked whether they know any other problems that are similar to the one just completed.

Based on our experiences with many dyscalculics, we are fairly certain that with the help of a competent tutor, with effort, discipline and structure, and appropriate concrete materials, dyscalculics can make a great deal of progress in mathematics learning and realize their potential.

Further readings and support:

• For Mahesh Sharma's UK courses and videos: Berkshire Mathematics
  
  
• For Mahesh Sharma's US courses and videos:
  
  • Center for Teaching/Learning of Mathematics, PO Box 3149, Framingham, MA 01701 Phone: 001 508 877 7895 Fax: 001 508 788 3600 ctlm@rcn.com
  • Mathematics Institute, Cambridge College, 1000 Massachusetts Ave., Cambridge, MA 02138 Phone: 001 617 873 0211 Fax: 001 617 876 2663
    
    
• Dyscalculia, Mahesh Sharma and Eugene Loveless, CT/LM, 1988
  
  
• Dyslexia, Dyscalculia, and other Mathematical Problems, Mahesh Sharma, CT/LM, 1989
  
  
• How to Teach Arithmetic Facts Easily, Mahesh Sharma, CT/LM, 2000
  
  
• Mathematics for Dyslexics: A Teaching Handbook, Chinn and Ashcroft, Whurr, 1997
  
  
• The Mathematical Brain, Brian Butterworth, Macmillan, 1999
  
  
• Working with Dyscalculia: Recognising Dyscalculia Overcoming Barriers to Learning in Maths, Anne Henderson, Fil Came and Mel Brough, Learning Works International. ISBN: 0-9531-0552-0.
  
  

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