3.  What forms of instruction are most effective?

Dyscalculic learners lack an intuitive grasp of numbers and have problems learning number facts and procedures by the usual methods of teaching. Even when these learners produce a correct answer or use a correct method, they may do so mechanically and without confidence; they are anxious about it.

One objective of remedial instruction should be to improve learners' self-esteem by giving them real-life exposure to mathematics as a part of everyday life: ingredients needed in baking a cake, checking the change after purchasing something, or making estimations.

The milestone concepts for learning mathematics are: understanding number, place value, fractions, integers, spatial sense and variability. Because a person's mathematics difficulties generally originate from some dysfunction in one of these milestone concepts, one should begin instruction in these areas systematically.

Individuals with dyscalculia need help in organizing and processing information related to quantity and space. Since mathematics is a form of language, one should spend time on its vocabulary, syntax and translation - from mathematics to English and from English to mathematics.

These individuals can benefit from tutoring that can accomplish three objectives. First, to help them make-up the missing arithmetic concepts. Second, to help them connect these to their current mathematical needs. And, third, to help them develop the prerequisite skills for mathematics learning.

Effective teaching combines direct instruction (teacher-directed tasks, discussion, and concrete models) with strategy instruction (teaching ways to learn, such as memorization techniques for arithmetic facts, study skills and metacognition - learners identify strategies that help them to learn). Such teaching include:

• Sequencing and task-analysis (breaking down the task into parts and then synthesizing the parts into a whole, providing step-by-step prompts).
  
  
• Repetition and practice (automatizing arithmetic facts, daily testing, sequenced review).
  
  
• Socratic questioning and responses (structured questioning where teacher asks process or content questions to scaffold learning).
  
  
• Control of task difficulty (the teacher provides necessary assistance or tasks sequenced from easy to difficult).
  
  
• Use of technology.
  
  
• Teacher-modelled problem solving.
  
  
• Strategy cues (reminders to use strategies).

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