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Mastering basic number facts

 

According to a book by Kate Garnett, Ph.D. :

Many learning disabled students have persistent trouble "memorizing" basic number facts in all four operations, despite adequate understanding and great effort expended trying to do so. Instead of readily knowing that 5+7=12, or that 4x6=24, these children continue laboriously over years to count fingers, pencil marks or scribbled circles and seem unable to develop efficient memory strategies on their own.

For some, this represents their only notable math learning difficulty and, in such cases, it is crucial not to hold them back "until they know their facts." Rather, they should be allowed to use a pocket-size facts chart in order to proceed to more complex computation, applications, and problem-solving. As the students demonstrate speed and reliability in knowing a number fact, it can be removed from a personal chart. Addition and multiplication charts also can be used for subtraction and division respectively. For specific use as a basic fact reference, a portable chart (back-pocket-size, for older students) is preferable to an electronic calculator. Having the full set of answers in view is valuable, as is finding the same answer in the same location each time since where something is can help in recalling what it is. Also, by blackening over each fact that has been mastered, overreliance on the chart is discouraged and motivation to learn another one is increased. For those students who have difficulty locating answers at the vertical/horizontal intersections, it helps to use cutout cardboard in a backward L-shape.

Several curriculum materials offer specific methods to help teach mastering of basic arithmetic facts. The important assumption behind these materials is that the concepts of quantities and operations are already firmly established in the student's understanding. This means that the student can readily show and explain what a problem means using objects, pencil marks, etc. Suggestions from these teaching approaches include:

  • Interactive and intensive practice with motivational materials such as games
    …attentiveness during practice is as crucial as time spent
  • Distributed practice, meaning much practice in small doses
    …for example, two 15-minute sessions per day, rather than an hour session every other day
  • Small numbers of facts per group to be mastered at one time
    …and then, frequent practice with mixed groups
  • Emphasis is on "reverses," or "turnarounds" (e.g., 4 + 5/5 + 4, 6x7/7x6)
    …In vertical. horizontal, and oral formats
  • Student self-charting of progress
    …having students keep track of how many and which facts are mastered and how many more there are to go
  • Instruction, not just practice
    …Teaching thinking strategies from one fact to another (e.g., doubles facts, 5 + 5, 6 + 6, etc. and then double-plus-one facts, 5 + 6, 6 + 7, etc.).


   
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