Effects of Premature Drill
William Brownell, 1930’s

• drill doesn’t promote memorization for all
• drill doesn’t change the way kids think
• drill doesn’t promote quantitative thinking
• drill does increase speed and accuracy
• drill is not enough; students need more

Goals For Learning Basic Facts
William Brownell, 1940’s

There are two major goals when you are teaching the basic facts:

• immediate responses
• justifying those answers by explaining why they have to be correct

Rate, Accuracy, and Process In Learning Multiplication
William Brownell, 1940’s

• 75% of kids who had a way to figure out the answer to a basic fact had memorized those facts by the end of the school year
• 60% of kids who were guessing or giving rote responses were still doing that at the end of the school year
• helping students learn thinking helps them memorize basic facts

Summer Retention Of Basic Facts
Ed Rathmell, 1970’s

• Kids who could justify the answers by a procedure other than counting dropped 8% over the summer
• Kids who could not justify their answers dropped 55% over the summer
• helping students learn thinking helps them retain facts
• helping students learn thinking helps them retain facts

Thinking Strategies for Subtraction
Carol Thornton and Paula Smith, 1980’s

At the end of the first grade:

• 60% of kids with drill approach were still counting
• 30% of kids with strategies approach were still counting
• helping students learn thinking helps them get beyond counting to answer facts
• 12% of kids with drill approach had facts memorized
• 55% of kids with strategies approach had facts memorized
• helping students learn thinking helps them memorize facts
• 20% of the responses were incorrect for the drill approach
• 2% of the responses were incorrect for the thinking strategies approac
• hhelping students learn thinking helps them become more accurate

Sample References

• “Action Research:  Strategies for Learning Subtraction Facts,” by Thornton and Smith in The Arithmetic Teacher, April, 1988, pp. 8-12.
  • This article includes convincing data for helping students learn thinking strategies.
• “Strategies for Basic-Facts Instruction,” by Isaacs and Carroll in Teaching Children Mathematics, May, 1999, pp. 508-515
  • This article includes what we currently know about teaching basic facts and some of the current issue

Thinking With Numbers
Rathmell, Leutzinger, Gabriele, 1990’s

A thinking approach to teaching the basic facts was more effective than a worksheet and drill approach in the following ways:

• better speed and accuracy
• better mental computation
• far fewer students used their fingers
• helping students learn thinking helps students develop number sense

Low ability students made the greatest gains in

• speed
• accuracy
• mental computation
• ability to use thinking strategies
• far fewer used their fingers
• all students can learn thinking strategies

After summer vacation, randomly selected students from the experimental class and the control class were interviewed

experimental students

• not one used their fingers
• all used at least one derived fact strategy
• all solved all three mental computation problems

control students

• all used their fingers at least once
• less than half used a derived fact strategy
• less than half solved as many as one of three mental computation problem

Thinking With Numbers

After 1 Year In One School, Percent of Students Not Proficient At Mathematics, 2002-2003

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