How Can Doubling a Known Fact Be Helpful to Find Products Mentally?

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Mental math...the bane of many a teacher's (and parents!) existence.  But it is a critical skill for becoming fluent in mathematics.  Doubling math facts is a great strategy to increase speed and accuracy for even the most difficult facts.

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The topic of becoming fluent with math facts is actually a hotly debated topic in education.  Teachers have been debating it for nearly 100 years!  Everyone agrees that they should be know the facts, but everyone has an opinion about how to get there.

Kids should know their facts and be able to use them.  This is part of the Information Processing Theory (automaticity is fundamental to success in higher mathematics).   

On this page I talk about why we should teach mental maths and provide some strategies.  But the specific question about doubling math facts has come up and I thought it would be a good idea to provide some research into the strategy.



5 Points About Doubling Math Facts

1.  Exposing students to continual drills doesn't work for many kids.  Providing a great foundation in number sense helps, but most students don't have the type of memory capacity to learn this way.

Research (Pinksy) has shown that a meaning-based approach is far more effective than drills. However, timed practice drills that are systematic and include pretesting produce measurable results with many special needs students as long as they are based on fact family instruction.

A meaning based approach is a teaching technique that connects what students already know with what they are learning.  The most effective types of meaning based approaches for fact fluency are:

  • Doubling Math Facts (variations)
  • Making a Ten


2.  Doubles facts teaches students to manipulate numbers.  This is a key strategy for future success in mathematics.  Kids are learning how numbers relate to each other and this provides a foundation for using effective strategies for solving other number sentences.

For example, 5 + 6 = 5 + 5 + 1.  Most young students do not understand that both sides of the equation have the same sum (value).  They do not instinctively recognize this.  By pointing out the doubles fact, you are not only explicitly teaching a strategy for solving 5 + 6.  You are also laying the foundation for success with automaticity.


3.  Doubling Math Facts assists learning disabled students to move from counting to an efficient direct retrieval method. 

These are your students that continue to start at a low number and count on to find the sum. 

Example:  they will start at 5 and count up 8 times (instead of thinking 5 + 5 + 3) which often ends up producing an incorrect response. They will struggle greatly with mastering math facts without utilizing the two meaning based approaches mentioned above.  


4.  Doubling works with large numbers as well, i.e. 50 + 60.  It is best utilized when the addends are relatively close together or can be deconstructed into an equation that makes sense (50 + 50 + 10).


5.  When we create a meaningful network of ideas, there are fewer details kids have to retain.  Our brains love patterns and sorting ideas into tidy "boxes," if you will.  Logical connections (such as doubling) make sense to us and once it is fully understood there will (should) be automatic recall.  Our students will use it without even knowing they are.



Final Thoughts on the Doubling Debate

Remember that doubling math facts is merely a strategy.

I'm certainly not saying that curriculum publishers have it right with their worksheets that have taken it way out of line (I've seen them too - have a look at this blog post about first grade math homework using doubles!)  I feel the author's pain and get it.  So much of this Common Core stuff is over the top.

I also don't think that teaching doubling through problem solving as linked to above is necessarily appropriate.  That is an application of the strategy.  In my mind, that type of worksheet would have been much more appropriate for a group setting where the students could discuss their thinking with the teacher to guide them.  I would have been justifiably irritated too if my first grader brought that home!

But doubling or even doubling plus one isn't a CC thing.  It has been around for years and it is a solid strategy for helping kids developing fluency (understanding) and automaticity (fast without thinking) with math facts.  .

The ultimate goal really is to no longer need a strategy.  After they understand what's going on, let's help them become quicker and get that automaticity. 

Kids ultimately have to just know their facts.


Sources Cited

1.  Developing Fact Fluency in Mathematics.  Winter 2010. Lee Pinsky Learning Center.
2.  Doubles Background Information for Teachers and Parents.  BrainPop.
 
3.  Thornton, Carol A.  "Strategies for the basic facts." Mathematics for the Young Child. Reston, VA. National Council for Teachers of Mathematics.  1990
4.  Woodward, John.  Developing automaticity in multiplication facts: integrating strategy instruction with timed practice drills. 2006.



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