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The Benefits of Memorizing Math Facts

By Margaret Groves, M.Phil., M.Ed. ELS

QuickReckoning, Inc.

Our free QuickMathFacts Software has been designed to very rapidly aid children in the memorization of math facts. Why?  Because, quite simply, a lack of fluency in basic math fact recall significantly hinders a child's subsequent progress with problem-solving, algebra and higher-order math concepts.  This lack of fluency will have a serious impact on overall self confidence and general academic performance in a child's elementary school experience and produce long term  learning hurdles in mathematics.

There has been controversy about the need to memorize math facts since the introduction of significant reforms in math curriculum in the 1990s, which largely replaced rote memorization with a new emphasis on integrative math teaching.  This involves teaching many different concepts at the same time instead of sequentially, and using manipulatives in place of numbers to illustrate mathematical concepts long after number sense should have been mastered.  Leading researchers have cautioned that this has resulted in a math curriculum that is too complex in the early grades, introducing advanced mathematical concepts before children have mastered basic computation.   

A report by Tom Loveless, Director of the Brown Center on Education Policy at the Brookings Institution, Washington DC, states that "Youngsters who have not mastered whole number arithmetic by the end of 4th grade are at risk of later becoming remedial students in mathematics" (http://www.ed.gov/rschstat/research/progs/mathscience/loveless.html) and urges that every student in the nation should receive a thorough grounding in arithmetic. 

Another article, "The Arithmetic Gap" by Tom Loveless and John Coughlan, published in Educational Leadership (February 2004; p55-59), looks at the National Assessment of Educational Progress (NAEP) math testing and explains that, although trends in overall math achievement are positive, this masks a very significant decline in computational skills over the last decade. Loveless and Coughlan suggest that students' ability to add, subtract, divide and multiply is partly suffering because of the use of calculators in elementary classrooms (4th graders who use calculators daily on classwork have significantly lower scores than those who do not) and partly because of the math "reform" standards and new National Council of Teachers of Mathematics (NCTM) curricula that became popular in the early 1990s.

A concept paper on the US Department of Education website (http://www.ed.gov/rschstat/research/progs/mathscience/concept_paper.pdf) comments on the growing controversy surrounding the reforms in math teaching methods, saying that these have de-emphasized learning basic mathematics facts and encouraged an inappropriate dependence on calculators.

State testing may be covering up the serious deficiency in math fact education by allowing the use of calculators even during the test in the elementary grades, and by using a very low score on math multiple choice tests as the level to meet the state standards.  You can visit your state's department of education website and find out what the "passing grade" is.  You might be surprised.

The NCTM has attempted to respond to the controversy by issuing its new Curriculum Focal Points, released on September 12th, 2006 and available as a free download from www.nctm.org. The NCTM argues that it never intended that teachers should throw out memorization of math facts, and the new guidelines state that second graders should be able to quickly recall basic addition and subtraction facts and fourth graders must have quick recall of multiplication and division facts.

States such as Oregon who have been lagging behind in math standards are now raising the bar for 3rd grade math achievement in an attempt to get children up to speed with math skills so that they can go on to succeed in higher grades (“Oregon considers higher math standards – mostly for elementary school students.” The Oregonian October 28th 2010)  What is the basic skill 3rd graders need to master?  Math fact fluency!

What can schools and parents do to help their students?  QuickMathFacts (Download QuickMathFacts Free Now! )is a simple software tool that helps children achieve math fact fluency in 10 minutes a day or less.  A recent study in students with disabilities showed the effectiveness of self-graphing to improve math fact fluency (PM Figarola, “Effects of self-graphing and goal setting on the math fact fluency of students with disabilities.” Behav Anal Pract 2008;1(2):36-41).  

QuickMathFacts, available in a school version which is networked, and a home version, automatically graphs student progress in real time and helps children continually improve speed of recall of math facts, in exactly the same way as this study found effective.  The lead investigator and author of the study told me in an email “I did have the opportunity to read about your program on your website. The fact that it incorporates a graphing component is something that very few, if any, math programs use.”  

 

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Last modified: September 10, 2014