Why Do Students Struggle Learning and Retaining Multiplication Facts?

At an early age students learn to skip count by 1’s, 2’s, 5’s, and 10’s.  They also learn their “turn around” facts (8 + 2 = 2 + 8) and their fact families:

8 + 2 = 10

2 + 8 = 10

10 – 2 = 8

10 – 8 = 2

Students begin to learn their multiplication facts with the ones that they learned to skip count by.  If you look at a 12 X 12 multiplication chart and you eliminate all the multiplication facts where you multiply by 1’s, 2’s, 5’s, 10’s and 11’s and all “turn around” facts there are only 28 facts left to learn. 

For years, memorization of these facts assumed that you had Numerical Fluency.  Students develop true Numerical Fluency when they develop Number Sense.  Understanding how numbers are composed and decomposed and the patterns and grouping found within our system help students master their multiplication facts.  Multiplying by two is related to doubles in addition.  Multiplying by four is just doubling multiplying by 2.  When students understand that numbers decompose into sums or differences of other numbers, they can easily use the distributive property to find partial products which they then put back together.  When asked to solve 7 X 8, someone with Number Sense may have memorized 56, but they would also be able to work out that 7 X 7 = 49 and then add 7 to make 56, or they may know that ten 7’s subtract two 7’s (70-14) gives the same answer. At Mathnasium, our main focus is Number Sense.  We teach students how numbers are composed and look at decomposing them mentally and efficiently.  It is useful to hold some math facts in memory, but we learn them by using them in different mathematical situations not by practicing them through times table repetition and timed tests.

Once students learn their basic multiplication facts, they apply them to their fact families with division and later  to two and three-digit multiplication facts.  Basic facts help understand equivalent fractions and finding common denominators for adding fractions with “unlike” denominators.  This knowledge also empowers them to understand factors, multiples, GCF and LCM.  Number Sense is the foundation for all higher-level mathematics (Feikes & Schwingendorf, 2008). Connect HERE for their study.  In Algebra for instance,  students transfer this knowledge to factoring polynomials and simplifying radicals.

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