It is important that children have a conceptual understanding of basic addition and multiplication facts before they memorize basic facts.
Students may progress through three stages in learning the meaning of addition and multiplication: concrete, semi-concrete and abstract. In memorizing basic facts, students may also progress through three stages: using counters, reasoning and total recall.
In the concrete stage of learning, students use different types of manipulatives to understand addition and multiplication concepts. Some sample manipulatives include using bowls for sets and counters such as beans in the bowls, french fry containers for sets and wood sticks or straws as counters, lily pads for sets and frogs on the lily pad for counters, etc. Using the bowl and bean manipulatives, the problem “2+3=5” may be represented with a bowl with 2 beans in it and a bowl with 3 beans. Next, the beans in the two bowls may be poured into a third bowl, showing that the sum is 5.
The multiplication problem “3x4=12” may be explained as 3 sets of 4 or 3 bowls with 4 beans in each bowl.
In the semi-concrete stage, drawings are used to represent sets and counters in sets. For example, circles can be used for sets and dots in the circles as counters. In the abstract stage, students understand addition and multiplication concepts without using manipulatives or drawings.
After students have mastered the conceptual understanding of addition and multiplication, it is important that students memorize basic addition and multiplication facts during their elementary school years. Memorizing basic math facts is not recommended by all math researchers, but it is important and will help students learn other mathematical concepts such as fractions in the middle grades and algebra beyond the middle grades.
Students usually go through three phases in memorizing addition and multiplication facts. In phase one, students use counting strategies such as blocks, fingers or tally marks to count.
In phase two, mental reasoning strategies are used to find relationships in the numbers. For example, when adding 6+7, the student may know that 6+6=12, so therefore 6+7 is one greater or 6+6+1=13.
In the third phase, students have memorized the addition or multiplication facts and can recall the answer with speed and accuracy.
Summer vacation is a perfect time for older students or adults to help younger students memorize basic addition or multiplication facts. Memorization is the most basic level of learning and can be achieved by most students.
