Math community blog; Helping people understand procedures, follow rules and find patterns

Why do Kids fail at memorization of the multiplication table?

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Math teachers and math tutors will help kids arrest the slide into math anxiety if they will radically change the way they teach math. Since math is built upon rules, procedures and patterns, helping kids understand math procedures and sustaining interest will go a long way in alleviating the misery some student’s face while learning math.

 

Careful observation of each kid to quickly spot kids who show sign of disengagement in school is of paramount importance to a teacher so as to provide needed intervention early before the kid gets frustrated. When intervention is provided, it should aim at improving the child’s perception abilities and critical thinking skills. This intervention will also arrest the slide into frustration, depending on the child’s level of disengagement.

A PISA survey conducted after the last PISA test found that interest in the task at hand is a factor that propels students to reach their full potentials. Kids who are helped to understand and uncover math procedures will do very well in math.

UNDERSTANDING THE MULTIPLICATION FACTS

Every kid needs to understand the multiplication facts if they are to do well in math. Making good progress in math requires the child to have a good knowledge of the multiplication table early in life. A better way to make progress and retain knowledge of the multiplication table is for kids to understand how it is constructed and be able to apply it to solving problems instead of memorization.

Saying 3 X 5 equals 15 or multiplication is repeated addition without helping the child uncover why it is so will amount to memorization strategy which will not help the kid derive proof for themselves.

A good teacher will carefully explain the process of formation of the multiplication table to the student and help the child build a good mathematical base and learn different solution strategies when learning the multiplication table.

Below is a picture of the 12 X 12 multiplication table.

 

 

multiplication grid for elementary school kids

Looking at the picture above, a good math teacher or tutor should help the kid derive the multiplication table to 12 and beyond, understand why multiplication is repeated addition and understand square numbers.

 

HOW A MATH TUTOR TEACHES THE MULTIPLICATION TABLE

As a math tutor in an online tutoring website, I make a picture of the multiplication table as shown above and present it to the student, allowing the child to study it for a while and see if they can make sense of it.

Then, I begin with the ‘YOU’ technique by asking the kid to spot as many patterns in the multiplication table as they can. Knowing that math is built on rules, procedures and patterns, the kid should be able to ask themselves when a math problem is presented, if there is a rule and procedure to be followed and if there is a pattern they can find, to arrive at the solution.

Next, I ask the kid to point at the patterns they identified from the multiplication table grid presented. I give them a heads up if they cannot make anything out of the grid by informing them to look at each row and each column closely.

Next, I inform the student that in row 1, each box is increasing by adding one to the preceding box to arrive at the numeral of the following box. Row 2 is increasing by adding 2 to the preceding box to arrive at the numeral in the succeeding box. This pattern continues to row 12.

The kid should simply view each succeeding box as increasing by adding the row number to the preceding box to obtain the numeral of the succeeding box. If the kid were to construct the multiplication table grid on their own and fill each box in the row going from left to right, Row(x) will be completed by inserting (x) in the first box, then adding (x) to the preceding box to obtain the numeral in the succeeding box.

Next we will look at the column with a view to spotting any patterns. I ask the kid to look at the column to find patterns. If the kid finds the patterns as similar to the row, I appreciate their alertness and continue helping them uncover the multiplication table grid. The patterns in the column are similar to that of the rows but it goes from top to bottom as compared to the rows that proceeds from left to right.

Column 1 will be completed by adding 1 to the box on top to arrive at the numeral of the box below. The numerals in column 2 are obtained by adding 2 to the box on top to arrive at the numeral of the box below. This pattern of obtaining the numerals in each column is similar going from column 1 to column 12.

What this means is that if the child were to complete a blank 12 X 12 multiplication table grid on their own, column (x) will be completed from top to bottom by inserting (x) in the first top box then, adding (x) to the numeral of the preceding box to obtain the numeral of the succeeding box.

To make sense of all this process and allow the kid to uncover proof for themselves, I proceed to help the child find the product of the factors 5 X 3. This I do by asking the child to draw a horizontal line with a rule and a pencil through row 5 and another vertical line through column 3. The product of 5 X 3 can be found at the intersection of both lines which is 15 from the multiplication table grid. I encourage the kid to try 7 X 8 using the same principle above to find the product of both factors.

Uncovering proof for themselves will help them retain knowledge of the times table.

 

WHAT IS REPEATED ADDITION?

Repeated addition is multiplication. This is what is taught in schools but, without the teacher helping the child understand why it is so will equate to no teaching.

2 X 4 is equal to 2 + 2 + 2 + 2 which is equal to 8. This will make sense to the student if they will look to row 2. While uncovering the multiplication table grid above we found that each box increases to the right of row 2. The kid should start with 2 in the first box then add 2 to the preceding box to arrive at the numeral or number of the succeeding box. 2 X 4 simply means begin by adding 2 to the first blank box of row 2. To find the numeral of the second box, we add 2 to the first box. The numeral of the second box will equal 4 (2 + 2 = 4). To find the numeral of the third box, we add 2 to the second box. This will equal 6 (2 + 4 = 6). Finally, to find the numeral in the fourth box, we add 2 to the third box. The numeral will equal 8 (2 + 6 = 8). This proves to the child that multiplication is repeated addition

SQUARE NUMBERS

Square numbers are by definition product of a number multiplied by itself. The numbers highlighted in the diagonal of the multiplication fact grid are square numbers because the number 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 when multiplied by themselves will produce the square numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144 as highlighted in the diagonal. 

The actions of learning and teaching cannot be separated. Assisting the student learn different strategies and methods of arriving at the solution of a problem will build confidence in the student and help them gain mastery of the topic.

When kids know that they have the right problem solving skills, interest will be boosted and confidence gained. This is the confidence the kid needs going forward into any test.

 

 

 Written by Charles Onwugbene of FX-FCTUTOR (@fxfctutor1)

 

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