Research on the practice of massaging the head of a baby with hot water and ointments in Ghana. By Dzamesi Yael (Ph.D. in Science Education)
Understanding the concept of quantity - Primary 1.
(4 children, ages: 6 to 7 years old).
Abstract.
The children in Primary 1 could not differentiate between adding a quantity and subtracting a quantity in term of counting or moving along the numbers on a ruler. They could not understand that adding a quantity to a number means to move along the increasing numbers to the right side of the initial number. And subtracting a quantity from a number would mean moving along the decreasing numbers to the left side of the initial number on the ruler.
Conceptual understanding of numbers and quantities means that they are products that can be changed by adding or subtracting a quantity from them. The changes can be described by mathematical symbols of addition and subtraction. The children in Primary 1 solved math formulas by counting with fingers, discs, or matchsticks. At the last term of Primary 1 they could solve math formulas of addition and subtraction separately even though when facing subtraction, they tended to see the subtraction sign many times as an addition sign. The teacher had to remind them that it was a subtraction formula. They also got confused when they faced addition and subtraction formulas together. The teacher tried to teach them to add and subtract numbers with the help of a ruler (Figure 1).
Figure 1: Using the ruler in addition and subtraction.
In Figure 1, the initial number or quantity is eight. The upper ruler demonstrates adding a quantity to number 8. Adding 5 to 8 means moving 5 numbers to the right side of number 8 along the bigger numbers and reaching number 13. The down ruler demonstrates subtracting a quantity from number 8. Subtracting 5 from 8 means moving 5 numbers to the left side of number 8 along the smaller numbers and reaching number 3. These two operations on the ruler were very difficult to Primary 1 children. They did not understand what it means to move along the bigger or increasing numbers (the right side of number 8 in Figure 1, up), or to move along the smaller or the decreasing numbers (the left side of number 8 in Figure 1, down). They started practicing the use of the ruler with addition math formulas, and they got used to the right side of the initial number. However, when they move to subtraction math formulas, they did not understand the difference between moving to the right or up and left or down in numbers. When they received mixed math formulas of addition and subtraction, they got completely confused on which side of the initial number they should count, the bigger numbers to the right side or the smaller numbers to the left side. No matter how many times things were explained to them, and they requested to show on the ruler on which side the numbers are increasing or decreasing, they continued to be confused. This indecisive behavior of the children shows on unstable cognitive processes, the same way they children confused between the (+) and (-) math symbols.
What could have contribute to the unstable cognitive process, upon all efforts of practical methods of teaching math?
See pages:
"Concluding what was counted in math".
"Grouping and separating of numbers".
"Interpreting a picture into a math formula".
"Addition and subtraction symbols".
The hot water massage on the front head could have damaged the frontal lobe (Picture 1 in "The structure of the brain") page where many abstract cognitive processes occur.