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)
Addition and subtraction symbols - Primary 1.
(4 children, ages: 6 to 7 years old).
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Figure 1: The confusion between (+) and (-) signs.
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If the children in Primary 1 stored meaningfully the operation of counting, achieving conceptual understanding of quantity and​ understanding the difference between addition and subtraction, why was the confusion between the signs?
1. Is the short span attention did not allow the children to notice the difference between (+) and (-) symbols?
Or...
2. Is there a difference between (+) and saying: "Add" or between (-) and saying: "Take away"?
And
3. Does the confusion between (+) to (-) symbols shows an unstable cognitive process?
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1. If we assume that the plus (+) and minus (-) signs are difficult to be differentiated under a short attention span, it should
have been expected to see the same confusion in handwriting of the small letters such as between 'm' and 'n', 'a' and 'u', 'i' and
'l', for example, but none of the Primary 1 children got confused between these letters or other similar letters. The answer,
therefore, to the first question is negative.
2. There is a difference in the process that the working memory passes between letters and mathematical signs.
Between the sign ‘m’ to its sound, there is a direct connection. However, between the sign (+) or (-) and the practical math operation there are more than one cognitive step (Figure 2).
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Figure 2: The difference in the number of cognitive steps of processing the meaning of a letter and the meaning of the math symbols (+) and (-).
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The answer to the second question is positive
In general, the subtraction operation is more difficult than the addition because it involves a higher abstract thinking. In this case, the confusion between the plus and the minus signs among the children could have been due to the difficulty of the working memory to shift from one set of complicated cognitive operations to another set of complicated cognitive operations. If there was a definite conceptual understanding of the addition and subtraction symbols it would not be difficult for the working memory to shift between the different information in the long-term memory [57].
When there is a lack of good conceptual understanding it leads to an un-organized storage of information in the long-term memory, which makes later all cognitive processes slow and inefficient [59]. Therefore, the answer on the third question is positive.
Lack of a good conceptual understanding causes an unstable cognitive process.
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If the pupils started to work with an addition math expression, they continue to solve the next subtraction expression as addition (Figure 1 A and B). If the pupils started to work with a subtraction math expression, they continue to solve the next addition expression as subtraction (Figure 1 C an D). In these cases, the teacher had to point on the sign of the (+) or (-) and ask the child "What sign is it?" The first answer was usually the wrong one. Then the child said the opposite sign while seeking the approval of the teacher. Once the child got the approval in the face expression of the teacher, he or she could correctly solve the math formula. They knew how to work addition and subtraction in small number in a practical method, such as with discs and objects, but always got confused with the abstract aspect of differentiating between (+) and (-) symbols.
The arrows show on stepping forward to another cognitive step in processing the information.
'm' → sound
(+) → the word "addition" → considering the two numbers to add → counting → summarizing the counting with the sum → writing the correct math formula.
(-) → the word "take away" → considering the two numbers; one to subtract from the other → counting in reverse → summarizing the counting with the sum → writing the correct math formula.
Abstract.
The children in Primary 1 were taught addition before subtraction. Even though they could answer well on additional math formula and separately on subtraction math formula, they could not answer well on exercise that contained both addition and subtraction math formulas.
If the first question was addition, they related to the subtraction symbol in the next question as addition and vice versa. This confusion was shown also when they were asked to translate a concrete task of adding objects or taking away objects from a picture into a math formula and taking decision which math symbol (+) or (-) to use.
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Teaching addition in Kindergarten 2 was done by practical methods of counting discs and other objects, drawing, and writing the math expression in the exercise book. However, expressing a process of an addition by math formula was difficult to the children. They continue to learn and practice addition in Primary 1. After mastering the addition, they were introduced to the practical process of subtraction and then to the symbol of subtraction. The pupils had to cancel the deducted items from pictures by drawing a line on them and then write the math expression. When they mastered the subtraction formula, they practice each symbol for some time without the help of the pictures (abstract method). When they master this we introduced both signs: giving simple addition and subtraction exercises together on one sheet of paper. All four pupils confused between the (-) and the (+) signs (Figure 1).