Studies show that students whose understanding of subtraction is only to take away will have difficulty learning other mathematical concepts.
There are three ways by which subtraction can be understood: (1) Taking Away, (2) Difference, and (3) Inverse relation to addition operation. Pupils’ first experience with subtraction involves taking away. The dash sign means minus and minus is taken to mean ‘take away’.
Subtraction as ‘taking away’
Here are formats of subtraction tasks that involve taking away:
- Marco has 12 twelve marbles. He gave 5 to his friend Precy. How many does he have left? (This problem is represented by the equation, 12 – 5 = ____.)
subtraction as taking away - Marco has 12 marbles. He gave some to his friend, Precy. If he had 7 marbles left, how many did he give to Precy? (This problem is represented by the equation, 12 – ____ = 7.)
- Marco gave his friend 5 marbles. If has 7 marbles left, how many did he have at the start? (This problem is represented by the equation, ____ – 5 = 7.)
Problem situation number 3 require subtraction representation but is actually an addition problem because the solution involve adding 5 and 7 instead of doing subtraction.
For most students this is all they understand about subtraction — to take away. This is probably because the use of subtraction in many daily life situations use this meaning. To compound this situation, many of the subtraction tasks in textbooks are also of this type. Very few, if there is any, will include problems that supports the development of the other meaning of subtraction. And when for a long time all one know about subtraction is to take away, it would be very hard to accept other meanings. Studies show that students whose conception of subtraction is only to take away will have difficulty learning other mathematical concepts.
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