There are so many cases in my teaching life, which the students did not master their basics such as addition, subtraction, multiplication or division and then in their later life these unskilled basics have had dramatic impact on their math ability but unfortunately they were not aware of it.
Why they could not do word problems well or grade 8 equations or grade 10 relation equations well despite I have so patiently explained the concepts and steps again and again? It is so sad for me to tell them they really should go back to basics like relearn fractions they had learned in elementary. They are already grade 9 and some of them are in grade 10 already so it is understandable that it is difficult for them to take the suggestion to go back to elementary math and re-work on fractions or times table.
I am writing this article to tell parents and students that children must master math basics before grade 4 and if you don't then it could be an uphill battle to try to constantly have to improve your math in later grades.
Without mastering basics math, the obstacles students could face later in their life are:
1. They are slow in response to teaching and often can not catch up to the speed the math teacher is presenting the new materials, so after class they only understand 50% of what the teacher is talking about or most of the time they do not understand at all.
2. They lose second nature or instinct to see the way to solve word problems. Even with the help of calculators, there are problems that calculators will not help or they will end up spend too much time on a few problems to try to use calculators to find the "way" and can not finish the problems in time. For example the following equation solving problem, 3 x = 24, it is really simple matter that both sides divided by 3 so one will get x = 8 but if the students have not mastered the basics then the student need to use a calculator to do it and simply can not do it mentally. They learn math without using their mental calculation ability but rely on external device so when asked to find out factors, these students will be very slow and will have difficulty in finding out LCD for relational equations.
For a bit complicated equation 3x – 2 = 5x + 3 then they just can't "see" that – 5 = 2x without doing nay more work. Sometimes, they make mistakes just because they need to write many extra steps to get their answers since they can't do simple mental calculations.
3. Since these students never mastered basics, their brains are not trained to do any basics math mentally so they have trouble to understand integers later. They can't do calculations easily by just looking at the signs.
The above are just 3 points out of many potential problems for those students who have not mastered basics could face later in their higher grades. My advice for those students who did not master the basics is to go back to elementary math and re-do those very basic calculations and lots of practice to the point that you can come up with answers orally with put using calculators.
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