Many moms secretly compare their kids to other kids. At times they feel anxious if they find their kid’s friends seem to be academically more advanced than their own child. ‘Is my child going to be alright? Shouldn’t s/he be learning more advanced materials just to be safe?’ When teaching students, I often find some parents are only interested in how advanced their child is studying. On one hand, that is understandable, because checking the level at which the child is studying seems be a simple way to gauge if they are doing well academically.
If you put sincere efforts into truly understanding your child’s real academic levels, however, you will realize ‘how advanced’ he/she is studying doesn’t necessarily mean much. I sometimes feel concerned when I see some ‘smart kids’ solving challenging problems just by memorizing solutions with no fundamental understanding. How do they solve these problems so quickly without ever thinking? Ironically, there are many students who can solve advanced problems while they cannot really answer more fundamental questions.
For example, let’s think about the multiplication table. Say there are two 2nd-grade elementary students. While one student has completely memorized the multiplication table, the other one has not memorized it yet, but s/he understands it is basically skip-counting or repeated addition. The following problem is given to both students.
'If you receive $5 a month from your parents, how much money will you have in 12 months?'
The first student replies, "I’ve never learned (memorized) 5 x 12 so I don’t know the answer." Since s/he has memorized only up to multiplication of 9, s/he doesn’t even try to solve the problem. The second student, on the other hand, knows s/he has to add 5 together 12 times, and slowly approaches to the answer, which is 60.
Although the example was about the multiplication table, this same principle can be applied to all levels of studying. Developing your own problem-solving skills based on a deep understanding of principles and fundamentals is much more powerful in the end, than just being able to answer quickly from memorizing solutions without true understanding, especially in more advanced grades. For that reason, the second student has more potential than the first one, and the parents shouldn’t be too concerned if their child hasn’t memorized the multiplication table yet. (Of course, memorizing the multiplication table will definitely expedite fast and accurate mathematical operation, and students should master it at some point. However, parents don’t need to panic if their children haven’t memorized it yet as a 2nd grader.)
I have seen a student whose school grades were top notch but solved problems without a true understanding of fundamental concept. So, when a problem was given in a slightly different way, he often did not understand the question. Often, this type of student or their parents are only interested in whether or not their answer is correct. They don’t value the process itself much. Therefore, they focus on “how to get the answer quickly” rather than “understanding fundamentals.” So instead of “wasting” their time struggling to solve problems, they sit and wait for their teacher to show them how to solve problems with mechanical skills. These students quickly absorb the techniques as soon as they are taught, by memorizing. What’s problematic is that equipped with good test-taking skills (at least on a superficial level), they become more confident in their study method, and less interested in spending time in understanding fundamentals. It truly creates a vicious cycle in their proper learning. Getting good school grades with this kind of superficial learning and thinking is, however, only possible in lower grades. If my child’s school grade dropped all of a sudden after high school, perhaps it was predictable, just like a building with weak foundations eventually collapses.
Once a student has realized that s/he lacks a deep understanding of fundamentals, the only option left is to go back to basics and understand the principle. But there is another problem. Many students lose their concentration when they go back and revisit the materials they learned previously. They think what they have already “heard” or “seen” before is what they “know”, and refuse to focus on the fundamentals. So really, the best way to learn "right" is to learn slowly but surely when you first learn the material. Before working on the calculation speed, it is more important to develop problem-solving skills via a deep understanding of basic concepts.
The curriculum in each grade is part of the large continuous learning spectrum, and it is organically connected from the previous grade to the following grade. So, in-depth study in the current grade level is naturally related to the next grade level, and sometimes it is even more advanced than some of the next grade-level problems. Therefore, instead of caring too much about how “advanced” my child is, try to understand where they truly are, and provide the right amount of challenges based on what they know. This will help them develop their own problem-solving skills.
Your child will eventually do better at school by studying at their own pace, making sure they understand from the basic to the most advanced level in the grade.