Math has unique characteristics that other subjects such as language art, social study, and the majority of science do not have. If you do not understand the characteristics well and treat Math and your child as other subjects, it causes a huge problem later.

**1. Layered skills and concepts**

Math requires a solid understanding of previously learned skills and concepts to learn a new concept. To understand addition, solid understanding of number sense is required. Understanding subtraction requires an understanding of addition. Multiplication involves addition. Division requires multiplication and subtraction. Fraction involves addition, subtraction, multiplication, and division. Understanding of division is crucial for a fraction. In Geometry, arithmetic skills are required to calculate angles, areas, and volumes. Many geometry questions require ratio to solve it.

Both time and measurement also require all arithmetic skills.

So, if your child does not have a solid number sense, all other concepts never become solid than the number sense. If your child does not have a solid addition skill, then he/she is not able to get better scores in all other areas that he/she learns later either.

On the other hand, other subjects such as language art and social study have no or less dependency on the previous concepts or area of study.

In other words, Math is a vertical subject, while other subjects are more horizontal and require no or small vertical dependency.

**The layered structure of Math concepts**

You may not concern so much if your child takes 70 points on one subject in Social Study or language art. But if you have the same level of concern on Math with other subjects, it is a huge mistake. As discussed above, math is a vertical subject. So, if you allow your child to keep taking 70 points, your child is almost guaranteed to have a tough time to keep up with Math around 4^{th} to 6^{th} grade.

Conceptually, 70% in number sense x 70% in addition x 70% in subtraction x 70% in multiplication x 70% in division x 70% fraction = 11.8%

How can he/she understand the ratio that comes next on top of just 11.8% of understanding?

You may think that this is too simplified. It could be. But watching many students struggled with Math starting fraction and ratio, and the majority of them do not have a solid understanding of the arithmetic, the above number aligns our experience.

**2. Proficiency**

Another unusual characteristic of Math is that it strongly requires proficiency and the proficiency of one area affects the following subjects. I see a significant discrepancy on the degree of emphasis on proficiency between Asian families and families in other races. Many Asian families put great focus on the proficiency of arithmetic.

Reality is that proficiency is crucial in the basic arithmetic, especially addition, subtraction, and multiplication. Knowing how to calculate is not enough at all, if it takes time to calculate, it is the same as not able to calculate in the real world even in elementary school. Many parents seem not to push their child enough to practice the calculation if they understand how to calculate even it takes time. It’s a huge mistake.

Unfortunately, if it takes a too long time to calculate an arithmetic problem, it is the same as not to able to solve it since all tests have a time limitation. So, you need to fully grasp that understanding the concept and being able to use it is completely different. For instance, many students understand how to calculate carryover, regrouping, and multiplication but take a too long time to calculate problems. So, they can not solve questions in time.

The worse is that the lack of proficiency hinders to learn the next concept. In the process of mastering multiplication, students use addition a lot to fill the gap of imperfect memorization of the multiplication table. For instance, to calculate 8 x 7, many students calculate 8 x 5 + 8 + 8 when they are not able to remember the answer of 8 x 7. The lack of proficiency of addition slows down the mastering multiplication.

Children need to remember combinations of two numbers that make 10, and 45 carryover patterns, and multiplication table and need to be able to answer all of them instantly. Memorizing these patterns is simple and requires limited efforts, usually two weeks or so for 45 carryover patterns and another two to three weeks for multiplication table. But becoming proficient to these calculation generates an unbelievable difference and confidence.

Many students who understand concepts but could not get good scores are due to lack of proficiency. Also, proficiency affects directly to the child’s confidence in Math.

If your child seems to understand how to calculate addition with carryover and subtraction with regrouping, but still struggling to get a good score, check the proficiency. Lack of proficiency hinders to learn new concepts such as multiplication, division, fraction. So, make sure that your child does not only understand the key concepts such as carryover and regrouping but also the proficiency enough on these.

**3. Concept and technique**

Another challenge that math has is difficult to distinguish whether your child understands a concept or the technique. Your child can remember combinations of addition and multiplication and how to calculate carryover and regrouping. They can remember tables and techniques without an understanding of the concepts. They can get a full score without understanding the concept with techniques. High dependency on techniques could be a downside of putting too much emphasis on proficiency.

These students who are great students following parents’ order, practicing a lot, and getting great scores and mastering the techniques. But these students tend to start struggling late in elementary school in 4^{th} grade or so.

It is a kind of sad story, but not uncommon.

Students who do not understand the number sense fully, start struggling in decimal and large numbers.

A similar thing happens to the students who master multiplication and division technically but not conceptually, struggle with word problems since they do not understand how to apply them.

Children who did not play with actual objects and count them tend to have this number sense problem. But this widely varies by individual. Some children get the idea instantly, and some students need a much longer time.

Fraction and ratio are not an exception. Students also need to understand the concepts to be able to apply them to word problems.

Please make sure that your child fully understands the concept then teach related techniques and have him/her practice for proficiency.

**Take outs**

- Math test score should be 100 points always as Math is a vertically integrated subject.
- Proficiency of arithmetic is crucial.
- Ensure that your child understands the concept fully.

### P.S.

Based on the research done by UC Irvine, The relative importance of adolescent skills and behaviors for adult earnings: A cross-national study, Math has the highest correlation with the completion of school and earnings among major subjects. Be sure that your child is good at math.