How to Improve Test Scores in Math

- Three points to check at and improve -

1. Not good at math?

There are many reasons a child might not be able to achieve good scores in math. As tutors, our first job is to identify what is preventing a child from consistently getting perfect scores and to then prioritize finding a solution. If your child is in first or second grade, it will be easier to determine the problem, as your child will only have exposure to limited topics in math at this point. As your child’s grade level and breadth of knowledge increase, it becomes more complicated and time-consuming to identify root causes.

2. Three major reasons

Though there may be many reasons your child is unable to consistently achieve a perfect score, the following three reasons are the primary causes. We will break down each of the three reasons into more specific ones that are directly associated with action items for improvement. Understanding these three reasons is very important, as the subsequent course of action to be taken varies significantly from reason to reason.

1) Lack of proficiency

This reason applies to addition, subtraction, multiplication, division, fractions, and more. If a child is typically scoring 40 to 70 points on tests, a lack of proficiency may be the primary cause. In the US, the lack of emphasis on proficiency causes a huge problem for years to come. Asian families tend to emphasize proficiency in basic arithmetic, thus paving the way for their children to succeed in STEM fields.

Knowing how to calculate and doing so accurately, within a reasonable amount of time, are entirely different matters. Even if your child knows how to add 8 + 9, methods like using fingers to count or breaking down 9 into 2 + 7 take too much time and indicate that your child is not proficient enough.

Many parents do not fully understand the importance of proficiency and leave their children at risk. Children need to know how to calculate. Additionally, they need to memorize addition and subtraction combinations, the same way one would memorize multiplication tables.

2) Lack of conceptual understanding

If a child is not able to answer certain types of questions at all (e.g. carryover addition, subtraction with regrouping, rounding, or decimals), a lack of conceptual understanding could be the underlying reason.

3) Comprehension

There is a group of students who are very good at calculations, but not at all good at word problems. Many students who attended Kumon fall into this group.

3. Typical cases

1) Lack of proficiency

If a child can achieve 60 to 70 points on the majority of math tests, but never a perfect score, we check for proficiency. Since the child was able to earn 60 to 70 points, he or she usually understands key concepts, but was unable to answer all the questions in time or made many mistakes.

2) Lack of conceptual understanding

If a child receives a significantly low score in a particular topic in comparison with other topics, this suggests that the child did not grasp a key concept. The child usually feels uncomfortable with a certain topic and needs to recognize that he or she does not fully understand the concept.

This often occurs when dealing with fractions, telling time, and approximations. Students who do not have a good understanding of number sense struggle with math when large numbers and decimals begin to come into play around fourth grade. Students know how to calculate, but do not fully know what each digit means. Therefore, when dealing with larger numbers or decimals, students are easily confused.

3) Comprehension

These children are good at math and generally score well, but make frequent mistakes when dealing with word problems or are unable to understand the meaning of questions.

4. Assessment

1) Do not ignore proficiency

If your child falls under case two (missing the concept) or case three (comprehension), the problem is usually clear and the child will recognize his or her weakness. The challenge is case one (proficiency), or case one coupled with another one of the two cases.

2) 80 points is not enough

If your child is not able to score more than 90 points on math tests, I strongly suggest checking your child’s proficiency in basic calculations. In general, the proficiency requirement in the US is too low – simply knowing how to calculate is often useless in the real world.

3) Avalanche effect

Your child needs to be able to perform calculations in addition, subtraction, and multiplication calculations quickly and accurately in order to move forward. These are fundamentals. Without using addition, students will not be able to make calculations in multi-digit multiplication. Without using multiplication and subtraction, students will not be able to do long division. Without understanding division, students will not be able to calculate fractions and ratios. Without using addition and subtraction, students will not be able to calculate time and angles. Without using multiplication, students will not be able to calculate area and volume.

All math and STEM subjects rely entirely on these fundamental skills in arithmetic. These skills should be proficient and accurate.

4) Addition and subtraction need memorization

Addition, subtraction, and multiplication require memorization of patterns. Knowing how to calculate is important, but not enough on its own. To be truly proficient, your child needs to memorize the patterns. This is where we often observe a gap. The majority of parents do not understand the need for memorization, and, as a result, leave their child behind.

It’s akin to building a multi-story building on unstable foundation.

5) Sad but common drop off pattern

This is essentially what you are doing if you see your child scoring 70 points on math tests in first/second grade and let them continue on. It’s easy to predict what will happen in the near future.

Conceptually: 70% (addition) x 70% (subtraction) x 70% (multiplication) x 70% (division) x 70% (fractions) = 17%

Reality is worse. Because multi-digit multiplication requires addition if your child scored 70 points when learning addition and multiplication: 70% (addition proficiency) x 70% (multiplication proficiency) = 49%. Since division requires multiplication and subtraction, it is even worse. Some students give up on math when it comes to division and fractions.

5. Countermeasures

1) Lack of proficiency

If your child has proficiency issues, you need to forget his or her grade level, return to core subject matter, and have your student practice that. It may be annoying for your child and you may face resistance. Some parents have complained to us that their child is in fifth grade and shouldn’t need to revert to practicing addition and multiplication. You need to understand the necessity of proficiency and explain to your child that simply knowing how to calculate is not enough. You must convey speed and accuracy requirements to your child.

You also need to understand that your child needs to memorize patterns.

In many instances, I have seen the test scores of my students jump after improving proficiency and a confidence boost.

In our experience, almost all students reached the goal of proficiency in less than two weeks per subject, with only 15 minutes of practice each day. Please consider that 15 minutes x 14 days = 3.5 hours. Dedicating just 3.5 hours could yield life-changing effects and put your student on track to become an A student instead of a potential dropout.

The practice may sound tedious, but I actually found the opposite: If we share a common goal, the majority of students enjoy doing the necessary exercises and tracking their progress. The closer students get to their target time, the more they are willing to practice to achieve their goal. Once they hit the target time, they feel satisfaction and confidence. Repeating these practices continue to build confidence and teach students how to overcome challenges.

2) Lack of conceptual understanding

Concept-related problems are relatively easy to fix – just revisit the concept. The point is to take the time to ensure that your child fully understands the concept. Because teachers have limited time to teach each subject, they are not able to wait for all students to grasp a concept. It would be best for you to sit down with your child and spend time going over each concept. However, we are all busy, and teaching a child is emotionally challenging for many parents. Asking a tutor or using other services may be the better option for you and your child.

It is essential to detect this issue as early as possible before the problem causes ripple effects.

Once your child has grasped the concept, please confirm your child’s knowledge by having him or her solve several problems. Understanding the concept and being able to properly apply it are separate matters.

3) Comprehension

Improving comprehension is challenging and requires a mindset change for your child. There are some techniques, but they are not perfect.

i) Change gears

Your child has been trained to solve basic calculations quickly and accurately, as we discussed in the above section on proficiency. Children who attended Kumon have been trained to be an excellent human calculator, which is not a bad thing. However, many children try to apply this same approach – speed – to word problems, which does not work at all.

They need to change gears and understand that they need to solve word problems using three steps:

ii) Three-step approach

The first step is the extraction of information. All word problems contain the information needed to solve the problem. In this first step, children need to perform two sub-steps: They need to understand what the question is, and they need to extract the information from the world problem that is going to help them solve it. Reading a word problem aloud a few times can help in changing gears and understanding the question at hand.

The second step is to construct an equation using the extracted information. This step is far trickier for children than adults might think, and requires practice. Many children can perform the first step, but not this one. Certain techniques may help in this area. For instance, if the question asks for a difference, the equation will utilize subtraction.

The third step is easy: solving the equation.

If you can solve several world problems with your child following these steps, your child will understand the steps and be able to apply them. Please note that the second step requires additional practice.

6. Additional considerations

If your child struggles with written/printed questions but doesn’t struggle as much when dealing with questions asked aloud, please check to see if your child might have dyslexia. Some research shows that about 8% of children have some extent of dyslexia.

7. Taking action

Whether your child struggles a little bit or a lot in math, please check the following:

1) Your child’s proficiency. If your child is not proficient, please have him or her practice.

2) Understanding of all key concepts. If this is lacking, take the time to ensure that your child comes to understand key concepts correctly and can properly apply them.

3) Ability to solve word problems. If your child struggles with word problems, share the steps with your child and practice them – especially the second step.