# The Most Effective Way to Improve Grades is Still to Practice Problems

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The most effective way to improve grades is still to practice problems! A few days ago, a colleague in the office shared a joke with us about her daughter's wrong answers. When answering the question inside the last parenthesis, the child directly used a ruler to measure the straight-line distance between the snail and the hedgehog. This approach was indeed unique. Especially after the implementation of the policy of subtracting points for wrong answers, the tactic of solving a large number of problems has become less popular, even though it was once widely used in learning. As a result, the burden on children has decreased, but the types of questions they have encountered have also sharply decreased! Therefore, it is not surprising that children often come up with many unique ideas when doing problems. After all, they haven't seen them before! If this were the only problem, it wouldn't matter much, but the most critical thing is that children encountering exam questions are becoming increasingly flexible. To be honest, I think that the most direct, simple, and effective way to solve this problem is to practice more problems. Moreover, practicing problems not only allows children to encounter more types of questions but also has many other benefits.

Benefits of practicing problems:

It can help children clearly understand what they know and what they don't know. Many things can only be known after actually doing them. Just like memorizing books, when you read them according to the book, you always feel like you have already memorized them, but when you close the book, your mind goes blank. The same goes for problem-solving. Children will only know which topics they are good or bad at after seeing the problems, doing them, and making mistakes. Relying solely on intuition will certainly not achieve this effect. Otherwise, why would there be the saying, "I know it when I see it, but I'm useless when I do it"? More importantly, during the process of practicing problems, children will have a deep impression of their mistakes, and even indirectly stimulate their awareness of checking and filling gaps on their own. Studies have shown that when students identify their weak areas in the first round of problem-solving, they will actively and consciously correct their mistakes in the second round of problem-solving. Therefore, in theory, practicing problems can fully stimulate children's internal drive!

2.Help children remember knowledge more accurately and firmly.

This is something I have experienced myself. I remember vividly when I was in primary school learning about the distributive law of multiplication, I couldn't seem to memorize the formula and its variations no matter how many times I recited them:

(a+b)×c=a×c+b×c; a×c+b×ca+b)×c

I tried reciting them multiple times but it didn't work. Later on, my grandma told me not to bother memorizing them and instead try solving a couple of problems using the formula. At that time, I thought to myself: "It's not that easy." But surprisingly, after doing just three problems using the formula, I had it memorized. So, if you want your knowledge to stick faster and more firmly, practicing problems is still the best way.

And I'm not the only one who thinks so. Henry Roediger and Jeffrey Karpicke, psychologists from Washington University, published an article on "practicing problems" in Psychological Science. In their article, they mentioned that simulated tests, i.e., practicing problems, have a significant impact on memory retention.

To verify this statement, they conducted tests with students and compared the effect of practicing problems versus memorizing learning materials on knowledge retention. The result showed that, although memorizing the material had good short-term effects, practicing problems had an absolute advantage in long-term memory retention.

From the bar chart above, you can see that within 5 minutes after learning, students who memorized the material had better memory retention, but after 2 days to one week, the group that practiced problems had twice as much memory retention compared to the memorization group. Moreover, research has shown that practicing problems not only improves memory retention but also accuracy. As shown in the figure below, compared with reading learning material (45% accuracy), practicing problems/testing helps retain knowledge more accurately (67% accuracy).

From these studies, we can see that practicing problems can really help children remember knowledge more firmly and accurately.

3.Change the structure of children's brains.

Seeing this title, some of you may think I'm exaggerating, saying that practicing problems can make your child smarter? Yes, it can. Because when practicing problems, our brains go through a process of retrieving and recalling stored knowledge.

In this process, our brains are not only recalling information but also engaging in a cognitive process of understanding, reasoning, extending and generating output. For example, a child can observe the surface of a clock or count the number of large and small squares on the dial to verify what their teacher taught them about clocks in class. This is a process of recalling and understanding. Writing down the correct answer is an output process.

However, while practicing problems, children may also have other thoughts such as: "Doesn't the clock have a second hand? Why wasn't it mentioned in class?" Curious children may even observe the movement of the second hand on a clock in real life. Although their conclusion based on personal observation may not be entirely accurate, it's still preparation for learning about the second hand in the future.

Therefore, practicing problems not only consolidates old knowledge but also prepares children adequately for new knowledge. As the saying goes, "Reviewing old topics enables one to learn new ones." However, while there are many benefits to practicing problems, giving your child a pile of questions to practice alone is not the best approach. This approach not only has no effect on improving your child's grades but can also damage their interest in learning.

4.What should you pay attention to when practicing problems?

Step 1: Choose appropriate difficulty level questions that expose weaknesses.

Especially after finishing a unit, we can find some basic comprehensive exercises for children to try. One thing to note is that always choose basic questions rather than advanced ones. My daughter and I sometimes do these exercises together, pretending that we are taking exams. Sometimes, I even grade her. In fact, the final score is not important. The key is to quickly identify the weak areas in your child's learning through these basic questions. This will prepare them for the actual "practice" phase of problem-solving, so that they won't practice aimlessly.

Step 2: Improve weaknesses exposed by children.

After finding weaknesses through one or two sets of basic questions, don't just start practicing lots of similar or transformed questions based on what they do not know. Doing so might result in more errors, be meaningless, and waste time, damaging your child's interest in learning. After discovering a child's weakness, first help them supplement and improve their weak knowledge points. See whether the child is having trouble recalling basic knowledge from the textbook or understanding the underlying logic of the question. Always go back to the textbook and make sure they understand the most basic theory before practicing problems. It's like building a road: first compact and level the base, then harden and pave it with asphalt to create a solid highway!

Step 3: Practice problems purposefully.

After handling all the basic issues, it's not the time to practice everything randomly. You still need some strategies. Original questions from textbooks must be practiced since these examples are typical and basic questions. Whether doing transformed questions or advanced-level questions, they are all derived from textbook examples. Another type of question to practice is your child's incorrect questions. Be sure to prepare a notebook for wrong answers. The questions in this book are critical questions from the process of practicing problems. This not only reduces your child's burden but also helps them to have an objective and purposeful approach to improve their learning efficiency.

Step 4: Choose typical questions to practice.

Although you are practicing problems, it doesn't mean that you should practice everything. For example, repetitive questions with too much similarity should be avoided. First, children may not want to do them as they find them boring. Second, doing similar questions repeatedly can develop habitual thinking, limiting a child's flexible application of knowledge.

Also, avoid calculation questions that are too difficult or too complex. Practicing calculation questions is to consolidate calculation rules and improve speed. Standard calculation questions usually achieve this goal. Questions that make you scratch your head and calculate without any simplification, reduction, or smart calculation should be avoided. What kind of questions should you practice? Those that have the same underlying theory but different directions, which means transformed questions that have many variations.

For example:

A classic primary school problem: Chicken and Rabbit in the same cage.

There are 20 chickens and rabbits with 44 feet in total. How many of each animal do you have?

A pen contains both birds and rabbits. The number of rabbits is four more than the number of birds. There are 76 feet in total. How many rabbits and birds are there?

If there are 200 chickens and rabbits with chicken feet 56 less than rabbit feet, how many chickens and rabbits are there?

There are 27 boxes of pens and pencils with a total of 300 pens/pencils. Each box of pens has 10 pens, and each box of pencils has 12 pencils. How many boxes of pens and pencils are there?

A large bottle of oil weighs 4 kg, while two small bottles weigh 1 kg. If there are 100 kg of oil in a total of 60 bottles, how many large and small bottles are there?

Benefits of practicing problems:

It can help children clearly understand what they know and what they don't know. Many things can only be known after actually doing them. Just like memorizing books, when you read them according to the book, you always feel like you have already memorized them, but when you close the book, your mind goes blank. The same goes for problem-solving. Children will only know which topics they are good or bad at after seeing the problems, doing them, and making mistakes. Relying solely on intuition will certainly not achieve this effect. Otherwise, why would there be the saying, "I know it when I see it, but I'm useless when I do it"? More importantly, during the process of practicing problems, children will have a deep impression of their mistakes, and even indirectly stimulate their awareness of checking and filling gaps on their own. Studies have shown that when students identify their weak areas in the first round of problem-solving, they will actively and consciously correct their mistakes in the second round of problem-solving. Therefore, in theory, practicing problems can fully stimulate children's internal drive!

2.Help children remember knowledge more accurately and firmly.

This is something I have experienced myself. I remember vividly when I was in primary school learning about the distributive law of multiplication, I couldn't seem to memorize the formula and its variations no matter how many times I recited them:

(a+b)×c=a×c+b×c; a×c+b×ca+b)×c

I tried reciting them multiple times but it didn't work. Later on, my grandma told me not to bother memorizing them and instead try solving a couple of problems using the formula. At that time, I thought to myself: "It's not that easy." But surprisingly, after doing just three problems using the formula, I had it memorized. So, if you want your knowledge to stick faster and more firmly, practicing problems is still the best way.

And I'm not the only one who thinks so. Henry Roediger and Jeffrey Karpicke, psychologists from Washington University, published an article on "practicing problems" in Psychological Science. In their article, they mentioned that simulated tests, i.e., practicing problems, have a significant impact on memory retention.

To verify this statement, they conducted tests with students and compared the effect of practicing problems versus memorizing learning materials on knowledge retention. The result showed that, although memorizing the material had good short-term effects, practicing problems had an absolute advantage in long-term memory retention.

From the bar chart above, you can see that within 5 minutes after learning, students who memorized the material had better memory retention, but after 2 days to one week, the group that practiced problems had twice as much memory retention compared to the memorization group. Moreover, research has shown that practicing problems not only improves memory retention but also accuracy. As shown in the figure below, compared with reading learning material (45% accuracy), practicing problems/testing helps retain knowledge more accurately (67% accuracy).

From these studies, we can see that practicing problems can really help children remember knowledge more firmly and accurately.

3.Change the structure of children's brains.

Seeing this title, some of you may think I'm exaggerating, saying that practicing problems can make your child smarter? Yes, it can. Because when practicing problems, our brains go through a process of retrieving and recalling stored knowledge.

In this process, our brains are not only recalling information but also engaging in a cognitive process of understanding, reasoning, extending and generating output. For example, a child can observe the surface of a clock or count the number of large and small squares on the dial to verify what their teacher taught them about clocks in class. This is a process of recalling and understanding. Writing down the correct answer is an output process.

However, while practicing problems, children may also have other thoughts such as: "Doesn't the clock have a second hand? Why wasn't it mentioned in class?" Curious children may even observe the movement of the second hand on a clock in real life. Although their conclusion based on personal observation may not be entirely accurate, it's still preparation for learning about the second hand in the future.

Therefore, practicing problems not only consolidates old knowledge but also prepares children adequately for new knowledge. As the saying goes, "Reviewing old topics enables one to learn new ones." However, while there are many benefits to practicing problems, giving your child a pile of questions to practice alone is not the best approach. This approach not only has no effect on improving your child's grades but can also damage their interest in learning.

4.What should you pay attention to when practicing problems?

Step 1: Choose appropriate difficulty level questions that expose weaknesses.

Especially after finishing a unit, we can find some basic comprehensive exercises for children to try. One thing to note is that always choose basic questions rather than advanced ones. My daughter and I sometimes do these exercises together, pretending that we are taking exams. Sometimes, I even grade her. In fact, the final score is not important. The key is to quickly identify the weak areas in your child's learning through these basic questions. This will prepare them for the actual "practice" phase of problem-solving, so that they won't practice aimlessly.

Step 2: Improve weaknesses exposed by children.

After finding weaknesses through one or two sets of basic questions, don't just start practicing lots of similar or transformed questions based on what they do not know. Doing so might result in more errors, be meaningless, and waste time, damaging your child's interest in learning. After discovering a child's weakness, first help them supplement and improve their weak knowledge points. See whether the child is having trouble recalling basic knowledge from the textbook or understanding the underlying logic of the question. Always go back to the textbook and make sure they understand the most basic theory before practicing problems. It's like building a road: first compact and level the base, then harden and pave it with asphalt to create a solid highway!

Step 3: Practice problems purposefully.

After handling all the basic issues, it's not the time to practice everything randomly. You still need some strategies. Original questions from textbooks must be practiced since these examples are typical and basic questions. Whether doing transformed questions or advanced-level questions, they are all derived from textbook examples. Another type of question to practice is your child's incorrect questions. Be sure to prepare a notebook for wrong answers. The questions in this book are critical questions from the process of practicing problems. This not only reduces your child's burden but also helps them to have an objective and purposeful approach to improve their learning efficiency.

Step 4: Choose typical questions to practice.

Although you are practicing problems, it doesn't mean that you should practice everything. For example, repetitive questions with too much similarity should be avoided. First, children may not want to do them as they find them boring. Second, doing similar questions repeatedly can develop habitual thinking, limiting a child's flexible application of knowledge.

Also, avoid calculation questions that are too difficult or too complex. Practicing calculation questions is to consolidate calculation rules and improve speed. Standard calculation questions usually achieve this goal. Questions that make you scratch your head and calculate without any simplification, reduction, or smart calculation should be avoided. What kind of questions should you practice? Those that have the same underlying theory but different directions, which means transformed questions that have many variations.

For example:

A classic primary school problem: Chicken and Rabbit in the same cage.

There are 20 chickens and rabbits with 44 feet in total. How many of each animal do you have?

A pen contains both birds and rabbits. The number of rabbits is four more than the number of birds. There are 76 feet in total. How many rabbits and birds are there?

If there are 200 chickens and rabbits with chicken feet 56 less than rabbit feet, how many chickens and rabbits are there?

There are 27 boxes of pens and pencils with a total of 300 pens/pencils. Each box of pens has 10 pens, and each box of pencils has 12 pencils. How many boxes of pens and pencils are there?

A large bottle of oil weighs 4 kg, while two small bottles weigh 1 kg. If there are 100 kg of oil in a total of 60 bottles, how many large and small bottles are there?

This item was added to our catalog on Friday 26 May, 2023.