Learning for junior high school entrance exams depends on how you teach! There is a huge difference in thinking ability
Note: This post is specialized in science thinking skills such as arithmetic and science.
Most children who aim to take the junior high school entrance exam attend a cram school for about 3 years from around the 4th grade of elementary school (at the latest to the 5th grade) to prepare for the entrance exam.
The major preparatory schools that children attend have repeatedly researched and produced original teaching materials, and instructors specializing in entrance exams will guide them according to the curriculum of the perfect teaching materials.
The teaching materials are really good, and it is surprising that elementary school children are devised to make elementary school students understand the units they learn in high school mathematics so that they can sometimes understand this and that, and they can naturally guide the solution to the problem with their own heads without making full use of formulas.
Since a professional instructor will teach this excellent teaching material for three years, and in a very soft-minded childhood, it may be natural that you will acquire your thinking skills and improve your brain.
Personally, I would like all children to use this excellent teaching material to learn, regardless of whether they take the junior high school entrance exam or not.
Because when going on to junior high school ~ high school,This is because what I learned in elementary school using this excellent teaching material will be my "ability to think theoretically" and "mathematically" in the future.
In fact, in the 2022 Common Test (Mathematics II.B), questions were asked that intertwined the number sequences learned in high school mathematics and the traveler's arithmetic learned by elementary school students in junior high school entrance exams.
The high school student I was teaching (no experience in junior high school entrance exams) understood the number sequence, but he did not notice the idea of "traveler's arithmetic (graph)" and lost points from (1) of the common test question. On the other hand, when I tried to solve it with a sixth-grade elementary school student, of course I couldn't solve the problem of the number sequence (solution using a gradient formula) in high school, but I have a shocking memory that I solved the problem of traveler's arithmetic (graph) and answered (1) of the big question correctly.
2023In the common test of the year, problems involving compound interest calculation and gradation formulas were asked in Mathematics II and B, and students who were interested in saving and investing would have understood the mechanism well and would have worked advantageously.
Unlike the previous center exam, the common test not only covers high school mathematics knowledge, but also junior high school mathematics and elementary school mathematics learning, and even mathematical knowledge as well as daily social and economic content.How important it is for future learning to have the ability to think deeply since elementary school and to be interested in and interested in various events!I feel it.
Again, the teaching materials produced by major junior high school entrance examination cram schools are closely related to daily life, and they are learning to draw line diagrams and designs and make you think without making full use of formulas as much as possible."Improve children's brains"There is no doubt that it will be.
However, when I look at the teaching methods and learning methods of instructors at junior high school entrance exams and cram school recently, I realize that there is a considerable difference from the teaching methods of professional cram school instructors I taught in elementary school.
Of course, I can understand that teaching methods are also changing with the changes of the times.I am worried that it is becoming a teaching method that cannot be concluded that "learning for junior high school entrance exams acquires thinking skills".
What does that mean? Let's give you a specific example.
[Number sequence problems learned in the 4th grade of elementary school]
"According to a certain rule, the numbers are arranged as follows
3, 9, 15, 21, 27・・・・・
(1) What is the number 20th from left?
(2) If you add up to the 20th number from left to right, what is the sum?
In fact, this sequence problem is also learned in high school mathematics.
In high school mathematics
You will learn how to find the general term of a sequence = first term tolerance × (n-1).
The same problem in elementary school math
The difference between 9~3 is 6, the difference between 15~9 is 6, and the difference between 21~15 is 6・・・・・
In other words, the numbers that have increased by 6 are lined up.
The number 20th is the number of 6 increased, and the number between the 1st to the 20th is 19, so the number of 19 times increased (from Ueki's calculation) = 19×6 = 114
However, since we are starting from 3, we add 3 to 114 3 = 117
What do you think?
In high school mathematics, the general term an=a with the first term a, tolerance d, and n as natural numbers.(n-1)While there are many high school students who learn with difficulty and do not understand the meaning of this formula and solve it,In elementary school mathematics, I have already learned to understand and solve the meaning of high school mathematics formulas.
As a result, when studying mathematics in high school, you can easily answer without the need for formulas such as general terms at all.
Furthermore, in high school mathematics, students learn the formula that seems very difficult, such as the sum of the equal difference sequence Sn = number of terms / 2× (first term last term).
However, the sum formula of this sequence (I will omit it here) also explains "Why is this happening?" in elementary school math materials, and "usually" even at cram schools, the instructor will guide you in detail with designs.
Therefore, after entering high school, I was able to take classes as a matter of course, not new knowledge at all.
Students who studied in junior high school entrance exams clearly had a high school math sequence.He understood the meaning of the essence of the sequence and acquired the ability to assemble and solve it by himself even if he did not memorize the formula.
howeverThere has been a change in cram school instruction in recent years.I feel. (This is not the case for all cram schools)
Among the students who attend the major cram schools I teach, there are many children who proudly chant formulas and subsume them, saying, "The □ is the first number tolerance × (□-1)...".
There are various reasons such as "the cram school teacher himself has no experience in taking the junior high school entrance examination", "it is more efficient to memorize the formula", and "there is no class time to explain the meaning of the formula", but this does not allow you to acquire "logical thinking skills" at all even if you study for the junior high school entrance exam.
Far from not being able to learn it, only self-esteem such as "I know advanced formulas" and "I know advanced solutions" grows, and furthermore, it creates the illusion that "I can do arithmetic (mathematics) by memorizing formulas", and when this becomes a habit, as I go to junior high school and high school,"Memory brain of solution techniques"It has become and does not fly, and lacks "logical thinking ability"I don't understand "thinking" itselfIt may end up getting worse.
"Guidance that you want to avoid at all costs"It can be said.
In the teaching method of junior high school entrance examinations, this danger has become noticeable not only in the number sequence but also in many units.
In the end, excellent teaching materials that cram schools have worked hard to produce over many years are meaningless in this kind of learning method.
Let me give you a few typical examples.
First of all, it is the number of cases.
[1. The problem of the number of cases learned in the 5th grade of elementary school]
１．『 A.B.C.D.E.F. will select one class leader and one vice-team leader in a group of 6 people. How do you choose a class leader and a deputy team leader?
２．『 Choose two of the six A.B.C.D.E.F day shifts. How do you choose?"
Number problems in these cases are learned in high school mathematics with permutations (P) and combinations (C).
In elementary school arithmetic, I first learned by having them write a tree diagram and count it.
And it was a teaching method that made students understand "why do you do ÷ 2 in problem 2?" by actually experiencing the difference between problems 1 and 2, but recently, cram school instructors have seen opportunities to teach "problem 1 is 6P2, so there are 30 ways of 6×5" and "problem 2 is 6C2, so there are 15 ways of 6×5÷ 2×1".
The student said, "P?C?" I wonder, "Why is it ÷ C?"
In question 2, my cram school has students write a tree diagram once.
Then, the child realized, "Oh, I'm counting the same thing twice~" and said, "Why do I have to divide the problem of 2 by 2?" I can understand it.
However, thisI feel a sense of crisis that the guidance of the instructor who gives me awareness from actual experience is fading.
There is also an example like this.
[2. The problem of "speed and ratio" learned in the 6th grade of elementary school]
"Mr. A leaves home at the same time every morning and goes to school. If you walk at a speed of 90 meters per minute, you will arrive at 8:25, but if you ride a bicycle at a speed of 300 meters per minute, you will arrive at 8:11. What time and minute does Mr. A leave the house every morning?"
In fact, these problems are also learned as applied problems in the "Equations" unit of junior high school mathematics.
However, in the math of elementary school students who have not learned equations, the child's "logical thinking ability" was acquired by teaching them as follows.
[Instructor]
"What is the ratio of speed to walking and cycling?"
[Student]
"90m/min: 300m/min, so 3:10"
[Instructor]
"That's right~! Simply put, walking in 1 minute means (3) and cycling (10)!"
"If so, how much time does it take to walk the same distance and ride a bicycle?"
[Student]
"Hmm~hmm? It takes a lot of time because you only go a little further on foot! I see! The ratio of time taken in the opposite of that ratio is walking: bicycle is 10:3 "
[Instructor]
It takes 10 hours to walk on the same school route, and it takes 3 to arrive by bicycle."
"In other words, there is a time difference of 10-3=7 between walking and cycling."
"If that's the case, there is a difference of 25 minutes - 11 minutes = 14 minutes between walking and cycling on the same school route, so this 7 is 14 minutes, and 1 is 2 minutes."
"The time it took to walk is 10, so 10×2 minutes = 20 minutes.
How about?
In the past, without making full use of formulas like this, guidance was given to easily guide you to the answer without even calculating it by imagining it in your head (once you get used to it).
On top of thatWhile enjoying the ability to think theoretically one by oneI led it.
In addition, elementary school arithmetic without making full use of formulas can also be used as a unique solution as follows.
[Instructor]
"Walking and cycling are the same school route, so let's set the distance to ○m yourself."
"It doesn't matter if it's 1m or 100m, but since you are going 90m or 300m in one minute, set it to 900m (the least common multiple of 90 and 300) to make it easier to calculate!"
"How many minutes does it take to walk 90 m/minute, or how many minutes does it take to ride a bicycle?"
[Student]
"If you walk, you will walk for 10 minutes at 900m÷90, and if you ride a bicycle, you will take 3 minutes at 900m÷300. Oh yes! Now that the difference is 14 minutes, the distance is doubled. The school route is 1800m! It took twice as long as it took to walk, and it took 20 minutes."
[Instructor]
"Oh yes, you can think like this."
Like thisIf you don't make full use of formulas, you can derive solutions from various ways of thinking and have a "flexible way of thinking"It will be like this.
This"Flexibility" has a great impact on future "mathematical ability"It is no exaggeration to say.
However, in recent cram schools,
"Put the walking time as □ minutes and the bicycle time as (□-14) minutes. The ratio of time to speed traveling the same distance is opposite, so the ratio of walking: bicycle speed is 90:300 = 3:10 is opposite...
Time to walk: Time spent on a bicycle = 10:3 = □:(□-14)
3×□＝10×（□－14）
3×□＝10×□－140
7×□＝140
□＝20
"It took 20 minutes to walk."
I began to see many students receiving this kind of guidance.
This is a solution based on the equation of a junior high school student.
Some people may think that "receiving preemptive guidance from junior high school students is advantageous for taking exams", but it is meaningful only when you acquire the "ability to think for yourself" in elementary school, and this kind of preemptive learning for children whose arithmetic skills are not yet perfect may prevent "thinking ability" more and more.
If this kind of "formula-assembling" learning method becomes a habit from elementary school, it will be impossible to visualize the phenomenon in your head at all.
If you can't visualize the phenomenon in your head, you won't be able to take science and mathematics subjects in junior high and high school first.
The reason is that students who are not good at mathematics are obsessed with constructing formulas and do not have the ability to imagine and think about phenomena.
It is no exaggeration to say that this is a problem with the fact that they have not developed the "ability to think" since elementary school.
And frighteningly, students who lack the ability to think are more difficult in junior high school ~ high school mathematics
We will lean towards formula-dependent learning methods.
I was obsessed with "which formula can I use to solve it?" and finallyIt becomes a "memory brain for solution techniques" and results in struggling with science and mathematics subjects in junior high and high school.It is clear.
To acquire the "ability to think",
"Don't teach or use formulas as much as possible"
"Practice and make people realize why this is the case."
I feel that it is important for cram school instructors to teach in this regard.
Also, recently
・Do not write line drawings or designs
・The notebook is beautifully listed like a junior high and high school student.
・Do not write stick figures and visualize the phenomenon in question in pictures.
I see a lot of students.
To imagine the phenomenon of arithmeticBy writing pictures, designs, and line diagrams in a notebook, you will deepen your understanding and develop your "ability to think"It is.
Without this work, you will never acquire "thinking skills".
If this learning method has not become a habit, let's review the teaching method of the instructor you attend the cram school again.
Parents should also be careful that if the teaching method is wrong, instead of acquiring the ability to think, they will only cultivate the "memory brain of solution techniques", which can affect junior high school ~ high school.
"Even if you are learning with the same teaching materials, there will be a big difference in your child's thinking ability in the teaching method."It is.
Don't be overconfident that "it's okay because you're studying at a cram school," and sometimes ask "How are you learning?" or "What kind of guidance are you getting?" I hope that you will actually look at the notebook and make an effort to check the teaching method.
Again,
"Learning for junior high school entrance exams depends on how you teach!It is.
This page has been automatically translated. Please note that it may differ from the original content.
Note: This post is specialized in science thinking skills such as arithmetic and science.
Most children who aim to take the junior high school entrance exam attend a cram school for about 3 years from around the 4th grade of elementary school (at the latest to the 5th grade) to prepare for the entrance exam.
The major preparatory schools that children attend have repeatedly researched and produced original teaching materials, and instructors specializing in entrance exams will guide them according to the curriculum of the perfect teaching materials.
The teaching materials are really good, and it is surprising that elementary school children are devised to make elementary school students understand the units they learn in high school mathematics so that they can sometimes understand this and that, and they can naturally guide the solution to the problem with their own heads without making full use of formulas.
Since a professional instructor will teach this excellent teaching material for three years, and in a very soft-minded childhood, it may be natural that you will acquire your thinking skills and improve your brain.
Personally, I would like all children to use this excellent teaching material to learn, regardless of whether they take the junior high school entrance exam or not.
Because when going on to junior high school ~ high school,This is because what I learned in elementary school using this excellent teaching material will be my "ability to think theoretically" and "mathematically" in the future.
In fact, in the 2022 Common Test (Mathematics II.B), questions were asked that intertwined the number sequences learned in high school mathematics and the traveler's arithmetic learned by elementary school students in junior high school entrance exams.
The high school student I was teaching (no experience in junior high school entrance exams) understood the number sequence, but he did not notice the idea of "traveler's arithmetic (graph)" and lost points from (1) of the common test question. On the other hand, when I tried to solve it with a sixth-grade elementary school student, of course I couldn't solve the problem of the number sequence (solution using a gradient formula) in high school, but I have a shocking memory that I solved the problem of traveler's arithmetic (graph) and answered (1) of the big question correctly.
2023In the common test of the year, problems involving compound interest calculation and gradation formulas were asked in Mathematics II and B, and students who were interested in saving and investing would have understood the mechanism well and would have worked advantageously.
Unlike the previous center exam, the common test not only covers high school mathematics knowledge, but also junior high school mathematics and elementary school mathematics learning, and even mathematical knowledge as well as daily social and economic content.How important it is for future learning to have the ability to think deeply since elementary school and to be interested in and interested in various events!I feel it.
Again, the teaching materials produced by major junior high school entrance examination cram schools are closely related to daily life, and they are learning to draw line diagrams and designs and make you think without making full use of formulas as much as possible."Improve children's brains"There is no doubt that it will be.
However, when I look at the teaching methods and learning methods of instructors at junior high school entrance exams and cram school recently, I realize that there is a considerable difference from the teaching methods of professional cram school instructors I taught in elementary school.
Of course, I can understand that teaching methods are also changing with the changes of the times.I am worried that it is becoming a teaching method that cannot be concluded that "learning for junior high school entrance exams acquires thinking skills".
What does that mean? Let's give you a specific example.
[Number sequence problems learned in the 4th grade of elementary school]
"According to a certain rule, the numbers are arranged as follows
3, 9, 15, 21, 27・・・・・
(1) What is the number 20th from left?
(2) If you add up to the 20th number from left to right, what is the sum?
In fact, this sequence problem is also learned in high school mathematics.
In high school mathematics
You will learn how to find the general term of a sequence = first term tolerance × (n-1).
The same problem in elementary school math
The difference between 9~3 is 6, the difference between 15~9 is 6, and the difference between 21~15 is 6・・・・・
In other words, the numbers that have increased by 6 are lined up.
The number 20th is the number of 6 increased, and the number between the 1st to the 20th is 19, so the number of 19 times increased (from Ueki's calculation) = 19×6 = 114
However, since we are starting from 3, we add 3 to 114 3 = 117
What do you think?
In high school mathematics, the general term an=a with the first term a, tolerance d, and n as natural numbers.(n-1)While there are many high school students who learn with difficulty and do not understand the meaning of this formula and solve it,In elementary school mathematics, I have already learned to understand and solve the meaning of high school mathematics formulas.
As a result, when studying mathematics in high school, you can easily answer without the need for formulas such as general terms at all.
Furthermore, in high school mathematics, students learn the formula that seems very difficult, such as the sum of the equal difference sequence Sn = number of terms / 2× (first term last term).
However, the sum formula of this sequence (I will omit it here) also explains "Why is this happening?" in elementary school math materials, and "usually" even at cram schools, the instructor will guide you in detail with designs.
Therefore, after entering high school, I was able to take classes as a matter of course, not new knowledge at all.
Students who studied in junior high school entrance exams clearly had a high school math sequence.He understood the meaning of the essence of the sequence and acquired the ability to assemble and solve it by himself even if he did not memorize the formula.
howeverThere has been a change in cram school instruction in recent years.I feel. (This is not the case for all cram schools)
Among the students who attend the major cram schools I teach, there are many children who proudly chant formulas and subsume them, saying, "The □ is the first number tolerance × (□-1)...".
There are various reasons such as "the cram school teacher himself has no experience in taking the junior high school entrance examination", "it is more efficient to memorize the formula", and "there is no class time to explain the meaning of the formula", but this does not allow you to acquire "logical thinking skills" at all even if you study for the junior high school entrance exam.
Far from not being able to learn it, only self-esteem such as "I know advanced formulas" and "I know advanced solutions" grows, and furthermore, it creates the illusion that "I can do arithmetic (mathematics) by memorizing formulas", and when this becomes a habit, as I go to junior high school and high school,"Memory brain of solution techniques"It has become and does not fly, and lacks "logical thinking ability"I don't understand "thinking" itselfIt may end up getting worse.
"Guidance that you want to avoid at all costs"It can be said.
In the teaching method of junior high school entrance examinations, this danger has become noticeable not only in the number sequence but also in many units.
In the end, excellent teaching materials that cram schools have worked hard to produce over many years are meaningless in this kind of learning method.
Let me give you a few typical examples.
First of all, it is the number of cases.
[1. The problem of the number of cases learned in the 5th grade of elementary school]
１．『 A.B.C.D.E.F. will select one class leader and one vice-team leader in a group of 6 people. How do you choose a class leader and a deputy team leader?
２．『 Choose two of the six A.B.C.D.E.F day shifts. How do you choose?"
Number problems in these cases are learned in high school mathematics with permutations (P) and combinations (C).
In elementary school arithmetic, I first learned by having them write a tree diagram and count it.
And it was a teaching method that made students understand "why do you do ÷ 2 in problem 2?" by actually experiencing the difference between problems 1 and 2, but recently, cram school instructors have seen opportunities to teach "problem 1 is 6P2, so there are 30 ways of 6×5" and "problem 2 is 6C2, so there are 15 ways of 6×5÷ 2×1".
The student said, "P?C?" I wonder, "Why is it ÷ C?"
In question 2, my cram school has students write a tree diagram once.
Then, the child realized, "Oh, I'm counting the same thing twice~" and said, "Why do I have to divide the problem of 2 by 2?" I can understand it.
However, thisI feel a sense of crisis that the guidance of the instructor who gives me awareness from actual experience is fading.
There is also an example like this.
[2. The problem of "speed and ratio" learned in the 6th grade of elementary school]
"Mr. A leaves home at the same time every morning and goes to school. If you walk at a speed of 90 meters per minute, you will arrive at 8:25, but if you ride a bicycle at a speed of 300 meters per minute, you will arrive at 8:11. What time and minute does Mr. A leave the house every morning?"
In fact, these problems are also learned as applied problems in the "Equations" unit of junior high school mathematics.
However, in the math of elementary school students who have not learned equations, the child's "logical thinking ability" was acquired by teaching them as follows.
[Instructor]
"What is the ratio of speed to walking and cycling?"
[Student]
"90m/min: 300m/min, so 3:10"
[Instructor]
"That's right~! Simply put, walking in 1 minute means (3) and cycling (10)!"
"If so, how much time does it take to walk the same distance and ride a bicycle?"
[Student]
"Hmm~hmm? It takes a lot of time because you only go a little further on foot! I see! The ratio of time taken in the opposite of that ratio is walking: bicycle is 10:3 "
[Instructor]
It takes 10 hours to walk on the same school route, and it takes 3 to arrive by bicycle."
"In other words, there is a time difference of 10-3=7 between walking and cycling."
"If that's the case, there is a difference of 25 minutes - 11 minutes = 14 minutes between walking and cycling on the same school route, so this 7 is 14 minutes, and 1 is 2 minutes."
"The time it took to walk is 10, so 10×2 minutes = 20 minutes.
How about?
In the past, without making full use of formulas like this, guidance was given to easily guide you to the answer without even calculating it by imagining it in your head (once you get used to it).
On top of thatWhile enjoying the ability to think theoretically one by oneI led it.
In addition, elementary school arithmetic without making full use of formulas can also be used as a unique solution as follows.
[Instructor]
"Walking and cycling are the same school route, so let's set the distance to ○m yourself."
"It doesn't matter if it's 1m or 100m, but since you are going 90m or 300m in one minute, set it to 900m (the least common multiple of 90 and 300) to make it easier to calculate!"
"How many minutes does it take to walk 90 m/minute, or how many minutes does it take to ride a bicycle?"
[Student]
"If you walk, you will walk for 10 minutes at 900m÷90, and if you ride a bicycle, you will take 3 minutes at 900m÷300. Oh yes! Now that the difference is 14 minutes, the distance is doubled. The school route is 1800m! It took twice as long as it took to walk, and it took 20 minutes."
[Instructor]
"Oh yes, you can think like this."
Like thisIf you don't make full use of formulas, you can derive solutions from various ways of thinking and have a "flexible way of thinking"It will be like this.
This"Flexibility" has a great impact on future "mathematical ability"It is no exaggeration to say.
However, in recent cram schools,
"Put the walking time as □ minutes and the bicycle time as (□-14) minutes. The ratio of time to speed traveling the same distance is opposite, so the ratio of walking: bicycle speed is 90:300 = 3:10 is opposite...
Time to walk: Time spent on a bicycle = 10:3 = □:(□-14)
3×□＝10×（□－14）
3×□＝10×□－140
7×□＝140
□＝20
"It took 20 minutes to walk."
I began to see many students receiving this kind of guidance.
This is a solution based on the equation of a junior high school student.
Some people may think that "receiving preemptive guidance from junior high school students is advantageous for taking exams", but it is meaningful only when you acquire the "ability to think for yourself" in elementary school, and this kind of preemptive learning for children whose arithmetic skills are not yet perfect may prevent "thinking ability" more and more.
If this kind of "formula-assembling" learning method becomes a habit from elementary school, it will be impossible to visualize the phenomenon in your head at all.
If you can't visualize the phenomenon in your head, you won't be able to take science and mathematics subjects in junior high and high school first.
The reason is that students who are not good at mathematics are obsessed with constructing formulas and do not have the ability to imagine and think about phenomena.
It is no exaggeration to say that this is a problem with the fact that they have not developed the "ability to think" since elementary school.
And frighteningly, students who lack the ability to think are more difficult in junior high school ~ high school mathematics
We will lean towards formula-dependent learning methods.
I was obsessed with "which formula can I use to solve it?" and finallyIt becomes a "memory brain for solution techniques" and results in struggling with science and mathematics subjects in junior high and high school.It is clear.
To acquire the "ability to think",
"Don't teach or use formulas as much as possible"
"Practice and make people realize why this is the case."
I feel that it is important for cram school instructors to teach in this regard.
Also, recently
・Do not write line drawings or designs
・The notebook is beautifully listed like a junior high and high school student.
・Do not write stick figures and visualize the phenomenon in question in pictures.
I see a lot of students.
To imagine the phenomenon of arithmeticBy writing pictures, designs, and line diagrams in a notebook, you will deepen your understanding and develop your "ability to think"It is.
Without this work, you will never acquire "thinking skills".
If this learning method has not become a habit, let's review the teaching method of the instructor you attend the cram school again.
Parents should also be careful that if the teaching method is wrong, instead of acquiring the ability to think, they will only cultivate the "memory brain of solution techniques", which can affect junior high school ~ high school.
"Even if you are learning with the same teaching materials, there will be a big difference in your child's thinking ability in the teaching method."It is.
Don't be overconfident that "it's okay because you're studying at a cram school," and sometimes ask "How are you learning?" or "What kind of guidance are you getting?" I hope that you will actually look at the notebook and make an effort to check the teaching method.
Again,
"Learning for junior high school entrance exams depends on how you teach!It is.
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