Never give them the answer!
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You should teach them how to think, not what to think.
There was a similar quote in the drama version of the manga "Dragon Zakura".
For children who want to eat fish, which would you rather do for them?
1) Catch the fish yourself and feed it to the children.
2) You don't catch the fish yourself, but you teach the children how to fish.
From a short-term perspective, you might think you want to catch the fish for them and feed it to them.
However, by doing so, the children might end up in the following situations:
"The children will develop the idea that fish are things you receive, not things you catch yourself."
"You will have to continue fishing for the children forever."
"The children can only eat the fish that you are skilled enough to catch."
"If you are no longer there, the children will not be able to eat fish."
Isn't this a lesson that should be remembered when teaching anything, not just fishing?
For example, to put it in a more easily understood case:
A child has been given homework.
The child says they don't understand it.
Would you then immediately give them the answer just because it would make the child happy?
You wouldn't do that, would you?
This is because you know that it is important for them to derive the answer "by themselves."
It is because you know that the result is not what is important, but the process is.
If you only provide the answer (the result of your own thinking), the person being taught may become someone who just "waits" for the answer and may stop considering that other answers might exist.
However, if you teach the way of thinking to derive the answer, they may become someone who can "search" for the answer.
They might even come up with an "answer" you never thought of yourself.
I think it is interesting to pay attention each time you are teaching to see whether you are teaching the "answer" or the "way of thinking."
Also, when someone else is teaching you something, consider whether they are telling you the "answer" or teaching you the "way of thinking."
I think it is even more interesting to think about that as well (^^)
The first condition for "improving one's ability to learn" is the awareness of "not having learned enough," the realization that there is "still so much I need to learn."
Now then, why don't you try solving a little arithmetic problem here? (Grin)
It's a nostalgic arithmetic word problem, so how about a little brain exercise for a change?
Believe it or not, when I was a university student, I worked part-time as a Kumon teacher for arithmetic (from 1st grade) and mathematics (up to 3rd year of high school), so I might be a little good at arithmetic.
For those who get all the questions right, there might be a special little gift from me (lol).
Well then, go ahead and give it some thought!?
1. Planting Problem
【Problem】
Along a 10-meter road, cherry trees are planted at 1-meter intervals.
How many cherry trees are needed?
The planting problem is a type of problem that appeared in arithmetic during the Edo period.
I think it can be done easily if you can do division, but there is a pitfall in an unexpected place.
So, how many trees do you all predict... that is the question.
Come on, give it a try!
2. Difference Problem
[Problem]
A squirrel has 63 acorns, and a flying squirrel has 55 acorns.
How many acorns should the squirrel give to the flying squirrel so that they both have the same number of acorns?
This is what we call difference calculation.
It is called difference calculation because you get the answer by dividing the difference between the two.
There are various ways to arrive at the answer for this as well.
Methods like dividing the difference, using the concept of the overall average, or using X... solving things in various ways is what builds your skills, isn't it? (^^)
3. Sum and Difference Calculation
[Problem]
An older brother and a younger brother have 15 coins in total.
The older brother has 3 more coins than the younger brother.
How many coins does each of them have?
I can almost hear people saying this is easy, but when I see problems like this, I think it would be fine to solve them using algebra with X and Y even in elementary school. (^^)
If you solve problems like crane-turtle calculation or sum and difference calculation using algebra, you won't need to memorize and distinguish between so many different types of word problems.
Solving this problem within the scope of arithmetic methods certainly has meaning in terms of learning various ways of thinking.
However, knowing how to solve it using X and Y broadens the scope of application, so let's try solving it with algebra!
4. Elimination Calculation
[Problem]
Buying 1 mandarin orange and 2 apples costs 50 yen.
Also, buying 1 mandarin orange and 1 apple costs 30 yen.
What is the price of one mandarin orange and one apple, respectively?
This is a problem where you determine the price of individual items from two different total prices.
Once you understand the concept through diagrams, you will be able to solve it quickly using algebra next time.
You know that algebra uses symbols like X and Y instead of numbers, right? (^^)
You can think of it as an equation of words.
Exactly, this is the fundamental concept behind equations.
5. Difference Calculation
【Problem】
Squirrel-kun planned to do 20 homework sheets a day during summer vacation.
However, he only did 15 sheets a day, so 100 sheets remained after summer vacation ended.
How many homework sheets were there in total?
It's called a difference calculation because you collect the difference between the days the homework was done and the days it wasn't.
Once you know the difference in the number of pages per day, the rest is easy.
Word problems can be solved by unraveling them little by little, just like untangling a thread (^^)
A great detective's mystery solving starts with gathering information, but in math word problems, all the information is already in the problem.
It's a battle of how to connect the little bits of information to get the answer!
6. Crane and Turtle Calculation
【Problem】
Six teams, A, B, C, D, E, and F, are playing soccer matches.
Each team plays every other team exactly once.
Points are awarded as follows: 3 points for a win, 1 point for a draw, and 0 points for a loss.
However, because Team F's participation was delayed, the five teams A through E played all their possible matches first, and the results are shown in the table below.
Team Points
A 10
B 9
C 4
D 3
E 1
How many draws were there in the matches played so far?
The crane and turtle calculation is a type of math problem that has existed in Japan for a long time.
This is the foundation of mathematics known as algebra, but before that, I think the problem is good.
Why is it good? Because the problem is so silly and funny (lol).
Counting the legs of cranes and turtles is generally unrealistic; I think you could just count the number of heads from the start, but it's funny to think about it seriously.
Some people ask why arithmetic is useful, but wouldn't saying, 'You can think about such interesting things,' be an answer?
7. Work Problems
【Problem】
The bears are currently building a school.
The rabbit and the squirrel are pouring concrete for the floor.
This job takes 10 days if done by the rabbit alone, and 15 days if done by the squirrel alone.
If they work together, how many days will it take?
This is a problem about thinking about work.
It's a problem that can be used in daily life, isn't it? (^^)
Work problems are the same type of problem as filling a pool with water.
There are various ways to think about it, but it is common to solve it as a ratio problem by considering the size of the pool as 1.
Let's master the way of thinking about ratios where the whole is 1!
It might even be useful sometimes (lol).
8. Age Problems
【Problem】
Currently, the older sister is 12 years old, the younger sister is 10 years old, and the mother is 38 years old.
In how many years will the sum of the older sister's and younger sister's ages be equal to the father's age?
Even though they are called age problems, there are various types of problems that deal with ages.
Age makes for an interesting problem, doesn't it? (^^)
9. Excess and Deficiency Problems
[Problem]
A traveler got lost and, since it was night, decided to sleep in a temple.
In the middle of the night, he heard voices outside and listened closely, only to find that some cloth thieves were discussing how to divide their stolen cloth.
"If we divide it into 5 bolts each, there are 3 bolts left over."
"If we divide it into 6 bolts each, we are 5 bolts short. How many thieves are there, and how many bolts of cloth are there?"
In a book of arithmetic from the Edo period called 'Jinkoki', there is a problem called 'The Silk Thief Problem'.
It is the problem above.
It's somewhat interesting to make thieves the subject of a problem, but it's also an interesting idea to listen to that and wonder how many there are and how many they stole, isn't it? (^^)
It's pitch black and you can't see, but can you figure it out if you think about it?
The thieves are interesting, but I think it's also interesting that you can figure it out through calculation.
10. Newton's Problems
[Problem]
In a certain pasture, if 300 cows graze, the grass runs out in 10 days, and if 600 cows graze, it runs out in 4 days.
Then, for how many days can 500 cows graze?
Assume that all cows eat the same amount of grass per day, and that the grass grows at a constant rate every day.
It's called a Newton's problem because Newton thought of it (^^)
While the aforementioned work problems are based on the inverse proportional relationship between the labor force (number of people) required to complete a task and the time it takes, Newton's problems are quite difficult because they involve a force that increases (hinders) or decreases (assists) the work at a constant rate while the work is being done, so they cannot be solved simply by using the concept of inverse proportion (^^;)
A characteristic of these various word problems is that they are not solved using equations or the like, but rather have individual solution methods for each type of problem (^^)
Furthermore, problems like the following are often featured in employment exams and civil service exams, so they might be good for mental gymnastics!
<Types of Word Problems>
[ Problems focusing on sums and differences ]
Planting problems
Crane and turtle problems
Sum and difference problems
Set problems
Regularity (in entrance exam arithmetic)
[ Problems focusing on ratios ]
Excess and deficiency problems
Reduction problems
Difference collection problems
Work problems
Unitary method problems (total sum problems)
Traveler problems
Passing problems
Newton's problems
Clock problems
Multiple problems
Distribution problems
Age problems
Flowing water problems
Water tank problems
Concentration problems
Profit and loss problems
Elimination problems
Equivalent problems
Average problems
Meeting problems
Catch-up problems
Assumption problems
Chicken, dog, and octopus problems
Reasoning problems
[ Others ]
Set theory problems
Reasoning problems
Algebraic systems
[ Other types of 'zan' problems ]
Komachi problems
Rat problems
Day-by-day doubling problems
Cryptarithmetic problems
Periodic problems
Square array problems
Calendar problems
Expansion problems
[ Reference articles, etc. ]
How to develop your own 'learning ability'?
Tatsuru Uchida wrote the following about learning ability, so I will introduce it here for your reference.
'There are three things necessary for the "ability to learn."
I will repeat them.
First, having a keen awareness of one's own ignorance, the feeling that "I must learn."
Second, being able to intuitively sense, "Ah, this person is my teacher."
Third, having a broad openness that makes that "teacher" want to teach.
To express these three conditions in a single sentence, it would be: "I want to learn. Teacher, please teach me."
It is not a matter of grades or scores that can be expressed numerically, but just these few words.
This is what I consider to be "academic ability."
A person who can honestly and clearly say this sentence is already, at that stage, a "person with academic ability."
Conversely, no matter how much knowledge or skill one has, a person who cannot say these words is a "person without academic ability."
It is not about not knowing English or not knowing mathematical formulas.'
They do not try to say the simple words, "I want to learn. Teacher, please teach me."
They feel that saying those words would be a great "loss," so if possible, they want to go through their whole life without ever having to say such a line.
They dislike asking someone for something because it feels like they are "in debt."
They think of themselves as having "high pride" or "backbone" for thinking that way.
I believe that is the essence of the situation known as 'academic decline'.
It is the learner themselves who decides whether what they have learned is useful, isn't it?
Value does not reside in knowledge, information, technology, or even money; it must be constructed by the person who uses it. However, when it comes to learning, I also believe that in our world, everyone has the potential to act as a mentor, so I hope you all find a great teacher!