Ninth graders often ask me in class: “Why do we need trigonometry?” And in the tenth-eleventh class, the question arises: “Why do we need integrals and a derivative? And the coordinate method in geometry? ”
All difficult topics raise similar questions. “Most likely, this will not be useful to us in life,” my students say. And if you analyze the statistics of graduates, they are right. Only a small part of them will use any of the above. And even less – to apply in future work all the mathematical knowledge from the school curriculum.
Let’s figure out what the meaning of the subject is and why it’s worth falling in love with mathematics.
Reason 1. Uniqueness
How did the reforms of Peter I influence the development of the state? Controversial topic. Why did Taras Bulba kill his son? Many articles have been written with varying interpretations. Can a legal state listen to its own citizens? The question is controversial.
And finally: 3x + 4x = 7x. Is always. Yesterday, 50 years ago, in Africa, in a crisis, in inclement weather.
Reason 2. The development of thinking
The child has learned to count, and if he will only deal with calculations, sooner or later he will stop in development. Yes, it can be considered verbally using complex algorithms in the mind, but only the speed of thinking will develop, not the depth.
What follows is an introduction to variables, geometry, trigonometry, stereometry, logarithms, and the antiderivative derivative. And each subsequent, more complex topic leads to the fact that the student develops intellectual abilities: skills of analysis and generalization, abstract thinking and the ability to think in concepts.
Reason 3. Ability to reflect on the abstract
We know that one platypus plus two platypuses will be three platypuses. Although few people, solving this problem, saw the platypus live. It is mathematics that teaches us to reflect on what we do not have in reality, to design. We use present information to plan long-term or short-term future. And the quality of such planning greatly depends on our mathematical abilities.
Reason 4. Making difficult decisions
If we have only n rubles, and on vacation we need n + 20 000 rubles, then we choose the cheaper option, since mathematics taught us to compare. And no matter how much we want to go on a dream vacation, the harsh mathematical reality tells us that it will not work.
Here is a classic problem for the fifth to sixth grade. 100 children live in city A, 300 children in city B. The distance between cities is 10 km. At what point do you need to build a school so that children together overcome the smallest possible distance? The answer is at the end of the article.
Reason 5. Yes, it is practically applicable
The influence of mathematics on the successful work of programmers, scientists and engineers is self-evident.
Many times I met engineers who use trigonometry in design. Successful office workers have a competitive advantage, being able to optimize their activities.
Reason 6. We learn algorithms
We do not think when we repeat everyday algorithms. We don’t think how to breathe, how to lace up shoes, we don’t plan a thousandth way to work. Yes, we mastered most of these skills long before we went to school.
But if we are talking about high-level algorithms, then mathematics helps us here. Make the right solution of the substance, perform the operation (the surgeon makes decisions based on the incoming information, and he will treat the same two patients equally), make logistic decisions and so on.
Also, mathematics tells us that it is foolish to do the same thing and hope for a different result. Your colleague brews coffee according to the usual algorithm, but the coffee machine does not work. He repeats the same action again, again – but there is still no coffee. Analyze his math level.
Reason 7. Generate and recognize false
It can be of different types.
A comic lie: “Perhaps this is the best article about mathematics from a mathematics teacher at Lifehacker for 2018.” Like narrowing the information field we can not only joke, but also mislead.
Statistics like a lie: “According to statistics, most of those who drank water died.” This is the most commonplace example. There is more gracefully, with the same misunderstanding of the correlation: “Everyone who has achieved success in life has seen a sunset or taken a bath, and maybe both. The conclusion is obvious. If you want to be successful, take a bath at sunset. ”
The next type of lie in statistics can harm not only those who read it, but also those who collect data. it sampling falsity. You open your own business and conduct a survey near a business center, for example, about confectionery. You got a sample of 1,500 people, realized what the future buyer wants to see, and open a candy store in your sleeping area, taking into account the wishes of the people. But customers do not go, and you are bankrupt.
This trap can be set specifically. For example, a study of the effectiveness of toothpaste in people who have just left a dentist. Student sports research and projection of results on the older generation. A study of public opinion via the Internet: “As an online survey shows, 100% of the population has access to the Internet.”
There is also falsehood. Not everyone evaluates correctly the relationship between events and the number of repetitions. The first example: if the probability that a house on the seashore floods, for example, 1/10 000, then when calculating the probability of flooding of two houses at once, we get 1/100 000 000. This is wrong, because if the house is flooded, it means that a natural disaster happened: heavy rain, big waves caused a flood. It is obvious that in such conditions many houses will be flooded, and the likelihood of flooding of the second house is much higher.
The second example is the number of repetitions. If we have a small probability of an event, but its conditions are often repeated, then it is likely to happen. Let’s say the probability of slipping in a bath without a rug is 1/5 000. How often do we take a shower? Once or twice a day. So, we can assume that if we do not put a rug on the bottom of the bathtub, then about once every 10 years we will slip, and here the outcome depends on dexterity and good luck.
Learn math, understand life.
The answer to the problem: you need to build a school in city B, however sad it is for the guys from city A.