2023November

Learning for the junior high school entrance exam depends on how you teach! There is a huge difference in thinking ability Note: This post is specialized in science thinking skills such as math and science. Most children who aim to take the junior high school entrance exam go to the junior high school entrance exam cram school for about three years from the 4th grade of elementary school (at the latest in the 5th grade) to prepare for the exam. All of the major preparatory schools that children attend do research and create 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 excellent, and it is amazing that they sometimes devise ways to make elementary school students understand the units they learn in high school mathematics, such as making elementary school children think about this and that, letting them naturally guide the solution to problems with their own minds without making full use of formulas, and making them understand the meaning of the formulas more deeply. This excellent teaching material is taught by a professional instructor for three years, and it is natural that the brain will improve as a child with a very soft mind. Personally, I would like all children, regardless of whether they take the junior high school entrance exam or not, to use this excellent material to learn. This is because when you go on to junior high school ~ high school, what you learn in elementary school using this excellent teaching material will be your "ability to think theoretically" and "mathematical ability" in the future. In fact, in the 2022 Common Test (Mathematics II.B), the content of the question was related to the number sequence learned in high school mathematics and the traveler's arithmetic learned by elementary school students in the junior high school entrance exam. The high school student I was teaching (who had no experience in junior high school entrance exams) understood the number sequence, but he was unaware of the idea of "traveler arithmetic (graph)" and lost points from (1) of the common test major question. On the other hand, when I tried to solve it with a sixth-grade elementary school student, I naturally couldn't solve the problem of the high school math sequence (solution using the recurrence formula), but I solved the problem of traveler arithmetic (graph) and answered (1) of the big question correctly. In the 2023 Common Test, Mathematics II.B also asked questions involving compound interest calculation and the recurrence formula, which would have been advantageous for students who are interested in saving and investing to understand how it works. Unlike the previous National Center Examination, the Common Test asks not only knowledge of high school mathematics, but also the study of junior high school mathematics and elementary school mathematics, and not only mathematics knowledge, but also content that is intertwined with daily socio-economic matters. I feel it. Again, the teaching materials produced by major junior high school entrance exams preparatory schools are closely related to daily life, and there is no doubt that they will definitely "improve children's minds" by making them think by drawing line diagrams and patterns without making full use of formulas as much as possible. However, when I look at the teaching methods and learning methods of the instructors at the junior high school entrance exam preparatory school these days, I realize that there is a considerable difference from the teaching methods of the professional cram school instructors I was instructed in elementary school. Of course, it is understandable that teaching methods will shift with the changing times, but I am afraid that it is becoming a teaching method that cannot be categorically concluded that "learning for junior high school entrance exams is to acquire the ability to think." What does that mean? Let me give you an example. [Number sequence problems learned in 4th grade] "According to a certain rule, arrange the numbers as follows: 3, 9, 15, 21, 27... (1) What is the 20th number from the left? (2) If you add the 20th number from the left to the 20th, what is the sum? In fact, this sequence problem is also studied in high school mathematics. In high school mathematics, you will learn the formula of how to find the general term of a sequence of numbers = first term tolerance × (n-1). In elementary school mathematics, the difference between 9~3 is 6, the difference between 15~9 is 6, the difference between 21~15 is 6, and the difference between 21~15 is 6. The number of the 20th number is 19 times from the 1st to the 20th, so the number increased 19 times (from the plant calculation) = 19×6 = 114 However, since it starts from 3, add 3 and 114 3 = 117 What do you think? In high school mathematics, the general term an=a in which the first term a, tolerance d, and n are natural numbers(n-1)While there are many high school students who learn difficult with D and solve problems by substituting this formula without knowing the meaning, they have already learned to understand and solve the meaning of the formula in high school mathematics in elementary school mathematics. As a result, when learning mathematics in high school, there is no need for formulas such as general terms, and it is easy to answer. Furthermore, in (2), you will learn a formula that seems difficult in high school mathematics, such as the sum Sn = number of terms / 2 × (first term last term) of a arithmetic sequence. However, the formula for the sum of this sequence (which I will omit here) is also explained in elementary school math teaching materials, and "usually" even at cram schools, the instructor will give detailed guidance with patterns. Therefore, after entering high school, I was able to take classes on the number sequences I learned in mathematics as a matter of course, not as new knowledge. The students who studied in the junior high school entrance exam clearly understood the meaning of the essence of the sequence in high school mathematics, and acquired the ability to assemble and solve problems on their own even if they did not memorize the formulas. However, I feel that there has been a change in cram school guidance in recent years. Among the students who attend the major cram schools I teach, there are many children who proudly recite the formula "The □ number tolerance is ×(□-1)...", and ask for it. There are various reasons for this, such as "the cram school instructor himself has no experience in taking the junior high school entrance exam", "it is more efficient to memorize the formula", "there is no class time to explain the meaning of the formula", etc., but this does not mean that even if you study for the junior high school entrance exam, you will not acquire "logical thinking skills" at all. Far from not being able to acquire it, the self-esteem of "I know advanced formulas" and "I know advanced solutions" increases, and furthermore, "I will be able to do arithmetic (mathematics) by memorizing formulas", and if this becomes a habit, as I go on to junior high school and high school, it will become a "memory brain of solving techniques", and I will lack "logical thinking ability" and "thinking" You may end up getting worse and worse if you don't know what it is. It can be said that it is "guidance that you want to avoid at all costs". In the teaching method for junior high school entrance exams, this danger has become noticeable not only in the number sequence but also in many units. At the same time, the excellent teaching materials that the cram school has painstakingly produced over many years are meaningless with this kind of learning method. Let's take a few typical examples. The first is the number of cases. [1. Numbers problem when learning in the 5th grade] 1. In the six-member A.B.C.D.E.F. group, one group leader and one deputy group leader will be selected. How many ways do you choose a group leader and a deputy group leader? 2．『 Out of the six A.B.C.D.E.F. members, choose two of them. How many ways do you choose?' The number problems in these cases are studied in high school mathematics by permutations (P) and combinations (C). In elementary school arithmetic, I learned by first drawing a tree diagram and counting. In addition, it was a teaching method to make students understand "why do ÷ 2 in problem 2" by actually experiencing the difference between problems 1 and 2, but recently I have seen opportunities where cram school instructors are teaching "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 asked, "P?C?" You may wonder, "Why do you ÷ C?" In problem 2, at my cram school, I have my students draw a tree diagram once. Then, the child realized, "Oh, I'm counting the same thing twice ~" and asked, "Why do I have to divide the problem of 2 by 2?" is understandable. However, I feel a sense of crisis that the guidance of instructors who give awareness from such actual experiences is fading. [...]