Ph\u1ea7n l\u1edbn h\u1ecdc sinh \u0111\u1ec1u s\u1ee3 ph\u1ea1m ph\u1ea3i sai l\u1ea7m, v\u00e0 h\u1ecd c\u1ed1 g\u1eafng tr\u00e1nh \u0111i\u1ec1u \u0111\u00f3 nhi\u1ec1u nh\u1ea5t c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c. Ph\u1ea7n l\u1edbn c\u00e1c gi\u00e1o vi\u00ean c\u0169ng kh\u00f4ng mu\u1ed1n h\u1ecdc sinh ph\u1ea1m ph\u1ea3i sai l\u1ea7m, cho n\u00ean h\u1ecd l\u00e0m vi\u1ec7c c\u1ea7n m\u1eabn \u0111\u1ec3 ng\u0103n c\u1ea3n h\u1ecdc sinh kh\u1ecfi ph\u1ea1m sai l\u1ea7m. \u0110\u1eb7c bi\u1ec7t \u1edf ch\u00e2u \u00c1, gi\u00e1o vi\u00ean s\u1ebd l\u00e0m b\u1ea5t k\u00ec c\u00e1i g\u00ec h\u1ecd c\u00f3 th\u1ec3 l\u00e0m \u0111\u1ec3 gi\u00fap cho h\u1ecdc sinh KH\u00d4NG ph\u1ea1m sai l\u1ea7m. \u0110\u00f4i khi h\u1ecd l\u1eb7p l\u1ea1i b\u00e0i gi\u1ea3ng nhi\u1ec1u l\u1ea7n \u0111\u1ec3 ch\u1eafc r\u1eb1ng h\u1ecdc sinh bi\u1ebft c\u00e2u tr\u1ea3 l\u1eddi hay cho h\u1ecdc sinh b\u00e0i h\u1ecdc th\u00eam, \u0111\u1ec3 cho h\u1ecdc sinh kh\u00f4ng ph\u1ea1m sai l\u1ea7m. Nh\u01b0ng t\u1ea1i sao ch\u00fang ta s\u1ee3 \u0111\u1ec3 h\u1ecdc sinh ph\u1ea1m sai l\u1ea7m?<\/p>\n
T\u1ea5t nhi\u00ean, kh\u00f4ng gi\u00e1o vi\u00ean n\u00e0o mu\u1ed1n th\u1ea5y h\u1ecdc sinh tr\u01b0\u1ee3t trong l\u1edbp c\u1ee7a h\u1ecd nh\u01b0ng c\u00f3 kh\u00e1c bi\u1ec7t trong c\u00e1c l\u1edbp h\u1ecdc ch\u00e2u \u00c1 v\u00e0 ph\u01b0\u01a1ng T\u00e2y. N\u1ebfu h\u1ecdc sinh tr\u01b0\u1ee3t trong l\u1edbp \u1edf M\u0129, h\u1ecd ph\u1ea3i h\u1ecdc l\u1ea1i l\u1edbp \u0111\u00f3 v\u00ec h\u1ecdc sinh ch\u1ecbu tr\u00e1ch nhi\u1ec7m cho vi\u1ec7c h\u1ecdc c\u1ee7a h\u1ecd. Cho h\u1ecdc sinh \u0111i\u1ec3m th\u1ea5p v\u00e0 l\u00e0m cho h\u1ecd ph\u1ea3i h\u1ecdc l\u1ea1i m\u00f4n h\u1ecdc cho t\u1edbi khi vi\u1ec7c h\u1ecdc c\u1ee7a h\u1ecd l\u00e0 vi\u1ec7c th\u00f4ng th\u01b0\u1eddng v\u00e0 ph\u1ea7n l\u1edbn h\u1ecdc sinh ch\u1ea5p nh\u1eadn \u0111i\u1ec1u \u0111\u00f3 nh\u01b0 m\u1ed9t ph\u1ea7n c\u1ee7a vi\u1ec7c h\u1ecdc c\u1ee7a h\u1ecd. \u1ede ch\u00e2u \u00c1, n\u1ebfu h\u1ecdc sinh tr\u01b0\u1ee3t m\u1ed9t l\u1edbp, gi\u00e1o vi\u00ean c\u1ea3m th\u1ea5y c\u00f3 tr\u00e1ch nhi\u1ec7m v\u00ec h\u1ecd quan t\u00e2m t\u1edbi vi\u1ec7c h\u1ecdc c\u1ee7a h\u1ecdc sinh v\u00e0 h\u1ecd kh\u00f4ng mu\u1ed1n th\u1ea5y h\u1ecdc sinh tr\u01b0\u1ee3t. Khi d\u1ea1y \u1edf ch\u00e2u \u00c1, t\u00f4i \u0111\u1ec3 \u00fd r\u1eb1ng ph\u1ea7n l\u1edbn c\u00e1c gi\u00e1o vi\u00ean \u0111\u1ec1u b\u00e1m theo k\u1ebf ho\u1ea1ch b\u00e0i gi\u1ea3ng m\u1ed9t c\u00e1ch nghi\u00eam ng\u1eb7t. H\u1ecd mu\u1ed1n bao qu\u00e1t m\u1ecdi th\u1ee9 trong n\u1ed9i dung, t\u1eeb \u0111\u1ea7u \u0111\u1ebfn cu\u1ed1i, cho n\u00ean h\u1ecd kh\u00f4ng c\u00f3 \u0111\u1ee7 th\u1eddi gian \u0111\u1ec3 h\u1ecdc sinh t\u1ef1 h\u1ecdc. Do th\u1eddi gian b\u1ecb gi\u1edbi h\u1ea1n trong l\u1edbp h\u1ecdc, nhi\u1ec1u ng\u01b0\u1eddi “d\u1ea1y c\u00e2u tr\u1ea3 l\u1eddi” thay v\u00ec \u0111\u1ec3 t\u1ef1 b\u1ea3n th\u00e2n h\u1ecdc sinh t\u00ecm ra c\u00e2u tr\u1ea3 l\u1eddi. N\u1ebfu h\u1ecdc sinh kh\u00f4ng hi\u1ec3u, h\u1ecd cho h\u1ecdc sinh c\u00e2u tr\u1ea3 l\u1eddi thay v\u00ec cho ph\u00e9p h\u1ecdc sinh c\u00f3 th\u1eddi gian suy ngh\u0129 v\u1ec1 c\u00e2u tr\u1ea3 l\u1eddi. M\u1ed9t gi\u00e1o vi\u00ean ch\u00e2u \u00c1 n\u00f3i v\u1edbi t\u00f4i: \u201cN\u1ebfu ch\u00fang t\u00f4i d\u1ea1y theo c\u00e1ch th\u1ea7y d\u1ea1y, ch\u00fang t\u00f4i s\u1ebd kh\u00f4ng bao gi\u1edd k\u1ebft th\u00fac \u0111\u01b0\u1ee3c n\u1ed9i dung m\u00f4n h\u1ecdc. Ch\u00fang t\u00f4i kh\u00f4ng c\u00f3 \u0111\u1ee7 th\u1eddi gian cho h\u1ecdc sinh; h\u1ecd ph\u1ea3i bi\u1ebft c\u00e2u tr\u1ea3 l\u1eddi \u0111\u1ec3 cho h\u1ecd c\u00f3 th\u1ec3 qua \u0111\u01b0\u1ee3c k\u00ec thi.\u201d B\u1eb1ng vi\u1ec7c cho c\u00e2u tr\u1ea3 l\u1eddi cho n\u00ean h\u1ecdc sinh c\u00f3 th\u1ec3 ghi nh\u1edb thay v\u00ec kh\u00e1m ph\u00e1 ra c\u00e2u tr\u1ea3 l\u1eddi theo c\u00e1ch ri\u00eang c\u1ee7a h\u1ecd, vi\u1ec7c d\u1ea1y n\u00e0y c\u0169ng l\u00e0m h\u1ecfng ch\u1ee7 \u0111\u1ecbnh c\u1ee7a vi\u1ec7c h\u1ecdc s\u00e2u.<\/p>\n
V\u00e0i n\u0103m tr\u01b0\u1edbc \u1edf ch\u00e2u \u00c1, t\u00f4i c\u00f3 c\u00f9ng d\u1ea1y m\u00f4n “Thu\u1eadt to\u00e1n ph\u1ea7n m\u1ec1m” v\u1edbi m\u1ed9t gi\u00e1o s\u01b0 kh\u00e1c. M\u1ed9t h\u00f4m, m\u1ed9t h\u1ecdc sinh tr\u00ecnh b\u00e0y m\u1ed9t thu\u1eadt to\u00e1n \u0111\u1ec3 gi\u1ea3i b\u00e0i to\u00e1n s\u1eafp x\u1ebfp. Th\u1ea7y gi\u00e1o n\u00e0y d\u01b0\u1eddng nh\u01b0 n\u1ed5i gi\u1eadn; \u00f4ng \u1ea5y la l\u00ean: \u201c\u0110\u1ea5y kh\u00f4ng ph\u1ea3i l\u00e0 c\u00e1ch \u0111\u00fang.\u201d H\u1ecdc sinh n\u00e0y b\u1ea3o v\u1ec7 gi\u1ea3i ph\u00e1p c\u1ee7a m\u00ecnh b\u1eb1ng vi\u1ec7c ch\u1ec9 ra r\u1eb1ng thu\u1eadt to\u00e1n c\u1ee7a anh ta c\u0169ng gi\u1ea3i quy\u1ebft \u0111\u01b0\u1ee3c b\u00e0i to\u00e0n n\u00e0y. Th\u1ea7y gi\u00e1o th\u1ea5t v\u1ecdng: \u201cNh\u01b0ng em ph\u1ea3i l\u00e0m n\u00f3 theo c\u00e1ch n\u00e0y. \u0110i\u1ec1u em l\u00e0m kh\u00f4ng ph\u1ea3i l\u00e0 c\u00e1ch \u0111\u00fang.\u201d M\u1eb7c d\u1ea7u anh ta l\u00e0 \u0111\u00fang v\u00ec \u0111i\u1ec1u h\u1ecdc sinh n\u00e0y \u0111\u00e3 l\u00e0m kh\u00f4ng ph\u1ea3i l\u00e0 gi\u1ea3i ph\u00e1p t\u1ed1t nh\u1ea5t, cho d\u00f9 n\u00f3 gi\u1ea3i quy\u1ebft \u0111\u01b0\u1ee3c v\u1ea5n \u0111\u1ec1, nh\u01b0ng th\u1ea7y gi\u00e1o kh\u00f4ng th\u1ec3 cho ph\u00e9p c\u00e1ch gi\u1ea3i kh\u00e1c trong l\u1edbp c\u1ee7a m\u00ecnh. Th\u1ea7y kh\u00f4ng mu\u1ed1n th\u1ea5y gi\u1ea3i ph\u00e1p kh\u00e1c v\u00ec n\u00f3 l\u00e0m cho h\u1ecdc sinh b\u1ecb l\u1eabn l\u1ed9n. Th\u1ea7y mu\u1ed1n m\u1ecdi h\u1ecdc sinh \u0111\u1ec1u \u0111i theo “c\u00e2u tr\u1ea3 l\u1eddi \u0111\u00fang” \u0111\u1ec3 qua \u0111\u01b0\u1ee3c k\u00ec thi. Th\u1ea7y s\u1ee3 r\u1eb1ng b\u1eb1ng vi\u1ec7c cho ph\u00e9p c\u00e1c gi\u1ea3i ph\u00e1p kh\u00e1c nhau, \u0111i\u1ec1u \u0111\u00f3 c\u00f3 th\u1ec3 l\u00e0m lo\u00e3ng vi\u1ec7c d\u1ea1y c\u1ee7a th\u1ea7y, cho n\u00ean th\u1ea7y mu\u1ed1n ch\u1eafc r\u1eb1ng m\u1ecdi h\u1ecdc sinh \u0111\u1ec1u h\u1ecdc “c\u00e1ch \u0111\u00fang” \u0111\u00e3 \u0111\u01b0\u1ee3c vi\u1ebft trong s\u00e1ch gi\u00e1o khoa. Nh\u01b0ng b\u1eb1ng vi\u1ec7c \u0111i theo m\u1ed9t gi\u1ea3i ph\u00e1p “c\u00f4ng th\u1ee9c”, \u0111i\u1ec1u \u0111\u00f3 ng\u0103n c\u1ea3n h\u1ecdc sinh h\u1ecdc cho b\u1ea3n th\u00e2n h\u1ecd. N\u1ebfu t\u00ecnh hu\u1ed1ng n\u00e0y x\u1ea3y ra \u1edf M\u0129, t\u00f4i s\u1ebd cho ph\u00e9p h\u1ecdc sinh gi\u1ea3i th\u00edch gi\u1ea3i ph\u00e1p c\u1ee7a anh ta trong l\u1edbp r\u1ed3i \u0111\u1ec3 l\u1edbp th\u1ea3o lu\u1eadn \u0111\u1ec3 \u0111i t\u1edbi gi\u1ea3i ph\u00e1p t\u1ed1t nh\u1ea5t.<\/p>\n
Khi h\u1ecdc sinh qu\u1ed1c t\u1ebf t\u1edbi l\u1edbp t\u00f4i \u1edf CMU, s\u1ebd ph\u1ea3i m\u1ea5t \u00edt nh\u1ea5t l\u00e0 m\u1ed9t n\u0103m hay h\u01a1n \u0111\u1ec3 \u0111\u1ed5i th\u00f3i quen h\u1ecdc t\u1eadp c\u1ee7a h\u1ecd. T\u00f4i bao gi\u1edd c\u0169ng y\u00eau c\u1ea7u h\u1ecd ngh\u0129 v\u1ec1 c\u00e2u tr\u1ea3 l\u1eddi hay tr\u00ecnh b\u00e0y gi\u1ea3i ph\u00e1p c\u1ee7a h\u1ecd trong l\u1edbp \u0111\u1ec3 th\u1ea3o lu\u1eadn. N\u1ebfu n\u00f3 l\u00e0 sai, h\u1ecd ph\u1ea3i l\u00e0m l\u1ea1i n\u00f3 tr\u01b0\u1edbc khi t\u00f4i cho h\u1ecd c\u00e2u tr\u1ea3 l\u1eddi \u0111\u00fang. H\u1ecdc sinh th\u01b0\u1eddng h\u1ecfi: \u201cT\u1ea1i sao th\u1ea7y l\u00e0m cho ch\u00fang em ngh\u0129 v\u00e0 \u0111\u01b0a t\u1edbi c\u00e2u tr\u1ea3 l\u1eddi sai nhi\u1ec1u l\u1ea7n r\u1ed3i th\u1ea7y ph\u1ea3i s\u1eeda l\u1ea1i n\u00f3? Cho ch\u00fang em c\u00e2u tr\u1ea3 l\u1eddi \u0111\u00fang c\u00f3 ph\u1ea3i d\u1ec5 d\u00e0ng h\u01a1n kh\u00f4ng?\u201d T\u00f4i gi\u1ea3i th\u00edch: \u201cPh\u1ea1m sai l\u1ea7m l\u00e0 \u0111\u01b0\u1ee3c. \u0110em t\u1edbi c\u00e2u tr\u1ea3 l\u1eddi sai l\u00e0 \u0111\u01b0\u1ee3c v\u00ec \u0111\u00f3 l\u00e0 c\u00e1ch c\u00e1c em h\u1ecdc. Vi\u1ec7c c\u1ee7a th\u1ea7y l\u00e0 gi\u00fap cho c\u00e1c em h\u1ecdc t\u1eeb sai l\u1ea7m c\u1ee7a c\u00e1c em. N\u1ebfu c\u00e1c em bi\u1ebft r\u1eb1ng c\u00e1c em sai th\u00ec l\u1ea7n sau c\u00e1c em s\u1ebd \u0111\u1ed5i c\u00e1ch ngh\u0129 v\u00e0 \u0111i t\u1edbi c\u00e2u tr\u1ea3 l\u1eddi \u0111\u00fang. C\u00f3 nhi\u1ec1u c\u00e1ch gi\u1ea3i v\u1ea5n \u0111\u1ec1, v\u00e0 th\u1ea7y mu\u1ed1n c\u00e1c em t\u1ef1 m\u00ecnh gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1. N\u1ebfu c\u00e1c em sai, c\u00e1c em c\u00f3 th\u1ec3 th\u1eed l\u1ea1i n\u00f3 cho t\u1edbi khi c\u00e1c em l\u00e0m \u0111\u01b0\u1ee3c n\u00f3 \u0111\u00fang. H\u1ecdc t\u1eeb sai l\u1ea7m kh\u00f4ng ph\u1ea3i l\u00e0 t\u1ef1 \u0111\u1ed9ng \u0111\u00e2u, cho n\u00ean c\u00e1c em ph\u1ea3i l\u00e0m n\u00f3 nhi\u1ec1u l\u1ea7n \u0111\u1ec3 c\u00f3 \u0111\u01b0\u1ee3c c\u00e2u tr\u1ea3 l\u1eddi \u0111\u00fang. Nh\u01b0ng m\u1ed9t khi c\u00e1c em \u0111\u00e3 c\u00f3 c\u00e2u tr\u1ea3 l\u1eddi \u0111\u00fang, c\u00e1c em h\u1ecdc vi\u1ec7c gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1; v\u00e0 t\u01b0 duy \u0111\u00f3 s\u1ebd \u1edf l\u1ea1i v\u1edbi c\u00e1c em trong th\u1eddi gian d\u00e0i. N\u1ebfu th\u1ea7y cho c\u00e1c em c\u00e2u tr\u1ea3 l\u1eddi \u0111\u00fang, \u0111\u00f3 l\u00e0 suy ngh\u0129 c\u1ee7a th\u1ea7y, kh\u00f4ng ph\u1ea3i c\u1ee7a c\u00e1c em; ch\u1eb3ng m\u1ea5y ch\u1ed1c c\u00e1c em s\u1ebd qu\u00ean n\u00f3 sau l\u1edbp v\u00e0 vi\u1ec7c h\u1ecdc kh\u00f4ng x\u1ea3y ra. C\u00f3 th\u1ec3 m\u1ea5t th\u1eddi gian \u0111\u1ec3 ph\u00e1t tri\u1ec3n k\u0129 n\u0103ng n\u00e0y b\u1eb1ng vi\u1ec7c h\u1ecdc t\u1eeb sai l\u1ea7m, nh\u01b0ng m\u1ed9t khi c\u00e1c em h\u1ecdc n\u00f3 r\u1ed3i, c\u00e1c em s\u1ebd kh\u00f4ng bao gi\u1edd qu\u00ean v\u00ec n\u00f3 t\u1edbi t\u1eeb c\u00e1c em.\u201d<\/p>\n
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—English version—<\/p>\n
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Learning from mistakes<\/p>\n
Most students are afraid of making mistakes, and they try to avoid it as much as possible. Most teachers also do not want students to make mistakes, so they work hard to prevent students from making mistakes. Especially in Asia, teachers will do whatever they can to help students NOT making mistakes. Sometimes they repeat an important lesson several times to make sure that students know the answer or provide an extra tutorial to students, so they do not make mistakes. But why are we afraid to let students make mistakes?<\/p>\n
Of course, no teachers want to see students fail in their classroom but there is a difference in the Asian and Western classroom. If students fail a class in the U.S., they have to repeat the class because students are responsible for their learning. Give students low grade and making them repeat a course until they learn is a common thing and most students accept that as part of their learning. In Asia, if students fail in class, the teachers feel responsible as they are concern about students\u2019 learning and they do not want to see them fail. When teaching in Asia, I notice that most teachers follow the lesson plan rigorously. They want to cover everything in the content, from the beginning to the end, so they do not have enough time for students to learn by themselves. Due to the limited time in the classroom, many \u201cTeach the answer\u201d rather than let students find the answer themselves. If students do not understand, they give them the answer instead of allowing students time to think about the answer. An Asian teacher told me: \u201cIf we teach the way you teach, we will never finish the course content. We do not have enough time for students; they must know the answer so they can pass the exam.\u201d By given the answer so students can memorize rather than discover the answer on their own, this teaching also defeats the purpose of deep learning.<\/p>\n
A few years ago in Asia, I co-taught the \u201cSoftware Algorithm\u201d course with another professor. One day, a student presented an algorithm to solve a sorting problem. The teacher seemed upset; he yelled: \u201cThat is not the correct way.\u201d The student defended his solution by pointed out that his algorithm can also solve the problem. The teacher was frustrated: \u201c But you must do it this way. What you do is not the right way.\u201d Although he was right because what the student did was not the best solution, even it did solve the problem, but the teacher could not allow another solution in his class. He did not want to see a different solution as it confused other students. He wanted all students to follow the \u201cright answer\u201d to pass the exam. He was afraid that by allowing different solutions, it might dilute his teaching, so he wanted to make sure that all students learn the \u201cright way\u201d that was written in the textbook. But by following a \u201cformula\u201d solution, it prevents students to learn for themselves. If this situation happens in the U.S., I will allow the student to explain his solution in class then let the class and discuss to come up with the best solution.<\/p>\n
When international students came to my class at CMU, it would take at least a year or more to change their learning habit. I always ask them to think about the answer or present their solution in class for discussion. If it is wrong, they have to do it again before I give them the correct answer. Students often ask: \u201cWhy make us think and come up with the wrong answer several times then you have to correct it? Would it be easier just to give us the right answer?\u201d I explain: \u201cIt is OK to make a mistake. It is OK to come up with the wrong answer because it is the way you learn. My job is to help you learn from your mistake. If you know that you are wrong then next time you will change your thinking and come up with the right answer. There are many ways to solve a problem, and I want you to solve the problem by yourselves. If you are wrong, you can try it again until you get it right. Learning from mistakes is not automatic, so you have to do it several times to get the right answer. But once you have the right answer, you learn to solve problem; and that thinking will stay with you for a long time. If I give you the right answer, it is my thinking, not yours; soon you will forget it after the class and learning do not happen. It may take the time to develop the skill by learning from mistakes, but once you learn it, you will never forget because it comes from you.\u201d<\/p>\n
<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
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