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In my last few weeks of the school term, I had many discussions in class about the education system in Singapore and countries elsewhere.
I'm not too sure when it was that I developed the passion to learn. I just happened to realize that every bit of knowledge that was available to me was the embodiment of what it was to be a human being. Everything was part of this giant cosmic web that I've only seen a small part of. I got hungry, I got famished. I needed to consume information and have my many questions answered. Since then, I've been an extremely eager student, and my teachers have noticed this.
I just found everything so fascinating, and it didn't even matter what it was. I used to hate Maths and Science because I didn't see the relevance of them and didn't have the passion for them. I made up excuses for my bad results in Math and in Biology and Chemistry, saying that I was "right-brained" or was naturally inclined towards the arts. Then I stopped, because I suddenly realized that what I was being stupid.
I took a tremendous amount of interest into everything, and I stopped thinking thoughts that went like this, "Why do I even need to learn trigonometry? I'm not going to be walking along the road one day and suddenly find myself with the urge to calculate the angle of inclination of some lamp." or other puerile nonsense.
Nothing was redundant, and as I've mentioned - everything was linked to something else. It was like an infinite dance of information, and I was in the front row. I could reach out and grab whatever I wanted.
Of course, I took precautions: I avoided learning how schools wanted me to. I made sure that the drive I had to learn was intrinsic – I didn't absorb facts for the sake of absorbing them. I became self-possessed and passionate. I believed that everything I could learn was beneficial to me as a person. I kept trying to see the beauty in things, and now being awed by numerals and mathematical concepts and the majesty of the Sciences comes naturally. The wonder which I have when I approach these subjects is genuine and real.
It's been observed that most of the students in Singapore are simply masters of absorbing facts and statistics. They do not see the relevance of anything and everything they learn in school. They've been labelled as sponges, they mindlessly absorb whatever is presented to them. When they're wrung - when they sit for an examination, facts are forced out of them.
I learn because I enjoy learning about what it is to be human, and everything that entails being one.
+ Show Spoiler +
I'm not entirely confident about where I was going with this blog. I guess I just wanted to share the wonderment of a starry-eyed schoolboy with regards to learning.
  
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Reading about the history of math is a fun way of seeing its relevance. ET Bell's "Men of Mathematics" gives short, entertaining biographies of famous mathematicians and traces the development of math. It is pretty amazing when you think about it all. Philosophy and literature have fascinating histories as well.
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I'm not sure what the proper way to respond to this blog is, but I approve its contents. Also, you always have nice music; I already have you to thank for discoving Rebecca Brandt and Bonobo, add Emancipator to that list 
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This is good! But why not question the primacy of utility to begin with? Where did our assumption about the value of utility come from anyways? Why must everything that is of value be useful, and everything useful be valueable?
The Master said: "The Superior Man is aware of Goodness, the inferior man is aware of advantage."
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Thanks, I didn't realize his new album came out.
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Keep in mind all science and math is philosophy, and you'll go far with learning.
PS Wasn't the whole right-brain left-brain thing debunked?
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Also it probably matters what you're studying. I don't know if anyone can say that every subject was interesting to them, so it probably makes more sense for you to say that you only have a passion to learn certain subjects (unless you really like *all* of them?). But maybe there are some people out there who genuinely enjoy learning about everything; I haven't seen many people like that. People usually like specializing in one area, and would be thoroughly depressed working as a shoe salesman (for example).
That's why you get the "puerile nonsense" like how am I going to use trigonometry in my daily life. But I don't think its childish or silly at all. I think you would probably do well to recognize that not everyone is like you, and not everyone has a passionate interest in learning math or the infinite connections associated with it. There are a lot of aspects of mathematics that they probably won't use for the rest of their life, so they shouldn't be forced to learn something that holds no innate interest to them. Of course there may be other arguments for learning the math that's taught at that level.
Incidentally, math gets 100x more interesting in university if you decide to specialize in math (I'm taking one such course now, the textbook is excellent, by Michael Spivak), but you better be a semi-genius or you'll have trouble!
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On March 17 2013 22:54 Iranon wrote:I'm not sure what the proper way to respond to this blog is, but I approve its contents. Also, you always have nice music; I already have you to thank for discoving Rebecca Brandt and Bonobo, add Emancipator to that list
I'm glad
On March 17 2013 23:46 Roe wrote:
Keep in mind all science and math is philosophy, and you'll go far with learning.
PS Wasn't the whole right-brain left-brain thing debunked?
I have no idea. I didn't bother to look up more info on the matter.
On March 18 2013 00:09 radscorpion9 wrote:
Also it probably matters what you're studying. I don't know if anyone can say that every subject was interesting to them, so it probably makes more sense for you to say that you only have a passion to learn certain subjects (unless you really like *all* of them?). But maybe there are some people out there who genuinely enjoy learning about everything; I haven't seen many people like that. People usually like specializing in one area, and would be thoroughly depressed working as a shoe salesman (for example).
That's why you get the "puerile nonsense" like how am I going to use trigonometry in my daily life. But I don't think its childish or silly at all. I think you would probably do well to recognize that not everyone is like you, and not everyone has a passionate interest in learning math or the infinite connections associated with it. There are a lot of aspects of mathematics that they probably won't use for the rest of their life, so they shouldn't be forced to learn something that holds no innate interest to them. Of course there may be other arguments for learning the math that's taught at that level.
Incidentally, math gets 100x more interesting in university if you decide to specialize in math (I'm taking one such course now, the textbook is excellent, by Michael Spivak), but you better be a semi-genius or you'll have trouble!
To be honest, I think it's because I only take a few subjects in school. That is:
-English
-Elementary Math
-Additional Math
-Chemistry
-Biology
-History/Social Studies
And because I'm only studying them all at a very basic level. I suppose that once I have to learn everything at a higher level, my interest for everything might wane. If we're talking about true passion, then mine lies in Literature. For this, I have sam!zdat and farvacola to thank ^_^
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Seeking education and knowledge for intrinsic purposes- because you truly want to obtain information and have those interesting and diverse conversations that only a well-rounded and educated person could have- is an incredibly worthwhile project, and one that educators wish all their students would believe in. Unfortunately, most motivators for education (at least, until students become adults) tend to be external (e.g., learn about this topic because you want a good grade, or do your homework because your parents and teachers want you to). And while those aren't terrible per se, they're not very helpful in the long run if they don't eventually create some level of inherent desire to learn as well. You'll tend to stop caring once you complete the task that's being asked of you, especially if educators are more focused on you regurgitating information than actually generating a high level of interest in the subject. But if you honestly have a thirst for knowledge, even if the purpose of it isn't immediately practical, you welcome debates and discussions and research and reading, even after you pass your class. And that's rare for many students, because many systems of education are more concerned with tangible results like grades than how students feel about their education. (One can make an argument that they're linked, although students have learned how to play the game of school and to do well in classes without truly learning or remembering anything. Because it's not their priority, especially if it doesn't seem like their teachers' priority. And it's much harder to quantify a love of learning than it is to look at one's grades.)
Thanks for calling my attention to your blog post It makes me happy- both as an educator and as a student- that some people can develop a thirst for knowledge on their own. I only hope it will be reinforced and even strengthened by those you meet in the future.
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Seeking education and knowledge for intrinsic purposes- because you truly want to obtain information and have those interesting and diverse conversations that only a well-rounded and educated person could have- is an incredibly worthwhile project, and one that educators wish all their students would believe in.
So how are educators actively trying to accomplish this?
Unfortunately, most motivators for education (at least, until students become adults) tend to be external (e.g., learn about this topic because you want a good grade, or do your homework because your parents and teachers want you to).
many systems of education are more concerned with tangible results like grades than how students feel about their education.
What do you think should be done so things can improve?
I'm glad you enjoyed my blog, and thanks for the well wishes
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The main reason I learn is because it's challenging and everything else is boring.
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On March 23 2013 18:47 Recognizable wrote:
The main reason I learn is because it's challenging and everything else is boring.
I'm only theorizing here, but isn't everything you do learning, in a sense? When you practice StarCraft, it's still falls under learning, since you're learning how to play better after all. When you listen to music, you're learning how to appreciate music, etc., so on and so forth. I hope you get the idea.
I think you only stop learning if your mind is stagnant and it's literally a blank.
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Yes. However, all those things you mentioned, games/music/movies just can't keep my mind occupied for long enough.
They do not see the relevance of anything and everything they learn in school. They've been labelled as sponges, they mindlessly absorb whatever is presented to them. When they're wrung - when they sit for an examination, facts are forced out of them.
Very true, there is this weird dichotomy in my school. Everyone that has chosen a science curriculum generally get's high grades and likes to actually learn, everyone that did not, doesn't. It's very understandable as well. Because something like History, at least on a high school level, requires almost no creativity whatsoever and it's just memorizing facts. Very boring and dull. The amount of times I've gotten, "so what can you do with Math/Physics?" Make me sick; I don't know and I don't care.
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On March 23 2013 19:20 Recognizable wrote:Yes. However, all those things you mentioned, games/music/movies just can't keep my mind occupied for long enough. Show nested quote +They do not see the relevance of anything and everything they learn in school. They've been labelled as sponges, they mindlessly absorb whatever is presented to them. When they're wrung - when they sit for an examination, facts are forced out of them. Very true, there is this weird dichotomy in my school. Everyone that has chosen a science curriculum generally get's high grades and likes to actually learn everyone that did not, doesn't. It's very understandable as well. Because something like History, at least on a high school level, requires almost no creativity whatsoever and it's just memorizing facts. Very boring and dull. The amount of times I've gotten, "so what can you do with Math/Physics?" Make me sick; I don't know and I don't care.
I am confident that I definitely understand what you're talking about. Soft subjects like History can be infinitely easier to do better in when you take it at a high school level. I'm not sure how the Sciences are tested in the Netherlands, but I would say that in Singapore, it's much harder to do well in the humanities. The reason for this is that how History is tested isn't just memorizing facts at all, although you still do it to a certain extent. The History tests I take here tests how well you can interpret a political cartoon/picture or whatever. With the inference you make from said picture, you then have to back up it up with the knowledge you have on the subject.
For example, there's a picture of Hitler shoving a piece of meat labelled Czechoslovakia into a meat grinder, and the product goes into a bowl labelled "the Reich". So you have to explain what you think of Hitler from that cartoon, by saying that he was expansionistic and so on. Then you have to reinforce this inference based on your knowledge on Hitler. You have to bring up the ideals that he expressed in Mein Kampf, or talk about the Czechoslovakian crisis in 1938.
Now let's consider how the Sciences are taught and examined in Singapore (in general). I learn a few things in school, exothermic and endothermic reactions, electrolysis, the calculation of moles, the whole works. But the approach which the teachers take to teaching these things are largely inspired abut what is going to come out on the test. I need to learn the first 20 elements in the periodic table because those are the elements that are going to appear in the test. The rest of the periodic table? Fuck `em. So what if they're interesting. You must memorize what happens when you add hydrochloric acid to Potassium. You must know how to prepare potassium nitrate from potassium hydroxide and nitric acid via titration.
Do you see what I'm trying to get across? Everything that I am taught that concerns the Sciences is just confined to this pre-defined box. I get sick of it sometimes, I really do. But then I realize that it's just what Science is. You're merely taking down observations of nature, that's why it seems like there is no creativity involved when learning it in school. I believe Neil deGrasse Tyson even said something like this once. Van Gogh painted starry night, and if he didn't, nobody would have painted it. But if Newton didn't discover the law of optics, somebody else would have discovered it. Because the study of science is already pre-defined, and art is not, it's one of the reasons why art fascinates me much more than science sometimes.
Of course, I understand that there is so much more to Science, and that innovative creativity is integral to scientific development, but still - I remain exponentially more interested in literature. It's because the laws of science is universal and unchanging. I guess what I'm trying to say is this - it takes different kinds of people. There are people that are thrilled by studying how the world works sans humans, and there are people that are interested in studying the world that humans create.
I have a feeling that I'm just spewing shit.
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I am confident that I definitely understand what you're talking about. Soft subjects like History can be infinitely easier to do better in when you take it at a high school level. I'm not sure how the Sciences are tested in the Netherlands, but I would say that in Singapore, it's much harder to do well in the humanities. The reason for this is that how History is tested isn't just memorizing facts at all, although you still do it to a certain extent. The History tests I take here tests how well you can interpret a political cartoon/picture or whatever. With the inference you make from said picture, you then have to back up it up with the knowledge you have on the subject.
Yes we have cartoons as well. Our last one on our exam was about Churchill and FDR sitting on a fishing boat, maybe you've seen it? They definitely strive to test critical thinking skills, however the solutions are very apparent and you just have to link a couple of things to what you've learnt. You aren't thinking across boundaries, the answer was somewhere exactly in the book, and if it was not, the reasoning is always so apparent it's hard not to stumble over the answer.
Now let's consider how the Sciences are taught and examined in Singapore (in general). I learn a few things in school, exothermic and endothermic reactions, electrolysis, the calculation of moles, the whole works. But the approach which the teachers take to teaching these things are largely inspired abut what is going to come out on the test. I need to learn the first 20 elements in the periodic table because those are the elements that are going to appear in the test. The rest of the periodic table? Fuck `em. So what if they're interesting.
This is beyond dumb. We get a book with basically all the information including the periodic table and we can use it at every exam.
You must memorize what happens when you add hydrochloric acid to Potassium. You must know how to prepare potassium nitrate from potassium hydroxide and nitric acid via titration.
Somewhere, probably beneath a layer of Mathematics and years of study, there are principles which explain why the things happen as they happen when you add hydrochloric acid to Potassium.
You're merely taking down observations of nature
I believe this to be a common misconception of science. Many of science wasn't done by observing nature and forming a theoretical model around the observations but by forming a theoretical model, which is where the creativity comes in, and confirming your theoretical model with nature.
Because the study of science is already pre-defined, and art is not, it's one of the reasons why art fascinates me much more than science sometimes.
Seeing as how art is made by humans whom are bounded by the same physical laws you could in theory form a theoretical model which explains why we humans enjoy art and what art will be succesful and whatnot. I'm just messing around :p
What is your opinion about Math? Seeing as how Math is the pinnacle of reasoning and creativity unbounded by physical laws. Well, you probably wouldn't know because they don't teach mathematical reasoning in high schools. Which is incredibly sad because it's what Mathematics is all about. I hope I can get good at it someday, because it's incredibly hard.
I should get back to studying.
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Then can't we just apply the same logic that you used for the humanities to the sciences? You said that you just get a book with all the information, so isn't it essentially the same thing - the answers are all found in the book, one way or another.
On March 23 2013 19:59 Recognizable wrote:I believe this to be a common misconception of science. Many of science wasn't done by observing nature and forming a theoretical model around the observations but by forming a theoretical model, which is where the creativity comes in, and confirming your theoretical model with nature.
But aren't they just observations of nature after all? Not too bastardize the whole scientific theory, but isn't it much like saying,"I think the sky is purple.". Then I go outside, check it out, and go, "Guess I'm wrong!".
On March 23 2013 19:59 Recognizable wrote:Show nested quote +Because the study of science is already pre-defined, and art is not, it's one of the reasons why art fascinates me much more than science sometimes. Seeing as how art is made by humans whom are bounded by the same physical laws you could in theory form a theoretical model which explains why we humans enjoy art and what art will be succesful and whatnot. I'm just messing around :p What is your opinion about Math? Seeing as how Math is the pinnacle of reasoning and creativity unbounded by physical laws. Well, you probably wouldn't know because they don't teach mathematical reasoning in high schools. Which is incredibly sad because it's what Mathematics is all about. I hope I can get good at it someday, because it's incredibly hard. I should get back to studying.
As you've mentioned, I don't learn mathematical reasoning, and I haven't been exposed that much to it. But I know there's something much more beneath and beyond everything I'm taught in school. So, I'm sad that I really don't have an opinion on Mathematics. However, I do know that Plexa is doing a PhD in Mathematics, pluripotential theory, if my memory serves me correctly.
I should get back to studying too
Edit:
If there's an easy way to introduce myself to mathematical reasoning, do tell.
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On March 23 2013 16:31 Azera wrote:Show nested quote +
Seeking education and knowledge for intrinsic purposes- because you truly want to obtain information and have those interesting and diverse conversations that only a well-rounded and educated person could have- is an incredibly worthwhile project, and one that educators wish all their students would believe in.
So how are educators actively trying to accomplish this?
I think that much of it can come from how teachers can get students actively engaged in the course material, motivate learning, and generate interest. This can occur through instructional methods (e.g., open class discussion and conversations as opposed to teachers just lecturing to students, boring them), as well as the specific projects and ideas that are organized by the teacher (either as a grading policy or just general philosophies that help students grow intellectually).
Unfortunately, I think many teachers feel that they need to focus more on testing and abiding by specific curricula, and are therefore not able to explore the variety of ideas they may have. Teachers often have to worry more about time restraints and the sheer quantity (not necessarily quality) of material that needs to be taught by the time class tests, course exams, and standardized testing occurs. As with any profession, feeling rushed tends to decrease performance, and a subject as important as education is something that truly should not be half-assed.
Show nested quote +
Unfortunately, most motivators for education (at least, until students become adults) tend to be external (e.g., learn about this topic because you want a good grade, or do your homework because your parents and teachers want you to).
Show nested quote +
many systems of education are more concerned with tangible results like grades than how students feel about their education.
What do you think should be done so things can improve? I'm glad you enjoyed my blog, and thanks for the well wishes
We can take a few pages out of other countries' books when it comes to educational policy. We can't copy everything that Finland or China or Singapore does, but we can work towards a culture that promotes the respect of educators and education (e.g., less hand-holding of students, making sure parents work together with teachers, and less political bullshit and walking on eggshells), as well as shifting the focus of standardized tests from an obsession that decides everything in life, to occasional benchmarks and general statistics. Granted, there are plenty of other educational problems that can't be solved at the teacher-level (e.g., federal funding and how that trickles down), but teachers can make sure that students are being mentally stimulated by the material, and not just in it for the grades.
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On March 23 2013 20:32 Azera wrote:Show nested quote +On March 23 2013 19:59 Recognizable wrote:Because the study of science is already pre-defined, and art is not, it's one of the reasons why art fascinates me much more than science sometimes. Seeing as how art is made by humans whom are bounded by the same physical laws you could in theory form a theoretical model which explains why we humans enjoy art and what art will be succesful and whatnot. I'm just messing around :p What is your opinion about Math? Seeing as how Math is the pinnacle of reasoning and creativity unbounded by physical laws. Well, you probably wouldn't know because they don't teach mathematical reasoning in high schools. Which is incredibly sad because it's what Mathematics is all about. I hope I can get good at it someday, because it's incredibly hard. I should get back to studying. As you've mentioned, I don't learn mathematical reasoning, and I haven't been exposed that much to it. But I know there's something much more beneath and beyond everything I'm taught in school. So, I'm sad that I really don't have an opinion on Mathematics. However, I do know that Plexa is doing a PhD in Mathematics, pluripotential theory, if my memory serves me correctly. I should get back to studying too Edit: If there's an easy way to introduce myself to mathematical reasoning, do tell.
I was raised on brain teasers and logic puzzles, and so my math classes usually seemed enjoyable, as I perceived the information through the lens of riddles and problem solving, rather than the regurgitation of theorems and facts. My math teachers weren't absolutely terrible either, which tends to be a huge determining factor in whether or not students get turned away from a specific subject. When I was a student teacher, one of the courses I taught was a high school geometry class, and I was forced to teach the topic that most students hate with a passion: proofs. Granted, there are some really interesting proofs out there, but the logic and reasoning portion of geometry does nothing to further the passion of mathematics. Students find out the hard way (read as: the wrong way) that mathematics prides itself on proof and logical consistency, but the proofs they have to perform are proving that triangles are congruent (SSS, SAS, ASA, blah blah blah) and then eventually again in trigonometry (using identities to prove that two trigonometric quantities are equal). These sections of the curricula seem almost purposely designed to turn people away from mathematics (or at least make it seem boring), when in reality we can be focusing on how important logic and reasoning and rational, consistent steps and the need for defending our ideas are.
Thinking mathematically often comes with experience. Students aren't accustomed to proving things (at least, past their usual extent of needing to defend their answers and claims, which doesn't happen nearly as much as it should), and they become uncomfortable with the fact that you can't just follow a simple mindless procedure (e.g., the order of operations) and have every math question solved for you. I was able to create some logic puzzles and brain teasers for my geometry students to give them in between the boring-but-necessary-for-the-test geometry proofs, and most students found the overall instruction to be entertaining and successful (I constantly asked for their feedback and input). So I salvaged some of geometry's reputation in my class, but only by introducing my own ideas and being flexible with my own pedagogy... and I feel that that's something that teachers in general should do more of, but are frequently unable to do because they're bound by time constraints and curricula.
As far as thinking mathematically is concerned, I find it to be very hard to do so if you're accustomed to thinking in other ways. There tends to be one right answer in mathematics, but you can take several paths to get there, and not all of them force you to think of things in terms of black and white, or boring, or "follow the procedure and you'll do it right".
+ Show Spoiler +In college, my bachelor's degree was in mathematics, and then I got my master's in math education. Currently, I'm doing a PhD in math education too
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On March 24 2013 01:25 DarkPlasmaBall wrote:Show nested quote +On March 23 2013 20:32 Azera wrote:On March 23 2013 19:59 Recognizable wrote:Because the study of science is already pre-defined, and art is not, it's one of the reasons why art fascinates me much more than science sometimes. Seeing as how art is made by humans whom are bounded by the same physical laws you could in theory form a theoretical model which explains why we humans enjoy art and what art will be succesful and whatnot. I'm just messing around :p What is your opinion about Math? Seeing as how Math is the pinnacle of reasoning and creativity unbounded by physical laws. Well, you probably wouldn't know because they don't teach mathematical reasoning in high schools. Which is incredibly sad because it's what Mathematics is all about. I hope I can get good at it someday, because it's incredibly hard. I should get back to studying. As you've mentioned, I don't learn mathematical reasoning, and I haven't been exposed that much to it. But I know there's something much more beneath and beyond everything I'm taught in school. So, I'm sad that I really don't have an opinion on Mathematics. However, I do know that Plexa is doing a PhD in Mathematics, pluripotential theory, if my memory serves me correctly. I should get back to studying too Edit: If there's an easy way to introduce myself to mathematical reasoning, do tell. I was raised on brain teasers and logic puzzles, and so my math classes usually seemed enjoyable, as I perceived the information through the lens of riddles and problem solving, rather than the regurgitation of theorems and facts. My math teachers weren't absolutely terrible either, which tends to be a huge determining factor in whether or not students get turned away from a specific subject. When I was a student teacher, one of the courses I taught was a high school geometry class, and I was forced to teach the topic that most students hate with a passion: proofs. Granted, there are some really interesting proofs out there, but the logic and reasoning portion of geometry does nothing to further the passion of mathematics. Students find out the hard way (read as: the wrong way) that mathematics prides itself on proof and logical consistency, but the proofs they have to perform are proving that triangles are congruent (SSS, SAS, ASA, blah blah blah) and then eventually again in trigonometry (using identities to prove that two trigonometric quantities are equal). These sections of the curricula seem almost purposely designed to turn people away from mathematics (or at least make it seem boring), when in reality we can be focusing on how important logic and reasoning and rational, consistent steps and the need for defending our ideas are. Thinking mathematically often comes with experience. Students aren't accustomed to proving things (at least, past their usual extent of needing to defend their answers and claims, which doesn't happen nearly as much as it should), and they become uncomfortable with the fact that you can't just follow a simple mindless procedure (e.g., the order of operations) and have every math question solved for you. I was able to create some logic puzzles and brain teasers for my geometry students to give them in between the boring-but-necessary-for-the-test geometry proofs, and most students found the overall instruction to be entertaining and successful (I constantly asked for their feedback and input). So I salvaged some of geometry's reputation in my class, but only by introducing my own ideas and being flexible with my own pedagogy... and I feel that that's something that teachers in general should do more of, but are frequently unable to do because they're bound by time constraints and curricula. As far as thinking mathematically is concerned, I find it to be very hard to do so if you're accustomed to thinking in other ways. There tends to be one right answer in mathematics, but you can take several paths to get there, and not all of them force you to think of things in terms of black and white, or boring, or "follow the procedure and you'll do it right". + Show Spoiler +In college, my bachelor's degree was in mathematics, and then I got my master's in math education. Currently, I'm doing a PhD in math education too
I've been wondering. What is different about the reasoning you learn in like Chemistry and Physics in High School and the reasoning you do in Mathematical proofs? I know they are different because I suck at the latter, but I can´t put my finger on it. I know almost no one in my class is comfortable with proofs, probably because we don't practice this nearly enough. Anyway, just look at this question: There is an object which sends out a wave under water with (whatever) speed which pulsates for 100ns, the wave hits a wall 12cm further away and bounces back. When the end of the wave hit's the pulsating object it starts to pulse again. Show that the frequency of the pulsating object is hearable. Why is this so different than: Here are a couple of triangles and circles, proof this angle is 3 times the other angle. Both exercices you reason based on information you have gotten. I have a great Math teacher by the way. He is just so happy to teach Math. I also had a great Physics teacher. He would always ask: Do you guys understand it? We would nod. "Yes, yes..... you always nod"
Yelling: "BUT DO YOU REALLY UNDERSTAND IT? Kudos for becoming a teacher
We can take a few pages out of other countries' books when it comes to educational policy. We can't copy everything that Finland or China or Singapore does, but we can work towards a culture that promotes the respect of educators and education
This is very important imo. I'm in class full of bright kids. None of them want to work in such an underappreciated profession.
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EPT
