Sadly, this thread shows how poor a job the system has done in teaching people HOW to read and think.
Woke Math mandatory for grade 9 - Ontario
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Most of us have met people who technically know a process step by step but because they do not understand why that process is what it is, they are completely lost the second they need to trouble shoot a solution.
I remember in my grade 9 math honors class we were given paper and scissors to figure out the formula for the surface area of a cylinder. Took us a while but when we finally realized we needed to build a cylinder we realized we had a rectangle and 2 circles and the answer was 2(pi*r)^2+LH ... this type of hands on learning is extremely helpful and teaches you to think outside the box.
There are infinite examples of people that asked themselves WHY they are doing things a certain way. Then they come up with improved or brand new ways of doing things, which moves everyone forward. It amazes me that some think that math is somehow untouchable.
See, I don't agree that "there's no value in rote learning" either.
One of the things I've found in the ongoing discussion about how to teach math is that people often seem to fall into one of two camps: all math should be taught through rote learning, or all math should be taught through discovery/understanding. I'm not sure why so often these tend to be viewed as mutually exclusive. I believe math education is most effective when each is employed, because either can be more appropriate for some circumstances, and (more to the point) they can actually serve to reinforce one another.
Some things in math are very repetitive. There are a lot of skills and basic facts that a person needs access to as you progress, and it is often not practical to figure those out from scratch every time. It is, for example, a heck of a lot more practical to first expect someone to learn that 3.14 is an approximation for pi than to teach them how pi is calculated to any particular degree of accuracy. But, as said, treating math as nothing but memorization is practically useless. It gives a student no capacity to solve problems that differ in any way from what they've seen before. And students who attempt to succeed in math primarily through memorization usually do pretty well up to a certain point, until their brain just can't retain any more and they hit the wall.
Some people just take the opposite approach, thinking they never really need to practice anything. They can just figure it all out. Or they saw it and it made sense, so now they can do it right? Except this is absolutely not what happens.
Let's consider the quadratic formula. It takes a bit more sophistication to understand how to develop the formula than it does to use it, so there's some logic in first asking people to learn the formula and repeatedly use it to solve quadratic equations. You can then also show students how to solve quadratic equations by completing the square. Then you can progress to deriving the formula by completing the square on the abstraction of a quadratic equation in standard form, and the knowledge you gained through practice makes it easier to develop the formula, because you know what pieces you need to see and you've done the process in specific cases. But if you are capable of deriving the formula, you also are going to get better at solving equations.
Ideally the development of math is an iterative process. You learn how to solve quadratic equations, which helps you understand where the process of solving equations comes from, which makes you better at solving equations. More generally, when you practice skills, you have an opportunity to explore what is happening at a deep level, and when you understand things at a deeper level, you get better at the skills.
A lot of math at high levels actually resembles this. Often there's a need for some brute force and repetitive calculations until patterns can be detected and a deeper analysis can take place. But then, a general understanding develops and procedural stuff becomes a lot easier.
I absolutely believe that students need constant opportunities to explore in math. What I've observed though is that this has somehow made some people think you don't need to learn your multiplication tables. We are best served by having both.
How frequent is "all the time"? Are there many examples to reinforce your statement. Or is this just off the top of your head?
Perhaps I should have said that rote learning has "little" value instead of "no" value and that's true of all skills. We're on the same page though. Practically speaking, it is impossible to learn any skill only with memorization especially since technology is constantly changing. We write things down, use computers, etc so that we don't have to remember sequences of steps. Not to mention it gives us a checklist to run through while we're doing critical tasks like operating machinery, flying a plane, etc.
The most hilarious part is after 8:30 because this person clearly dow
All the time means "regularly through history"
On a fun note, since the quadratic formal was mentioned, there is apparently a new, simpler, way of approaching these problems - might be too woke for the right though lmao
I'll leave the weirdos who think mathematics is static and inherently uniform or somehow derived naturally with this:
"What mathematicians can prove depends on their starting assumptions, not on any fundamental ground truth from which all answers spring."
www.quantamagazine.org
"What mathematicians can prove depends on their starting assumptions, not on any fundamental ground truth from which all answers spring."
How Gödel’s Proof Works
His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.
www.quantamagazine.org
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Well, see, I don't think we are completely on the same page with this, because I don't think rote learning has little value. I believe some learning through memorization and repetition is absolutely essential.
Returning to the multiplication tables for a moment: I've heard the argument that students don't need to do this because they'll have access to calculators which can multiply for them. I cringe at this. An immediate consequence is that processes take more time this way, especially situations where you effectively work in reverse such as factoring trinomials. But more than that, knowing your multiplication tables actually makes it easier to see what's happening a lot of the time. A student who knows the multiplication tables is much more likely to recognize a pattern in a process involving multiplication than one who doesn't. It is again this idea that it is more useful to think of "memorization" and "understanding" as iteratively linked rather than mutually exclusive.
This is all related to the zone of proximal development, a concept in education that is sometimes boiled down to the idea that there is a space within which a student learns by combining what they already know with the support of more knowledgeable others. Ultimately the idea is that neither having someone explain everything to you or discovering everything on your own is particularly effective.
I've seen this. I believe it's valuable to look at, just as we said that there is value in looking at multiple approaches to problems. However, I think it's highly debatable that the approach is simpler, because it involves multiple distinct steps that still ultimately resemble using formulas unless you want to derive them on the spot.
I think its more understanding principles, less memorizing formulas, but at this point I'll never forget the quadratic formula so for me it isn't helpful haha but I think I would have preferred it to memorizing the formula if I learned them simultaneously.
I was curious enough to watch this. You can debate the validity of some points in here, but there are some clear reasons he really doesn't know what he's talking about.
One of them actually is pretty much the same argument that has appeared in this thread: If 4 is the only correct answer to 2+2, then the question has an objectively correct answer, and so math is objective. The mistake here is to say that because some questions you might ask in math are entirely right or wrong, then that must mean all questions you might ask in math are entirely right or wrong. That's a logical fallacy. I've addressed this earlier, but for example reality can be a little more complex when you start asking questions about interpreting the results of mathematical models. But another area that hasn't really been discussed, and that came up in the video, is the assessment of math. Usually it's straightforward to mark something as correct when a student gets the right answer, although as already discussed there can be an argument for giving some penalty for such issues as form. But what about when something is definitely not correct? If a question is marked out of 4 and someone gets the wrong answer, how many marks is their solution worth? That is absolutely an area in which teachers have to draw upon professional expertise, and definitely one in which bias has a potential impact.
He also dismisses different ways of knowing as some kind of bs. This is ridiculous, as having different ways of knowing whether something is correct is a definite strength in math. Suppose, for example, that a student gets x=2 as one solution to the equation x^2+5x+6=0. How might one know that is not a correct solution? Well, there are a couple of traditional ways, such as doing a substitution or checking each step in the student's work until a mistake is spotted. But that's not all. You could, for example, recognize that each coefficient and the constant on the left side are all positive, and so if x is positive, then so is the left side. Since the right side is 0, we can see x cannot be positive. Different ways of knowing whether an answer might be correct, and recognizing each of them displays greater mastery, not less.
Does it matter if we are not completely the same page with this or any topic? Not quite sure why you need to nitpick on people that basically agree with your overall argument that there are multiple ways to look at problems. I would agree with you though that memorization and repetition go hand in hand. On the other hand, that process can be very frustrating and time consuming and that's where teachers, tutors, etc need to step in. IMO, I think understanding what exactly is happening when you do any numerical operation vs memorizing that 3 x 3 = 9.
Perhaps we need to step outside of math for a moment. In computer programming, there's no way you could memorize enough code. The field is too broad and ever changing. Instead, you learn some core concepts like variables, loops, functions, etc. that are basically the same no matter if you're writing Python, JavaScript, jQuery, etc. For everything else, you have books or Google to rely on. There are lots of differences between them, but the core logic is basically the same.
You're clearly knowledgeable in mathematical concepts so how about describing their practical application? How do the quadratic equation, factoring trinomials, etc. apply practically? I feel that most of teachers don't even know because they were also taught to memorize these concepts. Perhaps we need to be teaching math and some basic computer programming concepts at the same time so that students can visually see what is going on?
It's Ezra Levant, "he really doesn't know what he's talking about" is the safe default position to start from.
You will note that coding is now part of the 9th grade math curriculum.
Probably one of those things that is too woke I guess.
I really like this method. I would have appreciated it in school.
