00:01 Discovery learning is a student-centered approach to inquiry-based learning. 00:43 Discovery learning promotes student-centered, autonomous, problem-solving approach. 01:27 Discovery learning promotes hands-on, independent learning. 02:08 Discovery learning emphasizes higher order thinking and reasoning 02:51 Teachers must facilitate student learning and provide guidance 03:39 Discovery learning includes case studies and role playing 04:22 Teachers play a crucial role in guiding students' discovery learning process. 05:08 Discovery learning may disadvantage weaker students
I put my students in a group, and encouraged to explore and investigate, together, some numbers in the pursuit of calculus. Thus far, no differentials have been solved. They are still struggling with limits. I'm tempted to show them, but i think that they just need more time, patience and understanding. I know Newton and Leibnitz did it, so they can also, using these techniques. Any advice?
I'm currently a Calc II student. I am studying for ChemE, so I say this as to indicate I'm not a math major, though I'm interested and committed. I unfortunately do not always have the best ability to sit and analyze a situation from the get go, so I try the discovery method almost learning backwards, as though I were trying to set it up for someone else to learn. I want to help my friends and siblings do well, and I think this is the method of learning that opened my eyes. So, I have spent time tirelessly thinking about how you might phrase stuff so that. So at least on the limits, I found the best way to pose limits as just saying "this is a hypothetical, if you could do this." Stipulate on this fact that the value input and or output isn't necessarily there in the instance of observation. So like restrict y = x so that it as f(x) exists on D: [0,5), there is no value for f(5) but if you say limx-->5(-) you can ignore the restriction and still say the left-hand limit of f(x) here still produces 5. Maybe this is wrong in the case of a restriction, but it works on a Domain wherein an element is excluded from the reals such as f(x) = (x^2 -3x + 2)/(x-1) which we can see is ((x-2)(x-1))/(x-1). Under normal circumstances this is just a straight line cause x-1 cancels itself, however this causes a hole discontinuity. We all know the dual side limit works for it and that it would be allowing us to cancel those out, even though functionally we can't do this without the limit. Derivatives might be well stated to convey that we cannot take it over a zero distance but the limit allows for the elimination of the effort that would have to be taken each time to painstakingly find what it approaches, so you could entertain what it would be if you jumped straight to that converged value, suggesting you could still kill the function qualities. That's not to say the derivative is hypothetical, we all know it's not. We could just argue that we skip all the intermediate steps and broke out of the reality we normally sit in. Because like, infinity may sit on a respective side of 0 on the Reals, we know that it isn't a specific value and for the same reason we can't give sin(k/x) (wherein k is a constant) a value at 0, because neither instance centers itself on a number. Your students would have to be very involved and dedicated enough in their off time to be able to really put thought into what you're doing to make my next suggestion valid. Maybe, you could have them do that, reconvene and cement everything they intuited correctly, and ask for feedback as how to either better describe in the midst of your clarification or help them by setting up hints that might better suit the group. Personally the thinking doesn't need to be assigned to me, I do it in free time and to destress. Maybe re-contextualizing a variety of things they know in the every day so that it not only catches their attention but shocks them into thinking. Over this past summer, I was spurred into about a week of operating a paper compass like a madman. I was so inspired by Euclidean style constructions, but that would likely stray too far out of context for Calc, so I don't blame any dismissal of said idea. However, I did this to graphically represent the Method of Exhaustion. A good limit instance of a sandwich theorem "albeit you can't solve for the middle section, you can tell that you are at least constricting and capturing the value of pi. The two bounding formulae you get are ntan(pi/n) >= nsin(pi/n). I set the two equal for the sake of it, knowing that to do so I had to break out of numbers to do it. But you could use the idea of them having to go onto infinity as a point to asymptotic approach. I also find that specifying the integral is an infinite sum, not just of the outputs of the function in the plane but expanding the given function into the immediately higher dimension helps. I had the funny thought some time ago, doing solids of revolution, that if you failed to contextualize it as the infinitesimals being 2D objects essentially summed together into a 3D object in their 3D space, you could mistake it for being a regular function in the plane, and take it as simple area. This point drove home to me, that it was merely an infinite sum. This might press too much into Calc II content or might deal with stuff prematurely if you do AP Calc BC, but I figure the point being made is an eyeopener. Maybe all my points are rather dull and I do hope they didn't come off as patronizing. That said, I have furthered my thinking capabilities dealing with problems after I have learned the right ways and on the frontside now too for certain things, and this might help any of your current or future students. I will try to use it on those I will teach, and hopefully this input was useful, pretend maybe that I'm a past student. Anyhow, have a good day.
@@drakesmith471 I abandoned the discovery technique, instead using asymptotes as a proxy for limits, and using this bit of a crutch, they were able to pick it up in only a few lessons. Sometimes the old way is the best way, or at least the path of least resistance.
@@kidsteach938 You're absolutely right about the path of resistance. Everyone has their methods of doing stuff, and if the old way works, well on with the show then. XD That said, hopefully the ones who will be spurred on come to find that such method. But glad to see things worked out.
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00:01 Discovery learning is a student-centered approach to inquiry-based learning.
00:43 Discovery learning promotes student-centered, autonomous, problem-solving approach.
01:27 Discovery learning promotes hands-on, independent learning.
02:08 Discovery learning emphasizes higher order thinking and reasoning
02:51 Teachers must facilitate student learning and provide guidance
03:39 Discovery learning includes case studies and role playing
04:22 Teachers play a crucial role in guiding students' discovery learning process.
05:08 Discovery learning may disadvantage weaker students
Extremely useful for me. Im getting ready for BEd final exams and this clear, precise video gave a vivid explanation . Thanks a lot
I love your format. It’s been very helpful! 🙏🏻
I put my students in a group, and encouraged to explore and investigate, together, some numbers in the pursuit of calculus. Thus far, no differentials have been solved. They are still struggling with limits. I'm tempted to show them, but i think that they just need more time, patience and understanding. I know Newton and Leibnitz did it, so they can also, using these techniques. Any advice?
I'm currently a Calc II student. I am studying for ChemE, so I say this as to indicate I'm not a math major, though I'm interested and committed. I unfortunately do not always have the best ability to sit and analyze a situation from the get go, so I try the discovery method almost learning backwards, as though I were trying to set it up for someone else to learn. I want to help my friends and siblings do well, and I think this is the method of learning that opened my eyes. So, I have spent time tirelessly thinking about how you might phrase stuff so that. So at least on the limits, I found the best way to pose limits as just saying "this is a hypothetical, if you could do this." Stipulate on this fact that the value input and or output isn't necessarily there in the instance of observation. So like restrict y = x so that it as f(x) exists on D: [0,5), there is no value for f(5) but if you say limx-->5(-) you can ignore the restriction and still say the left-hand limit of f(x) here still produces 5. Maybe this is wrong in the case of a restriction, but it works on a Domain wherein an element is excluded from the reals such as f(x) = (x^2 -3x + 2)/(x-1) which we can see is ((x-2)(x-1))/(x-1). Under normal circumstances this is just a straight line cause x-1 cancels itself, however this causes a hole discontinuity. We all know the dual side limit works for it and that it would be allowing us to cancel those out, even though functionally we can't do this without the limit. Derivatives might be well stated to convey that we cannot take it over a zero distance but the limit allows for the elimination of the effort that would have to be taken each time to painstakingly find what it approaches, so you could entertain what it would be if you jumped straight to that converged value, suggesting you could still kill the function qualities. That's not to say the derivative is hypothetical, we all know it's not. We could just argue that we skip all the intermediate steps and broke out of the reality we normally sit in. Because like, infinity may sit on a respective side of 0 on the Reals, we know that it isn't a specific value and for the same reason we can't give sin(k/x) (wherein k is a constant) a value at 0, because neither instance centers itself on a number. Your students would have to be very involved and dedicated enough in their off time to be able to really put thought into what you're doing to make my next suggestion valid. Maybe, you could have them do that, reconvene and cement everything they intuited correctly, and ask for feedback as how to either better describe in the midst of your clarification or help them by setting up hints that might better suit the group. Personally the thinking doesn't need to be assigned to me, I do it in free time and to destress. Maybe re-contextualizing a variety of things they know in the every day so that it not only catches their attention but shocks them into thinking. Over this past summer, I was spurred into about a week of operating a paper compass like a madman. I was so inspired by Euclidean style constructions, but that would likely stray too far out of context for Calc, so I don't blame any dismissal of said idea. However, I did this to graphically represent the Method of Exhaustion. A good limit instance of a sandwich theorem "albeit you can't solve for the middle section, you can tell that you are at least constricting and capturing the value of pi. The two bounding formulae you get are ntan(pi/n) >= nsin(pi/n). I set the two equal for the sake of it, knowing that to do so I had to break out of numbers to do it. But you could use the idea of them having to go onto infinity as a point to asymptotic approach. I also find that specifying the integral is an infinite sum, not just of the outputs of the function in the plane but expanding the given function into the immediately higher dimension helps. I had the funny thought some time ago, doing solids of revolution, that if you failed to contextualize it as the infinitesimals being 2D objects essentially summed together into a 3D object in their 3D space, you could mistake it for being a regular function in the plane, and take it as simple area. This point drove home to me, that it was merely an infinite sum. This might press too much into Calc II content or might deal with stuff prematurely if you do AP Calc BC, but I figure the point being made is an eyeopener. Maybe all my points are rather dull and I do hope they didn't come off as patronizing. That said, I have furthered my thinking capabilities dealing with problems after I have learned the right ways and on the frontside now too for certain things, and this might help any of your current or future students. I will try to use it on those I will teach, and hopefully this input was useful, pretend maybe that I'm a past student. Anyhow, have a good day.
@@drakesmith471 I abandoned the discovery technique, instead using asymptotes as a proxy for limits, and using this bit of a crutch, they were able to pick it up in only a few lessons. Sometimes the old way is the best way, or at least the path of least resistance.
@@kidsteach938 You're absolutely right about the path of resistance. Everyone has their methods of doing stuff, and if the old way works, well on with the show then. XD That said, hopefully the ones who will be spurred on come to find that such method. But glad to see things worked out.
Very informative video
Thank you for this video. It was very good 👍
What is apk this tool to explain in your TH-cam?
👍
please take the guitar music out. I wanted to hear you talk.