Conic sections help a teacher out (1 Viewer)

[Kiraken]

lol i literally just said 'i don't want you to just tell me it's good' but if you disgree you have to justify your ideas properly to me or it'll just seem silly


I spent some time on grapher this afternoon making 3d interactive shit where you can see the different conic sections and change the equations of the planes that intersect the cone and see how that changes the shapes and shiz

also made a geogebra file with a circle and an ellipse with both foci on the origin of the circle. Major and minor semi-axes added in the the arms that maintain the same distance from both foci and a point as an animation has a point moving around the edge of the ellipse and an algebra thing on the side showing that the added distances are constant

i'm rambling again but I have definitely taken your ideas on board. i didn't do 4u at school doe. say i have a 1 hour lesson, is an intro to what conic sections are (slicing cones in this grapher thing i have made) then starting on ellipse (what is it, foci, radii, axes and deriving formulae, auxiliary circle) too much or what for a 1 hour lesson? I watched Nigel Simmons slide share lesson for ellipse and I didn't really like how quickly he went through deriving the formula, like sure i can memorise them but do I completely understand/would i be able to derive it myself if i forgot the formula? probs not. then again his lesson was only a 24 minute video. idk bros.

This is a very good idea imo as it will help students visualise the concepts better

 

[Alexis Texas]

also, not completely related to this thread but what do you guys think abotu a "flipped" classroom

like what if your homework was to watch a nigel simmons video on ellipses (http://www.slideshare.net/nsimmons/x2-t03-01-ellipse-2010)

then in class you spent more time doing problems. the idea is that you do the easy stuff at home and can fast-forward/rewind etc then do hard stuff in class with the teacher guiding you/working with peers etc

 

[Carrotsticks]

also, not completely related to this thread but what do you guys think abotu a "flipped" classroom

like what if your homework was to watch a nigel simmons video on ellipses (http://www.slideshare.net/nsimmons/x2-t03-01-ellipse-2010)

then in class you spent more time doing problems. the idea is that you do the easy stuff at home and can fast-forward/rewind etc then do hard stuff in class with the teacher guiding you/working with peers etc

Will respond to your other post later when I have time.

But for this one, I don't think doing that is a good idea. I can't imagine many students doing this and also it seems like a 'lazy way out' of teaching them the real stuff. By doing this, you're moreso being like a 'university tutor' since you're just doing problems. The role of a classroom teacher is to both be a 'lecturer and tutor' all-in-one. Also, students will lose confidence in your abilities if you're getting another teacher to teach them things instead of you doing it yourself.

If every single student did it, then that's great. However, realistically, not all students would do it.

 

[iBibah]

also, not completely related to this thread but what do you guys think abotu a "flipped" classroom

like what if your homework was to watch a nigel simmons video on ellipses (http://www.slideshare.net/nsimmons/x2-t03-01-ellipse-2010)

then in class you spent more time doing problems. the idea is that you do the easy stuff at home and can fast-forward/rewind etc then do hard stuff in class with the teacher guiding you/working with peers etc

My ext teacher does that sometimes...worst thing ever. All it takes is some kids who didn't watch the video, and the rest have to wait for them to be taught. Another problem is that the video may not explain things clearly enough, and you can't ask questions you need to while the concept is being taught.

 

[Alexis Texas]

Only bad teachers would "flip" the classroom in a way that makes it lazy. i think it opens up so much more opportunity for learning activities because you can raise the standard of work/make it more difficult and be there for when students ask questions. the types of questions definitely shouldn't be your standard text book questions.

I've seen year 9/10 kids being shown basic combinatorics videos and spending a lesson on figuring out how many 6-digit numbers there are so that when you multiply the products you get 720. the type of thinking I saw was incredible considering they were liek 15. like 'it can't have 7 because 7 doesn't go in to 720' and things like 6! is 720 and 'the humber can have max 2 1's in it because otherwise it wouldn't reach 720' like i don't think that is possible with the ol' chalk and talk, homework is for home method because you don't really engage in that kind of thinking when you just have to do x, y, z text book problems.

i definitely agree though like if someone doesn't do the work either they fall behind of everyone else waits and the harder applications/problem solving for 4-unit is probably too hard but idk i'd like to think students in 4unit would like the challenge? It's definitely easier to use this in the junior school when the maths isn't that difficult doe

 

[iBibah]

Only bad teachers would "flip" the classroom in a way that makes it lazy. i think it opens up so much more opportunity for learning activities because you can raise the standard of work/make it more difficult and be there for when students ask questions. the types of questions definitely shouldn't be your standard text book questions.

I've seen year 9/10 kids being shown basic combinatorics videos and spending a lesson on figuring out how many 6-digit numbers there are so that when you multiply the products you get 720. the type of thinking I saw was incredible considering they were liek 15. like 'it can't have 7 because 7 doesn't go in to 720' and things like 6! is 720 and 'the humber can have max 2 1's in it because otherwise it wouldn't reach 720' like i don't think that is possible with the ol' chalk and talk, homework is for home method because you don't really engage in that kind of thinking when you just have to do x, y, z text book problems.

i definitely agree though like if someone doesn't do the work either they fall behind of everyone else waits and the harder applications/problem solving for 4-unit is probably too hard but idk i'd like to think students in 4unit would like the challenge? It's definitely easier to use this in the junior school when the maths isn't that difficult doe

I think it would be good to do but not on a regular basis. Maybe only for the topics/parts of topics that spark discussion like mentioned above. But doing it for everything wouldn't work, everyone would slack off.

 

[enoilgam]

It's a nice idea in theory, but in practice, I doubt whether it will work. As has been mentioned above, most people wont do it so they will be left behind. Plus, a lot of people prefer having a teacher explain the work to them, so they can ask questions and stuff. It might be a bit more effective for an MX2 class, which is likely to be filled with more motivated and capable students. But even then, I'd still imagine that many would want the teacher to explain the stuff to them.

 

[Carrotsticks]

i definitely agree though like if someone doesn't do the work either they fall behind of everyone else waits and the harder applications/problem solving for 4-unit is probably too hard but idk i'd like to think students in 4unit would like the challenge? It's definitely easier to use this in the junior school when the maths isn't that difficult doe

I get what you mean about starting the class with a 'higher standard' so you can tackle more difficult problems, but even stronger students still need a couple of 'textbook problems' to gain familiarity with the methods involved, so then they can apply them to more difficult problems.

I think you might be over-estimating the ability of the average Extension 2 student.

Furthermore, actually being there also allows you to provide 'mathematical motivations' for students, which will facilitate them in 'discovering' and 'figuring out' what to do.

A lot of students, when they learn new things, often think "WTF how did they know to do this??". Part of being a strong Mathematics student is having the ability to 'see what to do', given some sort of motivation.

For example, I need to prove A. But the expression from A looks a bit like the expression from B, so that's perhaps where I should start.

This is an invaluable skill for students that is best done with a teacher actually being there.

 

[Alexis Texas]

I think we think we are arguing two extremes. you obviously can't do all flipped/pbl stuff that isn't practical especially because there is a final exam that requires students to answer somewhat standard questions

but i mean all you need to do to make a kid think is ask them something rather than telling them something, do you get what i mean?
like 'here is how we find the coordinates of the focus' vs 'what information do we need to find the coordinates of the focus'
doesn't really add much time and probably is more helpful in the long run because they figured it out. And that helps them develop the skills to know what to do. like rather than telling them, ask them questions that will help them know what to look for next time.

 

[braintic]

I think we think we are arguing two extremes. you obviously can't do all flipped/pbl stuff that isn't practical especially because there is a final exam that requires students to answer somewhat standard questions

but i mean all you need to do to make a kid think is ask them something rather than telling them something, do you get what i mean?
like 'here is how we find the coordinates of the focus' vs 'what information do we need to find the coordinates of the focus'
doesn't really add much time and probably is more helpful in the long run because they figured it out. And that helps them develop the skills to know what to do. like rather than telling them, ask them questions that will help them know what to look for next time.

Sounds great in theory. But I think you need a dose of reality in regard to what students are really like and what they expect. I take it you've booked a place at a selective high school on your graduation, because at most other schools you won't get to teach Ext 2 for years, and most of the time you will be teaching General and 2 unit. And I can assure you that these students at non-selective high schools won't take to your method.

 

[Kiraken]

Sounds great in theory. But I think you need a dose of reality in regard to what students are really like and what they expect. I take it you've booked a place at a selective high school on your graduation, because at most other schools you won't get to teach Ext 2 for years, and most of the time you will be teaching General and 2 unit. And I can assure you that these students at non-selective high schools won't take to your method.

lol she has to do it for a uni assignment so that stuff about teaching ext 2 in some years is kinda irrelevant

 

[Alexis Texas]

Sounds great in theory. But I think you need a dose of reality in regard to what students are really like and what they expect. I take it you've booked a place at a selective high school on your graduation, because at most other schools you won't get to teach Ext 2 for years, and most of the time you will be teaching General and 2 unit. And I can assure you that these students at non-selective high schools won't take to your method.

if students expect to walk in to my classroom and be spoon fed information they are in for a rude surprise.

did you even read what i posted thae change between telling them something and asking a question to make students think is hardly a radical shift in pedagogy.

i'm doing ext2 content for a uni assignment becuase i have to. i take it you have no clue abotu supply/demand of mathematics teachers in this country because I'm pretty much guaranteed any job i want and i'll probably have to teach ext2.
Uni's are retraining PE teachers as maths teachers because there are not enough. i know ~7 people doing the retraining course and at 2 schools I've worked at, 1/2 the new maths teachers are pe teachers, the others are a couple of years from retirement lol

 

[kaz1]

As a former 4unit maths student, I would have loved it if the teacher explained conics with ice cream cones and ice cream

 

[kaz1]

if students expect to walk in to my classroom and be spoon fed information they are in for a rude surprise.

did you even read what i posted thae change between telling them something and asking a question to make students think is hardly a radical shift in pedagogy.

i'm doing ext2 content for a uni assignment becuase i have to. i take it you have no clue abotu supply/demand of mathematics teachers in this country because I'm pretty much guaranteed any job i want and i'll probably have to teach ext2.
Uni's are retraining PE teachers as maths teachers because there are not enough. i know ~7 people doing the retraining course and at 2 schools I've worked at, 1/2 the new maths teachers are pe teachers, the others are a couple of years from retirement lol

fucking oath I would hate it if my 4unit maths teacher was a PE teacher

 

[Carrotsticks]

braintic is a very competent teacher, from what I've seen, and I'm pretty sure he's been teaching longer than you've been in school. So if anything, he would have the most 'clue' about the demand/supply of Mathematics teachers. Also, what's the guarantee that the school you're going to land in even offers Extension 2?

I understand that you dislike spoon-feeding, which is a great thing. However, I think there's some mis-understanding of my post. When I say that a teacher should be there to provide Mathematical motivation, it doesn't mean that you literally give it away. It involves the 'asking of questions' as you have mentioned.

For example, when I go through the proof of PS+PS'=2a, I always ask my students for what ideas they have in mind initially. If they don't have much of an idea, I give them clues (ie: "Do you know any formulas or expressions involving PS? Yep, PS=ePM would be a good start.)

Also, may I ask if you've taught Year 11/Year 12 students before? Or perhaps those who are at a more advanced level (ie: taking extension subjects)?

I get the feeling that you're applying techniques of teaching Junior HS to teaching Extension 2.

 

[braintic]

if students expect to walk in to my classroom and be spoon fed information they are in for a rude surprise.

did you even read what i posted thae change between telling them something and asking a question to make students think is hardly a radical shift in pedagogy.

i'm doing ext2 content for a uni assignment becuase i have to. i take it you have no clue abotu supply/demand of mathematics teachers in this country because I'm pretty much guaranteed any job i want and i'll probably have to teach ext2.
Uni's are retraining PE teachers as maths teachers because there are not enough. i know ~7 people doing the retraining course and at 2 schools I've worked at, 1/2 the new maths teachers are pe teachers, the others are a couple of years from retirement lol

Like you, when I left Uni I thought I knew everything about teaching. And although it took me a long time to admit it to myself, I really knew nothing at the start. Everything worthwhile I've learned about teaching I learned through experience. You will be the same. Think about the practicalities - at most ten hours of teaching per topic in Extension 2, and I still struggle to get through the content. How much of that time do you intend spending on investigation?

There is plenty of competition for places in selective schools, and I have not heard of a first year maths teacher getting a job at one of these schools, except as casual relief. At any other school except Grammar, there will be at most one Extension 2 class. And despite your claims, each school will have at least a handful of experienced teachers who are not going to give away their Ext 2 classes to a newly graduated teacher. And in many of those schools, the head teacher will allocate him/herself the Ext 2 class each year. Any head teacher who gives a new teacher an Extension 2 class without first making them teach the entire 2 unit course, and then the entire Ext 1 course is not doing the right thing by the students.

Whether we like it or not, at least half of the students who do Ext 2 are doing it simply because of how the scaling assists them to get a good ATAR. That is the reality. They want to know how to best pass the next test. And if you don't teach them explicitly, get ready for the complaints. As Carrotsticks said, we all employ questioning techniques designed to make the students think. And that is all there is time for if the course is to be taught thoroughly.

My prediction: you won't teach Ext 2 before the Australian curriculum arrives.

 

[seanieg89]

braintic is a very competent teacher, from what I've seen, and I'm pretty sure he's been teaching longer than you've been in school. So if anything, he would have the most 'clue' about the demand/supply of Mathematics teachers. Also, what's the guarantee that the school you're going to land in even offers Extension 2?

I understand that you dislike spoon-feeding, which is a great thing. However, I think there's some mis-understanding of my post. When I say that a teacher should be there to provide Mathematical motivation, it doesn't mean that you literally give it away. It involves the 'asking of questions' as you have mentioned.

For example, when I go through the proof of PS+PS'=2a, I always ask my students for what ideas they have in mind initially. If they don't have much of an idea, I give them clues (ie: "Do you know any formulas or expressions involving PS? Yep, PS=ePM would be a good start.)

Also, may I ask if you've taught Year 11/Year 12 students before? Or perhaps those who are at a more advanced level (ie: taking extension subjects)?

I get the feeling that you're applying techniques of teaching Junior HS to teaching Extension 2.

Yeah this Socratic style of teaching is effective and can lead to real understanding rather than superficial mimicry of a teachers calculations. Unfortunately I think the time constraints in a teaching year handcuff you somewhat in how much you can employ this.

 

[townie]

No wonder nobody wants to get into teaching if current people in the profession are so overwhelmingly negative about how a passionate a student teacher is. For all y'all are going on about the 'best' way to teach - nobody seems to be applying the same principles to teaching Alexis about teaching.

/2c

 

[nerdasdasd]

No wonder nobody wants to get into teaching if current people in the profession are so overwhelmingly negative about how a passionate a student teacher is. For all y'all are going on about the 'best' way to teach - nobody seems to be applying the same principles to teaching Alexis about teaching.

/2c

What about the disrespect that teachers face in the classroom?

 

[braintic]

No wonder nobody wants to get into teaching if current people in the profession are so overwhelmingly negative about how a passionate a student teacher is. For all y'all are going on about the 'best' way to teach - nobody seems to be applying the same principles to teaching Alexis about teaching.

/2c

Last time I checked, Alexis was not my student. Given that, why would I try to teach someone who has made it clear they won't be receptive to the methods I use, and who seems more intent on teaching us? A balance between idealism and practicality is what is needed.