Conic sections help a teacher out (1 Viewer)

[Alexis Texas]

Sup brahs

i'm doing maths teaching and i have to write a unit of work about conic sections and i want YOUR feelpinions about this
I have to present ONE (1) lesson to my course coordinator as if she is a student (which will be intimidating as fuck so help me out yo)


ok so I was thinking showing this video (maybe not all of it)

http://www.youtube.com/watch?v=GcKiG-CuvtA

and going in to conic sections, particularly the ellipse (also maybe sort of introduce hyperbole/parabolic trajectories/sections as 'what we will be doing next lesson')

getting an ellipse up, labelling axes and focal points and shit
and then using this information to determine planetary orbits or figuring out scales or obits or some shit i need to figure out the actual lesson details which will be easy but what i want to know is


conceptually, would this make the topic more interesting/do you think it is a good idea?

 

[braintic]

You know, I don't know if I'd want my children to have a teacher who swears unprovoked on a public forum. Forum rhymes with decorum.

 

[iBibah]

You know, I don't know if I'd want my children to have a teacher who swears unprovoked on a public forum. Forum rhymes with decorum.

A lot of high school teachers swear in and out of the class room. Whether it be minor or major words, most do it.

 

[SpiralFlex]

What kind of topics in conic - sections? How relevant do they have to be with the high school syllabus?

 

[Carrotsticks]

Sup brahs

i'm doing maths teaching and i have to write a unit of work about conic sections and i want YOUR feelpinions about this
I have to present ONE (1) lesson to my course coordinator as if she is a student (which will be intimidating as fuck so help me out yo)


ok so I was thinking showing this video (maybe not all of it)

http://www.youtube.com/watch?v=GcKiG-CuvtA

and going in to conic sections, particularly the ellipse (also maybe sort of introduce hyperbole/parabolic trajectories/sections as 'what we will be doing next lesson')

getting an ellipse up, labelling axes and focal points and shit
and then using this information to determine planetary orbits or figuring out scales or obits or some shit i need to figure out the actual lesson details which will be easy but what i want to know is


conceptually, would this make the topic more interesting/do you think it is a good idea?

For what grade is this? How 'interesting' it is is quite reliant on their current abilities.

Though honestly, I wouldn't show them that video. The content is great, but I cannot imagine it being appealing to high school students. Have you thought about showing them how conic sections are the projections of light rays upon surfaces? ie: shine a torch at a certain angle and we get an ellipse, another angle yields a hyperbola etc etc.

 

[Kiraken]

im assuming this is for extension 2 maths, tbh most students in extension 2 would probably not really care about that video but perhaps it would be interesting for you to go through kepler's thing quickly yourself or do something else that might emphasise the practical applications of it really quickly.

I mean maybe along with labelling the focal points etc. You can derive some relevant formulas for the ellipse and go through the equations, how to find important points etc. Not sure how long the lesson is but all that should take up most of a 1 hour lesson if done in detail

 

[Alexis Texas]

Would students care about a torch shining on a tabletop, though?

I literally just have to do this for a uni assessment. I understand students taking 4unit don't exactly need extra motivation other than to get dat atar but my marking rubric says it has to be innovative, link to the history or practical applications of maths and me motivating"

Call me a nerberger but don't you think it's cool that a couple of degrees made that much difference to whether or not mathematicians/astronomers could say the orbit is circular and eventually they found out is was an ellipse. there are also other problems like the gravitational two-body problem/kepler problem that are interesting.

like wouldn't introducing it this way be slightly more interesting than "ok today we are doing conic section this is an ellipse here is the formula, memorise it then apply it kthxbye"

i need to present what would be a 1 hour lesson

so maybe 1/2 that video then go in to formula/properties etc. give students a diagram/thing in GeoGebra measure all important info and determine the equation


I am not just saying 'i want you to tell me how good this is" but I just thought it was a good idea to show the idea of focus points as a tangible "thing" where you can actually and that actually mean something.

Opposed to reading it out of a text book. I mean "what are foci??? oh ok the sun is an example of a focus in an elliptical orbit". also sort of showing the dependent relationship all aspects of an ellipse have with each other rather than this thing being an ellipse and the foci are one the characteristics. i'm rambling and i hope what I'm saying makes sense if it's a shit idea just tell me but i think it's more interesting/accessible/meaningful than 'slice a cone look what you get isn't this cool'



(but in my tut, my lecturer talked about brahe and kepler in passing and how much she loved astronomy so i'm just trying to brown nose a bit also. but i legit think it's a good idea)

 

[Alexis Texas]

also i would only probably show like 2 minutes of that video


edit: also i'm not planning on being the kind of teacher that hands info to students on a platter to be memorised. you little punks are going to have to think so hard your brain will literally hurt

 

[Sy123]

Would students care about a torch shining on a tabletop, though?

I literally just have to do this for a uni assessment. I understand students taking 4unit don't exactly need extra motivation other than to get dat atar but my marking rubric says it has to be innovative, link to the history or practical applications of maths and me motivating"

Call me a nerberger but don't you think it's cool that a couple of degrees made that much difference to whether or not mathematicians/astronomers could say the orbit is circular and eventually they found out is was an ellipse. there are also other problems like the gravitational two-body problem/kepler problem that are interesting.

like wouldn't introducing it this way be slightly more interesting than "ok today we are doing conic section this is an ellipse here is the formula, memorise it then apply it kthxbye"

i need to present what would be a 1 hour lesson

so maybe 1/2 that video then go in to formula/properties etc. give students a diagram/thing in GeoGebra measure all important info and determine the equation


I am not just saying 'i want you to tell me how good this is" but I just thought it was a good idea to show the idea of focus points as a tangible "thing" where you can actually and that actually mean something.

Opposed to reading it out of a text book. I mean "what are foci??? oh ok the sun is an example of a focus in an elliptical orbit". also sort of showing the dependent relationship all aspects of an ellipse have with each other rather than this thing being an ellipse and the foci are one the characteristics. i'm rambling and i hope what I'm saying makes sense if it's a shit idea just tell me but i think it's more interesting/accessible/meaningful than 'slice a cone look what you get isn't this cool'



(but in my tut, my lecturer talked about brahe and kepler in passing and how much she loved astronomy so i'm just trying to brown nose a bit also. but i legit think it's a good idea)

Why not just display mathematics for its beauty?

Example, use this: http://www.geogebra.org/cms/en/
(for example) To show what happens if you squash a circle by some factor.
Explain how the Conic Sections are derived by showing an actual Cone being cut in different ways.

etc etc. There are many mathematical ways of showing interest in Conics, rather than having to refer to 'real life applications'.

 

[Alexis Texas]

you didn't actually link me to a specific geogebra file you just linked the main site

are you guys dumb do you even know how uni works
you get a rubric and you do what it says or you fail my rubric says real life apps/history of maths/some sort of cool motivating thing

"shine a torch on a table"
"show cones being sliced!!!!!"

ugh

 

[brent012]

I can't watch that video since I'm on my phone at uni and didn't do 4u in the hsc anyway, but real life examples sound good. Who cares if actual students (on here at least) would rather just learn the textbook/exam style stuff. It's obviously what your marker wants and some students would definitely appreciate it.

 

[enoilgam]

you didn't actually link me to a specific geogebra file you just linked the main site

are you guys dumb do you even know how uni works
you get a rubric and you do what it says or you fail my rubric says real life apps/history of maths/some sort of cool motivating thing

"shine a torch on a table"
"show cones being sliced!!!!!"

ugh

Not to blow smoke up his butt, but I would definitely give carrot's ideas some more thought considering that he is a pretty damn good at this sort of thing (I have seen him teach and he is excellent at getting people engaged). I dont think there is anything wrong with the whole shinning the torch idea, it's a simple but practical way of illustrating a concept and I think it is something which your tutor would appreciate. Sometimes, the simplest things can be the most effective and engaging.

 

[braintic]

you didn't actually link me to a specific geogebra file you just linked the main site

are you guys dumb do you even know how uni works
you get a rubric and you do what it says or you fail my rubric says real life apps/history of maths/some sort of cool motivating thing

"shine a torch on a table"
"show cones being sliced!!!!!"

ugh

Is that how you you intend to talk to students in your class who don't understand you. After all, anyone who doesn't give you the answer you are looking for must just be plain stupid, right?

 

[Kiraken]

you didn't actually link me to a specific geogebra file you just linked the main site

are you guys dumb do you even know how uni works
you get a rubric and you do what it says or you fail my rubric says real life apps/history of maths/some sort of cool motivating thing

"shine a torch on a table"
"show cones being sliced!!!!!"

ugh

tbh shining a torch and actually showing that practical application is far more engaging and motivating than just telling them to watch a bit of a youtube video imo

 

[enoilgam]

tbh shining a torch and actually showing that practical application is far more engaging and motivating than just telling them to watch a bit of a youtube video imo

Agreed 100%, it shows that you have given the assignment far more thought and effort as well.

 

[Sy123]

you didn't actually link me to a specific geogebra file you just linked the main site

are you guys dumb do you even know how uni works
you get a rubric and you do what it says or you fail my rubric says real life apps/history of maths/some sort of cool motivating thing

"shine a torch on a table"
"show cones being sliced!!!!!"

ugh

I'm not supposed to do your assignment for you, make your own, its not hard.

Is that how you you intend to talk to students in your class who don't understand you. After all, anyone who doesn't give you the answer you are looking for must just be plain stupid, right?

Nah this thread is intended for people to give praise for silly teaching method OP has, instead of giving helpful criticisms and suggestions, because after all forums aren't used for the latter, right?

 

[Alexis Texas]

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.

 

[iBibah]

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.

imo this is actually a really good way to start. My tutor started with this and it made a lot of sense to me, and brought more meaning to the otherwise boring-seeming topic.

 

[Carrotsticks]

You might want to check this out, it makes MUCH more sense as to how the conic sections work (and relation to generating spheres etc).

http://en.wikipedia.org/wiki/Dandelin_spheres

I think deriving formulae can be restricted a bit (especially the equation of the ellipse, because it is very long). Also, specific formulas for the ellipse such as directrix, focus, equation of ellipse etc can be quoted. Nevertheless, best to give them a rough idea of where these things come from.

It's great to see that you put in effort into making the '3d interactive shit' to demonstrate specific features of the conic section. That is something that would be most valuable to the student. Suggestion: See if you can also incorporate the property that PS=ePM into it, and relate it to their study of "Geometry of the Parabola" and how the property PS=PM is a special case of PS=ePM, where e=1. Students (in my experience) seem to really like it when I relate a more advanced concept to something that they've already done (even if its just a simple case of it).

You can probably comfortably fit the following into an hour:

1. Introduction as to what conics are, and name the different types of conics.

2. Where these shapes come from (concept of cutting inverted cones)

3. Uses of conic sections in real life (be sure to mention the elliptical billiard table and the Whispering Tubes/Galleries in Questacon, trilateration etc).

4. Recap of "Geometry of the Parabola" (which the school SHOULD have done by the time Conics is visited), and its extension to the Ellipse.

5. Question: "You studied the directrix and foci, but what are they actually? Cool story bro, the directrix is the line x=a/e, but what is its significance?"

6. Relation to Dandelin Spheres (look this up on Youtube because I admit the concept is quite daunting to begin with).

7. Rough derivations of equation of ellipse/foci/directrix.

 

[Alexis Texas]

i can defs do intro to conics, show the different slices on this grapher thing i made, let """student""" play around with it for like 2 minutes, applications/relevance of conics (might just make/find a .gif to show planetary motion and provide links as ~extra info~)

Then recap of focus, directrix and definition of an ellipse in regards to it's foci and directrices

then derive equations and use this geogebra thing to "show" foci, directrices etc. also how elliptical properties relate to a circle or vice versa (?)

let "students" play around with it. what happens to equation when the centre isn't the origin? what if the major axis is on the y-axis not x-axis? all those sorts of questions hopefully people will be thinking.
then auxiliary circle etc.
done.



But I don't really want to just "teach" I want it to be more me responding to observations/questions. Like, show students the geogebra animation and think about what's going on. Ask questions like what happens when it shifts etc. play with the geogebra stuff and actually learn how to learn nomsaying. Obvs i'm not just going to give them a computer and be like 'here you go' but i don't want to just write on the board, even if i explain things really well, then set text book questions that is so boring.

Do you guys think it would be too difficult to start to figure out where the equations for an ellipse come from if you had a teacher sort of scaffolding/asking prompting questions?