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Advice on Full Time Community College Math Instructor Position
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I have to do a teaching demo on the following:
Please treat the committee as students in your Calculus II class. Please take 12-15 minutes to introduce your lesson on the Taylor Series and its applications. Take the final two minutes to indicate how you would finish your lesson for the day
Here's my plan:
1) Begin by stating that a Taylor Series is an expansion of a function into an infinite sum of terms.
2) Present the taylor expansion for $cos x=1-x^2/2!+x^4/4!+...$ as an example
3) Use Desmos (a computer will be provided) to show how the more sequence of terms that we have, the better the approximation of the $cos x$ graph. Example:
The red line is the cos x graph and the blue line is the approximation
4) Talk quickly about why the formula works (getting $c_0, c_1, c_2$) using $f(x) = c_0 + c_1(x-a) + c_2(x-a)^2 + c_3(x-a)^3+... $ to obtain $f(x) = f(a) + f'(a)/1! (x-a) + f''(a)/2!(x-a)^2 + f'''(a)/3!(x-a)^3 + ...$
5) Use this formula to obtain the taylor series expansion of $cos x$
6) Have a student centered formative assessment last 2-3 minutes and find the taylor expansion for sin x
My only concern is: Is this too much for a 12-15 minute demo?
community-colleges
asked 4 hours ago
Gerardo
24518
add a comment |Â
up vote
1
down vote
favorite
I have to do a teaching demo on the following:
Please treat the committee as students in your Calculus II class. Please take 12-15 minutes to introduce your lesson on the Taylor Series and its applications. Take the final two minutes to indicate how you would finish your lesson for the day
Here's my plan:
1) Begin by stating that a Taylor Series is an expansion of a function into an infinite sum of terms.
2) Present the taylor expansion for $cos x=1-x^2/2!+x^4/4!+...$ as an example
3) Use Desmos (a computer will be provided) to show how the more sequence of terms that we have, the better the approximation of the $cos x$ graph. Example:
The red line is the cos x graph and the blue line is the approximation
4) Talk quickly about why the formula works (getting $c_0, c_1, c_2$) using $f(x) = c_0 + c_1(x-a) + c_2(x-a)^2 + c_3(x-a)^3+... $ to obtain $f(x) = f(a) + f'(a)/1! (x-a) + f''(a)/2!(x-a)^2 + f'''(a)/3!(x-a)^3 + ...$
5) Use this formula to obtain the taylor series expansion of $cos x$
6) Have a student centered formative assessment last 2-3 minutes and find the taylor expansion for sin x
My only concern is: Is this too much for a 12-15 minute demo?
community-colleges
asked 4 hours ago
Gerardo
24518
To me, this looks like more than 15 minutes worth, but you may be faster than I, or think about things differently than I. Honestly, the best way to determine if you can do the demo in 12-15 minutes is to get in front of a white board or projector and actually do the demo...
– Xander Henderson
2 hours ago
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have to do a teaching demo on the following:
Please treat the committee as students in your Calculus II class. Please take 12-15 minutes to introduce your lesson on the Taylor Series and its applications. Take the final two minutes to indicate how you would finish your lesson for the day
Here's my plan:
1) Begin by stating that a Taylor Series is an expansion of a function into an infinite sum of terms.
2) Present the taylor expansion for $cos x=1-x^2/2!+x^4/4!+...$ as an example
3) Use Desmos (a computer will be provided) to show how the more sequence of terms that we have, the better the approximation of the $cos x$ graph. Example:
The red line is the cos x graph and the blue line is the approximation
4) Talk quickly about why the formula works (getting $c_0, c_1, c_2$) using $f(x) = c_0 + c_1(x-a) + c_2(x-a)^2 + c_3(x-a)^3+... $ to obtain $f(x) = f(a) + f'(a)/1! (x-a) + f''(a)/2!(x-a)^2 + f'''(a)/3!(x-a)^3 + ...$
5) Use this formula to obtain the taylor series expansion of $cos x$
6) Have a student centered formative assessment last 2-3 minutes and find the taylor expansion for sin x
My only concern is: Is this too much for a 12-15 minute demo?
community-colleges
asked 4 hours ago
Gerardo
24518
I have to do a teaching demo on the following:
Please treat the committee as students in your Calculus II class. Please take 12-15 minutes to introduce your lesson on the Taylor Series and its applications. Take the final two minutes to indicate how you would finish your lesson for the day
Here's my plan:
1) Begin by stating that a Taylor Series is an expansion of a function into an infinite sum of terms.
2) Present the taylor expansion for $cos x=1-x^2/2!+x^4/4!+...$ as an example
3) Use Desmos (a computer will be provided) to show how the more sequence of terms that we have, the better the approximation of the $cos x$ graph. Example:
The red line is the cos x graph and the blue line is the approximation
4) Talk quickly about why the formula works (getting $c_0, c_1, c_2$) using $f(x) = c_0 + c_1(x-a) + c_2(x-a)^2 + c_3(x-a)^3+... $ to obtain $f(x) = f(a) + f'(a)/1! (x-a) + f''(a)/2!(x-a)^2 + f'''(a)/3!(x-a)^3 + ...$
5) Use this formula to obtain the taylor series expansion of $cos x$
6) Have a student centered formative assessment last 2-3 minutes and find the taylor expansion for sin x
My only concern is: Is this too much for a 12-15 minute demo?
community-colleges
community-colleges
asked 4 hours ago
Gerardo
24518
asked 4 hours ago
Gerardo
24518
asked 4 hours ago
Gerardo
24518
asked 4 hours ago
Gerardo
24518
asked 4 hours ago
Gerardo
24518
24518
To me, this looks like more than 15 minutes worth, but you may be faster than I, or think about things differently than I. Honestly, the best way to determine if you can do the demo in 12-15 minutes is to get in front of a white board or projector and actually do the demo...
– Xander Henderson
2 hours ago
add a comment |Â
To me, this looks like more than 15 minutes worth, but you may be faster than I, or think about things differently than I. Honestly, the best way to determine if you can do the demo in 12-15 minutes is to get in front of a white board or projector and actually do the demo...
– Xander Henderson
2 hours ago
To me, this looks like more than 15 minutes worth, but you may be faster than I, or think about things differently than I. Honestly, the best way to determine if you can do the demo in 12-15 minutes is to get in front of a white board or projector and actually do the demo...
– Xander Henderson
2 hours ago
To me, this looks like more than 15 minutes worth, but you may be faster than I, or think about things differently than I. Honestly, the best way to determine if you can do the demo in 12-15 minutes is to get in front of a white board or projector and actually do the demo...
– Xander Henderson
2 hours ago
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
1
down vote
Caveat: I'm just a random Internet poster, not an instructor, so take this with a grain of salt. And get some advice from blooded veterans.
A. It's too much. 1 and 2 are plenty for 12 minutes.
B. Write out the entire 50 minute lecture, practice it at once, and write up a synthesis of the last 35 minutes. I suggest something like topic, time, key points, perhaps purpose (you can draw a 4 column table and fill it out in the 3 minute). Make it simple enough so that you can actually explain it in 2 minutes. Test yourself to see that you can (it is simple enough summary).
C. Your beginning should have some intro that is a little more motivational, less dry (1 is too theoretical). Maybe something like "sins and cosines are complicated and polynomials are easy so we like to change them into something easier to work with" Or "you will need this in physics" or whatever the practical rationale is for why this is in the curriculum (not too real analysis-y, please). [I do quite like 2, though.]
D. Remember that your target audience at a juco is not math superstars. They are a lower skill set than you or even than an AP calculus class. Good people who want to get through this to support their chem/physics class or nursing degree or what have you. They are looking to progress and get jobs or to transfer to lower level state schools (and then get jobs). Have some sympathy for this and for them (without being obvious or patronizing about it either).
E. I suspect the interview committee wants to see that you can manage time, organize your thoughts, are practiced, command the room, have some energy, etc. And can get through the topic without getting too tied up into every nuance. I think you have plenty of math chops and that will not be their main worry (that you know the topic well). Sure review the standard lesson and be absolutely up to speed on it (especially if they probe...but if they don't, don't feel a need to flaunt.). But the objective is probably 20% math skill (and mostly about being above a skill threshold rather than how high above it). 80% is instructional ability...which is very, very strongly correlated to planning the lecture and practicing it at least 3 times. [Don't bother with that level of time investment when doing the job, except for first lecture, but definitely for the interview.]
F. Do a little reconnaissance and figure out what text they use. See how it addresses this topic and work the homework problems in that text.
G. Really this whole topic is a little bit of a pain for the student and not the most important material. Maybe even why they picked it. Show you can get the kids through the damned thing.
answered 1 hour ago
guest
40414
add a comment |Â
up vote
1
down vote
Please take 12-15 minutes to introduce your lesson
Your intuition is correct that this is far too much for a 12-15 minute lesson. The committee knows that there is no way you could deliver a whole lesson, even an introductory one, on this topic.
Since you've only got 15 minutes, plan to use it to spark interest in the topic, knowing that you're only showing the committee the very beginning.
For example, why not show students the cosine function on a small interval around $x=0$, and ask them what polynomial it reminds them of? "Does it look like some kind of $x^2$ or $x^3$?" Let them decide which one, and then graph their guess on top of $y=cos(x)$. You will have the opportunity to discuss the vertical intercept and the width of the graph -- that it can be adjusted (by multiplying a term by a constant). In this way, your lesson could start as a game about building the cosine function from simpler functions, and students will be involved in the guessing process. I see this occupying up to 5 minutes. Then do your steps 1 and 2, and you're probably out of time.
In my opinion, using your lesson time to draw on your students' previous experience with trig and power functions helps them see that they are already capable of doing much of the intuitive work leading to Taylor polynomials, and it validates that this new thing is something that doesn't have to seem like just applying another magic math formula.
You should definitely plan to tell the committee what else the lesson would include (if you had the time), but I also would tell them what they should already know. [e.g. "Hey, class...let's remember back when we studied graphs of power functions. Do you all remember how to draw the graph of $y=-x^2$?"]
Have a student centered formative assessment last 2-3 minutes and find the taylor expansion for sin x
You could considerably simplify this assessment (for an introduction) by asking them what just the first term of the series expansion should be. If you took the time to remind them of the "long-run behavior" of a polynomial when you discussed the cosine function, you could let them use their calculators to determine what the 2nd term of the series expansion of $sin(x)$ is.
answered 8 mins ago
Nick C
1,502522
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Caveat: I'm just a random Internet poster, not an instructor, so take this with a grain of salt. And get some advice from blooded veterans.
A. It's too much. 1 and 2 are plenty for 12 minutes.
B. Write out the entire 50 minute lecture, practice it at once, and write up a synthesis of the last 35 minutes. I suggest something like topic, time, key points, perhaps purpose (you can draw a 4 column table and fill it out in the 3 minute). Make it simple enough so that you can actually explain it in 2 minutes. Test yourself to see that you can (it is simple enough summary).
C. Your beginning should have some intro that is a little more motivational, less dry (1 is too theoretical). Maybe something like "sins and cosines are complicated and polynomials are easy so we like to change them into something easier to work with" Or "you will need this in physics" or whatever the practical rationale is for why this is in the curriculum (not too real analysis-y, please). [I do quite like 2, though.]
D. Remember that your target audience at a juco is not math superstars. They are a lower skill set than you or even than an AP calculus class. Good people who want to get through this to support their chem/physics class or nursing degree or what have you. They are looking to progress and get jobs or to transfer to lower level state schools (and then get jobs). Have some sympathy for this and for them (without being obvious or patronizing about it either).
E. I suspect the interview committee wants to see that you can manage time, organize your thoughts, are practiced, command the room, have some energy, etc. And can get through the topic without getting too tied up into every nuance. I think you have plenty of math chops and that will not be their main worry (that you know the topic well). Sure review the standard lesson and be absolutely up to speed on it (especially if they probe...but if they don't, don't feel a need to flaunt.). But the objective is probably 20% math skill (and mostly about being above a skill threshold rather than how high above it). 80% is instructional ability...which is very, very strongly correlated to planning the lecture and practicing it at least 3 times. [Don't bother with that level of time investment when doing the job, except for first lecture, but definitely for the interview.]
F. Do a little reconnaissance and figure out what text they use. See how it addresses this topic and work the homework problems in that text.
G. Really this whole topic is a little bit of a pain for the student and not the most important material. Maybe even why they picked it. Show you can get the kids through the damned thing.
answered 1 hour ago
guest
40414
add a comment |Â
up vote
1
down vote
Caveat: I'm just a random Internet poster, not an instructor, so take this with a grain of salt. And get some advice from blooded veterans.
A. It's too much. 1 and 2 are plenty for 12 minutes.
B. Write out the entire 50 minute lecture, practice it at once, and write up a synthesis of the last 35 minutes. I suggest something like topic, time, key points, perhaps purpose (you can draw a 4 column table and fill it out in the 3 minute). Make it simple enough so that you can actually explain it in 2 minutes. Test yourself to see that you can (it is simple enough summary).
C. Your beginning should have some intro that is a little more motivational, less dry (1 is too theoretical). Maybe something like "sins and cosines are complicated and polynomials are easy so we like to change them into something easier to work with" Or "you will need this in physics" or whatever the practical rationale is for why this is in the curriculum (not too real analysis-y, please). [I do quite like 2, though.]
D. Remember that your target audience at a juco is not math superstars. They are a lower skill set than you or even than an AP calculus class. Good people who want to get through this to support their chem/physics class or nursing degree or what have you. They are looking to progress and get jobs or to transfer to lower level state schools (and then get jobs). Have some sympathy for this and for them (without being obvious or patronizing about it either).
E. I suspect the interview committee wants to see that you can manage time, organize your thoughts, are practiced, command the room, have some energy, etc. And can get through the topic without getting too tied up into every nuance. I think you have plenty of math chops and that will not be their main worry (that you know the topic well). Sure review the standard lesson and be absolutely up to speed on it (especially if they probe...but if they don't, don't feel a need to flaunt.). But the objective is probably 20% math skill (and mostly about being above a skill threshold rather than how high above it). 80% is instructional ability...which is very, very strongly correlated to planning the lecture and practicing it at least 3 times. [Don't bother with that level of time investment when doing the job, except for first lecture, but definitely for the interview.]
F. Do a little reconnaissance and figure out what text they use. See how it addresses this topic and work the homework problems in that text.
G. Really this whole topic is a little bit of a pain for the student and not the most important material. Maybe even why they picked it. Show you can get the kids through the damned thing.
answered 1 hour ago
guest
40414
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Caveat: I'm just a random Internet poster, not an instructor, so take this with a grain of salt. And get some advice from blooded veterans.
A. It's too much. 1 and 2 are plenty for 12 minutes.
B. Write out the entire 50 minute lecture, practice it at once, and write up a synthesis of the last 35 minutes. I suggest something like topic, time, key points, perhaps purpose (you can draw a 4 column table and fill it out in the 3 minute). Make it simple enough so that you can actually explain it in 2 minutes. Test yourself to see that you can (it is simple enough summary).
C. Your beginning should have some intro that is a little more motivational, less dry (1 is too theoretical). Maybe something like "sins and cosines are complicated and polynomials are easy so we like to change them into something easier to work with" Or "you will need this in physics" or whatever the practical rationale is for why this is in the curriculum (not too real analysis-y, please). [I do quite like 2, though.]
D. Remember that your target audience at a juco is not math superstars. They are a lower skill set than you or even than an AP calculus class. Good people who want to get through this to support their chem/physics class or nursing degree or what have you. They are looking to progress and get jobs or to transfer to lower level state schools (and then get jobs). Have some sympathy for this and for them (without being obvious or patronizing about it either).
E. I suspect the interview committee wants to see that you can manage time, organize your thoughts, are practiced, command the room, have some energy, etc. And can get through the topic without getting too tied up into every nuance. I think you have plenty of math chops and that will not be their main worry (that you know the topic well). Sure review the standard lesson and be absolutely up to speed on it (especially if they probe...but if they don't, don't feel a need to flaunt.). But the objective is probably 20% math skill (and mostly about being above a skill threshold rather than how high above it). 80% is instructional ability...which is very, very strongly correlated to planning the lecture and practicing it at least 3 times. [Don't bother with that level of time investment when doing the job, except for first lecture, but definitely for the interview.]
F. Do a little reconnaissance and figure out what text they use. See how it addresses this topic and work the homework problems in that text.
G. Really this whole topic is a little bit of a pain for the student and not the most important material. Maybe even why they picked it. Show you can get the kids through the damned thing.
answered 1 hour ago
guest
40414
Caveat: I'm just a random Internet poster, not an instructor, so take this with a grain of salt. And get some advice from blooded veterans.
A. It's too much. 1 and 2 are plenty for 12 minutes.
B. Write out the entire 50 minute lecture, practice it at once, and write up a synthesis of the last 35 minutes. I suggest something like topic, time, key points, perhaps purpose (you can draw a 4 column table and fill it out in the 3 minute). Make it simple enough so that you can actually explain it in 2 minutes. Test yourself to see that you can (it is simple enough summary).
C. Your beginning should have some intro that is a little more motivational, less dry (1 is too theoretical). Maybe something like "sins and cosines are complicated and polynomials are easy so we like to change them into something easier to work with" Or "you will need this in physics" or whatever the practical rationale is for why this is in the curriculum (not too real analysis-y, please). [I do quite like 2, though.]
D. Remember that your target audience at a juco is not math superstars. They are a lower skill set than you or even than an AP calculus class. Good people who want to get through this to support their chem/physics class or nursing degree or what have you. They are looking to progress and get jobs or to transfer to lower level state schools (and then get jobs). Have some sympathy for this and for them (without being obvious or patronizing about it either).
E. I suspect the interview committee wants to see that you can manage time, organize your thoughts, are practiced, command the room, have some energy, etc. And can get through the topic without getting too tied up into every nuance. I think you have plenty of math chops and that will not be their main worry (that you know the topic well). Sure review the standard lesson and be absolutely up to speed on it (especially if they probe...but if they don't, don't feel a need to flaunt.). But the objective is probably 20% math skill (and mostly about being above a skill threshold rather than how high above it). 80% is instructional ability...which is very, very strongly correlated to planning the lecture and practicing it at least 3 times. [Don't bother with that level of time investment when doing the job, except for first lecture, but definitely for the interview.]
F. Do a little reconnaissance and figure out what text they use. See how it addresses this topic and work the homework problems in that text.
G. Really this whole topic is a little bit of a pain for the student and not the most important material. Maybe even why they picked it. Show you can get the kids through the damned thing.
answered 1 hour ago
guest
40414
answered 1 hour ago
guest
40414
answered 1 hour ago
guest
40414
answered 1 hour ago
guest
40414
40414
add a comment |Â
add a comment |Â
up vote
1
down vote
Please take 12-15 minutes to introduce your lesson
Your intuition is correct that this is far too much for a 12-15 minute lesson. The committee knows that there is no way you could deliver a whole lesson, even an introductory one, on this topic.
Since you've only got 15 minutes, plan to use it to spark interest in the topic, knowing that you're only showing the committee the very beginning.
For example, why not show students the cosine function on a small interval around $x=0$, and ask them what polynomial it reminds them of? "Does it look like some kind of $x^2$ or $x^3$?" Let them decide which one, and then graph their guess on top of $y=cos(x)$. You will have the opportunity to discuss the vertical intercept and the width of the graph -- that it can be adjusted (by multiplying a term by a constant). In this way, your lesson could start as a game about building the cosine function from simpler functions, and students will be involved in the guessing process. I see this occupying up to 5 minutes. Then do your steps 1 and 2, and you're probably out of time.
In my opinion, using your lesson time to draw on your students' previous experience with trig and power functions helps them see that they are already capable of doing much of the intuitive work leading to Taylor polynomials, and it validates that this new thing is something that doesn't have to seem like just applying another magic math formula.
You should definitely plan to tell the committee what else the lesson would include (if you had the time), but I also would tell them what they should already know. [e.g. "Hey, class...let's remember back when we studied graphs of power functions. Do you all remember how to draw the graph of $y=-x^2$?"]
Have a student centered formative assessment last 2-3 minutes and find the taylor expansion for sin x
You could considerably simplify this assessment (for an introduction) by asking them what just the first term of the series expansion should be. If you took the time to remind them of the "long-run behavior" of a polynomial when you discussed the cosine function, you could let them use their calculators to determine what the 2nd term of the series expansion of $sin(x)$ is.
answered 8 mins ago
Nick C
1,502522
add a comment |Â
up vote
1
down vote
Please take 12-15 minutes to introduce your lesson
Your intuition is correct that this is far too much for a 12-15 minute lesson. The committee knows that there is no way you could deliver a whole lesson, even an introductory one, on this topic.
Since you've only got 15 minutes, plan to use it to spark interest in the topic, knowing that you're only showing the committee the very beginning.
For example, why not show students the cosine function on a small interval around $x=0$, and ask them what polynomial it reminds them of? "Does it look like some kind of $x^2$ or $x^3$?" Let them decide which one, and then graph their guess on top of $y=cos(x)$. You will have the opportunity to discuss the vertical intercept and the width of the graph -- that it can be adjusted (by multiplying a term by a constant). In this way, your lesson could start as a game about building the cosine function from simpler functions, and students will be involved in the guessing process. I see this occupying up to 5 minutes. Then do your steps 1 and 2, and you're probably out of time.
In my opinion, using your lesson time to draw on your students' previous experience with trig and power functions helps them see that they are already capable of doing much of the intuitive work leading to Taylor polynomials, and it validates that this new thing is something that doesn't have to seem like just applying another magic math formula.
You should definitely plan to tell the committee what else the lesson would include (if you had the time), but I also would tell them what they should already know. [e.g. "Hey, class...let's remember back when we studied graphs of power functions. Do you all remember how to draw the graph of $y=-x^2$?"]
Have a student centered formative assessment last 2-3 minutes and find the taylor expansion for sin x
You could considerably simplify this assessment (for an introduction) by asking them what just the first term of the series expansion should be. If you took the time to remind them of the "long-run behavior" of a polynomial when you discussed the cosine function, you could let them use their calculators to determine what the 2nd term of the series expansion of $sin(x)$ is.
answered 8 mins ago
Nick C
1,502522
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Please take 12-15 minutes to introduce your lesson
Your intuition is correct that this is far too much for a 12-15 minute lesson. The committee knows that there is no way you could deliver a whole lesson, even an introductory one, on this topic.
Since you've only got 15 minutes, plan to use it to spark interest in the topic, knowing that you're only showing the committee the very beginning.
For example, why not show students the cosine function on a small interval around $x=0$, and ask them what polynomial it reminds them of? "Does it look like some kind of $x^2$ or $x^3$?" Let them decide which one, and then graph their guess on top of $y=cos(x)$. You will have the opportunity to discuss the vertical intercept and the width of the graph -- that it can be adjusted (by multiplying a term by a constant). In this way, your lesson could start as a game about building the cosine function from simpler functions, and students will be involved in the guessing process. I see this occupying up to 5 minutes. Then do your steps 1 and 2, and you're probably out of time.
In my opinion, using your lesson time to draw on your students' previous experience with trig and power functions helps them see that they are already capable of doing much of the intuitive work leading to Taylor polynomials, and it validates that this new thing is something that doesn't have to seem like just applying another magic math formula.
You should definitely plan to tell the committee what else the lesson would include (if you had the time), but I also would tell them what they should already know. [e.g. "Hey, class...let's remember back when we studied graphs of power functions. Do you all remember how to draw the graph of $y=-x^2$?"]
Have a student centered formative assessment last 2-3 minutes and find the taylor expansion for sin x
You could considerably simplify this assessment (for an introduction) by asking them what just the first term of the series expansion should be. If you took the time to remind them of the "long-run behavior" of a polynomial when you discussed the cosine function, you could let them use their calculators to determine what the 2nd term of the series expansion of $sin(x)$ is.
answered 8 mins ago
Nick C
1,502522
Please take 12-15 minutes to introduce your lesson
Your intuition is correct that this is far too much for a 12-15 minute lesson. The committee knows that there is no way you could deliver a whole lesson, even an introductory one, on this topic.
Since you've only got 15 minutes, plan to use it to spark interest in the topic, knowing that you're only showing the committee the very beginning.
For example, why not show students the cosine function on a small interval around $x=0$, and ask them what polynomial it reminds them of? "Does it look like some kind of $x^2$ or $x^3$?" Let them decide which one, and then graph their guess on top of $y=cos(x)$. You will have the opportunity to discuss the vertical intercept and the width of the graph -- that it can be adjusted (by multiplying a term by a constant). In this way, your lesson could start as a game about building the cosine function from simpler functions, and students will be involved in the guessing process. I see this occupying up to 5 minutes. Then do your steps 1 and 2, and you're probably out of time.
In my opinion, using your lesson time to draw on your students' previous experience with trig and power functions helps them see that they are already capable of doing much of the intuitive work leading to Taylor polynomials, and it validates that this new thing is something that doesn't have to seem like just applying another magic math formula.
You should definitely plan to tell the committee what else the lesson would include (if you had the time), but I also would tell them what they should already know. [e.g. "Hey, class...let's remember back when we studied graphs of power functions. Do you all remember how to draw the graph of $y=-x^2$?"]
Have a student centered formative assessment last 2-3 minutes and find the taylor expansion for sin x
You could considerably simplify this assessment (for an introduction) by asking them what just the first term of the series expansion should be. If you took the time to remind them of the "long-run behavior" of a polynomial when you discussed the cosine function, you could let them use their calculators to determine what the 2nd term of the series expansion of $sin(x)$ is.
answered 8 mins ago
Nick C
1,502522
answered 8 mins ago
Nick C
1,502522
answered 8 mins ago
Nick C
1,502522
answered 8 mins ago
Nick C
1,502522
1,502522
add a comment |Â
add a comment |Â
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To me, this looks like more than 15 minutes worth, but you may be faster than I, or think about things differently than I. Honestly, the best way to determine if you can do the demo in 12-15 minutes is to get in front of a white board or projector and actually do the demo...
– Xander Henderson
2 hours ago