Take-Home Examination on Ordinary Differential Equations?Students use WolframAlpha. Can we change calculus instruction to exploit it while discouraging 'cheating'?How to design a fair oral exam for >10 students?Grading scale: how to handle multiple choice questions with different number of choicesExam Writing: Combining Topics on Exams in New WaysTheme of a Differential Equations CourseShould I teach Laplace Transforms? How much?Why do we study ordinary differential equations?Are there any math certificates/qualifications on high school maths that you can do after high school?How to teach ordinary differential equations to good students?
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Take-Home Examination on Ordinary Differential Equations?
Students use WolframAlpha. Can we change calculus instruction to exploit it while discouraging 'cheating'?How to design a fair oral exam for >10 students?Grading scale: how to handle multiple choice questions with different number of choicesExam Writing: Combining Topics on Exams in New WaysTheme of a Differential Equations CourseShould I teach Laplace Transforms? How much?Why do we study ordinary differential equations?Are there any math certificates/qualifications on high school maths that you can do after high school?How to teach ordinary differential equations to good students?
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I am planning to give my students a take-home examination on ODE. The main topic that I would like to cover is Linear Differential Equations of Order Greater than One. For example, I will give my students question such as
Solve the following Differential Equation:
$$y''+y'=x^2+2x.$$
But my concern is, if the students are allowed to answer such questions in a take-home examination, there is almost no reasonable way that I can prevent them from using some online ODE solvers, such as WolframAlpha or this one.
Since some solvers not only give the solutions but also the details, it will defeat the purpose of this take-home examination. I can make "no Differential Equation Solvers" as a rule for this take-home examination, but I am not sure how to monitor my students and thus enforcing the rule.
Surely, having an in-class exam solves the problem. But if it is not possible, is there a way to reasonably test ODE's in the format of a take-home examination?
Edit: I gave them the take-home exam asking them to sign to promise that they have not used any unauthorised resources when finishing the exam. From my observation, all of them seem to have finished the exam honestly. By the way, I work in a small religious college where most students have very high moral values.
undergraduate-education exams differential-equations test-design
asked Oct 16 at 18:53
ZurielZuriel
2,6717 silver badges27 bronze badges
$endgroup$
add a comment
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$begingroup$
I am planning to give my students a take-home examination on ODE. The main topic that I would like to cover is Linear Differential Equations of Order Greater than One. For example, I will give my students question such as
Solve the following Differential Equation:
$$y''+y'=x^2+2x.$$
But my concern is, if the students are allowed to answer such questions in a take-home examination, there is almost no reasonable way that I can prevent them from using some online ODE solvers, such as WolframAlpha or this one.
Since some solvers not only give the solutions but also the details, it will defeat the purpose of this take-home examination. I can make "no Differential Equation Solvers" as a rule for this take-home examination, but I am not sure how to monitor my students and thus enforcing the rule.
Surely, having an in-class exam solves the problem. But if it is not possible, is there a way to reasonably test ODE's in the format of a take-home examination?
Edit: I gave them the take-home exam asking them to sign to promise that they have not used any unauthorised resources when finishing the exam. From my observation, all of them seem to have finished the exam honestly. By the way, I work in a small religious college where most students have very high moral values.
undergraduate-education exams differential-equations test-design
asked Oct 16 at 18:53
ZurielZuriel
2,6717 silver badges27 bronze badges
$endgroup$
11
$begingroup$
You could have two components to the assignment. A take-home portion could be assigned knowing that students have access to technology. The questions could be conceptual in nature, asking students to explain an idea; or they could involve heavy computations that you wouldn't ask them to do during a timed, paper exam. Meanwhile, an in-class portion could ask them to solve simple examples by hand, like the one you mentioned. Dividing it in this way makes it clearer to students what they'll be expected to do.
$endgroup$
– Brendan W. Sullivan
Oct 16 at 18:55
$begingroup$
@BrendanW.Sullivan, thanks for the comment! But even for the heavy computations they can let a computer do the job for them. For conceptual ones, google will probably tell them the answer.
$endgroup$
– Zuriel
Oct 16 at 18:58
$begingroup$
@Namaste, I can do it but I am running behind my schedule of this course and would love to save one class period to cover some materials if possible.
$endgroup$
– Zuriel
Oct 16 at 20:51
add a comment
|
$begingroup$
I am planning to give my students a take-home examination on ODE. The main topic that I would like to cover is Linear Differential Equations of Order Greater than One. For example, I will give my students question such as
Solve the following Differential Equation:
$$y''+y'=x^2+2x.$$
But my concern is, if the students are allowed to answer such questions in a take-home examination, there is almost no reasonable way that I can prevent them from using some online ODE solvers, such as WolframAlpha or this one.
Since some solvers not only give the solutions but also the details, it will defeat the purpose of this take-home examination. I can make "no Differential Equation Solvers" as a rule for this take-home examination, but I am not sure how to monitor my students and thus enforcing the rule.
Surely, having an in-class exam solves the problem. But if it is not possible, is there a way to reasonably test ODE's in the format of a take-home examination?
Edit: I gave them the take-home exam asking them to sign to promise that they have not used any unauthorised resources when finishing the exam. From my observation, all of them seem to have finished the exam honestly. By the way, I work in a small religious college where most students have very high moral values.
undergraduate-education exams differential-equations test-design
asked Oct 16 at 18:53
ZurielZuriel
2,6717 silver badges27 bronze badges
$endgroup$
I am planning to give my students a take-home examination on ODE. The main topic that I would like to cover is Linear Differential Equations of Order Greater than One. For example, I will give my students question such as
Solve the following Differential Equation:
$$y''+y'=x^2+2x.$$
But my concern is, if the students are allowed to answer such questions in a take-home examination, there is almost no reasonable way that I can prevent them from using some online ODE solvers, such as WolframAlpha or this one.
Since some solvers not only give the solutions but also the details, it will defeat the purpose of this take-home examination. I can make "no Differential Equation Solvers" as a rule for this take-home examination, but I am not sure how to monitor my students and thus enforcing the rule.
Surely, having an in-class exam solves the problem. But if it is not possible, is there a way to reasonably test ODE's in the format of a take-home examination?
Edit: I gave them the take-home exam asking them to sign to promise that they have not used any unauthorised resources when finishing the exam. From my observation, all of them seem to have finished the exam honestly. By the way, I work in a small religious college where most students have very high moral values.
undergraduate-education exams differential-equations test-design
undergraduate-education exams differential-equations test-design
asked Oct 16 at 18:53
ZurielZuriel
2,6717 silver badges27 bronze badges
asked Oct 16 at 18:53
ZurielZuriel
2,6717 silver badges27 bronze badges
edited Nov 1 at 21:10
Zuriel
asked Oct 16 at 18:53
ZurielZuriel
2,6717 silver badges27 bronze badges
asked Oct 16 at 18:53
ZurielZuriel
2,6717 silver badges27 bronze badges
asked Oct 16 at 18:53
ZurielZuriel
2,6717 silver badges27 bronze badges
2,6717 silver badges27 bronze badges
11
$begingroup$
You could have two components to the assignment. A take-home portion could be assigned knowing that students have access to technology. The questions could be conceptual in nature, asking students to explain an idea; or they could involve heavy computations that you wouldn't ask them to do during a timed, paper exam. Meanwhile, an in-class portion could ask them to solve simple examples by hand, like the one you mentioned. Dividing it in this way makes it clearer to students what they'll be expected to do.
$endgroup$
– Brendan W. Sullivan
Oct 16 at 18:55
$begingroup$
@BrendanW.Sullivan, thanks for the comment! But even for the heavy computations they can let a computer do the job for them. For conceptual ones, google will probably tell them the answer.
$endgroup$
– Zuriel
Oct 16 at 18:58
$begingroup$
@Namaste, I can do it but I am running behind my schedule of this course and would love to save one class period to cover some materials if possible.
$endgroup$
– Zuriel
Oct 16 at 20:51
add a comment
|
11
$begingroup$
You could have two components to the assignment. A take-home portion could be assigned knowing that students have access to technology. The questions could be conceptual in nature, asking students to explain an idea; or they could involve heavy computations that you wouldn't ask them to do during a timed, paper exam. Meanwhile, an in-class portion could ask them to solve simple examples by hand, like the one you mentioned. Dividing it in this way makes it clearer to students what they'll be expected to do.
$endgroup$
– Brendan W. Sullivan
Oct 16 at 18:55
$begingroup$
@BrendanW.Sullivan, thanks for the comment! But even for the heavy computations they can let a computer do the job for them. For conceptual ones, google will probably tell them the answer.
$endgroup$
– Zuriel
Oct 16 at 18:58
$begingroup$
@Namaste, I can do it but I am running behind my schedule of this course and would love to save one class period to cover some materials if possible.
$endgroup$
– Zuriel
Oct 16 at 20:51
11
11
$begingroup$
You could have two components to the assignment. A take-home portion could be assigned knowing that students have access to technology. The questions could be conceptual in nature, asking students to explain an idea; or they could involve heavy computations that you wouldn't ask them to do during a timed, paper exam. Meanwhile, an in-class portion could ask them to solve simple examples by hand, like the one you mentioned. Dividing it in this way makes it clearer to students what they'll be expected to do.
$endgroup$
– Brendan W. Sullivan
Oct 16 at 18:55
$begingroup$
You could have two components to the assignment. A take-home portion could be assigned knowing that students have access to technology. The questions could be conceptual in nature, asking students to explain an idea; or they could involve heavy computations that you wouldn't ask them to do during a timed, paper exam. Meanwhile, an in-class portion could ask them to solve simple examples by hand, like the one you mentioned. Dividing it in this way makes it clearer to students what they'll be expected to do.
$endgroup$
– Brendan W. Sullivan
Oct 16 at 18:55
$begingroup$
@BrendanW.Sullivan, thanks for the comment! But even for the heavy computations they can let a computer do the job for them. For conceptual ones, google will probably tell them the answer.
$endgroup$
– Zuriel
Oct 16 at 18:58
$begingroup$
@BrendanW.Sullivan, thanks for the comment! But even for the heavy computations they can let a computer do the job for them. For conceptual ones, google will probably tell them the answer.
$endgroup$
– Zuriel
Oct 16 at 18:58
$begingroup$
@Namaste, I can do it but I am running behind my schedule of this course and would love to save one class period to cover some materials if possible.
$endgroup$
– Zuriel
Oct 16 at 20:51
$begingroup$
@Namaste, I can do it but I am running behind my schedule of this course and would love to save one class period to cover some materials if possible.
$endgroup$
– Zuriel
Oct 16 at 20:51
add a comment
|
2 Answers
2
active
oldest
votes
$begingroup$
This is not really a math problem, it's a social problem. Some schools, such as West Point and Cal Tech, have their own honor code systems for this sort of thing. From what I understand, they work very well. However, most schools do not have any such system. Social scientists and psychologists have studied what factors promote or prevent cheating. Cheating is promoted by the following factors:
- a perception that everyone does it
- having a single, high-stakes exam, or a small number of such exams, rather than systematic, ongoing assessment
- a lack of self-efficacy.
At a school that doesn't have an honor code, it's going to be hard to avoid the issue that everyone will think they have to cheat in order to keep up with others who are cheating.
You don't say in your question how many exams you plan to give this term. For example, I'm giving 8 short exams over the course of 15 weeks in one of my classes this semester. If I was having the problem, as you describe, of running low on time, I would just cut one exam and do 7 exams. If you're doing only a couple of high-stakes exams, such as a midterm and a final, then you have one of the risk factors in place, and you're asking for trouble if you make the midterm a take-home.
I think you're kidding yourself if you think that the only issue is that students will use software to solve problems. They can also get help from human beings online. For example, there is a service called Chegg that many students on my campus use to cheat in STEM courses. They sign up for a recurring credit card charge, and in return they get full solutions to textbook problems and can also get help on problems they post. We have even had students use Chegg on their phones during a test to get live help, when the teacher wasn't vigilant enough about preventing access to phones. I believe they were both cooperating with each other and getting help from people off campus. You can't get out of this problem by constructing problems that are AI-proof.
If your problem is lack of time, one good option is not to give in to the assumption that students will never read a textbook and must be spoon-fed every fact and method. Tell them what chapters of the book they're responsible for, and focus class time on helping them over any hard parts.
answered Oct 16 at 23:27
Ben CrowellBen Crowell
10k23 silver badges60 bronze badges
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Comment-answer, but too long for a comment:
I think you are thinking about this wrong.
Tests are some of the MOST valuable hours in a course. They are high stakes performances (like in music or sports). Preparation for them drives a lot of learning. Then the actual execution and subsequent feedback is often much more valuable training than routine drill problems, because of caring about the result. You should maximize test utility versus another hour of lecture (which probably has less learning impact even than an hour of them working drill problems).
In addition, by using a take home you are trying to get an extra hour of their time. In addition, take homes are very hard to control from assistance (book, roommate, online). Can you really expect them to be rigid about a time limit when taking a test at home? If unlimited, then now you're taking more of their time.
In addition, take home tests often lead to instructors giving non ideal questions (ones that are too much like research projects for instance). This is not the case here--your question is fine. However, your urge to ask some sort of strange, hard to cheat on question may already be driving you away from what would be the normal best question in a controlled setting.
In general, ODE books have too much content for a one quarter or one semester course. It is very normal not to cover it all. So if you're already shaving some lessons off, just shave one more off. And learn the core of the topic well. And good tests are key to good learning. Don't shave this 2nd order ODE with constant coefficients off. It's the key part of the course! Very high gain. But surely there is some other lesson (existence, Wronskians, predator prey, transforms, Sturm Louisville, series, etc.) you can skip to allow use of class time for examination.
And I love all the topics and would love to have you cover everything. But you need to prioritize. You got a lifeboat with 15 spots and 25 people, pick the best 15 to live. 2nd order constant coefficient ODE, with a forcing function, will be seen all over the place in physics, engineering, chemistry applications. So it lives. Some other topics go in the water. And the test time needs to live. It's "high gain".
In theory, you could cover more content by telling the kids to learn a lesson sans lecture. But I get the impression you're not training superstars here. They will be unhappy without the scaffolding of some lecture time and Q&A time on the topic. So, just treat this as an optimization problem and do a little less, but do it well.
[Moderator may cut my other answer.]
answered Oct 17 at 2:47
guestguest
1211 bronze badge
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6
$begingroup$
I would argue precisely the opposite of this. There is no point whatever in testing people's ability to grind through the solution to problems like the OP's, because even the most basic computer algebra system can get the solution faster and more reliably. On the other hand, understanding something about Sturm Liouville theory, Laplace (and other) transforms, phase-plane diagrams, existence and uniqueness of solutions, etc, is about insight, which is the one thing that can't be automated. The fact that many undergraduate courses haven't changed for 50 years is relevant, of course.
$endgroup$
– alephzero
Oct 17 at 10:57
3
$begingroup$
Most of his students are going to be going into engineering or science. Being able to work diffy Qs, comes up all the time in STE. If you're weak on manipulational skill you'll have a hard time doing homework problems in junior year physics (mechanics, E&M, quantum) or in mechE (fluids, thermo, controls) or in EE (circuits). You'll have a hard time even following derivations. (You could make the same argument that knowing fractions or basic algebra is not important...but if you have to look everything up or run to a CAS, you're not going to follow the subject matter well.)
$endgroup$
– guest
Oct 17 at 11:30
1
$begingroup$
I also think having a good foundation in analytical solution techniques, first, will make it easier when dealing with the more detailed topics like series solutions or Sturm Louisville or transforms. And it tends to "build" in that you get a new lens to look at familiar topics. Humans are not computers...we have practical limits to our brains, but seeing the same thing a couple different ways, helps makes things make sense and stick. For instance seeing the similarity of parallel/series resistors in circuits and head losses in a fluid system.
$endgroup$
– guest
Oct 17 at 11:39
2
$begingroup$
Note, once you HAVE experienced things well and done a lot of practical manipulation, it may be absolutely fine to start using a calculator for tedious arithmetic or a CAS for solving equations. But at this point, you are a sophisticated user. This is a very different thing to saying a student should never bother to learn initially. Personally, I don't see how you can sit and read a paper, if you can't follow derivations and run to a computer (and having experience working problems makes it easier to follow work, even if not practiced now...just having done it before.)
$endgroup$
– guest
Oct 17 at 11:45
1
$begingroup$
The theme of this answer - that tests are hugely important - is absolutely true. Many folks who did not experience that value in earlier forms of university may not realize it and have missed out. I just completed a masters and it was well less valuable than the undergrad and the too-easy and/or too-little-thought-out exams that did not focus on deep problem solving were a big reason.
$endgroup$
– javadba
Oct 17 at 20:07
|
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2 Answers
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2 Answers
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$begingroup$
This is not really a math problem, it's a social problem. Some schools, such as West Point and Cal Tech, have their own honor code systems for this sort of thing. From what I understand, they work very well. However, most schools do not have any such system. Social scientists and psychologists have studied what factors promote or prevent cheating. Cheating is promoted by the following factors:
- a perception that everyone does it
- having a single, high-stakes exam, or a small number of such exams, rather than systematic, ongoing assessment
- a lack of self-efficacy.
At a school that doesn't have an honor code, it's going to be hard to avoid the issue that everyone will think they have to cheat in order to keep up with others who are cheating.
You don't say in your question how many exams you plan to give this term. For example, I'm giving 8 short exams over the course of 15 weeks in one of my classes this semester. If I was having the problem, as you describe, of running low on time, I would just cut one exam and do 7 exams. If you're doing only a couple of high-stakes exams, such as a midterm and a final, then you have one of the risk factors in place, and you're asking for trouble if you make the midterm a take-home.
I think you're kidding yourself if you think that the only issue is that students will use software to solve problems. They can also get help from human beings online. For example, there is a service called Chegg that many students on my campus use to cheat in STEM courses. They sign up for a recurring credit card charge, and in return they get full solutions to textbook problems and can also get help on problems they post. We have even had students use Chegg on their phones during a test to get live help, when the teacher wasn't vigilant enough about preventing access to phones. I believe they were both cooperating with each other and getting help from people off campus. You can't get out of this problem by constructing problems that are AI-proof.
If your problem is lack of time, one good option is not to give in to the assumption that students will never read a textbook and must be spoon-fed every fact and method. Tell them what chapters of the book they're responsible for, and focus class time on helping them over any hard parts.
answered Oct 16 at 23:27
Ben CrowellBen Crowell
10k23 silver badges60 bronze badges
$endgroup$
add a comment
|
$begingroup$
This is not really a math problem, it's a social problem. Some schools, such as West Point and Cal Tech, have their own honor code systems for this sort of thing. From what I understand, they work very well. However, most schools do not have any such system. Social scientists and psychologists have studied what factors promote or prevent cheating. Cheating is promoted by the following factors:
- a perception that everyone does it
- having a single, high-stakes exam, or a small number of such exams, rather than systematic, ongoing assessment
- a lack of self-efficacy.
At a school that doesn't have an honor code, it's going to be hard to avoid the issue that everyone will think they have to cheat in order to keep up with others who are cheating.
You don't say in your question how many exams you plan to give this term. For example, I'm giving 8 short exams over the course of 15 weeks in one of my classes this semester. If I was having the problem, as you describe, of running low on time, I would just cut one exam and do 7 exams. If you're doing only a couple of high-stakes exams, such as a midterm and a final, then you have one of the risk factors in place, and you're asking for trouble if you make the midterm a take-home.
I think you're kidding yourself if you think that the only issue is that students will use software to solve problems. They can also get help from human beings online. For example, there is a service called Chegg that many students on my campus use to cheat in STEM courses. They sign up for a recurring credit card charge, and in return they get full solutions to textbook problems and can also get help on problems they post. We have even had students use Chegg on their phones during a test to get live help, when the teacher wasn't vigilant enough about preventing access to phones. I believe they were both cooperating with each other and getting help from people off campus. You can't get out of this problem by constructing problems that are AI-proof.
If your problem is lack of time, one good option is not to give in to the assumption that students will never read a textbook and must be spoon-fed every fact and method. Tell them what chapters of the book they're responsible for, and focus class time on helping them over any hard parts.
answered Oct 16 at 23:27
Ben CrowellBen Crowell
10k23 silver badges60 bronze badges
$endgroup$
add a comment
|
$begingroup$
This is not really a math problem, it's a social problem. Some schools, such as West Point and Cal Tech, have their own honor code systems for this sort of thing. From what I understand, they work very well. However, most schools do not have any such system. Social scientists and psychologists have studied what factors promote or prevent cheating. Cheating is promoted by the following factors:
- a perception that everyone does it
- having a single, high-stakes exam, or a small number of such exams, rather than systematic, ongoing assessment
- a lack of self-efficacy.
At a school that doesn't have an honor code, it's going to be hard to avoid the issue that everyone will think they have to cheat in order to keep up with others who are cheating.
You don't say in your question how many exams you plan to give this term. For example, I'm giving 8 short exams over the course of 15 weeks in one of my classes this semester. If I was having the problem, as you describe, of running low on time, I would just cut one exam and do 7 exams. If you're doing only a couple of high-stakes exams, such as a midterm and a final, then you have one of the risk factors in place, and you're asking for trouble if you make the midterm a take-home.
I think you're kidding yourself if you think that the only issue is that students will use software to solve problems. They can also get help from human beings online. For example, there is a service called Chegg that many students on my campus use to cheat in STEM courses. They sign up for a recurring credit card charge, and in return they get full solutions to textbook problems and can also get help on problems they post. We have even had students use Chegg on their phones during a test to get live help, when the teacher wasn't vigilant enough about preventing access to phones. I believe they were both cooperating with each other and getting help from people off campus. You can't get out of this problem by constructing problems that are AI-proof.
If your problem is lack of time, one good option is not to give in to the assumption that students will never read a textbook and must be spoon-fed every fact and method. Tell them what chapters of the book they're responsible for, and focus class time on helping them over any hard parts.
answered Oct 16 at 23:27
Ben CrowellBen Crowell
10k23 silver badges60 bronze badges
$endgroup$
This is not really a math problem, it's a social problem. Some schools, such as West Point and Cal Tech, have their own honor code systems for this sort of thing. From what I understand, they work very well. However, most schools do not have any such system. Social scientists and psychologists have studied what factors promote or prevent cheating. Cheating is promoted by the following factors:
- a perception that everyone does it
- having a single, high-stakes exam, or a small number of such exams, rather than systematic, ongoing assessment
- a lack of self-efficacy.
At a school that doesn't have an honor code, it's going to be hard to avoid the issue that everyone will think they have to cheat in order to keep up with others who are cheating.
You don't say in your question how many exams you plan to give this term. For example, I'm giving 8 short exams over the course of 15 weeks in one of my classes this semester. If I was having the problem, as you describe, of running low on time, I would just cut one exam and do 7 exams. If you're doing only a couple of high-stakes exams, such as a midterm and a final, then you have one of the risk factors in place, and you're asking for trouble if you make the midterm a take-home.
I think you're kidding yourself if you think that the only issue is that students will use software to solve problems. They can also get help from human beings online. For example, there is a service called Chegg that many students on my campus use to cheat in STEM courses. They sign up for a recurring credit card charge, and in return they get full solutions to textbook problems and can also get help on problems they post. We have even had students use Chegg on their phones during a test to get live help, when the teacher wasn't vigilant enough about preventing access to phones. I believe they were both cooperating with each other and getting help from people off campus. You can't get out of this problem by constructing problems that are AI-proof.
If your problem is lack of time, one good option is not to give in to the assumption that students will never read a textbook and must be spoon-fed every fact and method. Tell them what chapters of the book they're responsible for, and focus class time on helping them over any hard parts.
answered Oct 16 at 23:27
Ben CrowellBen Crowell
10k23 silver badges60 bronze badges
edited Oct 16 at 23:56
answered Oct 16 at 23:27
Ben CrowellBen Crowell
10k23 silver badges60 bronze badges
answered Oct 16 at 23:27
Ben CrowellBen Crowell
10k23 silver badges60 bronze badges
answered Oct 16 at 23:27
Ben CrowellBen Crowell
10k23 silver badges60 bronze badges
10k23 silver badges60 bronze badges
add a comment
|
add a comment
|
$begingroup$
Comment-answer, but too long for a comment:
I think you are thinking about this wrong.
Tests are some of the MOST valuable hours in a course. They are high stakes performances (like in music or sports). Preparation for them drives a lot of learning. Then the actual execution and subsequent feedback is often much more valuable training than routine drill problems, because of caring about the result. You should maximize test utility versus another hour of lecture (which probably has less learning impact even than an hour of them working drill problems).
In addition, by using a take home you are trying to get an extra hour of their time. In addition, take homes are very hard to control from assistance (book, roommate, online). Can you really expect them to be rigid about a time limit when taking a test at home? If unlimited, then now you're taking more of their time.
In addition, take home tests often lead to instructors giving non ideal questions (ones that are too much like research projects for instance). This is not the case here--your question is fine. However, your urge to ask some sort of strange, hard to cheat on question may already be driving you away from what would be the normal best question in a controlled setting.
In general, ODE books have too much content for a one quarter or one semester course. It is very normal not to cover it all. So if you're already shaving some lessons off, just shave one more off. And learn the core of the topic well. And good tests are key to good learning. Don't shave this 2nd order ODE with constant coefficients off. It's the key part of the course! Very high gain. But surely there is some other lesson (existence, Wronskians, predator prey, transforms, Sturm Louisville, series, etc.) you can skip to allow use of class time for examination.
And I love all the topics and would love to have you cover everything. But you need to prioritize. You got a lifeboat with 15 spots and 25 people, pick the best 15 to live. 2nd order constant coefficient ODE, with a forcing function, will be seen all over the place in physics, engineering, chemistry applications. So it lives. Some other topics go in the water. And the test time needs to live. It's "high gain".
In theory, you could cover more content by telling the kids to learn a lesson sans lecture. But I get the impression you're not training superstars here. They will be unhappy without the scaffolding of some lecture time and Q&A time on the topic. So, just treat this as an optimization problem and do a little less, but do it well.
[Moderator may cut my other answer.]
answered Oct 17 at 2:47
guestguest
1211 bronze badge
$endgroup$
6
$begingroup$
I would argue precisely the opposite of this. There is no point whatever in testing people's ability to grind through the solution to problems like the OP's, because even the most basic computer algebra system can get the solution faster and more reliably. On the other hand, understanding something about Sturm Liouville theory, Laplace (and other) transforms, phase-plane diagrams, existence and uniqueness of solutions, etc, is about insight, which is the one thing that can't be automated. The fact that many undergraduate courses haven't changed for 50 years is relevant, of course.
$endgroup$
– alephzero
Oct 17 at 10:57
3
$begingroup$
Most of his students are going to be going into engineering or science. Being able to work diffy Qs, comes up all the time in STE. If you're weak on manipulational skill you'll have a hard time doing homework problems in junior year physics (mechanics, E&M, quantum) or in mechE (fluids, thermo, controls) or in EE (circuits). You'll have a hard time even following derivations. (You could make the same argument that knowing fractions or basic algebra is not important...but if you have to look everything up or run to a CAS, you're not going to follow the subject matter well.)
$endgroup$
– guest
Oct 17 at 11:30
1
$begingroup$
I also think having a good foundation in analytical solution techniques, first, will make it easier when dealing with the more detailed topics like series solutions or Sturm Louisville or transforms. And it tends to "build" in that you get a new lens to look at familiar topics. Humans are not computers...we have practical limits to our brains, but seeing the same thing a couple different ways, helps makes things make sense and stick. For instance seeing the similarity of parallel/series resistors in circuits and head losses in a fluid system.
$endgroup$
– guest
Oct 17 at 11:39
2
$begingroup$
Note, once you HAVE experienced things well and done a lot of practical manipulation, it may be absolutely fine to start using a calculator for tedious arithmetic or a CAS for solving equations. But at this point, you are a sophisticated user. This is a very different thing to saying a student should never bother to learn initially. Personally, I don't see how you can sit and read a paper, if you can't follow derivations and run to a computer (and having experience working problems makes it easier to follow work, even if not practiced now...just having done it before.)
$endgroup$
– guest
Oct 17 at 11:45
1
$begingroup$
The theme of this answer - that tests are hugely important - is absolutely true. Many folks who did not experience that value in earlier forms of university may not realize it and have missed out. I just completed a masters and it was well less valuable than the undergrad and the too-easy and/or too-little-thought-out exams that did not focus on deep problem solving were a big reason.
$endgroup$
– javadba
Oct 17 at 20:07
|
show 1 more comment
$begingroup$
Comment-answer, but too long for a comment:
I think you are thinking about this wrong.
Tests are some of the MOST valuable hours in a course. They are high stakes performances (like in music or sports). Preparation for them drives a lot of learning. Then the actual execution and subsequent feedback is often much more valuable training than routine drill problems, because of caring about the result. You should maximize test utility versus another hour of lecture (which probably has less learning impact even than an hour of them working drill problems).
In addition, by using a take home you are trying to get an extra hour of their time. In addition, take homes are very hard to control from assistance (book, roommate, online). Can you really expect them to be rigid about a time limit when taking a test at home? If unlimited, then now you're taking more of their time.
In addition, take home tests often lead to instructors giving non ideal questions (ones that are too much like research projects for instance). This is not the case here--your question is fine. However, your urge to ask some sort of strange, hard to cheat on question may already be driving you away from what would be the normal best question in a controlled setting.
In general, ODE books have too much content for a one quarter or one semester course. It is very normal not to cover it all. So if you're already shaving some lessons off, just shave one more off. And learn the core of the topic well. And good tests are key to good learning. Don't shave this 2nd order ODE with constant coefficients off. It's the key part of the course! Very high gain. But surely there is some other lesson (existence, Wronskians, predator prey, transforms, Sturm Louisville, series, etc.) you can skip to allow use of class time for examination.
And I love all the topics and would love to have you cover everything. But you need to prioritize. You got a lifeboat with 15 spots and 25 people, pick the best 15 to live. 2nd order constant coefficient ODE, with a forcing function, will be seen all over the place in physics, engineering, chemistry applications. So it lives. Some other topics go in the water. And the test time needs to live. It's "high gain".
In theory, you could cover more content by telling the kids to learn a lesson sans lecture. But I get the impression you're not training superstars here. They will be unhappy without the scaffolding of some lecture time and Q&A time on the topic. So, just treat this as an optimization problem and do a little less, but do it well.
[Moderator may cut my other answer.]
answered Oct 17 at 2:47
guestguest
1211 bronze badge
$endgroup$
6
$begingroup$
I would argue precisely the opposite of this. There is no point whatever in testing people's ability to grind through the solution to problems like the OP's, because even the most basic computer algebra system can get the solution faster and more reliably. On the other hand, understanding something about Sturm Liouville theory, Laplace (and other) transforms, phase-plane diagrams, existence and uniqueness of solutions, etc, is about insight, which is the one thing that can't be automated. The fact that many undergraduate courses haven't changed for 50 years is relevant, of course.
$endgroup$
– alephzero
Oct 17 at 10:57
3
$begingroup$
Most of his students are going to be going into engineering or science. Being able to work diffy Qs, comes up all the time in STE. If you're weak on manipulational skill you'll have a hard time doing homework problems in junior year physics (mechanics, E&M, quantum) or in mechE (fluids, thermo, controls) or in EE (circuits). You'll have a hard time even following derivations. (You could make the same argument that knowing fractions or basic algebra is not important...but if you have to look everything up or run to a CAS, you're not going to follow the subject matter well.)
$endgroup$
– guest
Oct 17 at 11:30
1
$begingroup$
I also think having a good foundation in analytical solution techniques, first, will make it easier when dealing with the more detailed topics like series solutions or Sturm Louisville or transforms. And it tends to "build" in that you get a new lens to look at familiar topics. Humans are not computers...we have practical limits to our brains, but seeing the same thing a couple different ways, helps makes things make sense and stick. For instance seeing the similarity of parallel/series resistors in circuits and head losses in a fluid system.
$endgroup$
– guest
Oct 17 at 11:39
2
$begingroup$
Note, once you HAVE experienced things well and done a lot of practical manipulation, it may be absolutely fine to start using a calculator for tedious arithmetic or a CAS for solving equations. But at this point, you are a sophisticated user. This is a very different thing to saying a student should never bother to learn initially. Personally, I don't see how you can sit and read a paper, if you can't follow derivations and run to a computer (and having experience working problems makes it easier to follow work, even if not practiced now...just having done it before.)
$endgroup$
– guest
Oct 17 at 11:45
1
$begingroup$
The theme of this answer - that tests are hugely important - is absolutely true. Many folks who did not experience that value in earlier forms of university may not realize it and have missed out. I just completed a masters and it was well less valuable than the undergrad and the too-easy and/or too-little-thought-out exams that did not focus on deep problem solving were a big reason.
$endgroup$
– javadba
Oct 17 at 20:07
|
show 1 more comment
$begingroup$
Comment-answer, but too long for a comment:
I think you are thinking about this wrong.
Tests are some of the MOST valuable hours in a course. They are high stakes performances (like in music or sports). Preparation for them drives a lot of learning. Then the actual execution and subsequent feedback is often much more valuable training than routine drill problems, because of caring about the result. You should maximize test utility versus another hour of lecture (which probably has less learning impact even than an hour of them working drill problems).
In addition, by using a take home you are trying to get an extra hour of their time. In addition, take homes are very hard to control from assistance (book, roommate, online). Can you really expect them to be rigid about a time limit when taking a test at home? If unlimited, then now you're taking more of their time.
In addition, take home tests often lead to instructors giving non ideal questions (ones that are too much like research projects for instance). This is not the case here--your question is fine. However, your urge to ask some sort of strange, hard to cheat on question may already be driving you away from what would be the normal best question in a controlled setting.
In general, ODE books have too much content for a one quarter or one semester course. It is very normal not to cover it all. So if you're already shaving some lessons off, just shave one more off. And learn the core of the topic well. And good tests are key to good learning. Don't shave this 2nd order ODE with constant coefficients off. It's the key part of the course! Very high gain. But surely there is some other lesson (existence, Wronskians, predator prey, transforms, Sturm Louisville, series, etc.) you can skip to allow use of class time for examination.
And I love all the topics and would love to have you cover everything. But you need to prioritize. You got a lifeboat with 15 spots and 25 people, pick the best 15 to live. 2nd order constant coefficient ODE, with a forcing function, will be seen all over the place in physics, engineering, chemistry applications. So it lives. Some other topics go in the water. And the test time needs to live. It's "high gain".
In theory, you could cover more content by telling the kids to learn a lesson sans lecture. But I get the impression you're not training superstars here. They will be unhappy without the scaffolding of some lecture time and Q&A time on the topic. So, just treat this as an optimization problem and do a little less, but do it well.
[Moderator may cut my other answer.]
answered Oct 17 at 2:47
guestguest
1211 bronze badge
$endgroup$
Comment-answer, but too long for a comment:
I think you are thinking about this wrong.
Tests are some of the MOST valuable hours in a course. They are high stakes performances (like in music or sports). Preparation for them drives a lot of learning. Then the actual execution and subsequent feedback is often much more valuable training than routine drill problems, because of caring about the result. You should maximize test utility versus another hour of lecture (which probably has less learning impact even than an hour of them working drill problems).
In addition, by using a take home you are trying to get an extra hour of their time. In addition, take homes are very hard to control from assistance (book, roommate, online). Can you really expect them to be rigid about a time limit when taking a test at home? If unlimited, then now you're taking more of their time.
In addition, take home tests often lead to instructors giving non ideal questions (ones that are too much like research projects for instance). This is not the case here--your question is fine. However, your urge to ask some sort of strange, hard to cheat on question may already be driving you away from what would be the normal best question in a controlled setting.
In general, ODE books have too much content for a one quarter or one semester course. It is very normal not to cover it all. So if you're already shaving some lessons off, just shave one more off. And learn the core of the topic well. And good tests are key to good learning. Don't shave this 2nd order ODE with constant coefficients off. It's the key part of the course! Very high gain. But surely there is some other lesson (existence, Wronskians, predator prey, transforms, Sturm Louisville, series, etc.) you can skip to allow use of class time for examination.
And I love all the topics and would love to have you cover everything. But you need to prioritize. You got a lifeboat with 15 spots and 25 people, pick the best 15 to live. 2nd order constant coefficient ODE, with a forcing function, will be seen all over the place in physics, engineering, chemistry applications. So it lives. Some other topics go in the water. And the test time needs to live. It's "high gain".
In theory, you could cover more content by telling the kids to learn a lesson sans lecture. But I get the impression you're not training superstars here. They will be unhappy without the scaffolding of some lecture time and Q&A time on the topic. So, just treat this as an optimization problem and do a little less, but do it well.
[Moderator may cut my other answer.]
answered Oct 17 at 2:47
guestguest
1211 bronze badge
answered Oct 17 at 2:47
guestguest
1211 bronze badge
answered Oct 17 at 2:47
guestguest
1211 bronze badge
answered Oct 17 at 2:47
guestguest
1211 bronze badge
1211 bronze badge
6
$begingroup$
I would argue precisely the opposite of this. There is no point whatever in testing people's ability to grind through the solution to problems like the OP's, because even the most basic computer algebra system can get the solution faster and more reliably. On the other hand, understanding something about Sturm Liouville theory, Laplace (and other) transforms, phase-plane diagrams, existence and uniqueness of solutions, etc, is about insight, which is the one thing that can't be automated. The fact that many undergraduate courses haven't changed for 50 years is relevant, of course.
$endgroup$
– alephzero
Oct 17 at 10:57
3
$begingroup$
Most of his students are going to be going into engineering or science. Being able to work diffy Qs, comes up all the time in STE. If you're weak on manipulational skill you'll have a hard time doing homework problems in junior year physics (mechanics, E&M, quantum) or in mechE (fluids, thermo, controls) or in EE (circuits). You'll have a hard time even following derivations. (You could make the same argument that knowing fractions or basic algebra is not important...but if you have to look everything up or run to a CAS, you're not going to follow the subject matter well.)
$endgroup$
– guest
Oct 17 at 11:30
1
$begingroup$
I also think having a good foundation in analytical solution techniques, first, will make it easier when dealing with the more detailed topics like series solutions or Sturm Louisville or transforms. And it tends to "build" in that you get a new lens to look at familiar topics. Humans are not computers...we have practical limits to our brains, but seeing the same thing a couple different ways, helps makes things make sense and stick. For instance seeing the similarity of parallel/series resistors in circuits and head losses in a fluid system.
$endgroup$
– guest
Oct 17 at 11:39
2
$begingroup$
Note, once you HAVE experienced things well and done a lot of practical manipulation, it may be absolutely fine to start using a calculator for tedious arithmetic or a CAS for solving equations. But at this point, you are a sophisticated user. This is a very different thing to saying a student should never bother to learn initially. Personally, I don't see how you can sit and read a paper, if you can't follow derivations and run to a computer (and having experience working problems makes it easier to follow work, even if not practiced now...just having done it before.)
$endgroup$
– guest
Oct 17 at 11:45
1
$begingroup$
The theme of this answer - that tests are hugely important - is absolutely true. Many folks who did not experience that value in earlier forms of university may not realize it and have missed out. I just completed a masters and it was well less valuable than the undergrad and the too-easy and/or too-little-thought-out exams that did not focus on deep problem solving were a big reason.
$endgroup$
– javadba
Oct 17 at 20:07
|
show 1 more comment
6
$begingroup$
I would argue precisely the opposite of this. There is no point whatever in testing people's ability to grind through the solution to problems like the OP's, because even the most basic computer algebra system can get the solution faster and more reliably. On the other hand, understanding something about Sturm Liouville theory, Laplace (and other) transforms, phase-plane diagrams, existence and uniqueness of solutions, etc, is about insight, which is the one thing that can't be automated. The fact that many undergraduate courses haven't changed for 50 years is relevant, of course.
$endgroup$
– alephzero
Oct 17 at 10:57
3
$begingroup$
Most of his students are going to be going into engineering or science. Being able to work diffy Qs, comes up all the time in STE. If you're weak on manipulational skill you'll have a hard time doing homework problems in junior year physics (mechanics, E&M, quantum) or in mechE (fluids, thermo, controls) or in EE (circuits). You'll have a hard time even following derivations. (You could make the same argument that knowing fractions or basic algebra is not important...but if you have to look everything up or run to a CAS, you're not going to follow the subject matter well.)
$endgroup$
– guest
Oct 17 at 11:30
1
$begingroup$
I also think having a good foundation in analytical solution techniques, first, will make it easier when dealing with the more detailed topics like series solutions or Sturm Louisville or transforms. And it tends to "build" in that you get a new lens to look at familiar topics. Humans are not computers...we have practical limits to our brains, but seeing the same thing a couple different ways, helps makes things make sense and stick. For instance seeing the similarity of parallel/series resistors in circuits and head losses in a fluid system.
$endgroup$
– guest
Oct 17 at 11:39
2
$begingroup$
Note, once you HAVE experienced things well and done a lot of practical manipulation, it may be absolutely fine to start using a calculator for tedious arithmetic or a CAS for solving equations. But at this point, you are a sophisticated user. This is a very different thing to saying a student should never bother to learn initially. Personally, I don't see how you can sit and read a paper, if you can't follow derivations and run to a computer (and having experience working problems makes it easier to follow work, even if not practiced now...just having done it before.)
$endgroup$
– guest
Oct 17 at 11:45
1
$begingroup$
The theme of this answer - that tests are hugely important - is absolutely true. Many folks who did not experience that value in earlier forms of university may not realize it and have missed out. I just completed a masters and it was well less valuable than the undergrad and the too-easy and/or too-little-thought-out exams that did not focus on deep problem solving were a big reason.
$endgroup$
– javadba
Oct 17 at 20:07
6
6
$begingroup$
I would argue precisely the opposite of this. There is no point whatever in testing people's ability to grind through the solution to problems like the OP's, because even the most basic computer algebra system can get the solution faster and more reliably. On the other hand, understanding something about Sturm Liouville theory, Laplace (and other) transforms, phase-plane diagrams, existence and uniqueness of solutions, etc, is about insight, which is the one thing that can't be automated. The fact that many undergraduate courses haven't changed for 50 years is relevant, of course.
$endgroup$
– alephzero
Oct 17 at 10:57
$begingroup$
I would argue precisely the opposite of this. There is no point whatever in testing people's ability to grind through the solution to problems like the OP's, because even the most basic computer algebra system can get the solution faster and more reliably. On the other hand, understanding something about Sturm Liouville theory, Laplace (and other) transforms, phase-plane diagrams, existence and uniqueness of solutions, etc, is about insight, which is the one thing that can't be automated. The fact that many undergraduate courses haven't changed for 50 years is relevant, of course.
$endgroup$
– alephzero
Oct 17 at 10:57
3
3
$begingroup$
Most of his students are going to be going into engineering or science. Being able to work diffy Qs, comes up all the time in STE. If you're weak on manipulational skill you'll have a hard time doing homework problems in junior year physics (mechanics, E&M, quantum) or in mechE (fluids, thermo, controls) or in EE (circuits). You'll have a hard time even following derivations. (You could make the same argument that knowing fractions or basic algebra is not important...but if you have to look everything up or run to a CAS, you're not going to follow the subject matter well.)
$endgroup$
– guest
Oct 17 at 11:30
$begingroup$
Most of his students are going to be going into engineering or science. Being able to work diffy Qs, comes up all the time in STE. If you're weak on manipulational skill you'll have a hard time doing homework problems in junior year physics (mechanics, E&M, quantum) or in mechE (fluids, thermo, controls) or in EE (circuits). You'll have a hard time even following derivations. (You could make the same argument that knowing fractions or basic algebra is not important...but if you have to look everything up or run to a CAS, you're not going to follow the subject matter well.)
$endgroup$
– guest
Oct 17 at 11:30
1
1
$begingroup$
I also think having a good foundation in analytical solution techniques, first, will make it easier when dealing with the more detailed topics like series solutions or Sturm Louisville or transforms. And it tends to "build" in that you get a new lens to look at familiar topics. Humans are not computers...we have practical limits to our brains, but seeing the same thing a couple different ways, helps makes things make sense and stick. For instance seeing the similarity of parallel/series resistors in circuits and head losses in a fluid system.
$endgroup$
– guest
Oct 17 at 11:39
$begingroup$
I also think having a good foundation in analytical solution techniques, first, will make it easier when dealing with the more detailed topics like series solutions or Sturm Louisville or transforms. And it tends to "build" in that you get a new lens to look at familiar topics. Humans are not computers...we have practical limits to our brains, but seeing the same thing a couple different ways, helps makes things make sense and stick. For instance seeing the similarity of parallel/series resistors in circuits and head losses in a fluid system.
$endgroup$
– guest
Oct 17 at 11:39
2
2
$begingroup$
Note, once you HAVE experienced things well and done a lot of practical manipulation, it may be absolutely fine to start using a calculator for tedious arithmetic or a CAS for solving equations. But at this point, you are a sophisticated user. This is a very different thing to saying a student should never bother to learn initially. Personally, I don't see how you can sit and read a paper, if you can't follow derivations and run to a computer (and having experience working problems makes it easier to follow work, even if not practiced now...just having done it before.)
$endgroup$
– guest
Oct 17 at 11:45
$begingroup$
Note, once you HAVE experienced things well and done a lot of practical manipulation, it may be absolutely fine to start using a calculator for tedious arithmetic or a CAS for solving equations. But at this point, you are a sophisticated user. This is a very different thing to saying a student should never bother to learn initially. Personally, I don't see how you can sit and read a paper, if you can't follow derivations and run to a computer (and having experience working problems makes it easier to follow work, even if not practiced now...just having done it before.)
$endgroup$
– guest
Oct 17 at 11:45
1
1
$begingroup$
The theme of this answer - that tests are hugely important - is absolutely true. Many folks who did not experience that value in earlier forms of university may not realize it and have missed out. I just completed a masters and it was well less valuable than the undergrad and the too-easy and/or too-little-thought-out exams that did not focus on deep problem solving were a big reason.
$endgroup$
– javadba
Oct 17 at 20:07
$begingroup$
The theme of this answer - that tests are hugely important - is absolutely true. Many folks who did not experience that value in earlier forms of university may not realize it and have missed out. I just completed a masters and it was well less valuable than the undergrad and the too-easy and/or too-little-thought-out exams that did not focus on deep problem solving were a big reason.
$endgroup$
– javadba
Oct 17 at 20:07
|
show 1 more comment
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$begingroup$
You could have two components to the assignment. A take-home portion could be assigned knowing that students have access to technology. The questions could be conceptual in nature, asking students to explain an idea; or they could involve heavy computations that you wouldn't ask them to do during a timed, paper exam. Meanwhile, an in-class portion could ask them to solve simple examples by hand, like the one you mentioned. Dividing it in this way makes it clearer to students what they'll be expected to do.
$endgroup$
– Brendan W. Sullivan
Oct 16 at 18:55
$begingroup$
@BrendanW.Sullivan, thanks for the comment! But even for the heavy computations they can let a computer do the job for them. For conceptual ones, google will probably tell them the answer.
$endgroup$
– Zuriel
Oct 16 at 18:58
$begingroup$
@Namaste, I can do it but I am running behind my schedule of this course and would love to save one class period to cover some materials if possible.
$endgroup$
– Zuriel
Oct 16 at 20:51