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Asking students to define “unique”
Can we save the word “unique”?Unique candidate that failsWhat is a good way to explain the Lebesgue integral to non-math majors?Advantages of learning different topics simultaneouslyHow to get students in a under-graduate linear algebra course interested in determinants?Should we “program” calculus students, like the physicists seem to want us to?Unique steps leading to a non-unique answerTeaching undergraduates who expect a high-school-like learning environmentInability to work with an arbitrary mathematical objectLearning proofs in introductory analysis coursesMacLane-Birkhoff's “Algebra” vs Jacobson's “Basic Algebra I,II” vs Lang's “Algebra”
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
Context: This is for introductory linear algebra course, near the beginning.
As a sort of "exit survey" after one of my lectures, I would like to ask my students to try and define what "unique" is from a mathematical perspective. I would then talk about that next time. However, I am not sure
- whether that's a good idea; or
- how to phrase the question so that I don't get answers like "it means you're really special".
undergraduate-education assessment
asked 8 hours ago
Avi SteinerAvi Steiner
2351 silver badge8 bronze badges
$endgroup$
add a comment
|
$begingroup$
Context: This is for introductory linear algebra course, near the beginning.
As a sort of "exit survey" after one of my lectures, I would like to ask my students to try and define what "unique" is from a mathematical perspective. I would then talk about that next time. However, I am not sure
- whether that's a good idea; or
- how to phrase the question so that I don't get answers like "it means you're really special".
undergraduate-education assessment
asked 8 hours ago
Avi SteinerAvi Steiner
2351 silver badge8 bronze badges
$endgroup$
$begingroup$
Related (though not a duplicate): Can we save the word unique?
$endgroup$
– Namaste
8 hours ago
$begingroup$
Do you address uniqueness in you class, prior to exit surveys? (Eg., unique solution, to a system of equations, if it exits, which comes up frequently in linear algebra) and/or do you expand on how to prove uniqueness in general within your class? Do you ask, in your exit survey, to define "unique solution" in the context of linear algebra, or the definition of "unique" in general?
$endgroup$
– Namaste
8 hours ago
$begingroup$
@Namaste I want this to be more of a "pre-assessment" prior to discussing unique solutions
$endgroup$
– Avi Steiner
8 hours ago
$begingroup$
Ahhh, that clarifies matters somewhat. I would simply suggest asking students, in a linear algebra class, to define what they think a "unique solution" means, in terms of solving a system of equations, prior to your addressing it in a lecture. I agree with the answer in that asking students: "Define what "unique" means mathematically" prior to previous exposure to the concept of "uniqueness" in mathematics," is like inviting what you want to avoid in $2$.
$endgroup$
– Namaste
7 hours ago
add a comment
|
$begingroup$
Context: This is for introductory linear algebra course, near the beginning.
As a sort of "exit survey" after one of my lectures, I would like to ask my students to try and define what "unique" is from a mathematical perspective. I would then talk about that next time. However, I am not sure
- whether that's a good idea; or
- how to phrase the question so that I don't get answers like "it means you're really special".
undergraduate-education assessment
asked 8 hours ago
Avi SteinerAvi Steiner
2351 silver badge8 bronze badges
$endgroup$
Context: This is for introductory linear algebra course, near the beginning.
As a sort of "exit survey" after one of my lectures, I would like to ask my students to try and define what "unique" is from a mathematical perspective. I would then talk about that next time. However, I am not sure
- whether that's a good idea; or
- how to phrase the question so that I don't get answers like "it means you're really special".
undergraduate-education assessment
undergraduate-education assessment
asked 8 hours ago
Avi SteinerAvi Steiner
2351 silver badge8 bronze badges
asked 8 hours ago
Avi SteinerAvi Steiner
2351 silver badge8 bronze badges
asked 8 hours ago
Avi SteinerAvi Steiner
2351 silver badge8 bronze badges
asked 8 hours ago
Avi SteinerAvi Steiner
2351 silver badge8 bronze badges
asked 8 hours ago
Avi SteinerAvi Steiner
2351 silver badge8 bronze badges
2351 silver badge8 bronze badges
$begingroup$
Related (though not a duplicate): Can we save the word unique?
$endgroup$
– Namaste
8 hours ago
$begingroup$
Do you address uniqueness in you class, prior to exit surveys? (Eg., unique solution, to a system of equations, if it exits, which comes up frequently in linear algebra) and/or do you expand on how to prove uniqueness in general within your class? Do you ask, in your exit survey, to define "unique solution" in the context of linear algebra, or the definition of "unique" in general?
$endgroup$
– Namaste
8 hours ago
$begingroup$
@Namaste I want this to be more of a "pre-assessment" prior to discussing unique solutions
$endgroup$
– Avi Steiner
8 hours ago
$begingroup$
Ahhh, that clarifies matters somewhat. I would simply suggest asking students, in a linear algebra class, to define what they think a "unique solution" means, in terms of solving a system of equations, prior to your addressing it in a lecture. I agree with the answer in that asking students: "Define what "unique" means mathematically" prior to previous exposure to the concept of "uniqueness" in mathematics," is like inviting what you want to avoid in $2$.
$endgroup$
– Namaste
7 hours ago
add a comment
|
$begingroup$
Related (though not a duplicate): Can we save the word unique?
$endgroup$
– Namaste
8 hours ago
$begingroup$
Do you address uniqueness in you class, prior to exit surveys? (Eg., unique solution, to a system of equations, if it exits, which comes up frequently in linear algebra) and/or do you expand on how to prove uniqueness in general within your class? Do you ask, in your exit survey, to define "unique solution" in the context of linear algebra, or the definition of "unique" in general?
$endgroup$
– Namaste
8 hours ago
$begingroup$
@Namaste I want this to be more of a "pre-assessment" prior to discussing unique solutions
$endgroup$
– Avi Steiner
8 hours ago
$begingroup$
Ahhh, that clarifies matters somewhat. I would simply suggest asking students, in a linear algebra class, to define what they think a "unique solution" means, in terms of solving a system of equations, prior to your addressing it in a lecture. I agree with the answer in that asking students: "Define what "unique" means mathematically" prior to previous exposure to the concept of "uniqueness" in mathematics," is like inviting what you want to avoid in $2$.
$endgroup$
– Namaste
7 hours ago
$begingroup$
Related (though not a duplicate): Can we save the word unique?
$endgroup$
– Namaste
8 hours ago
$begingroup$
Related (though not a duplicate): Can we save the word unique?
$endgroup$
– Namaste
8 hours ago
$begingroup$
Do you address uniqueness in you class, prior to exit surveys? (Eg., unique solution, to a system of equations, if it exits, which comes up frequently in linear algebra) and/or do you expand on how to prove uniqueness in general within your class? Do you ask, in your exit survey, to define "unique solution" in the context of linear algebra, or the definition of "unique" in general?
$endgroup$
– Namaste
8 hours ago
$begingroup$
Do you address uniqueness in you class, prior to exit surveys? (Eg., unique solution, to a system of equations, if it exits, which comes up frequently in linear algebra) and/or do you expand on how to prove uniqueness in general within your class? Do you ask, in your exit survey, to define "unique solution" in the context of linear algebra, or the definition of "unique" in general?
$endgroup$
– Namaste
8 hours ago
$begingroup$
@Namaste I want this to be more of a "pre-assessment" prior to discussing unique solutions
$endgroup$
– Avi Steiner
8 hours ago
$begingroup$
@Namaste I want this to be more of a "pre-assessment" prior to discussing unique solutions
$endgroup$
– Avi Steiner
8 hours ago
$begingroup$
Ahhh, that clarifies matters somewhat. I would simply suggest asking students, in a linear algebra class, to define what they think a "unique solution" means, in terms of solving a system of equations, prior to your addressing it in a lecture. I agree with the answer in that asking students: "Define what "unique" means mathematically" prior to previous exposure to the concept of "uniqueness" in mathematics," is like inviting what you want to avoid in $2$.
$endgroup$
– Namaste
7 hours ago
$begingroup$
Ahhh, that clarifies matters somewhat. I would simply suggest asking students, in a linear algebra class, to define what they think a "unique solution" means, in terms of solving a system of equations, prior to your addressing it in a lecture. I agree with the answer in that asking students: "Define what "unique" means mathematically" prior to previous exposure to the concept of "uniqueness" in mathematics," is like inviting what you want to avoid in $2$.
$endgroup$
– Namaste
7 hours ago
add a comment
|
1 Answer
1
active
oldest
votes
$begingroup$
To avoid misinterpretations, I'd give it to them in a mathematical sentence and ask them to explain what they believe 'unique' means in this context.
For lack of knowing where you are in the course, I might give them an exit ticket such as
Consider the sentence, "The equation x^3 - 2x + 3 = 0 has a unique
solution." What do you think the word "unique" means in this context?
Contrast this with the ways you might use "unique" in standard
English.
However, this sentence has a problem in that the word 'unique' can meaningfully only be interpreted in one way (or perhaps I'm uncreative); perhaps give them a mathematical sentence which is not quite so obvious.
answered 8 hours ago
Opal EOpal E
1,7108 silver badges27 bronze badges
$endgroup$
$begingroup$
I agree with establishing such context in any such survey:
$endgroup$
– Namaste
8 hours ago
$begingroup$
Context matters.
$endgroup$
– paul garrett
6 hours ago
add a comment
|
Your Answer
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1 Answer
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1 Answer
1
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oldest
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oldest
votes
active
oldest
votes
$begingroup$
To avoid misinterpretations, I'd give it to them in a mathematical sentence and ask them to explain what they believe 'unique' means in this context.
For lack of knowing where you are in the course, I might give them an exit ticket such as
Consider the sentence, "The equation x^3 - 2x + 3 = 0 has a unique
solution." What do you think the word "unique" means in this context?
Contrast this with the ways you might use "unique" in standard
English.
However, this sentence has a problem in that the word 'unique' can meaningfully only be interpreted in one way (or perhaps I'm uncreative); perhaps give them a mathematical sentence which is not quite so obvious.
answered 8 hours ago
Opal EOpal E
1,7108 silver badges27 bronze badges
$endgroup$
$begingroup$
I agree with establishing such context in any such survey:
$endgroup$
– Namaste
8 hours ago
$begingroup$
Context matters.
$endgroup$
– paul garrett
6 hours ago
add a comment
|
$begingroup$
To avoid misinterpretations, I'd give it to them in a mathematical sentence and ask them to explain what they believe 'unique' means in this context.
For lack of knowing where you are in the course, I might give them an exit ticket such as
Consider the sentence, "The equation x^3 - 2x + 3 = 0 has a unique
solution." What do you think the word "unique" means in this context?
Contrast this with the ways you might use "unique" in standard
English.
However, this sentence has a problem in that the word 'unique' can meaningfully only be interpreted in one way (or perhaps I'm uncreative); perhaps give them a mathematical sentence which is not quite so obvious.
answered 8 hours ago
Opal EOpal E
1,7108 silver badges27 bronze badges
$endgroup$
$begingroup$
I agree with establishing such context in any such survey:
$endgroup$
– Namaste
8 hours ago
$begingroup$
Context matters.
$endgroup$
– paul garrett
6 hours ago
add a comment
|
$begingroup$
To avoid misinterpretations, I'd give it to them in a mathematical sentence and ask them to explain what they believe 'unique' means in this context.
For lack of knowing where you are in the course, I might give them an exit ticket such as
Consider the sentence, "The equation x^3 - 2x + 3 = 0 has a unique
solution." What do you think the word "unique" means in this context?
Contrast this with the ways you might use "unique" in standard
English.
However, this sentence has a problem in that the word 'unique' can meaningfully only be interpreted in one way (or perhaps I'm uncreative); perhaps give them a mathematical sentence which is not quite so obvious.
answered 8 hours ago
Opal EOpal E
1,7108 silver badges27 bronze badges
$endgroup$
To avoid misinterpretations, I'd give it to them in a mathematical sentence and ask them to explain what they believe 'unique' means in this context.
For lack of knowing where you are in the course, I might give them an exit ticket such as
Consider the sentence, "The equation x^3 - 2x + 3 = 0 has a unique
solution." What do you think the word "unique" means in this context?
Contrast this with the ways you might use "unique" in standard
English.
However, this sentence has a problem in that the word 'unique' can meaningfully only be interpreted in one way (or perhaps I'm uncreative); perhaps give them a mathematical sentence which is not quite so obvious.
answered 8 hours ago
Opal EOpal E
1,7108 silver badges27 bronze badges
answered 8 hours ago
Opal EOpal E
1,7108 silver badges27 bronze badges
answered 8 hours ago
Opal EOpal E
1,7108 silver badges27 bronze badges
answered 8 hours ago
Opal EOpal E
1,7108 silver badges27 bronze badges
1,7108 silver badges27 bronze badges
$begingroup$
I agree with establishing such context in any such survey:
$endgroup$
– Namaste
8 hours ago
$begingroup$
Context matters.
$endgroup$
– paul garrett
6 hours ago
add a comment
|
$begingroup$
I agree with establishing such context in any such survey:
$endgroup$
– Namaste
8 hours ago
$begingroup$
Context matters.
$endgroup$
– paul garrett
6 hours ago
$begingroup$
I agree with establishing such context in any such survey:
$endgroup$
– Namaste
8 hours ago
$begingroup$
I agree with establishing such context in any such survey:
$endgroup$
– Namaste
8 hours ago
$begingroup$
Context matters.
$endgroup$
– paul garrett
6 hours ago
$begingroup$
Context matters.
$endgroup$
– paul garrett
6 hours ago
add a comment
|
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$begingroup$
Related (though not a duplicate): Can we save the word unique?
$endgroup$
– Namaste
8 hours ago
$begingroup$
Do you address uniqueness in you class, prior to exit surveys? (Eg., unique solution, to a system of equations, if it exits, which comes up frequently in linear algebra) and/or do you expand on how to prove uniqueness in general within your class? Do you ask, in your exit survey, to define "unique solution" in the context of linear algebra, or the definition of "unique" in general?
$endgroup$
– Namaste
8 hours ago
$begingroup$
@Namaste I want this to be more of a "pre-assessment" prior to discussing unique solutions
$endgroup$
– Avi Steiner
8 hours ago
$begingroup$
Ahhh, that clarifies matters somewhat. I would simply suggest asking students, in a linear algebra class, to define what they think a "unique solution" means, in terms of solving a system of equations, prior to your addressing it in a lecture. I agree with the answer in that asking students: "Define what "unique" means mathematically" prior to previous exposure to the concept of "uniqueness" in mathematics," is like inviting what you want to avoid in $2$.
$endgroup$
– Namaste
7 hours ago