Questions tagged [concept-motivation]
For questions how to motivate a mathematical concept (i.e., the motivation and examples of definitions, theorems, etc.) or general concepts of mathematics. Please use the [student-motivation] tag for questions about how to motivate students in general.
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Truth tables. What does a truth valuation of a formula even mean?
What does a truth table even mean? Does anyone actually spell it out anywhere? (reference please). People feel like the are not taught rigorously like limits are.
Edit: What does it mean for a (non-...
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How can we motivate that Newton's method is useful?
If you teach Newton's method for finding roots of real functions on the high school (or freshmen) level, I think some students may reason like a variant of the following:
Why do I need learn such a &...
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Course materials for developing a mathematical theory from "natural questions to ask"
Educational setting.
I'm teaching math courses - typically consisting of lectures, weekly homework sheets, and an exercise class where the homework questions are discussed - for undergraduate and ...
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How can we best motivate the study of polynomials to high-school students?
We all know how important and ubiquitous polynomials are in mathematics. However, when faced with a (not so much in love with the subject) 14-year-old asking us why they should care about these things,...
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Any meaning/interpretation for $\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\dots (= \mathrm e)$ (sum of reciprocals of factorials)?
One common way to introduce Euler's number $\mathrm e$ is $$\mathrm e = \lim_{n\to \infty} \left(1+\frac{1}{n}\right)^n,$$ where the right-hand expression has an "interest rate interpretation&...
user18187
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Is this motivation for the concept of a limit a good one?
tldr: There is a simple intuitive definition of a limit for monotone sequences, and I suggest that it can be used to motivate the (more complicated) standard definition. I am asking for feedback on my ...
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Does induction really avoid proving an infinite number of claims?
I am teaching calculus $1$ this semester, and I saw the following motivation for using induction by another teacher:
Since we can't go over "manually proving" all claims $1,2,\ldots$ and ...
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Favorite linear programming (not integer) examples?
I am wondering what examples you like to give when introducing linear programming, where the examples are not clearly better suited as integer linear programs. I would like a few examples where we can ...
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How well can students learn abstract concepts through concrete examples?
In my own personal experience in teaching linear algebra, where many students encounter abstract ideas for the first time, I find that most students have trouble consolidating observations from ...
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Introducing direct substitution in an intro calculus course
I'm revisiting the materials I've put together for students taking a non-proof-based intro to calculus, and my goal is for them to have a clear but rough sense of a limit as a bound (basically enough ...
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Probability — analytical results instead of simulations
After students learn how to use probabilistic simulations, what strategies can one use to encourage them to understand analytical results anyway? For example, I'm struggling to find a compelling ...
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How to explain loss of significance in numerical analysis?
As I have myself struggled a bit with this concept, I would like to present my own explanation of it.
Context:
Loss of significance is a loss of precision, not necessarily accuracy.
And for a long ...
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An introductory example for Taylor series (12th grade)
I (a student) am doing a presentation on Taylor series in my class (12th grade, in Germany if this is relevant). I am looking for a good example where you can see when Taylor series might be useful. ...
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How to teach the Pythagorean theorem in a satisfying way to high school students?
I've been pretty dissatisfied with the way the Pythagorean theorem is usually taught, mainly for two reasons:
The chosen proof feels like magic and I don't feel like I have a better understanding of ...
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Replacement for the Pac-Man grid analogy
To most people, a torus is a donut-like shape. Topologists like to describe the torus differently: you start with a square, and "identify opposite sides". We can imagine gluing together one ...
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