Most Popular
1500 questions
12
votes
5 answers
How to motivate the geometric definition of trigonometric functions on the unit circle
Suppose your students know already the geometric definition of $\sin$ $\cos$ and $\tan$ for angles between $0^{\circ}$ and $90^{\circ}$.
How can I motivate the definition of $\sin$, $\cos$ and $\tan$ for angles between $0^{\circ}$ and $360^{\circ}$…
Julia
- 1,265
- 2
- 12
- 21
12
votes
1 answer
Effective use of Moodle (or similar)
Currently we are using Moodle to manage our courses here. It has meant structuring the publication and turn in of homework, and has helped in distributing lecture notes and shorter documents to the students.
But Moodle has also functionality like…
vonbrand
- 12,306
- 3
- 27
- 59
12
votes
3 answers
Conceptual Mathematics by Lawvere & Schanuel as text for bridging course?
I have recently come across Conceptual Mathematics: A First Introduction to Categories by Lawvere & Schanuel. It is a gentle introduction to Category Theory and strikes me as a potential alternative text for a bridging course to abstract…
J W
- 4,654
- 2
- 22
- 44
12
votes
3 answers
Is it a dead end to define differentials as finite differences on the tangent line?
In a freshman calculus text (Larson), I was surprised to find a definition of differentials as finite differences on the tangent line, and even more surprised to learn later that this definition apparently dates back to Leibniz. My main source on…
user507
12
votes
4 answers
Mathematics Education Graduate Program List and Rankings
U.S. News and World Report publishes school rankings for many different disciplines, including mathematics. Is there any ranking for mathematics education graduate programs?
Weaker question: Is there a guide to selecting a math education graduate…
David Ebert
- 3,895
- 2
- 22
- 36
12
votes
7 answers
Why should or shouldn't we teach functions to 15 year olds?
Background
The students in my country are supposed to be able to work with and answer questions about functions at the age of around 15. This is asserted in the standard mathematics curriculum for middle school students.
Personally, I think the…
Improve
- 1,881
- 14
- 24
12
votes
2 answers
How to divide up readings in a flipped classroom?
Next semester I plan to experiment with "flipping" a classroom, by assigning required readings from the textbook (perhaps with supplementary notes) so that lecture doesn't have to "cover all the material", freeing up some class time for discussions,…
Mike Shulman
- 6,560
- 21
- 53
12
votes
4 answers
Reasons to teach Thales' theorem
In a classical course on Euclidean, compass-and-ruler geometry, Thales' theorem has always had a prominent place. However, as the Wikipedia article says,
It is equivalent to the theorem about ratios in similar triangles,
which seems to be…
mbork
- 1,299
- 9
- 14
12
votes
3 answers
Usefulness of $u$-substitution in and beyond early Calculus?
My students, when presented with an integral (source) like
$$\int (2x+2)e^{x^2+2x+3} \ dx$$
are apt to recognize derivative patterns like $u' e^{u}$ and reverse-engineer anti-derivatives rather than to utilize $u$-substitution.
With something…
Carser
- 798
- 6
- 12
12
votes
4 answers
How do you teach students about the concept of a proof?
I get this question a lot from new students who are taking their first proof-based math class. They are struggling because they don't have that fluency with proofs, to begin with. They don't know what constitutes valid proof or they have trouble…
iYOA
- 241
- 1
- 6
12
votes
6 answers
Question formats for online tests, to deter cheating
I'm teaching calculus 1 online this term and anticipate being plagued by the perennial problem of cheaters. I have seen suggestions for how to arrange the testing time to accommodate for traditional tests (such as this previous question and the…
Opal E
- 3,986
- 18
- 45
12
votes
6 answers
How do you explain concavity of a polynomial without any calculus?
How do you explain the concavity of a polynomial without any calculus?
As the title suggests, I am struggling to explain when given a graph of a polynomial, how we determine when it is concave up or concave down without using any calculus or tangent…
2132123
- 231
- 2
- 5
12
votes
1 answer
How, now, shall we teach math online?
Now that everyone has had the experience of teaching math in an online/remote/synchronous/asynchronous format, and looking forward to more of this in the Summer and Fall terms, how do we change our practices?
In the recent question How Shall We…
Nick C
- 9,436
- 25
- 59
12
votes
1 answer
Proof by contradiction - more than one case
I am looking for some examples of when proof by contradiction is used in a problem with more than one case.
In all the elementary examples, there are only two options (eg rational/irrational, infinite/finite), so you assume the opposite, show it…
PhysicsMathsLove
- 381
- 1
- 5
12
votes
8 answers
Are these assumptions in statistics correct or beneficial?
(I hope the question in in scope, please see my question on Meta about that)
My 15 yo son (2nde in France, this is the first year of the equivalent of a High School) is going through basic statistics. One of the exercises in his book made me wonder…
WoJ
- 1,388
- 1
- 9
- 19