Community Digest

Top new questions this week:

Parentheses around negative numbers

We teach students that a notation like $$17 - -59$$ is not acceptable or at least not good. Instead we want them to write $$17-(-59)$$ The main reason seems to be that it's more readable if you ...

undergraduate-education notation negative-numbers  
user avatar asked by realGottlob Score of 14
user avatar answered by Tommi Score of 36

How to teach that $10000x^2$ c$^2$m$^2$ is wrong?

How do you teach to teenagers or kids that if we have a square with side length $x$ m (that is, $100x$ cm), then its area is $x^2$ m$^2,$ but not $10000x^2$ c$^2$m$^2$ ?

user avatar asked by guest Score of 3
user avatar answered by ryang Score of 4

Interpreting the derivative as instantaneous rate of change in real phenomena

When interpreting the meaning of the derivative in real phenomena, it may seem that the interpretation is in conflict with the definition of the derivative itself. The confusion is caused by the units ...

undergraduate-education calculus derivative  
user avatar asked by Mahdi Majidi-Zolbanin Score of 1
user avatar answered by guest philosopher Score of 6

Best category theory textbook for undergraduate students

Title is pretty self explanatory. All recommendations welcome. Comments and answers which reject the premise of the question will be met with eye rolling. If I don't see a good enough answer I'll have ...

undergraduate-education textbooks category-theory  
user avatar asked by cheyne Score of 1
user avatar answered by Steven Gubkin Score of 4

What is an example of something you might see outside of math class and how would you model that thing as a set?

In mathematics, we have sets, such as $\begin{Bmatrix}1, 2, 3 \end{Bmatrix}$ or the real-numbers, usually denoted as $\mathbb{R}$. When teaching students about sets for the first time, it can ...

user avatar asked by Samuel Muldoon Score of 1
user avatar answered by Samuel Muldoon Score of 1

Greatest hits from previous weeks:

Impressive common misleading interpretations in statistics to make students aware of

Statistics are used everywhere; politicians, companies, etc. argue with the help of statistics. Since calculations are needed for the interpretation of statistics, such things should be taught in ...

undergraduate-education secondary-education statistics mathematics-in-daily-life  
user avatar asked by Markus Klein Score of 72
user avatar answered by Noah Score of 59

Early vs. late transcendentals

There seem to be two approaches to calculus education: Early transcendentals: introduce polynomials, rational functions, exponentials, logarithms, and trigonometric functions at the beginning of the ...

user avatar asked by Paul Siegel Score of 29
user avatar answered by AndrewC Score of 12

Combative students in proofs classes

When teaching my first discrete math class recently, I found a subset of about 5 out of 35 of my primarily computer science students who I struggled to reach. If these students simply struggled with ...

undergraduate-education student-motivation classroom-management classroom-interaction  
user avatar asked by Opal E Score of 36
user avatar answered by Daniel R. Collins Score of 25

Student asked me if it is necessary to simplify fractions at the end of answering a question. I'm not sure how to respond

I was just tutoring someone and we went through some sort of diagnostic test thing, when the following question came up. Question: Here is some information about $50$ people who took the driving test:...

secondary-education exams fractions  
user avatar asked by Adam Rubinson Score of 21
user avatar answered by Xander Henderson Score of 19

What are the comparative advantages of open-book versus closed-book exams?

I would like to know the advantages and disadvantages of open-book exams as compared to closed-book exams, particularly in standard undergraduate courses like calculus or linear algebra. My practice ...

reference-request exams  
user avatar asked by JDH Score of 30
user avatar answered by Sue VanHattum Score of 22

What are some research-level opportunities in mathematics that do not focus on proofs?

The research level of mathematics (what is done by professors and upper-level graduate students) tends to be heavily portrayed as focused on writing proofs to the exclusion of most anything else math-...

undergraduate-education student-motivation graduate-education  
user avatar asked by Robert Columbia Score of 15
user avatar answered by Dave L Renfro Score of 28

How does one tutor an A-level student past the derivative paradox?

Background: I am new to this site, but have 1500 reputation on the main Maths Stack. I am (age-wise) a secondary student of maths, but for a very long time have been informally learning at home and ...

secondary-education calculus teaching derivative  
user avatar asked by FShrike Score of 15
user avatar answered by Daniel R. Collins Score of 27
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