All Questions

0
votes
1answer
73 views

Integrating derivatives over functions problem

I had a question from a student which I'm unable to answer. We were practicing the rule $\int \frac{f'(x)}{f(x)} \, dx=\ln(f(x))$. A student noticed that if applied naively it gives the following ...
4
votes
3answers
196 views

Don't these word problems seem designed to be confusing?

I'm a fairly new private math tutor, and I'm good at math (I have a BS from Caltech with lots of graduate level math), but becoming good at teaching math is something else, which I strive to improve ...
4
votes
1answer
62 views

Using discrete examples in the beginning of integration

In Germany, one usual example to start teaching about integrals is to look at a simple (piecewise constant or with constant slope) functions that make up a water flow vs. time diagram and ask about ...
-4
votes
0answers
103 views

Should we relabel the slope formulas to prevent confusion with exponents? [on hold]

When you teach about slope in Algebra 1, should we relabel the slope formula to: $$m = \frac{y_b-y_a} {x_b-x_a}$$ and also temporarily relabel the slope-point formula to: $$y−y_a=m(x−x_a)$$ where ...
1
vote
0answers
70 views

Writing Up Solutions To G.H. Hardy's A COURSE IN PURE MATHEMATICS?

Ok, this may be a ridiculous question and if so, you guys will shut it down. But I didn't know where else to ask it-it certainly doesn't belong on Math Overflow. Does anyone know if anyone ever ...
4
votes
0answers
76 views
+50

Flow diagrams and summarizing strategies in proof-computation courses: good or bad for learning? Unsuitable for Inquiry-based learning?

For concreteness lets keep our discussion to calculus courses where there is a balance of proof and computations (computing limits but also doing epsilon-delta proofs) I can understand that in more ...
4
votes
2answers
99 views

What are some suggestions fo teaching statistics concepts to struggling college students?

I'm a private math tutor. I'm fairly new at this, and this semester is the first time I've been tutoring for a statistics class at a community college. I enjoy experimenting and learning about ways to ...
-4
votes
0answers
26 views

Negation of logic [closed]

I’m trying to negate the underlined formula(in the attached picture)but can’t seems to comes in terms with my solution. Your expert inputs are welcomed.
6
votes
0answers
105 views

Are there standard questions for testing how an instructor grades calculus?

My institution is now in the process of "standardizing" our calculus classes. One issue we have is the variation among instructors in grading problems. I am interested if there are ways to objectively ...
-3
votes
0answers
74 views

Find a bounded function $f$ such that $sin(x)<f'(x)<sin(x)+1$ [closed]

This question came up in my diffyqs discussion today. I was curious as to what you fine people had to say. My intuition says it can't happen because the derivative is mostly positive... but my ...
9
votes
5answers
231 views

Iconic image to explain the fundamental theorem of calculus?

Is there some single, persuading visualization that can be used to convince students of the intuitive truth of the fundamental theorem of calculus, in the form $$ \int_a^b f(t) \, dt = F(b) - F(a) \;?...
2
votes
1answer
91 views

How to explain the sample space of Monty Hall problem?

I am now pretending to be a newbie student. I write the following sample space for the Monty Hall problem (It is a famous brain teaser, I assume you know it). $$ S=\{ (C,G1),(C,G2), (G1,G2), (G2,G1) \...
0
votes
0answers
103 views

why did common core remove so many topics from Algebra II?

I don't understand why common core: High School Algebra II (NYC, NY, USA) removed so many topics. I think these ideas are pretty important and useful (especially since a handful of these topics come ...
0
votes
0answers
79 views

Algebra I common core is too short? [closed]

I feel that the common core: High School Algebra I (NYC, NY, USA) curriculum is too short and tedious. For one, it can be completed in 5 months even with a lot of prolonging. For me, there isn't a ...
5
votes
4answers
260 views

Students understand during course but can't solve exam

I am teaching a math class where the students, most of them, tell me that they can understand the materials given by me during the course. I test them during the course too and they seem to get it. ...
5
votes
3answers
140 views

What to include in an “elevator pitch” for an undergraduate statistics class

I'm going to be giving a five minute "elevator pitch" presentation to undergraduate math majors in order to advertise an introduction to statistics class that I'll be teaching in the spring. It's an ...
7
votes
2answers
207 views

Why do we state the antiderivative of $\sec x$ as $\ln |\sec x +\tan x|$?

One easy integration of $\sec x$ substitutes $u=\sin x$, viz.$$\int\frac{\cos x}{1-\sin^2 x}\,\mathrm{d}x=\frac{1}{2}\ln\left|\frac{1+\sin x}{1-\sin x}\right|+C.$$Multiplying top and bottom by $1+\sin ...
7
votes
1answer
89 views

How to organize a “cheatsheet-making session” with students

I am in charge in my institution of a class where students prepare math interviews to enter university. Part of the time is devoted to the review of the topics of PreCalculus and Calculus the students ...
0
votes
2answers
55 views

Hardware for real time streaming of writings and drawings

Looking for the necessary hardware to share, in real time streaming, the writings and drawings done in a paper or notebook. It looked like something easy to find but after two hours goggling, nothing ...
7
votes
4answers
152 views

Beyond cubic polynomials: Applications?

Cubic polynomials are crucially important in computer graphics: for example, cubic Bézier curves/surfaces, and cubic splines, which have many practical applications. Essentially visual continuity ...
8
votes
4answers
223 views

Intuition for the mean for elementary school kids

I was teaching elementary school kids (aged 10) about the mean. The intuition I gave them is roughly as follows: You are trying to find a value such that the sum of all the distances from the mean ...
5
votes
4answers
264 views

Why do we study Cantor Set?

For finding counter examples. That does not sound convincing enough, at least not always. Why as a object in its own right the study of Cantor Set has merit ?
2
votes
0answers
93 views

How to remedy the “freshman's dream”? [duplicate]

I am teaching a mid-level calculus course, and I see my students making the freshman's dream mistake of thinking that every function is a homomorphism. In particular, they think that exponents can be ...
0
votes
1answer
97 views

Verifying Simple Expression Equivalence in a Spreadsheet

For simple expressions with easily derived canonical forms (eg polynomials and simple rational expressions), is there a way to leverage existing tools to verify that two expressions are equal when ...
2
votes
0answers
149 views

Succinct description of situations where naively obvious is correct, but for far more complicated reasons?

What is the name for a situation where the obvious thing turns out to be true, but the reasoning is more complicated? In abstract algebra we can say the rational numbers - the fractions, $\mathbb{Q}...
4
votes
1answer
137 views

Is it feasible to expose undergraduates to a “map”-centric point of view early on?

Question: Would it be feasible to teach undergraduate math students a "map"-centric view early on? If so, how early on? Now that I'm preparing for a phd program, I'm also reflecting on my ...
3
votes
2answers
215 views

Teaching math by serving it as games with rules first, not intuition?

Just now I'm thinking a crazy reversed idea: Is it good to teach math to elementary students without starting from its real world motivation or making it intuitive first, but rather by realizing that ...
3
votes
0answers
95 views

On concentration inequalities [closed]

I would like suggestions for a good text on concentration inequalities (examples here https://en.wikipedia.org/wiki/Concentration_inequality). I am looking for sources (texts) that can give strong ...
3
votes
0answers
43 views

Are there any studies evaluating the impact of the Mathematics Vision Project?

I have found very little online that compares & critiques the MVP vs traditional curricula. Any suggestions & pointers would be welcomed. The MVP is an implementation of Common Core Standards ...
7
votes
3answers
483 views

Math Everywhere Activities

Question Does anyone have a nice list of "no effort" activities that parents can employ to promote numeracy? I am primarily interested in K-8 activities. Exposition Often parents ask me about what ...
1
vote
0answers
135 views

Intro to Proof: if $x$ divides $y$, then $ x \leq y$

I am teaching a very small intro to proofs class with Dana Ernst IBL book, and came to theorem 2.56. The section is about proof by contradiction but I felt that the solution I came up with is ...
3
votes
0answers
52 views

When to use row or column vectors in points and translations

A course that my kids are doing in conic sections insists that all positions are represented as standard 2D cartesian coordinates $(x,y)$ (i.e. row vectors), and all translations are written as 2D ...
4
votes
5answers
771 views

How to correct visualization of mathematical expressions?

This happens a lot when I try to explain the commutative property, mostly in elementary grade levels. I say 2 + 3 = ? and then the student usually replies with 5. Albeit they're not wrong, it's ...
10
votes
3answers
327 views

Examples (for beginners) of real functions which are not given by elementary formulae

Question: What are good examples of functions $f: \Bbb R \rightarrow \Bbb R$ (or $f: D \rightarrow \Bbb R$ with $D \subseteq \Bbb R$) which are not just given by "a formula" (or finitely many formulae ...
3
votes
1answer
65 views

Automated drilling sites with some specific problems

I am teaching a student basic equations. For now, I want him to drill: Multiplication Exponentiation (by exponents 2,3 4 and 5) Substituting values in first degree equations (what is $(x-2)(5x+3)+3x+...
6
votes
4answers
2k views

What is it called when terms disappear when reducing fractions?

If $a = \frac{x}{b}$ and $a = \frac{c}{b}$, and I solve for $x$ I get $x = c$. $b$ has been removed because it appeared in the numerator and the denominator. What is it called in English what ...
3
votes
1answer
145 views

Can we solve math just by speaking and not using any other extra devices?

I have been thinking, is it possible, or a good thing to do when learning from a textbook without ever writing anything down. But have to verbally give out the solution from beginning to the end with ...
2
votes
0answers
121 views

a theorem to simplify continuity in Stewart's calculus: early transcendentals

I'm covering section 2.5 of Stewart (on continuity) and stewarts treatment seems needlessly complicated. It seems like the following theorem would streamline a lot of it: If $f(x)$ and $g(x)$ are ...
8
votes
5answers
814 views

'Low-algebra' examples of induction

What are good examples of proofs by induction that are relatively low on algebra? Examples might include simple results about graphs. My aim is to help students get a sense of the logical form of an ...
3
votes
2answers
299 views

How is it correct for a lecturer to prove and “explain” a proof while explicitly knowing students are not familiar with logic itself?

I often see a situation when professors use words "logic", "mathematical proof" and even prove logically while actually knowing that students are not even familiar with logic itself, i.e. no formal ...
7
votes
1answer
243 views

Third Grade Question — This makes no sense to me?

Third grade grandchild had this for homework. I don't even know the intent here?
1
vote
0answers
94 views

I’m considering buying Art of Problem Solving. For those who read it, what’s your review of it? [closed]

As you know, Art of Problem Solving includes 11 books that comes with their solutions and they are PreAlgebra, Introduction to Algebra, Introduction to Counting and Probability, Introduction to ...
1
vote
0answers
46 views

Geometry sample tests

I am teaching intro to Geometry using Moise and Downs textbook. It is an excellent text but somewhat old. Does anyone know if there are sample tests that are available for use with this textbook?
4
votes
4answers
365 views

Is This Trick Helpful?

I am no professional educator; I am a student myself! But apparently I come up with useful tricks that help my younger brother do better in maths. I just want to hear your feedback, is all. My ...
2
votes
3answers
282 views

Harnessing misuse of equals sign

Students often misuse the equals sign to indicate "I've done this operation" rather than the proper use indicating numerical equivalence. Eg. Tax is paid using the rule: \$3 572 plus 32.5c per \$1 ...
5
votes
2answers
109 views

Teaching math long distance

I have a 13-year-old nephew that liked learning with me, but I've recently moved 400km away. I wonder if it is possible to still learn with him long distance. The subjects I care about are maths and ...
1
vote
1answer
93 views

A robot to simulate differential equations for undergraduate students. [closed]

I was recently at EPFL drone days and enjoyed a demo of a robot that could follow a black line like in the sketch (I can improve the sketch on demand): Then I remembered my good all times at the ...
2
votes
6answers
195 views

Undergraduate Math Seminar topic

** Edit Thanks everyone for some great suggestions. I should have been more clear though. I am actually looking for a college level proof that pertains to algebra or leads to algebra in some form. ...
9
votes
5answers
316 views

Motivation for polynomial long division

In the U.S. students in grades $\{9,10,11\}$ often learn long division of two polynomials, e.g.: $$ \frac{x^4 + 6x^2 + 2}{x^2 + 5} = x^2 + 1 - \frac{3}{x^2 + 5} \;. $$ I believe it is fair to say that ...
5
votes
4answers
143 views

Automatically creating homework worksheets from textbook problems

This semester I am a TA for a Calc 2 course. At my first meeting with my instructor, he mentioned in passing that "Homework is always easier than an exam, because homework questions come from the ...

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