All Questions

3
votes
0answers
12 views

What are some tips for framing a graph in the most readable, relevant, and aesthetic way, for secondary education mathematics?

When I say "framing," I mean things like choosing zoom, x-axis/y-axis step, horizontal/vertical shift from the origin, choosing how/when to number steps, labeling axes, as well as, purely aesthetic ...
0
votes
0answers
31 views

What should I say about elementary number theory?

I need to give an option talk about elementary number theory module. I will discuss how it is study of positive integers particularly the primes and give some cryptography applications. What is a good ...
1
vote
0answers
119 views

why don't we do labs in/for math?

(this is in the US and at a high school level) why don't we dedicate a day of the week each week to do a lab for math for exploration? I mean we already do that for Earth Science, Physics, Chemistry ...
1
vote
2answers
107 views

Selected Exercise for Linear Algebra Done Right Edition 3 [on hold]

I am self learning the book Linear Algebra Done Right. I tried to complete all exercises in each chapter. I am currently at Chapter 3 and found that it is not feasible to complete all of the exercises....
-1
votes
0answers
103 views

Parents teaching kids math [on hold]

How could an ideal journey a parent well versed in mathematics teaching their children about mathematics be described? What would the steps be, according to what gets taught, and how, at the various ...
-5
votes
0answers
60 views

How to explain why 'it's usually physicists who can solve the trickiest integrals' to a 17-year-old? [on hold]

I'm referring to this Reddit comment: https://old.reddit.com/r/math/comments/1qpus4/master_of_integration/cdffrnv/ and its daughter comment by u/gobearsandchopin: We're usually the only ones ...
-4
votes
0answers
89 views

How to explain why an easily graphable definite integral can be knotty to evaluate to a 17-year-old? [on hold]

I'm referring to definite integrals that can effortlessly be graphed on CAS, which e graph can be understood by high schoolers like: $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,...
2
votes
0answers
81 views

Unconstrained/Constrained optimization real life example

I am in charge of some practice lesson for Calculus II. I have to show how to apply the theory for unconstrained optimization (mainly Hessian analysis) and constrained optimization (Lagrange ...
5
votes
3answers
165 views

Why is it difficult to freely change between points and vectors?

I have noticed working with bright undergraduates that it is not uncommon for them to have difficulty easily converting between a point—say, a point $p$ on a surface $S \subset \mathbb{R}^3$&...
3
votes
6answers
2k views

How to convince students of the implication truth values? [duplicate]

How can I convince students that "P implies Q" is true when P is false, independent of what truth value Q takes? Is there any real life or a convincing argument for this? I have given the analogy ...
4
votes
1answer
111 views

Complex numbers and encourage justification

In remedial algebra, we learn that the graph of $y=(\sqrt x)^2$ is only in the first quadrant. We know this is the correct graph for the equation. This is because we know $y=x$ and $x \ge 0$. However,...
-3
votes
0answers
92 views

Why are students taught to take notes in class in secondary school? [closed]

It's been more than 10 years since I finished high school and at that time, I was taught to take notes during class so I'm assuming a lot of secondary schools are still teaching students to do that ...
-2
votes
1answer
104 views

How was higher learning taught without Math equations in the past? [closed]

Can Physics, engineering, or otherwise be taught without equations? How was math taught before there were equations? For example: How would string theory be explained to someone without the Math ...
6
votes
1answer
123 views

Best practices in teaching math to future elementary teachers

This question is about references in current best practices in teaching math to future elementary teachers at a university level. I am asking it because I do not see any question so far on this site ...
1
vote
2answers
91 views

Lower-division complex analysis textbook

I'm looking for recommendations for a good textbook to use for a hypothetical lower-division course in complex analysis, at a level of sophistication comparable to a second or third semester course in ...
-2
votes
1answer
87 views

What is the best way of introducing set theory? [closed]

The students are aware of mathematical logic and proof but have not come across any of the notions of a set. What is the most natural and motivating way to introduce set theory?
0
votes
1answer
80 views

Roadmap to studying PDEs for analyzing Quantum Physics better

I am studying the basics of Quantum Physics (involving the characteristics of Schrodinger's Wave equation without actually analyzing it rigorously mathematically) this semester. I was wondering, ...
8
votes
3answers
203 views

How to make students comfortable with the use of axiom of choice in analysis

I am teaching introductory real analysis this term and realize that my students have problem coming up with sequence in some arguments in real analysis. Let's take this example: Theorem: Given a ...
5
votes
4answers
198 views

Is the education system in Finland particularly good?

Inspired by this question: What makes education in Finland so good? Finland has marketed itself as a top country in education. Indeed, at some time, the Pisa results in Finland were quite good. ...
0
votes
0answers
98 views

What makes education in Finland so good?

This is a question more about education in general than math education but there is no general education Stack Exchange website so I decided to write this question here. If this question is more ...
0
votes
1answer
149 views

Should schools get students to do discovery math?

I think the traditional approach doesn't work very well on some students. I once read on the internet that some students learn the law $(a + b)^2 = a^2 + 2ab + b^2$ then incorrectly apply it to ...
-1
votes
1answer
67 views

Could students be taught the concept of rational numbers the same way as in the Formal construction section of the Wikipedia article rational number?

According to this answer, some students 14-18 are still struggling to understand fractions. Maybe some students know how to perform the calculations on rational numbers given in fraction notation but ...
3
votes
1answer
139 views

Geogebra for Blind People

I work in the University with students in a situation of disability, specifically, teaching them math and related things. I have a few students that are very visually impaired; they work with JAWS or ...
5
votes
5answers
304 views

When should students stop receiving tutoring for mathematics?

I work in a University Tutor Lab that covers content up to Calculus II. However, when a student in a Calculus III or Differential Equations class comes in, some other tutors and I will still tutor ...
0
votes
1answer
167 views

Future in mathematics

My sibling is done with high school and has always scored A in Maths and am not in position to advise her on the future in line of her niche. She's not yet in university and she's in her vacation but ...
4
votes
1answer
174 views

How is math taught in elementry school in Finland?

I read on the internet that Finland has the best education system in the world at that in Finland, students are taught to love mistakes and that's how they learn and become smarter. I could not find ...
0
votes
1answer
126 views

Integrated math curriculum in different countries

One of the selling points of re-hashed American 1990s high school math programs is that they are "integrated", that is, combine algebra, geometry, statistics, trigonometry just like the European ...
9
votes
3answers
197 views

How to motivate students to do proofs?

I am finding it difficult to motivate students on why they should how to prove mathematical results. They learn them just to pass examinations but show no real interest or enthusiasm for this. How can ...
2
votes
3answers
163 views

How to explain to pupils that “$\frac n{100}$ OF $a$” is equivalent to “$a$ TIMES $\frac{n}{100}$”?

How to explain to pupils that "$\frac n{100}$ OF $a$" is equivalent to "$\frac{n}{100}\times a$"? There is some difficulty in explaining that the first sentence, containing "OF" (which could suggest ...
2
votes
1answer
91 views

Classical references on equation solving

If I'm not in error, old style algebra books ( before 1945) concentrated on equation solving, and modern ones concentrate more on functions and their graphs ( as a preparation to calculus). Are there ...
4
votes
6answers
3k views

Where do students learn to solve polynomial equations these days?

When I was a math undergraduate 30 years ago in India, we were taught what was then called "classical algebra" (as opposed to abstract algebra), and we were taught among other things solving ...
4
votes
0answers
123 views

Which countries adopt metacognition in their official math curricula?

I know Singapore and Brazil explicitly adopt metacognition as one of their maths curricular pillars. The relevance of metacognition is recognized by OECD that has written a state-of-the-art report ...
1
vote
0answers
88 views

Missouri EOC and the best Geometry book

I am a Missouri High School Geometry teacher. WE are adopting textbooks this year. I would like opinions on which books are most closely aligned with the Missouri Learning Standards because at the ...
1
vote
2answers
107 views

Where to find good exercises for term operations?

I'm searching for exercises for practising operations with terms. They should involve working with decimal numbers and fractions (ideally one should convert decimal numbers to simple fractions like ...
4
votes
2answers
144 views

Collaborative note taking

I have been encouraging my classmates to connect with me on Google Docs to work collaboratively on taking notes. Still, no takers though. I imagine that if I were a professor, I would attempt to get ...
1
vote
1answer
104 views

Could this visual explanation of horizontal shift be helpful ? …( if not beautiful…)

With the image below I try to explain in which way substituting (x-a) ( with a> 0) for x in the expression defining a function results in a shift to the right, although " intuition" tells us it ...
1
vote
3answers
77 views

How to verbalize the correct statement of mixed units?

I want help phrasing the instructions in a math question. The issue is the correct way to express mixed units. For example, if an answer is “25 inches,” I don’t want to accept “25 inches” or “1 foot ...
7
votes
3answers
140 views

Physical devices for exploring calculus or pre-calculus

I saw this partial derivative machine yesterday, and it got me excited about other physical devices for exploring calculus concepts in a "lab" setting (e.g. make a prediction, collect data, etc.) Do ...
2
votes
1answer
117 views

Revision Lecture, what are the aims?

I will give a 2-hour long revision lecture on a Mathematics area. The aim of this lecture is to help the students prepare for the exam test. The course was rather long, covering 5 chapters and a ...
19
votes
6answers
2k views

Teaching indefinite integrals that require special-casing

I encountered the following concern when teaching indefinite integrals. I believe that many of us may overlook this. May I be wrong? Let's consider the following example. Find the indefinite ...
6
votes
3answers
145 views

Notation for change of basis matrix

As far as I can tell, it's only a slight exaggeration to say that every text has a different notation for a change of basis matrix from (say) $\mathcal{B}$ to $\mathcal{C}$. That's not even to talk ...
11
votes
9answers
3k views

How to explain what's wrong with this application of the chain rule?

Yesterday a student in my calculus class attempted something like this: Problem statement: Find the derivative of $3^{(5x+1)}$ with respect to $x$. Proposed solution: Let the inner function be ...
5
votes
3answers
249 views

Teaching a child time and hours in a digital world

My child, now four (soon five) years old, is interested in time, knowing what time it is and how long until something happens. We do not, at the moment, have analog clocks and a digital clock is not ...
5
votes
0answers
217 views

Mimic lecturing on blackboard, but facing audience [closed]

I teach mathematics at MSc and PhD levels. My preferred method of teaching is old-fashioned: talking and writing on the blackboard at the same time. Why? Because it has many advantages: Handwriting: ...
6
votes
4answers
164 views

Group theory by geometry

I'm introducing my kids to the concepts of group theory. To make abstract things tangible, I'm trying the geometry way, adopting Arnold's in "Abel's Theorem", so far I've explained, by using symmetry ...
5
votes
0answers
255 views

What books properly address the properties of $a^b$?

Many students think $\sqrt{a} \sqrt{b}=\sqrt{a\ b}$ $\sqrt{a^2}=a$ $\frac{1}{\sqrt{a}}=\sqrt{\frac{1}{a}}$ but none of the above are true when (a) and (b) are negative. To avoid such problems, ...
8
votes
1answer
260 views

Real World use of the Function $(\sin{x})^x$

Today in my calculus class we were going over L'Hopital's Rule and were dealing with limits of the following form $$h(x)=f(x)^{g(x)}$$ Three examples we considered are as follows: $(1)\; \...
4
votes
3answers
193 views

Analogy for multiplying modulo N

Sometimes I want to explain to laymen/new students/laywomen how addition modulo N works. There are some instructive analogies: Addition on the clock (12), Addition on weekdays (7). They illustrate the ...
10
votes
9answers
2k views

Vocabulary for giving just numbers, not a full answer

I am a math teacher from China, teaching a course in English. Some students of mine are really good at finding answers for math problems designed in a quiz, however they are unable to write down ...
2
votes
2answers
189 views

Learning proofs in introductory analysis courses

I have browsed the website a lot and I encountered many similar questions but not a question that asks the same question as I intend to. In introductory undergraduate classes in Analysis, usually, ...

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