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Measuring ones mathematics ability regularly - how to avoid getting better at the tests

This question might not suit the site, if so I apologise. I'd like to regularly test my maths skills, essentially finding out if I'm getting better or worse at a maths in general and then plot the ...
2
votes
0answers
29 views

Is There Book on Collection of Theorems?

For example, there is a book titled "Synopsis of Elementary Results in Pure and Applied Mathematics: Containing Propositions, Formulae, And Methods Of Analysis, With Abridged Demonstrations" (...
1
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1answer
78 views

How do I assimilate mathematical concept?

Already knowing that the famous quotation "there is no royal road to mathematics", I believe that the most efficient and best way to learn mathematics is to make it intuitive to oneself, at least to ...
0
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0answers
49 views

How to teach students how to find the domain and range of a function, using DESMOS? [closed]

My question is about using DESMOS.com to find the domain and range of a function. Please note, I am not looking for for domain and range restrictions in the application; this is easy, for me. I want ...
3
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3answers
523 views

The term “unique” for functions and operations

This is long so... TLDR: Proposing the math community steer away from the misleading term unique, with respect to functions and algebraic operations. Instead, use unambiguous. Why not? Analysis below....
5
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2answers
139 views

Algebra/trig/precalculus review questions that elicit common student errors

This semester I have decided to give students a simple question or two at the beginning of every calculus class that will trap them into making the most common errors that we all know...e.g. the ...
2
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2answers
116 views

Introducing quadric surfaces in high school

I am presenting an enrichment session on 3D geometry and quadric surfaces to support 15-year-old secondary school students. They know algebra but not calculus. They have learned about equations of ...
-1
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0answers
40 views

Tauberian operators [closed]

Let $X$ be a Banach space non reflexive and $T$ from $l2(X)$ to $l2(X) $ a bounded operator defined by : $$T(x_n )= \frac{x_n }{n}.$$ We know that : $$T^{**-1}(l_2(X)=\{x_n^{**} \in l_2 (X^{**}): \...
-5
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0answers
84 views

Should we try to redefine matrix multiplication in the opposite way?

By the "opposite" way I mean multiplying column-by-row instead of row-by-column. After toying with some formulas, I think one can easily convert the LaTeX codes of existing linear algebra textbooks (...
1
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0answers
53 views

How can I make a shift to applied mathematics? [closed]

I have done dual degree with bachelors in computer science. I am currently a software developer (India). I always have had interest in mathematics. But once was I got into college I did not work ...
4
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0answers
90 views

Combinatorial problems which can be solved with polynomials

Can someone please post some (relatively easy, high school level) combinatorial problems which can be solved with polynomials (but not generating functions). Here is an example of one such problem: ...
4
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4answers
200 views

What math courses should I take in order to become a secondary math educator?

Seeing as this is the math educator site, perhaps someone can help me out: I am looking to become a math teacher, but I am having a hard time figuring out which math courses I need to be taking. ...
4
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1answer
67 views

EdX Courses for Self-Study

I have been independently considering two edX courses in mathematics. The first, a course on probability theory drawing from a financial crisis case study, appeared to me plausibly comparable in ...
0
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0answers
43 views

Is it too late to study physics properly now that I am a 3rd year undergrad? [closed]

This may seem a bit silly. I am 21 years old 3rd physics undergraduate. Even, after taking a three year undergrad physics course it feels like I haven't really understood what I learnt, didn't learn ...
13
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6answers
2k views

How much symbolic calculations before plugging in actual values?

My son is in high school (France, 2nde) and I was watching how he solves math exercices. This led me to the following question: when are students expected to plug in actual values in their ...
6
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7answers
2k views

Teaching Calculus I to engineers

I am in a research project where one of our jobs is improving the first year university experience for our students. One of the topics we are looking into is changing the way we teach our introductory ...
7
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4answers
264 views

How is $\frac{a}{b}$ interpreted?

I was having a discussion with a colleague who is in the process of writing some curriculum, and we ended up having a discussion about what $\frac{a}{b}$ (with all the standard restrictions) meant. We ...
5
votes
4answers
1k views

Acceptability of creative questions in assessments

I am a math teacher and I have been for a decade now. One of the foundations of my philosophical approach to teaching has to do with Synthesis. For the purposes of this query, I consider Synthesis to ...
10
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7answers
3k views

Are there any proofs of Euler's Formula that do not rely on calculus?

The most common way I have seen Euler's formula $$ re^{i\theta} = r(\cos\theta+i\sin\theta) $$ introduced in a classroom environment is to substitute $i\theta$ into the series expansion of the ...
2
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3answers
116 views

How to teach integrals motivated by the work done in moving an object?

I am now teaching Calculus of several variables this semester. In apllications of integrals, the problem of finding the work done in moving an object under a force $F$ is one of the most common ...
1
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1answer
140 views

Math undergrad courses [closed]

Awhile back I was very weak with my trigonometry so I came to this site asking for help, and it turned out the few answers I got made a huge difference. I excelled at the trigonometry section in my ...
2
votes
1answer
178 views

Is there a numerical base that is in any way “better” for simple mathematical calculations than others?

I want to know if there are any numerical bases that are notably well-suited for humans to learn and use at an elementary or grade-school level. I know that different numerical bases (i.e. decimal/...
8
votes
2answers
120 views

How to read chained equalities out loud?

I find that my community-college students are usually very hazy on the status and meaning of chained equality statements (or other relational statements). This seems like a really critical element of ...
3
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2answers
103 views

Are there any more mathematical journals or websites with the “problems and solutions”?

Are there any more mathematical journals or websites with the "problems and solutions"? such as , the American Mathematical Monthly and Crux Mathematicorum
4
votes
1answer
135 views

Notation in the definition of matrix multiplication

When matrix multiplication is introduced, it is usually introduced with an additional variable: Given two multiplicable matrices $A$, $B$, one defines the product $C=AB$ to be the matrix given by some ...
15
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7answers
5k views

Lack of intuition, retention while self studying

I am a first year undergraduate student, currently in second semester. So basically I learnt most of the first year stuff in high school, so I have a lot of free time in this year (currently in ...
9
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5answers
5k views

Is short division taught these days and if not, why not?

tl;dr I'm interested in opinions on short division. Below I discuss my experience dealing with young children and long division versus short division. For those that don't know of it, wikiHow has a ...
0
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0answers
88 views

How to teach year 3 undergraduate courses to high school students?

I see on the webpage of a high school math summer program, SuMac, that they will cover some algebraic topology in a period of several weeks. And they covered every aspect of this subject, including ...
5
votes
1answer
127 views

Fun, impressive, or compelling examples of scaling of the standard deviation like $1/\sqrt{n}$?

I'm teaching a class where statistics is not the main topic, but I would like to introduce the idea that if you take $n$ measurements of a variable that are independent, identically distributed, and ...
7
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3answers
446 views

Doing research projects when one's knowledge is limited: is it preferable?

In some universities, high schools, and summer programs, students are required to do their own research project in maths and write their own essays/research papers. At the same time, however, many ...
16
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4answers
3k views

Does anyone teach logarithms via slide rules?

I just inherited two slide rules from my grandfather-in-law, one wood with smooth action despite nearly a century without use.1 (I used a K+E slide rule myself as an undergraduate in the 1970's.) It ...
5
votes
1answer
153 views

Misdirected, Side-Tracked, and Distorted Ramanujan: Problems in Basic Math Education?

I read that- “The tragedy of Ramanujan was not that he died young, but that his genius was misdirected, side-tracked, and to a certain extent : distorted. The years between 18 and 25 are ...
24
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6answers
2k views

What is the quantitative data on effectiveness of “modern” teaching methods?

What research has been done on how much and in what circumstances various non-lecture types of teching are effective with regards to student knowledge and performance? Meta/review studies preferred ...
14
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7answers
2k views

Should we teach simple content quickly or slowly?

The title might be a bit not specific, so let me give an example. In China, Japan, Korea, etc, there is a type of problem about chickens (or crane, or anything with two legs) and rabbits (4 legs) in ...
5
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4answers
213 views

How to convince parents that Mathematical puzzles/games help students in their academics too

I write content and conduct workshops for an education firm and also in schools where I try to make them realise how beautifully mathematics and rational thinking complement each other (on elementary ...
1
vote
1answer
89 views

How to teach geometric patterns? [closed]

I would like to know how to teach geometric patterns in secondary school. I want to elaborate worksheets, which could include different kinds of strategies related to this topic. Are there resources ...
12
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4answers
2k views

How should I introduce the Chain Rule

I'm halfway through my first year of teaching AP Calculus to high school seniors. It's been going generally well, but I'm feeling like I really could have done better getting them into the Chain Rule....
9
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1answer
172 views

Equality as “makes” vs equality as “equals”

A problem I often encounter while introducing students to equations is that of changing the conceptual image of the equation symbol $=$ from "results to" to "is equal to". To be more precise: In the ...
6
votes
3answers
200 views

Are there standard notations for 'number talks' / ‘math talks?'

I’m a homeschool teacher of a nine-year-old, and we sometimes have one-on-one ‘number talks’ (a.k.a. 'math talks') similar to the activity used in primary school classrooms. Part of this process ...
5
votes
2answers
248 views

Redesigning college math courses and curriculum to be self-paced

I imagine there must exist a fair amount of literature and discussion about the idea of somehow redesigning college math courses, and the entire college math curriculum, to be self-paced. Question: ...
6
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3answers
302 views

Cardinal vs. ordinal: When learned? When needed?

Is the distinction between cardinal numbers and ordinal numbers taught as part of mathematics (as opposed to part of learning the language distinction between "one" and "first") in pre-college or ...
2
votes
1answer
143 views

Why teaching undergraduate-level mathematics is so complicated? [closed]

Many of my professors are experts in their field, but they are just not able to teach. I mean: most of the times they are confusing, don't follow a logic sequence in their speech or keep a superior ...
26
votes
6answers
9k views

Should we stop differentiating between ln and log?

In many U.S. middle schools and high schools, $\ln$ and $\log$ are treated differently, with the intent that $\log$ is equivalent to $\log_{10}$. However, in undergraduate courses and in the academic ...
4
votes
2answers
160 views

Resources for Learning Multiplication Facts

A recent question (@Namaste) made me realize that it would be good to pull together the best resources for learning the multiplication facts. When seen as a rote memory task, this can turn students ...
9
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7answers
6k views

Is this primarily a “rote computational trick” for multiplication by 9?

I tried uploading a gif, but was unable to do so. What I can do, is share a link to the gif here. (SE software seems to have allowed me to share the link, but not upload it.) What it shows, ...
2
votes
1answer
128 views

Using video games as an introductory tool for game theory? Can video games illustrate game theoretic concepts?

A friend of mine is planning to create an educational video dealing with Game theory. His teaching strategy is to introduce the subject via video games. For example, he told me that the game "...
3
votes
2answers
308 views

How to teach linear programming and reductions?

Do you know any textbook with problems+solutions to support teaching of linear programming and reductions, and in particular, cover standard and slack forms, formulation of problems as linear programs,...
6
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3answers
319 views

How do I convince my teachers that a book on maths must focus on conceptual understanding?

I am a senior teacher at this school. We have to select the textbooks for the upcoming session. I am proposing that we have to select books (in maths) that focus more on conceptual understanding and ...
17
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7answers
5k views

Learn university maths or train for high school competitions: which is better?

I sometimes see people arguing against concentrating too many resources in high school maths competition (such as IMO) training. Their reasons they give are usually the following: Competitions are a ...
9
votes
1answer
675 views

How to (or should one) distinguish between lowercase and uppercase letters orally when lecturing?

I sometimes teach calculus in English whereas it's not my native language. For example, during a course about antiderivatives, how do you (orally) pronounce $f$ vs $F$? Which are the best? "the ...

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