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Questions tagged [secondary-education]

For questions about teaching mathematics in secondary education (in most countries approx. ages 10-18).

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English translation of Sung-Dae Hong's The Art of Mathematics

The Art of Mathematics by Sung-Dae Hong is the standard high-school mathematics textbook in South Korea. The series gets new editions and reprints since 1966. Wikipedia has a page for it. Had it ever ...
Anton Tarasenko's user avatar
14 votes
2 answers
2k views

The use of "$\therefore$" and "$\because$"

In schools, many students learn the usage of "$\therefore$" and "$\because$" in proofs. Such three-dot notation are popular in many high-school books and exams, but are almost ...
Ma Joad's user avatar
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12 votes
1 answer
471 views

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 ...
Nick C's user avatar
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5 votes
4 answers
1k views

Falling into the calculus trap

I am a student, in my last year of school(17 years old) When I was about 13 years old I fell into the calculus trap by starting off learning trigonometry on my own, when I was supposed to factor ...
pjmathematician's user avatar
2 votes
2 answers
3k views

Curriculum in USA vs. Canada

(1) When do students in Canada learn about the four triangle centres (centers), circumcenter, incenter, orthocenter, and centroid? In the USA (more precisely, Indiana), the math curriculums are by ...
Jessie's user avatar
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7 votes
6 answers
1k views

Efficient methods to receive and grade online mathematics assessments?

I am UK-based but I guess this issue currently affects all maths educators and has probably been addressed by those how have been delivering courses through online channels for the past few years. ...
Clive Long's user avatar
4 votes
2 answers
156 views

Teaching Approach at primary, middle and higher level

I would like to have a comparison or a big picture of how and why the approach for teaching math varies from primary (or pre primary) to middle to higher classes. I understand at every level one ...
gpuguy's user avatar
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30 votes
6 answers
3k views

How to motivate an adolescent who has fallen behind in conceptual development?

I tutor a 16 year old girl. As far as I can tell, she has average talent and interest in math. However, her knowledge of math is that of a 10 year old or even below. She knows the basic operations on ...
BKE's user avatar
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21 votes
6 answers
6k views

How rigorous should high school calculus be?

In the UK, calculus taught in secondary school focuses mainly on computation of derivatives and integrals and solving simple differential equations. There is a small amount of discussion about limits ...
A. Goodier's user avatar
  • 1,725
13 votes
7 answers
3k views

Content for a 40-minute lecture on graph theory for high schoolers

I'm due to deliver a session on graph theory for 16–17-year old students (UK sixth formers) as a taster of what studying mathematics at university is like. What would you recommend as content, and a '...
dbmag9's user avatar
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27 votes
10 answers
9k views

Should LaTeX be taught in high school? [closed]

This semester, I was forced to learn LaTeX for my Real Analysis class. The professor wanted all homework assignments to be typed in LaTeX in order to produce "high-quality" work. At first I was ...
FoiledIt24's user avatar
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14 votes
8 answers
5k views

Fun set theory for kids

Are there some fun results in set theory to set as landmarks while introducing to kids? For example, while introducing graph theory to kids, I could explain isomorphism via a pentagon and pentagram, ...
athos's user avatar
  • 777
6 votes
4 answers
2k views

Courses equivalent to College Algebra in other countries?

In USA, there is a course called College Algebra and a course description may look like the following: This course provides students an opportunity to gain algebraic knowledge needed in ...
Zuriel's user avatar
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12 votes
8 answers
2k views

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....
WoJ's user avatar
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3 votes
1 answer
161 views

Dolciani and Sorgenfrey textbook collaboration

Would it be possible to get a complete list of math textbooks written jointly by Dr. Mary Dolciani and Dr. Robert Sorgenfrey? I'm particularly interested in focusing on how they collaborated while ...
user 85795's user avatar
6 votes
1 answer
220 views

Resources for improving computational skills at the high school/university transition

Teaching first year undergraduates, I've noticed that what gives them the most trouble is simple computations like factoring, expanding, handling fractions, powers, especially when variables and other ...
Thomas Richard's user avatar
6 votes
5 answers
937 views

How to define "axes with the same scale" in Secondary/High School?

It's easy to recognize visually when an orthogonal coordinate system has its axes in the same scale. See, for instance, the following image. But I'm trying to write down a precise definition of it. ...
Humberto José Bortolossi's user avatar
1 vote
2 answers
266 views

Topics for undergraduate seminar for mathematics educators

There are some general questions about potential topics for undergraduate seminars: topics for an undergraduate Math seminar Undergraduate Math Seminar topic I am looking for topics for a 15-hour ...
Earthliŋ's user avatar
  • 111
4 votes
3 answers
1k views

Should we stop using traditional compass in schools & start/encourage adopting compasses like "Slide N Measure" or "Safe-T" compasses instead?

I think using the traditional compass with those styluses that can literally be used to hurt or accidentally hurt someone are very dangerous. Most people don't use these in day-to-day life anyways, ...
ytrkptl's user avatar
  • 127
11 votes
2 answers
256 views

2D drawings of 3D objects in printed school textbooks: orthogonal or perspective?

There is a tradition in the use of orthogonal projections to represent 3D objects in printed school math textbooks. On the other hand, perspective projections represent better the way as we "see" real ...
Humberto José Bortolossi's user avatar
12 votes
5 answers
1k views

About the effectiveness of self-studying maths (compared with other subjects)

An important feature of mathematics is that it is relatively easy (compare to many other subjects) to know whether or not one's understanding is correct. There are plenty of ways to check: one can ...
Ma Joad's user avatar
  • 1,673
9 votes
3 answers
333 views

Evaluating textbooks in math and physics

I’m currently interested in textbooks, especially the ones in math and physics that are used at the high school, undergraduate and graduate levels and, given the experience of the people on this ...
lorenzo's user avatar
  • 251
6 votes
5 answers
2k views

What are strategies for teaching that the altitude of a right triangle creates two similar triangles?

If you draw the altitude to the right triangle as shown, it is easily seen that $$\triangle KLM\sim\triangle KNL\sim\triangle LNM.$$ This in turn leads to several interesting proportional relations ...
Matthew Daly's user avatar
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10 votes
5 answers
777 views

How should I convince a student who thinks they proved $1=-1$

One of my high school students who has ZERO knowledge on complex numbers and the modulus function has showed me the following algebra: $$(16)^{\frac{1}{2}}=(16)^{\frac{2}{4}}=((16)^2)^{\frac{1}{4}}=...
Ekaveera Gouribhatla's user avatar
0 votes
2 answers
184 views

I find high school math very hard compared to middle school? [closed]

i hope i can get some help on how to get better at high school maths i find them very difficult compared to middle school. Whats the big difference so i can work on it ?
Badr eddine's user avatar
4 votes
4 answers
243 views

Has the equation $\log(x-10)=3+\log(x-3)$ a *substitutable* solution in $\mathbb{R}$?

Could we say it has one when substituting the $x$ value into the original equation? Obviously, to solve the trascendental equation one has to operate the two terms with logarithms, reducing the ...
Tavasanis's user avatar
  • 161
2 votes
1 answer
60 views

On a special degenerate conic

I have a question on MSE that maybe can be better posed here. The question is about degenerate conics, and especially the case of two parallel lines, as in the equation $ 𝑥^2+2𝑥𝑦+𝑦^2=1$. ...
Emilio Novati's user avatar
40 votes
14 answers
20k views

Why is learning mathematics compulsory?

In most education systems, Mathematics is a compulsory subject from primary school all the way to the start of university. A common reason given is that essential concepts like addition and ...
Axel Tong's user avatar
  • 873
39 votes
18 answers
10k views

How do I show students the Beauty of Mathematics?

I teach many high school students, and all of them complain about being unable to fully understand mathematical concepts. I try to show them the joy of learning and deepen their understanding through ...
Axel Tong's user avatar
  • 873
5 votes
5 answers
906 views

How to intuitively understand how the trig ratios are calculated

I've asked a question on Math Stack Exchange, but it was suggested it might be a better idea to post it on this Educators instead. Here's the question link: https://math.stackexchange.com/questions/...
user523384's user avatar
5 votes
2 answers
171 views

Tips and References for a 15 days Course on Math

I'm going to participate in a course (as a teacher) where I'm suppose to teach high school math to high school students in about 15 days during the year. Each class has about 1 hour long. Now, I think ...
MathMath's user avatar
  • 151
32 votes
6 answers
3k views

Allowing nonstandard mathematical language and/or notation

How important is enforcing standard mathematical language and/or notation? Today, I was questioned by a writing instructor as to how vital it is to correct students when they explain something using ...
Nick C's user avatar
  • 9,699
3 votes
2 answers
207 views

Introducing quadric surfaces in high school

I am presenting an enrichment session on 3D geometry and quadric surfaces to able 15-year-old secondary school students. They know algebra but not calculus. They have learned about equations of ...
A. Goodier's user avatar
  • 1,725
6 votes
1 answer
347 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: We ...
nonuser's user avatar
  • 390
5 votes
4 answers
1k 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. ...
Burt's user avatar
  • 694
14 votes
6 answers
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 ...
WoJ's user avatar
  • 1,398
8 votes
4 answers
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 ...
Mark B's user avatar
  • 133
11 votes
8 answers
8k 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 ...
Simply Beautiful Art's user avatar
1 vote
0 answers
115 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 ...
Ma Joad's user avatar
  • 1,673
7 votes
3 answers
488 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 ...
Ma Joad's user avatar
  • 1,673
15 votes
7 answers
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 ...
Ma Joad's user avatar
  • 1,673
1 vote
1 answer
124 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 ...
Carlos Torres's user avatar
15 votes
8 answers
4k 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....
Matthew Daly's user avatar
  • 5,629
9 votes
1 answer
293 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 ...
Vassilis Markos's user avatar
19 votes
7 answers
7k 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 ...
Ma Joad's user avatar
  • 1,673
10 votes
4 answers
1k views

Co-curricular lessons between geometry and chemistry?

My school is hyped about the promise of co-curricular education and they are giving the math and science teachers paid days off to develop lesson plans that synergize our learning goals. I'm on ...
Matthew Daly's user avatar
  • 5,629
7 votes
4 answers
798 views

Favorite secondary math manipulatives?

I read this is the mathematics educators stack exchange so hopefully this is the right place for this question. I was curious what is your favorite math toys, manipulatives, math games, or tools to ...
randomgirl's user avatar
21 votes
5 answers
2k views

Teaching a student who refuses to learn

How to deal with a student who refuses to learn? I've met a few of those over the years as a a private-class math teacher. They don't want to learn anything about the subject. Some of them are just ...
Mefitico's user avatar
  • 349
4 votes
1 answer
117 views

In preparation for exams: question bank or questions with omitted particulars?

I have been doing a little bit of experimenting when it comes time to review with the class in preparation for the final exam. The last handout I have been giving my students has usually been a ...
Andrew Chin's user avatar
19 votes
8 answers
6k views

Prisoner's dilemma formulation for children

I am preparing an introductory course on Game Theory for children (between 10 and 17 years old). In the course description, I want to include a prisoner's dilemma in order to catch children's ...
Kikolo's user avatar
  • 299

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