# Questions tagged [secondary-education]

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

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### What is an algebraic explanation of why the product of the slopes of perpendicular lines is $-1$? [duplicate]

Q: What is a succinct, clear and purely algebraic explanation of why the product of the slopes of perpendicular lines is $-1$? Here I am aiming for high-school students (in the U.S.). I have a purely ...
668 views

### I'm in 8th grade and just finished Algebra 2. What math would I do for the next 4 years? [closed]

I'm in 8th grade and just finished Algebra 2. What math would I do for the next 2 years? In what order would math I would do in 9th, 10th, 11th, and 12th grade. Thanks!
255 views

### When are students taught implicit and parametric representations of curves?

Do students learn implicit equations (such as $x^2+y^2-r^2 = 0$) and parametric equations (e.g., $x=a t^2,\;y= 2 a t$) in a first course in algebra, which in the US would be early high school, maybe ...
258 views

### How important is it to come up with or learn an elementary solution?

Note: by "elementary" I mean "without using more advanced theory and tools". Students are sometimes required or encouraged to solve very difficult problems using limited number of ...
598 views

### Advice: How to cite literature for high-school students?

Suppose one were writing a book aimed at high-school students (and their teachers), where "high-school" in the US means grades 9,10,11,12 (where college/university starts at 13). The book is ...
580 views

### Teaching Mathematics to a Younger Sibling

I always wanted to teach my siblings mathematics, and one, ten years of age, is particularly eager. For the purposes of specializing recommendations, I will add he can use arithmetic up to ...
414 views

### Should students get another chance at a math question because of English troubles?

The question is John has locked a 4 digit combination lock with each of the numbers 0-9. He knows the numbers 1,4,6, appears exactly once, but he does not remember the position of the numbers and he ...
169 views

### How do I teach my kid [closed]

I am struggling with teaching my 9th grade kid to solve math problems that are just outside of routine. For e.g., An example problem given by math teacher at school. x, y, z are in geometric ...
219 views

### Should a student have another chance at a math test question when they have a english problem? [closed]

A student has a english problem, should he get another chance and have another chance?
3k views

### Can we skip Newton's Method?

I am teaching an introductory calculus course for high school juniors and seniors. It is not formally described as an AP Calculus course, but it is supposed to map roughly onto Calculus AB. The ...
144 views

### Trying to explain(understand?) combinations

Let us assume that we have 30 balls( 7 green, 10 black, 13 white). I was trying to explain to someone how we count the number of possibilities of getting 3 greens, 3 black, and 3 white balls in a ...
252 views

### What are some famous problems, which are not difficult to understand, for senior high school students

I hope I am asking my question in the right forum. I am trying to introduce some mathematical problems (Better to be famous in the math community) to a group of senior high school students with a ...
79 views

### Math websites/apps for high school students

I am undergraduate math student who is interested in being a high school math teacher. I have been given an assignment to present to my class (for a total of about 20 minutes) a teaching tool or a ...
149 views

### Would the SMSG textbooks provide adequate extracurricular study?

Context: I'm a Grade 11 IBDP student and very fond of math. Assuming that I get the spare time to self-study material alongside the syllabus, I wish to spend it constructively (the only step I've ...
459 views

### Definitions of factors and terms

I have come across this question in a textbook How many factors are there in the term $5ab(x+y)$? State what they are It is being praised because it encourages thinking, which it does. However, I'm ...
428 views

### How much more skilled in the topic should you be in order to teach the topic?

For sake of argument, consider that skill of a topic is spectrum from "new and learner" to "experienced and expert." Where should you relatively be in order to teach the topic ...
174 views

### What is a good place for teachers to share self-created content?

I am a high school mathematics teacher and I regularly create problems and their solutions for my students. It has always lingered in my mind that this content can also benefit others. What would be a ...
169 views

### What are the resources to learn prerequisite knowledge to latter High school and undergrad prep textbooks?

I use textbook study and am planning on studying Spivak's Calculus, Mathematics It's Content, Methods, and Meaning, How to Prove it by Velleman, etc. However, I'm worried I lack the prerequisite ...
160 views

### Would it make sense for math courses to be pass/fail?

I have a theory that if standardized grading were abolished for a pass/fail system, people would be more mathematically competent. Bear with me here. With graded homework, especially homeworks that ...
263 views

### Is There Such Thing as Reaching Half a Standard?

I like the Common Core State Standards for Math as they focus on objectives that students need to reach. However, some standards have way too many parts for them. For instance, the standard CCSS.MATH....
523 views

### Logic and proofs in secondary school

Inspired by the question When do college students learn rigorous proofs?, I became curious when pupils in secondary schools learn about proofs, what kinds of proofs they are, how rigorously they are ...
229 views

### 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 ...
481 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 ...
398 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 ...
605 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 ...
1k 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 ...
948 views

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. ...
138 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 ...
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 ...
5k 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 ...
2k 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 '...
8k views

### Should LaTeX be taught in high school?

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 ...
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, ...
618 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 ...
1k 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....
119 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 ...
144 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 ...
377 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. ...
161 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 ...
225 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, ...
192 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 ...
786 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 ...
236 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 ...
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 ...
474 views

### How should I convince a student who 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}}=...
137 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 ?
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### 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 ...
56 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 $𝑥^2+2𝑥𝑦+𝑦^2=1$. ...