Questions tagged [secondary-education]

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

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3
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4answers
525 views

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 ...
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1answer
104 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!
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3answers
162 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 ...
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1answer
229 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 ...
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2answers
590 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 ...
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2answers
519 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 ...
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1answer
272 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 ...
3
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3answers
164 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 ...
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2answers
210 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?
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4answers
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 ...
3
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1answer
140 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 ...
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2answers
205 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 ...
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0answers
69 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 ...
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0answers
77 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 ...
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6answers
417 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 ...
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2answers
409 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 ...
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1answer
168 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 ...
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2answers
125 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 ...
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2answers
136 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 ...
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0answers
248 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....
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2answers
474 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 ...
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1answer
156 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 ...
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2answers
321 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 ...
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1answer
339 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 ...
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4answers
442 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 ...
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2answers
855 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 ...
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6answers
895 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. ...
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2answers
133 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 ...
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6answers
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 ...
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6answers
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 ...
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7answers
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 '...
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10answers
7k 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 ...
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8answers
4k 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, ...
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4answers
224 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 ...
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8answers
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....
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1answer
96 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 ...
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1answer
126 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 ...
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5answers
248 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. ...
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2answers
120 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 ...
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2answers
145 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, ...
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2answers
166 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 ...
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5answers
411 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 ...
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3answers
201 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 ...
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5answers
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 ...
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4answers
453 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}}=...
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2answers
124 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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4answers
185 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 ...
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1answer
50 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$. ...
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14answers
16k 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 ...
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17answers
7k 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 ...

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