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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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Resources to introduce Modular arithmetic

We have Clock arithmetic in grades 5 , 6 and thereafter nothing related to the Modular arithmetic is taught until students enter to the universities. Since this is very important topic in Number ...
Janaka Rodrigo's user avatar
0 votes
3 answers
433 views

What is this symbol called?

I know how to pronounce the first symbol as "theta", but the other symbol that looks like a circle with a vertical slash, I don't know what to call it. I would appreciate any help. Thank you
Teacher's user avatar
  • 17
23 votes
6 answers
8k views

What skills do algebra teachers wish their students had mastered before taking algebra?

I am designing 10 hour weekly summer math learning opportunities for students taking algebra next school year. I would like to know from algebra teachers what skills they wish their students had ...
Thomas McLoughlin's user avatar
1 vote
1 answer
156 views

Theory of semiotic mediation in teaching math at high school [closed]

I am working on the theory of semiotic mediation in teaching math at high school. According to the theory I need an artefact that is appropriate for high school (secondary school). In many papers ...
ryuk's user avatar
  • 131
0 votes
1 answer
112 views

Markov chains - how to translate mathematically the fact that the state at $n+1$ only depends on the state at $n$? [closed]

In a Markov chain of, say, three states $1,2,3$, when proving that the probabilistic state at $n+1$ ($\pi_n$) is equal to the probabilistic state at $n$ times the transition matrix, one has to use the ...
niobium's user avatar
  • 225
2 votes
0 answers
57 views

Math textbook for secondary school using Logo like language

What math textbooks for kids do you know that use Logo or similar languages with visual robots like Turtle (in "The Turtle Geometry") that demonstrate space motions, transformations of all ...
paus's user avatar
  • 83
1 vote
1 answer
96 views

Math textbook for secondary school using Logo like syntax

What math textbooks for kids do you know that use Logo or similar languages with visual robots like Turtle (in "The Turtle Geometry") that demonstrate space motions, transformations of all ...
paus's user avatar
  • 83
2 votes
3 answers
253 views

How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?

The mainstream way to show $V[aX+b]= a^2 V[X]$ is by using LOTUS. However, LOTUS seems to me too powerful and out-of-reach for a last-year high-school student. Therefore I was wondering if we could ...
niobium's user avatar
  • 225
3 votes
1 answer
77 views

International Baccalaureate - where to find the detail of the math programs?

Does anyone know what is the exact program of the International Baccalaureate in math? I've been looking for the MYP and DP programs in the website of the International Baccalaureate Institute but ...
niobium's user avatar
  • 225
2 votes
2 answers
114 views

Real-World Problems for Teaching Extrema and Derivative Tests in STEM Education

For educational purposes, I am seeking example problems in the realm of natural sciences, engineering, and business that satisfy the following criteria: Consider a one-dimensional real function $f$ (...
Julia's user avatar
  • 1,265
4 votes
0 answers
130 views

When can students understand the intersection of two circles?

I'm interested in learning two transitions: (1) When can students reason (intuitively, but accurately) to conclude that two circles in the plane could intersect in $0$, $1$, or $2$ points, or are ...
Joseph O'Rourke's user avatar
3 votes
4 answers
460 views

Why use the vague notion of "vector" when you have $\mathbb R^2,\mathbb R^3,\mathbb R^4,\ldots$?

I'm reading an introductory course on groups. In this course, the author illustrates concepts using the vectors of the plane. For example, "the set of vectors in the plane(or in space) is a group ...
Stéphane Jaouen's user avatar
9 votes
11 answers
3k views

Applications of High School Geometry

Sometimes I struggle to give my students a sufficient number of reasons why they should study Geometry in high school, other than that it helps them think and increases their understanding of the ...
Nate's user avatar
  • 91
5 votes
1 answer
379 views

Any known platform to post self made math questions

Background I am a class 10 student who is fond of maths. I like making math questions. Question I do not know of any platform where I can post these questions for others to practice and learn. I ...
GameTime With Aryan's user avatar
2 votes
1 answer
221 views

About a difficult exercise for 12 years pupils

You have to go from a point $A$ (start) to a point $B$ (arrival) by crossing a river $(d)$ and traveling as little distance as possible. Pupils first do a search by trying several paths $1,2,3,4$ and ...
Stéphane Jaouen's user avatar
1 vote
1 answer
564 views

Is integrated math class the same as mathematics class?

The first high school I went to I did Integrated Math 1 my Freshman year, Integrated 2 my Sophomore year, and Integrated 3 my junior year. My junior year I transferred to a continuation school where I ...
Natalie's user avatar
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5 votes
7 answers
2k views

Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

I am planning to become a math high-school teacher and have the following question: What Probability Theory should I base myself on to teach probabilities to students ? The classical approach is via ...
niobium's user avatar
  • 225
1 vote
0 answers
129 views

1st time math teacher 1st test feedback appreciated

I'm not a math teacher but I've stepped into the role to assist a small private school who lost their math teacher during the holidays (I'm a mechanical engineer by trade). The course is Algebra 1 (...
Dan S's user avatar
  • 19
2 votes
2 answers
158 views

International mathematical olympiad-type competitions at lower levels, and if they exist, their educational usefulness?

Educators in many countries have found that preparing highly motivated students for national and international mathematical olympiads can be useful in training them in mathematical ways of thinking. ...
tell's user avatar
  • 131
4 votes
2 answers
178 views

Infinite descent method in geometry

What are the examples we can use to explain infinite descent as an efficient method of proofs in geometry? I think one of the best may be proving medians of a triangle are concurrent by the infinite ...
Janaka Rodrigo's user avatar
7 votes
6 answers
2k views

How can we motivate that Newton's method is useful?

If you teach Newton's method for finding roots of real functions on the high school (or freshmen) level, I think some students may reason like a variant of the following: Why do I need learn such a &...
Julia's user avatar
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0 votes
2 answers
130 views

In what ways could or couldn't having students do homework in $\LaTeX$ for extra credit be helpful for them at the college level? High school level? [duplicate]

Do you think having students turn in homework in $\LaTeX$ say for extra credit is helpful for them at the college level? At the high school level? There could also be a few assignments that have to be ...
Matthew Albano's user avatar
2 votes
1 answer
990 views

Do you think with the advent of Desmos/GeoGebra, the Moore Method is more accessible to high school?

When I was a grad student, I taught a Calculus I course during the summer. Somehow I came across Robert Moore and I ended up reading his book which I connected with. Rather than being a great student, ...
Matthew Albano's user avatar
6 votes
3 answers
2k views

What are common mistakes that students will make when solving "What's the original price" percentage problems?

Take this question for an example: A smartphone is now $\$500$ after a $20\%$ discount. What was its original price? Now, this is an example of a type of math problem that students face usually in ...
CrSb0001's user avatar
  • 295
18 votes
11 answers
4k views

Topological fun facts for high school students

I'm going to give a class to highschoolers about topology. I've prepared the beginning of the class where I introduce what is topology and give them different ways we use to describe spaces, but ...
bml64's user avatar
  • 311
7 votes
7 answers
1k views

Special topics for introductory probability

I am helping to design a low-level college course whose purpose is to teach critical thinking, logic, finance and probability. I have been tasked with developing the probability section. I am ...
dt688's user avatar
  • 173
1 vote
1 answer
114 views

Speed math appropriate for middle-school students

There are many "rules" for speed arithmetic. List of some reference links showing speed methods or rules: https://ofpad.com/multiplication-tricks-for-mental-math/ https://ofpad.com/mental-...
EngrStudent's user avatar
9 votes
3 answers
1k views

Is there a standard convention for interpreting ambiguous absolute value expressions?

Consider the expression $$|x + 2|x + 3|x + 4|.$$ One way to interpret this is that there are two products being added together: $$|x+2|x \hspace{1cm} + \hspace{1cm} 3|x+4|$$ But you could also ...
Justin Skycak's user avatar
3 votes
12 answers
3k views

Importance of complex numbers knowledge in real roots

Many students question the importance of complex numbers in real life. We can find many important applications of imaginary numbers in Engineering field and physics. This question is not related to ...
Janaka Rodrigo's user avatar
5 votes
4 answers
364 views

Educational resources commonly address slant asymptotes. Why not general polynomial asymptotes?

Back in 2018, I wrote a post about asymptotes of rational functions in which I addressed not only horizontal and slant/oblique asymptotes, but also the general case of "polynomial asymptotes.&...
Justin Skycak's user avatar
1 vote
3 answers
516 views

Basic skill requirement suspension

Oregon appears to have suspended the "basic skills" requirement for graduation; see this. What will be the effect of this on the mathematical proficiency of the graduating class? Follow-up ...
Mikhail Katz's user avatar
  • 2,240
2 votes
4 answers
403 views

How can one lone picture prove the Triangle Inequality, $|x−y|≤|x|+|y|$, $|x|−|y|≤|x−y|$, and the Reverse Triangle Inequality?

I always showcase separate pictures of Triangle Inequality, and Reverse, to 16-years-old students in 1st class. I reshow pictures in 2nd class. I preachify Please remember these 4 inequalities. ...
user27289's user avatar
  • 139
1 vote
1 answer
207 views

Identifying Trigonometrical proofs

How can we identify trigonometrical proofs from geometrical proofs, do we have purely trigonometrical proof of Pythagoras theorem as claimed by two high school students ? https://www....
Janaka Rodrigo's user avatar
5 votes
13 answers
17k views

To 17 year olds, how can I explain that two numbers with arbitrarily small difference are equal?

$|a – b| < ε, \forall ε > 0 \iff a = b$ resurfaces on standardized tests to 17 year old (y.o.) students, who can memorize and regurgitate the proof to earn full marks. But the glut of duplicates ...
user95017's user avatar
  • 429
27 votes
7 answers
17k views

Why not think of derivatives as fractions?

Back in high school—back in the 1900s, as my sons say—when our calculus teacher was introducing the chain rule... $\frac{dy}{dx} = \frac{dy}{dt} \cdot \frac{dt}{dx}$ ...he made a special point of ...
adam.baker's user avatar
2 votes
5 answers
985 views

Geometrical verifications for Algebraic formulae

What is the importance of using approaches related to Geometric Algebra in teaching,is it only useful when introducing Algebra to the students or can it be helpful to improve creative skills in ...
Janaka Rodrigo's user avatar
6 votes
5 answers
6k views

What benefit is there to obfuscate the geometry with algebra?

Consider: In a right triangle: sin(2x + 4) = cos (46) What is the value of x? The question above is from standardized tests for a geometry course. If my goal is to have students understand ...
Lenny's user avatar
  • 1,068
0 votes
1 answer
69 views

Seeking References on Deterministic and Stochastic Phenomena Suitable for High School Students

Can anyone recommend good and didactic references that delve into the dualism between deterministic and stochastic phenomena? Ideally, I'm seeking materials that provide a conceptual explanation along ...
Humberto José Bortolossi's user avatar
9 votes
2 answers
2k views

Explaining Sigma-Notation

I attempted to introduce the summation notation $\Sigma$ to my students. The notation was unfamiliar to the students beforehand. I worked through many examples with them, but for most of them, working ...
wayne's user avatar
  • 193
6 votes
1 answer
150 views

Remote Teaching by Video Conferencing

I am in my early 70's and licensed to teach 8-12 math in Texas. I have an advanced degree in the same area. I used to teach in high school decades ago but have since quit because the student's ...
A.Magnus's user avatar
  • 161
0 votes
0 answers
40 views

Apps to make mathematics much interesting by sharing creative ideas with others

I think proofs without words is much important topic when we want to improve students interest in subject using their skills other than in mathematics. Recently I could able to find that kind of proof ...
Janaka Rodrigo's user avatar
1 vote
1 answer
103 views

highschool's mathematics journal which citable in Google Scholar

I'm a high school Mathematics teacher and I want to issue some research articles for highschool students to improve their math problem resolve skills. Is there any valuable Math journal for high ...
mbzadegan's user avatar
1 vote
2 answers
270 views

Responding to students' questions that aren't directly relevant to their exams

What would you suggest as the best way to deal with students' questions that seem irrelevant to their upcoming exams? When I was studying for my university-entrance exam, I came across a couple of ...
Janaka Rodrigo's user avatar
0 votes
1 answer
271 views

Limitations of applying the factor theorem

Here are three situations in which students might try to apply the factor theorem. Proving that $x + 1$ is a factor of the polynomial $x^3 + x + 2$ can be done using the factor theorem by showing ...
Janaka Rodrigo's user avatar
1 vote
1 answer
135 views

Pythagoras and Trigonometry sequencing

In teaching the high school curriculum Pythagoras is usually bundled with Trigonometry. They might be justified by way of proof of some sort. They are used to solve 2d and 3d geometry problems for ...
pdmclean's user avatar
  • 967
4 votes
2 answers
628 views

What is Algebra 1 and 2 as it is in US highschool education?

I am a pre-university student who wants to help students with Algebra 1 and 2 in high school. I am curious to how the curriculum was built and what the goal of teaching both algebra 1 and 2 might be. ...
muuzzmolz's user avatar
  • 171
11 votes
7 answers
3k views

How can we best motivate the study of polynomials to high-school students?

We all know how important and ubiquitous polynomials are in mathematics. However, when faced with a (not so much in love with the subject) 14-year-old asking us why they should care about these things,...
Federico's user avatar
  • 219
1 vote
3 answers
181 views

Whole numbers as sets vs abstracted properties of sets

I recently landed on a book written for elementary school teachers which introduced the concept of whole numbers in the following manner: We have a set $\{\alpha, \beta, \gamma\}$. There are other ...
Harshit Rajput's user avatar
12 votes
8 answers
938 views

Any meaning/interpretation for $\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\dots (= \mathrm e)$ (sum of reciprocals of factorials)?

One common way to introduce Euler's number $\mathrm e$ is $$\mathrm e = \lim_{n\to \infty} \left(1+\frac{1}{n}\right)^n,$$ where the right-hand expression has an "interest rate interpretation&...
user avatar
9 votes
6 answers
2k views

Can this be a better way of defining subsets?

I remember my high school days where subsets were defined in the following manner: Given two sets A and B, if every element of B is an element of A, then B is called a subset of A. A common ...
Harshit Rajput's user avatar

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