Questions tagged [secondary-education]

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

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16
votes
9answers
3k views

What is the rationale for distinguishing between proper and improper fractions?

I cannot recall ever hearing the terms "improper fraction" and "proper fraction" outside of an elementary and middle school setting. At some point in my mathematics education ...
0
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2answers
168 views

Advice on teaching advanced mathematics to high school students

I am a high school student really into algebra and algebraic geometry. I want to expose this sort of math to other high school students that have the motivation and ability. For a long time, I had no ...
2
votes
3answers
347 views

Why do so many people hate math?

I love mathematics and I know pretty much everyone in this community does too! That feeling of being stuck on a mathematical problem for days as you try to unearth the complexity in front of you is ...
35
votes
18answers
8k 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 ...
7
votes
2answers
207 views

How to get student with ADHD to practice exercises consistently

Background I have recently started tutoring a 14-year-old student who is diagnosed with ADHD and was struggling with passing a basic math course (think basic linear equations systems, first and second ...
15
votes
7answers
2k views

An introductory example for Taylor series (12th grade)

I (a student) am doing a presentation on Taylor series in my class (12th grade, in Germany if this is relevant). I am looking for a good example where you can see when Taylor series might be useful. ...
3
votes
2answers
178 views

The value of making students copy your derivations exactly

I have a hypothesis that I have not yet implemented, and am seeking guidance before I do. I have always taught algebra (and above) in such a way that the students understand the derivations. I check ...
1
vote
3answers
395 views

Why is highschool math so unrigorous?

I am an highschool student (I'm starting soon the italian equivalent of 12th grade) and I have many problems with the way hs math education works. I don't understand why everything is explained only ...
12
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16answers
6k views

How does one tutor an A-level student past the derivative paradox?

Background: I am new to this site, but have 1500 reputation on the main Maths Stack. I am (age-wise) a secondary student of maths, but for a very long time have been informally learning at home and ...
3
votes
2answers
106 views

Math Modeling search results data set

This year, I will be teaching a Math Modeling course to a group of motivated high school students. One topic we will discuss is providing good search results from an online query. Here's the problem. ...
5
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5answers
2k views

Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?

Specifically the one updated by Martin Gardner. I'm not studying as part of a high school or college course (I, in the near future, will though) just as a personal project.
33
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13answers
9k views

Should I be teaching point-slope formula to high school algebra students?

I'm student teaching this semester, and so far I'm loving it! Our next section in the book teaches point-slope formula, and my cooperating teacher (a 24-year veteran teacher) is convinced that point-...
4
votes
1answer
184 views

Research on Waldorf/Steiner mathematics education

I am broadly interested in research on mathematics education in the Waldorf/Steiner educational context, primarily in the upper secondary school setting, but not exclusively. Information about Waldorf/...
6
votes
0answers
170 views

Are there measurements of how much mathematics people remember after high-school?

These days I got curious about something: Are there measurements of how much mathematics people remember after high-school?
0
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1answer
70 views

Which grade students should be able to solve applied economy / business / profit prediction exercises?

I've designed a few applied problems with business analytics/money calculations. However, I'm not sure which age (or rather, which grade) are those best to introduce. on one hand, solution uses only +...
-1
votes
2answers
78 views

Can anyone help give pointers of Mathematics Story Telling Animated Videos for Age Group 10 - 15?

Ideally, these videos should talk about a real life problem which student can relate to and then showing logically how the problem can be solved. Later bringing in the right mathematical tool to solve ...
12
votes
3answers
364 views

Resources on interdisciplinary curricula

As I try to incorporate more history, science, language, computing, and art into my math class I keep finding the lessons to be very successful and my students always seem to enjoy them. While I know ...
7
votes
3answers
413 views

Resources for mathematics for sustainability

I am looking for resources (books, websites, etc.) for mathematics relevant to or in the context of sustainability, broadly construed, at upper secondary or early undergraduate level - so not ...
3
votes
2answers
191 views

Teaching words with multiple meanings in Mathematics and English

We want to teach about words that have multiple meanings, in mathematics and English for middle school children (e.g., function, root, or, volume, angle, constant). This is for students who are ...
39
votes
22answers
9k views

Response to Students Who Say "This Is Not Important"

Lately, my students keep telling me why what we are learning is not important. They ask me when will we use this in the real world? I explain how math is important in gambling, cooking, finance, ...
-2
votes
1answer
292 views

Why are math test scores dropping in America? Lack of student responsibility movement [closed]

Someone asked me this question today. Why do you honestly believe that high school math test scores in America (particularly the United States) are low compared to other countries? I thought about ...
7
votes
5answers
427 views

Creating an Engaging Class Atmosphere

I would like to start out next year by creating a classroom community. This year I noticed a lot of burnout towards the second half of the year. Basically, I want to see what kinds of games/activities ...
4
votes
2answers
250 views

Applications of the annihilator from linear algebra

I am currently assisting a course for future teachers at university level for a joint education in maths and physics in Germany and I have a question regarding the use and possible application of the ...
5
votes
1answer
198 views

Making the leap from Pre-Calculus to Calculus

This question is targeted at teachers who taught both low and high level mathematics. I have a group of students that I'm currently teaching precalculus and they seem to be doing really well in all ...
4
votes
5answers
313 views

Is it a good idea for elementary school students to observe and discover the "circle perimeter formula" themselves without being dictated to?

Let them discover $\;\ell=2\pi R\;$ by their own, at least the invariance of $\ell/R$ Do you think that the following method works well in a mathematics class of elementary school? What do you think ...
10
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4answers
1k views

Different Teaching Styles for Different Genders?

I was recently looking through job listings in my local area (US high school, ages 14-18) and I found two boarding schools with vacancies, one was male-only and the other was female-only. This got me ...
4
votes
2answers
200 views

Are there any list of mathematical constructions which can challenge 12-16 year old students?

Mathematical (geometric) constructions are an interesting way to engage students. It also helps in better understanding of different geometrical properties. For example, Sierpinski triangle or square, ...
15
votes
2answers
399 views

Is there a math curriculum that is aware of CAS and the internet?

About 15 years ago, I heard a math education professor give a talk about how computer algebra systems would change the kinds of questions teachers would ask high school and first year college students....
5
votes
1answer
168 views

Are there any mathematics based game apps which require students (between 10 - 16 years) to apply their maths knowledge to play the game

So, what we essentially mean is students will apply their knowledge on divisibility, factorization, prime numbers, lcm, gcf, decimals, fractions, etc to play the game. A somewhat different approach to ...
2
votes
3answers
195 views

If one wants to conduct a 1/2 day workshop in Mathematics for 12-16 year old students - how one should go about preparing the workshop

The questions that I want ask are the following: What are the most important and effective topics to conduct a workshop? What fraction of workshop should include lectures, activity, problem solving, ...
8
votes
2answers
186 views

Importance of asking questions in a mathematics class

It is observed many times that students do not ask the right questions in the classroom. They just attend the lectures passively. Rather than asking the questions o get their doubt cleared, they ...
1
vote
0answers
60 views

What are different Mathematical concepts which can be introduced to 12-16 year students in an activity based way

Activities are a great way to engage students with Mathematics. And that also helps them to visualise mathematical facts. For example, Pi in its decimal form appears to have no pattern (we used to say)...
3
votes
2answers
174 views

Looking for an educational game from long ago, possibly called Mother Goose [closed]

OK so this is really old school. Back in the 1980s, as a latchkey kid, I played on the computers in the library in elementary and middle school. There was this one bizarre educational game that I'd ...
12
votes
7answers
8k views

Why should or shouldn't we teach functions to 15 year olds?

Background The students in my country are supposed to be able to work with and answer questions about functions at the age of around 15. This is asserted in the standard mathematics curriculum for ...
6
votes
6answers
588 views

Why do we write $x$ instead of $1x$?

I am currently student teaching for an Integrated Math 1 class (which is similar to Algebra 1) that consists of 9th graders. I have been teaching my students how to solve linear systems using ...
6
votes
4answers
629 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 ...
7
votes
2answers
301 views

When working with 12-16 year olds, how should I graph functions when the domain technically isn't $\mathbb{R}$?

Let us assume that I want to graph any of the functions below. A) A can of soda costs $\$1$. Draw a graph depicting the total cost as a function of the number of cans you buy. Comment: One cannot ...
15
votes
3answers
2k views

How many of "The Seven Laws of Teaching" are still relevant for teaching maths today?

Wikipedia shows that in 1886 John Milton Gregory outlined his "The Seven Laws of Teaching"; asserting that a teacher should: Know thoroughly and familiarly the lesson you wish to teach; ...
-1
votes
2answers
168 views

What research has been done on the effects of requiring students to learn to count in an alternative number base such a binary or base eight? [closed]

What research has been done on the effects of requiring students to learn to count and do some easy arithmetic in an alternative number base, for example binary, base four, base six, base eight, base ...
17
votes
4answers
3k views

How does the workload of a high-school mathematics teacher compare to a university-level instructor?

This question could be very broad, and so I'd like to make it more specific. In the United States, mathematics educators generally work in secondary education or college education (elementary school ...
7
votes
7answers
4k views

What is the preferred way to denote the Pythagorean theorem equation?

I am teaching 12-16 year olds. How should I write down the Pythagorean theorem equation? Some alternatives: $a^2 + b^2 = c^2$ $\text{leg}^2 + \text{leg}^2 = \text{hypotenuse}^2$ $\text{leg}_1^2 + \...
7
votes
2answers
308 views

Phase shift vs. horizontal shift, and frequency vs. angular frequency in sinusoidal functions

TL;DR version: It seems to me that high school curricula no longer distinguish between "horizontal shift" and "phase shift", or between "frequency" and "angular ...
12
votes
5answers
795 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 ...
5
votes
7answers
670 views

What is a good second book in high school geometry?

I have been looking at questions on Math Stack Exchange and I am frequently coming across topics that sound as if they could have been optional chapters in a high school geometry class, but I have ...
22
votes
10answers
3k views

Is 'estimating' still considered a valuable skill?

I was with a 2nd year high school class, preparing for our (US) state's standardized test. I asked the class how they would solve this, and they flipped through the sheets to find $$V=\frac{1}{3}\pi ...
24
votes
5answers
978 views

A Series of Unfortunate Examples!

All of us know, when teaching, the "right" choice of examples is important. Though, making the "right" choice is one of those things that are easier said than done. Here is the ...
6
votes
1answer
299 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 ...
20
votes
8answers
5k views

Why do we teach the Rational Root Theorem? (high school algebra 2)

Main question: Does anyone have any good/interesting applications of the rational root theorem or ways to teach it that don't involve conveniently ignoring computer-based tools in order to avoid rote ...
3
votes
1answer
108 views

High school algebra books that encourage creative/novel problem solving

Circumstance Hello, I am looking for books that encourage creative problem-solving at the high school level. I attended secondary school in the United States and I have noticed that there are ...
16
votes
8answers
946 views

Rationale for not dividing both sides of an equation by $x$ (ex: $6x^2 = 12x$)

this came up in class yesterday and I feel like my explanation could have been more clear/rigorous. The students were given the task of finding the zeros of the following equation $$6x^2 = 12x$$ and ...

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