Questions tagged [secondary-education]

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

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4answers
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 ...
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5answers
5k 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 ...
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0answers
86 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 ...
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3answers
437 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 ...
13
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7answers
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 ...
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1answer
87 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 ...
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4answers
2k 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....
9
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1answer
171 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 ...
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7answers
5k 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 ...
10
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4answers
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 ...
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4answers
584 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 ...
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5answers
779 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 ...
4
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1answer
78 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 ...
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8answers
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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 ...
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22answers
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Quote to show students don't have to fear making mistakes

I have some high school students which seem to be afraid of making mistakes. They are hesitant to make exercises in class because they want their course notes to be super clean, without any mistakes. ...
2
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2answers
168 views

High school maths textbook for talented students

I am looking for a math textbook. I'm 15 and I'd like to complete algebra 2 geometry and perhaps something about probability/ number theory or trigonometry would be nice too. Later I wanna do ...
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5answers
440 views

Would a 1990's educated person need additional content knowledge to tutor high school mathematics today?

Have there been any major content (not pedagogical) changes in the basic US high school mathematics curriculum since the mid-1990's? More specifically, if I wanted to become a tutor of high school ...
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7answers
314 views

How to show $3(\log_2 n)^5 < \sqrt{n}$

I am teaching final year high school students and needed to persuade them of the following fact: There exists an $n_0 > 0$ such that for all $n>n_0$, $$3(\log_2 n)^5 < \sqrt{n}$$ Plotting ...
8
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1answer
502 views

An alternative to “two column” geometry proofs

I'm a high school teacher in New York State (US), starting in on my first year of teaching Geometry. One of the things that really intrigues me is that the Regents exam (the state-mandated final exam)...
8
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1answer
194 views

When (and why) did geometric means of more than two numbers exit the secondary curriculum?

In contemporary US secondary mathematics textbooks, geometric means occasionally make a brief appearance. For example: In Geometry, students learn that when an altitude is dropped to the hypotenuse ...
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4answers
407 views

Why is absolute value difficult?

My understanding is that students find absolute value to be challenging to learn or understand. Off the top of my head, I can come up with two possible reasons for this. Absolute value is a piecewise ...
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1answer
102 views

Entry Test for Statistical/Data Science class

If there is a Data Science class (for final year high school students, not necessarily from the same school) with the following syllabus: Python programming (first 3 meetings) Data cleaning and ...
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4answers
255 views

Inefficient methods

I see many teachers use slow methods to solve a given problem where there's another faster methods that doesn't demand much more effort. I'm not looking for mistakes like saying that $a$ is the slope ...
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2answers
171 views

Interpretation of how to define “bigger” and “smaller” real numbers

This is a variant on the question small real numbers. I have a disagreement with someone about the meaning of "bigger" real numbers. Say we have the real number $-1.$ Is $0$ "bigger" or "smaller" ...
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1answer
193 views

Scientific results on the usefulness of physical units in secondary education?

When we encounter "real world problems" in math, one can chose different levels of detail with regard to units: from leaving them out completely up to using them everywhere. I'd argue that both ...
3
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6answers
257 views

What is an interesting high-school level topic to discuss using Mathematica or Geogebra?

I have to choose a topic to give a presentation. The topic should be high-school level or at most Linear Algebra 1 and Calculus 1. Conics and polygons in the Euclidean geometry are some fine topics ...
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1answer
116 views

How to formulate this type of arcsin problem?

Reading and commenting on What are some common ways students get confused about finding an inverse of a function? I was kindly set straight that the use of $\sin^{^{-1}}(x)$ to mean $\arcsin(x)$ has ...
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1answer
105 views

Explicit Cross Method

When factoring quadratic expressions $ax^2+bx+c$ it is common to the guess and check factors (AKA the cross method). This would involve factoring $a$ and $c$ and considering particular combinations ...
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2answers
134 views

Curriculum for Advanced 6th Graders

Next year I volunteered to lead the math class for a group of 6th graders (ages 11 - 12). Here are the pertinent details: About 5 - 8 (U.S.) students, for about 45 minutes, 3 days a week (they'll ...
6
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2answers
161 views

What are some tips for framing a graph in the most readable, relevant, and aesthetic way, for secondary education mathematics?

When I say "framing," I mean things like choosing zoom, x-axis/y-axis step, horizontal/vertical shift from the origin, choosing how/when to number steps, labeling axes, as well as, purely aesthetic ...
2
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0answers
177 views

why don't we do labs in/for math?

(this is in the US and at a high school level) why don't we dedicate a day of the week each week to do a lab for math for exploration? I mean we already do that for Earth Science, Physics, Chemistry ...
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3answers
231 views

Complex numbers and encourage justification

In remedial algebra, we learn that the graph of $y=(\sqrt x)^2$ is only in the first quadrant. We know this is the correct graph for the equation. This is because we know $y=x$ and $x \ge 0$. However,...
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1answer
175 views

Integrated math curriculum in different countries

One of the selling points of re-hashed American 1990s high school math programs is that they are "integrated", that is, combine algebra, geometry, statistics, trigonometry just like the European ...
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4answers
346 views

Why do standard geometry textbooks not start with trigonometry?

Throughout my geometry course, I was given many theorems and postulates, which I was were expected to memorize and apply. At the time, I sorta went along with it, but I couldn’t help but wonder where ...
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6answers
310 views

Book recommendations on mathematics education focusing on geometry

I will be teaching Euclidean geometry to future teachers, and I am feeling a bit lost (I know geometry, but I am not that familiar with mathematics education). Is there some recent (as concise as ...
3
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2answers
130 views

Mathematics Research at Secondary Level (High school Level)

I am a future teacher and am interested in incorporating a mathematics research unit where my students do their own research on an unsolved problem. I have a couple ideas on problems, but am ...
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3answers
114 views

How can I measure the mathematical computation skills of high school students through a test?

How to analyze the level of difficulty of mathematical computation of a problem on a standard mathematical test designed for high school students? I mean how to choose some indices that can reflect ...
7
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4answers
309 views

How to deal with students who object to me teaching material that won't be in the exam?

I sometimes encounter students who ask questions like 'Why are we learning this if it won't be on the exam?' If there is time to spare I like to teach interesting applications or natural extensions of ...
4
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2answers
176 views

How can I help a student who is constantly struggling in an honors Algebra II (high school) class

I am tutoring a student who is in an honors Algebra II class. The class is definitely advanced and the student hasn't been exposed to this kind of material. The teacher is going beyond algebra II and ...
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3answers
323 views

The royal road to calculus

In the early 1900s Felix Klein lay out his vision for secondary mathematics curriculum. He wanted schools to teach calculus, so that universities would not be burdened by it. And at the core of the ...
6
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2answers
271 views

Mainstreaming math student

I'm working one-on-one with a student who is part of a sponsored refugee family. He's bright and a good learner, but has had a lot of interruptions to his education. No indication of any learning ...
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0answers
218 views

Teaching methods to make a weak student good at math? (particularly student from social science background)

I am currently teaching a high-school student, 1st grade Social Science. He is weak in mathematics. My initial strategy was to explain basic concept but with high repetitions, so that he can have a ...
28
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3answers
6k views

Difference between high school and college calculus courses

I am curious why students who take calculus in high school often do so poorly in college calculus. I am an instructor at an engineering college and I've noticed a decent number of students who have ...
4
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1answer
97 views

Making modular arithmetic interesting for school kids

This is a pattern even school kids could discover (when gently pointed to). I never did conciously, and cannot remember to have been pointed to explicitly, neither at school nor later: $$\color{red}{\...
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2answers
183 views

Presenting ways to find a resultant force

To begin with I am working in a high school classroom where the students are working on the applications of vectors. The beginning of the lesson is about calculating direction and magnitude of vectors ...
4
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1answer
187 views

How to explain angle hunting to students

$I$ is a point of the circle of diameter $JK$. The perpendicular bisector of $JK$ cut the semi-circle not containing $I$ at $M$. Let $N$ and $P$ be the orthogonal projections of $M$ on $IJ$ and $IP$. ...
9
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4answers
617 views

Is the constant term a coefficient?

I'm a baby boomer who was taught that the constant term of a polynomial is a coefficient, being the constant factor for the x^0 term. That's not what's taught today. Current text books are vague on ...
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7answers
666 views

List of realistic extremum problems

I am a student who would like to become a teacher, so I am currently following courses in education. One of the things I learned, is that students like authentic, realistic problems. However, much of ...
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1answer
97 views

UK Secondary School - how advanced (or not) is level 5-8?

My son has just finished his first half-term at secondary school (year 7). I have just received an email saying that the school has set him in a maths class based on current and previous results, and ...
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2answers
371 views

Integrating derivatives over functions problem

I had a question from a student which I'm unable to answer. We were practicing the rule $\int \frac{f'(x)}{f(x)} \, dx=\ln(f(x))$. A student noticed that if applied naively it gives the following ...