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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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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 ...
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156 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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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 ...
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3answers
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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 ...
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1answer
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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
149 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 ...
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120 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 $IP$. ...
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4answers
365 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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484 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
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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
349 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 ...
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When to use row or column vectors in points and translations

A course that my kids are doing in conic sections insists that all positions are represented as standard 2D cartesian coordinates $(x,y)$ (i.e. row vectors), and all translations are written as 2D ...
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'Low-algebra' examples of induction

What are good examples of proofs by induction that are relatively low on algebra? Examples might include simple results about graphs. My aim is to help students get a sense of the logical form of an ...
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4answers
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Is This Trick Helpful?

I am no professional educator; I am a student myself! But apparently I come up with useful tricks that help my younger brother do better in maths. I just want to hear your feedback, is all. My ...
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5answers
342 views

Motivation for polynomial long division

In the U.S. students in grades $\{9,10,11\}$ often learn long division of two polynomials, e.g.: $$ \frac{x^4 + 6x^2 + 2}{x^2 + 5} = x^2 + 1 - \frac{3}{x^2 + 5} \;. $$ I believe it is fair to say that ...
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Can undergraduate math courses be taught at a high school level? [closed]

Can these be taught at a high school level? multivariable calculus linear algebra abstract algebra real analysis complex analysis (non-measure theoretic) probability theory Maybe even other more ...
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What are teachers' expectations on private tutoring in secondary education?

By "tutoring", I mean when parents hire someone to help their child one-on-one. I am referring to secondary education. This "help" can take many forms, some of which are: Re-teaching concepts that ...
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2answers
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Is AP Calculus AB really necessary?

High school student here... This coming school year I'm scheduled to start AP Calculus AB and then my school is looking into taking Multivariable Calculus at a local university. The school's calculus ...
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1answer
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Books similar to “Teaching Developmentally”, but for high school math

I've been extremely excited by my reading of the book Elementary and Middle School Mathematics: Teaching Developmentally by Johan A. Van de Walle et al. Does anyone know of similar books (or other ...
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1answer
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Evaluation and feedback using Optical Mark Recognition systems in secondary school

OMR in exit tickets I plan to use an OMR, Optical Mark Recognition systems at the end of (some of) my classes. I want to use the same OMR system for exit tickets scattered over the academic year (...
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4answers
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Small 'new things' to confront talented high-schoolers with

Something my students* often struggle with is how to react on being confronted by 'new things', including functions, notation or definitions for which they are given sufficient definition but with ...
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6answers
320 views

Simple, elegant ways to teach the idea of what functions are for the first time

The context In my country, when the concept of function needs to be introduced in math classes, most teachers will simply talk about $f(x)=c$, $f(x)=ax+b$ and $f(x)=1/x$ (constant, linear and inverse ...
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Reference for study about good teachers in a US state

Several years ago I have read about a study in a US state where standard test scores were used to identify teachers whose students consistently improved far above the average and then film and analyse ...
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2answers
158 views

Why bother completing the square to find the minimum/maximum of a quadratic function?

Given a question like Find the coordinates of the minimum point on the curve $y=3x^2+2x+9$. students are often taught to solve this by completing the square. The class I am currently teaching ...
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0answers
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Is there a simple rationale for learning “reference angle” I can give a 9th grader?

I'm helping a 9th grader review for his Algebra 2 Regents exam (New York State). They need to know how to find the "reference angle." (I did read Why teach reference angles?.) I haven't found a ...
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5answers
186 views

Why teach absolute mean deviation?

I was helping my niece (7th grade) with homework and one of the topics was the absolute mean deviation. It's basically the same thing as standard deviation except instead of squaring the difference ...
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2answers
283 views

Middle / High School Math Teachers and LaTeX

All of the middle and high school math educators I´ve encountered choose not to use LaTeX in preparing their documents or presentations. I would assume that most of them had to use the program in the ...
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How to introduce trigonometric ratios (HS) through a cognitive model?

I'm teaching a precalculus course and also taking a class on how to teach mathematics constructing a specific cognitive model for different topics. So, I have this assignment to build a cognitive ...
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1answer
141 views

Calculus via a constructivist approach

A high-school teacher in the US whom I know, is teaching AP AB Calculus for the first time. He would like to use a constructivist approach: students explore mathematical problems and ideas and then,...
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1answer
115 views

How can I introduce a speech about the Fibonacci sequence creativiely?

I am a high school senior student. Soon, I am giving a presentation about the Fibonacci sequence and I am searching for a creative way to start my speech. I was wondering whether someone in this ...
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2answers
170 views

Experiences with Venn diagrams as didactic tool for factors, GCD, LCM?

Venn diagrams have got to infiltrate the modern curricula as a way to explain probability theory, discussing sets of events. Not surprising, and we can say that they never left us really in topology ...
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4answers
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How can I help a student who has a “wrong” kind of enthusiasm?

Alice (not real name) is a student in one of my Math 100 (calculus) classes. It's a course offered by my college as a dual credit course at a high school, so the whole class is about 17/18 years old, ...
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Why does result depend on procedure in my calculation of surface area using Guldin? [closed]

At present, I teach Guldin's rules for surface and volume of rotation, and give an example task from the textbook. The textbook uses procedure 1 (below) for calculation (below), but I advocate that ...
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4answers
190 views

Teaching congruent triangles non-rigorously

I've just started teaching congruent triangles to a class of 14/15 year olds in the UK. All that they are required to know for the purpose of national exams here is that two triangles are congruent if ...
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3answers
333 views

How to Teach Middle School Students to Read Square Roots?

This exact quote from my standard American Algebra 1 textbook states when first introducing rational square roots: $\sqrt{49} = 7$ is read "The positive square root of $49$ equals $7$." $-\...
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implication vs equivalence when solving equations

I remember we were taught in high school (Eastern Europe) the difference between implication ($\Rightarrow$) and equivalence ($\Leftrightarrow$) and were instructed, when solving equations to be ...
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3answers
157 views

Introducing an axiomatic method to high-school students

As well as mathematics I teach IB Theory of Knowledge, which includes mathematics as an area of knowledge. The class are mainly not students with a maths focus, although they all study at least some ...
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8answers
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Helping students who make no effort to figure things out for themselves

When I was a student, it was very much frowned upon to ask for help without making an effort, like how math.stackexchange.com operates (for the most part). In the high school where I work, it is ...
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4answers
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Why is polynomial factorization over the integers part of secondary school curricula?

By "polynomial factorization over the integers", I mean problems and solutions like the following: Problem: Find a factorization into irreducible polynomials for $24x^2 +x - 10$ and ...
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3answers
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The Way We Teach Square Roots

Recently I was watching this interview of Andrew Wiles where a secondary school teacher asked this question: How do you teach square roots? He doesn't answer the question so I'd like to ask it ...
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3answers
174 views

High School Math Course focused on Sports

I am an high school math teacher and want to develop a math course that is totally focused on sports. It would be a senior level course and would focus on the math and analytics of sports. I just ...
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Are there any high school level summer program that teaches Analysis?

All summer programs I know for highschool students focuses on number theory, combinatory, graph theory, logic, and all kinds of stuffs in discrete mathematics. (I am mainly interested in UK, US, ...
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How should a student's inefficient calculation be pointed out?

One time I watched a student solve the equation $0 = (x-2)^2-9$ for $x$ like this. $$\begin{align*} 0 &= (x-2)^2-9 \\0 &= (x^2-4x+4)-9 \\0 &= x^2-4x-5 \\0 &= (x+1)(x-...
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1answer
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Situation involving the application of addition or subtraction of algebraic fraction

I am preparing a unit on operations with algebraic fractions; But, particularly addition/subtraction of algebraic fraction such as $$\frac{3}{b} + \frac{2}{a} ; \frac{x+1}{3}- \frac{2x+3}{4}; \frac{...
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3answers
654 views

What are the minimum criteria when checking homework for completion only?

I know that some instructors collect homework and "grade that on the basis of completion" (e.g., item #2 on this answer). In fact, I tried this myself for several years, based on advice from my mentor ...
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1answer
149 views

How do I work in creating education standards?

I'm interested in playing a role in determining mathematics curriculum and goals for K-12 students. I'm currently a college student. How do I even begin down this path? Math? Political Science? ...
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2answers
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What can I teach a talented student who is enthusiastic about math?

I have a very clever student in Grade 7. Due to carelessness and English (which is not his native language), he failed the placement test and can't learn Grade 8 math (algebra 1) in school. School ...
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How to teach a student algebra who misses too much previous knowledge?

I am now tutoring a student in Grade 9, who falls behind in math study. He lacks the basic understanding of operations and inverse operations, and have trouble dealing with negative numbers and ...
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App to show exercises solved by students in real time

I'm looking for an app that can be used when the teacher gives a set of exercises to his class to show for each exercise how many students solved it, how many students tried to solve it, etc. The ...
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4answers
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Might it be helpful for students to have different symbols for subtraction (-) and negation ( _ )?

Might it be helpful for students to have two different symbols for subtraction (-) and negation ( _ )? Subtraction, after all is a binary operation (with 2 operands). Negation is a unary operation (...