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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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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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0answers
52 views

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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5answers
814 views

'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
365 views

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
316 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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6answers
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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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0answers
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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
216 views

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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0answers
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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
268 views

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
305 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
155 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
184 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
272 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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0answers
50 views

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
127 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
113 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
156 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
557 views

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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0answers
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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
155 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
324 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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175 views

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
149 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
6k views

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
270 views

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
435 views

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
172 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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0answers
104 views

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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10answers
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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
149 views

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
634 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
148 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
196 views

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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3answers
272 views

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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0answers
52 views

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
173 views

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 (...
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3answers
101 views

Phone app or webpage to link HS students to free math tutor?

I have been doing volunteer high-school math tutoring in person. But nowadays, I think there should also be an online way of connecting a student in need of help, with someone willing to help them. ...
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1answer
191 views

Are students being adversely affected by cranks or trolls in online math forums?

Does anyone know of any cases of students being adversely affected by cranks or trolls in online math forums (e.g. sci.math)? Are they even a minor problem? Dan
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3answers
144 views

Tasks that encourage argumentation

I am looking for resources that have tasks such as the one below that encourage argumentation. I want tasks that 8th graders could do but would also be appropriate for high school students. I want to ...
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0answers
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Compare depth and scope of math syllabus between Malaysia's STPM, Gao Kao and A level

Are the math syllabi of these three exams comparable? Which syllabus' scope is wider and deeper? Which helps students to be better prepared for math in undergraduate level? I believe that A level is ...
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2answers
144 views

Problem based learning (PBL) for pupils with educational difficulties

I taught IT in an engineering school during three years in problem based learning (PBL) only. Now I teach maths to pupils between 10 and 15 years old who have a lot of educational difficulties. I'm ...
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7answers
1k views

How to teach sum of fractions to students?

I think almost every middle school student in my country has learned sum of two fractions in this non reflexive way (I'm included when I was kid), doing the following steps: They calculate the lcm. ...
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3answers
481 views

Stating identity is not the same as knowing value

A discussion with a frustrated 10th grade student sent me here. I had provided two linear function expressions, $f(x)=2x+2$ and $g(x)=-\frac{1}{2}x-2$, now find the intersection of the two lines! ...
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6answers
281 views

Ideas for a 2 weeks project focused in polynomial functions

Right now I’m teaching precalculus in high school and I want to propose a project to my students about polynomial functions. They already know enough about quadratic functions and we study variation ...
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4answers
315 views

Difficulty with word problem interpretation

I've tutored math SAT prep for some years now, and have developed a routine with certain texts and exercises that I have found to be fairly successful in improving scores overall. I recognize that ...
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2answers
102 views

How can I get a better result making math videos with a tablet?

First question in this stack. Here it goes: So, I had this 2 or 3 year old intuos tablet and I said why not? And started doing my own videos. I've been making my own videos for my students last ...