Questions tagged [secondary-education]

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

-2
votes
2answers
117 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" ...
-5
votes
0answers
62 views

A KinderGarten of binomial coefficients [closed]

I tell the beginners that $(-n)!= \pm \infty$, if $n \in N$. Next, I tell them that the definition of ${\nu \choose k}$ as $$ \frac{\nu (\nu-1) (\nu-2) (\nu -3) ...(\nu-k+1)}{k!}~~~~(1)$$ is the most ...
7
votes
1answer
170 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
votes
6answers
248 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 ...
1
vote
1answer
86 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 ...
1
vote
1answer
91 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 ...
5
votes
2answers
114 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
votes
2answers
146 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 ...
1
vote
0answers
161 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 ...
5
votes
3answers
215 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,...
0
votes
1answer
134 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 ...
5
votes
4answers
324 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 ...
8
votes
6answers
241 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
votes
2answers
109 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 ...
0
votes
3answers
103 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
votes
4answers
291 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
votes
2answers
148 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 ...
10
votes
3answers
299 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
votes
2answers
249 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 ...
5
votes
0answers
205 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 ...
26
votes
3answers
4k 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
votes
1answer
88 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}{\...
5
votes
2answers
165 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 ...
3
votes
0answers
129 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 $IP$. ...
8
votes
4answers
478 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 ...
7
votes
7answers
547 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 ...
5
votes
1answer
93 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 ...
1
vote
2answers
366 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 ...
3
votes
0answers
60 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 ...
8
votes
5answers
892 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 ...
4
votes
4answers
397 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 ...
9
votes
5answers
470 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 ...
1
vote
6answers
1k views

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 ...
1
vote
0answers
181 views

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 ...
1
vote
2answers
314 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 ...
3
votes
1answer
128 views

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 ...
1
vote
1answer
152 views

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 (...
8
votes
4answers
277 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 ...
7
votes
6answers
348 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 ...
2
votes
0answers
65 views

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 ...
4
votes
2answers
180 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 ...
1
vote
0answers
110 views

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 ...
8
votes
5answers
213 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 ...
11
votes
2answers
390 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 ...
1
vote
0answers
55 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 ...
2
votes
1answer
198 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,...
1
vote
1answer
128 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 ...
4
votes
2answers
194 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 ...
30
votes
4answers
726 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, ...
2
votes
0answers
101 views

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 ...