Questions tagged [secondary-education]
For questions about teaching mathematics in secondary education (in most countries approx. ages 10-18).
644 questions
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How to teach high school students to analyze diagrams in a proof?
I work as a math intervention teacher with high school sophomores who are currently taking geometry. The sequence of instruction is as followed (so far this year):
Introduction to geometry - naming ...
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Good ways to help students overcome the mistake that $ 2a - 3b + 7a + 4b = -5a + 7b$
I often encounter students who incorrectly think that $ 2a - 3b + 7a + 4b = -5a + 7b,$ rather than $9a + b,$ due to the misapprehension that
$$ 2a - 3b + 7a + 4b = \color{red}{2a -}\ \color{lightblue}{...
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Solve $1 < 2$. Does it make sense to ask this?
I am translating GeoGebra's step-by-step solver (https://www.geogebra.org/solver/en) from English to Brazilian Portuguese.
When asking GeoGebra to solve $1 < 2$, the following explanation is given ...
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Ideas how to make slides easily
I am studying to become a math teacher. I received feedback to make my slides visually more attractive. I'm not skilled in graphical design, but I know the basics of LaTeX, CSS, and HTML. Which is the ...
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Is Induction implied within Definition of Recursion? [closed]
Hi I was reading about definition of Addition:
n + 0 = n
n + S(m) = S(n + m)
Between these two above mentioned steps, moving ...
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What kind of sequence is between an arithmetic and a geometric sequence?
In school we teach arithmetic and geometric sequences. Students should notice that arithmetic sequences (with common difference greater than $0$) grow steadily, while geometric sequences (with common ...
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How can a church or other non-academic institution find and hire math teachers?
We'd like to set up a remedial math program in our church. To do so, we would need to hire at least two teachers who could design courses in middle school and high school math, and teach them.
I'm a ...
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What are signs your high school algebra II (arithmetic) course plan focuses heavily on the first half and neglects depth in the second half?
What are signs your algebra II course plan focuses heavily on the first half and skimmed the second half?
I'm trying to figure out whether I'm going evenly.
I'm trying to figure out whether students ...
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Assigning a semi-independent project for current math I students to learn a topic in Math II overlap with math I, and teach a math II class, how to?
How can I foster a growth mindset and sense of belonging to the intellectual realm among Algebra II students by having them undertake a semi-independent project where they learn to teach an ...
user24309
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Examples of different languages with mathematically different names for concepts
Multilingual classroom
Having pupils of many different native languages, and many languages in general, has been getting quite common in Norwegian classrooms, too. In many other countries this has ...
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Resources to introduce Modular arithmetic
We have Clock arithmetic in grades 5 , 6 and thereafter nothing related to the Modular arithmetic is taught until students enter to the universities. Since this is very important topic in Number ...
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What is this symbol called?
I know how to pronounce the first symbol as "theta", but the other symbol that looks like a circle with a vertical slash, I don't know what to call it.
I would appreciate any help. Thank you
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What skills do algebra teachers wish their students had mastered before taking algebra?
I am designing 10 hour weekly summer math learning opportunities for students taking algebra next school year. I would like to know from algebra teachers what skills they wish their students had ...
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Theory of semiotic mediation in teaching math at high school [closed]
I am working on the theory of semiotic mediation in teaching math at high school. According to the theory I need an artefact that is appropriate for high school (secondary school). In many papers ...
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Markov chains - how to translate mathematically the fact that the state at $n+1$ only depends on the state at $n$? [closed]
In a Markov chain of, say, three states $1,2,3$, when proving that the probabilistic state at $n+1$ ($\pi_n$) is equal to the probabilistic state at $n$ times the transition matrix, one has to use the ...
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Math textbook for secondary school using Logo like language
What math textbooks for kids do you know that use Logo or similar languages with visual robots like Turtle (in "The Turtle Geometry") that demonstrate space motions, transformations of all ...
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Math textbook for secondary school using Logo like syntax
What math textbooks for kids do you know that use Logo or similar languages with visual robots like Turtle (in "The Turtle Geometry") that demonstrate space motions, transformations of all ...
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How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?
The mainstream way to show $V[aX+b]= a^2 V[X]$ is by using LOTUS. However, LOTUS seems to me too powerful and out-of-reach for a last-year high-school student.
Therefore I was wondering if we could ...
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International Baccalaureate - where to find the detail of the math programs?
Does anyone know what is the exact program of the International Baccalaureate in math?
I've been looking for the MYP and DP programs in the website of the International Baccalaureate Institute but ...
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Real-World Problems for Teaching Extrema and Derivative Tests in STEM Education
For educational purposes, I am seeking example problems in the realm of natural sciences, engineering, and business that satisfy the following criteria:
Consider a one-dimensional real function $f$ (...
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When can students understand the intersection of two circles?
I'm interested in learning two transitions:
(1) When can students reason (intuitively, but accurately) to conclude that two circles in the plane
could intersect in $0$, $1$, or $2$ points, or are ...
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Why use the vague notion of "vector" when you have $\mathbb R^2,\mathbb R^3,\mathbb R^4,\ldots$?
I'm reading an introductory course on groups. In this course, the author illustrates concepts using the vectors of the plane. For example, "the set of vectors in the plane(or in space) is a group ...
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Applications of High School Geometry
Sometimes I struggle to give my students a sufficient number of reasons why they should study Geometry in high school, other than that it helps them think and increases their understanding of the ...
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Any known platform to post self made math questions
Background
I am a class 10 student who is fond of maths. I like making math questions.
Question
I do not know of any platform where I can post these questions for others to practice and learn. I ...
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About a difficult exercise for 12 years pupils
You have to go from a point $A$ (start) to a point $B$ (arrival) by crossing a river $(d)$ and traveling as little distance as possible.
Pupils first do a search by trying several paths $1,2,3,4$ and ...
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Is integrated math class the same as mathematics class?
The first high school I went to I did Integrated Math 1 my Freshman year, Integrated 2 my Sophomore year, and Integrated 3 my junior year. My junior year I transferred to a continuation school where I ...
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Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?
I am planning to become a math high-school teacher and have the following question:
What Probability Theory should I base myself on to teach probabilities to students ?
The classical approach is via ...
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1st time math teacher 1st test feedback appreciated
I'm not a math teacher but I've stepped into the role to assist a small private school who lost their math teacher during the holidays (I'm a mechanical engineer by trade). The course is Algebra 1 (...
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International mathematical olympiad-type competitions at lower levels, and if they exist, their educational usefulness?
Educators in many countries have found that preparing highly motivated students for national and international mathematical olympiads can be useful in training them in mathematical ways of thinking.
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Infinite descent method in geometry
What are the examples we can use to explain infinite descent as an efficient method of proofs in geometry?
I think one of the best may be proving medians of a triangle are concurrent by the infinite ...
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How can we motivate that Newton's method is useful?
If you teach Newton's method for finding roots of real functions on the high school (or freshmen) level, I think some students may reason like a variant of the following:
Why do I need learn such a &...
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In what ways could or couldn't having students do homework in $\LaTeX$ for extra credit be helpful for them at the college level? High school level? [duplicate]
Do you think having students turn in homework in $\LaTeX$ say for extra credit is helpful for them at the college level? At the high school level? There could also be a few assignments that have to be ...
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Do you think with the advent of Desmos/GeoGebra, the Moore Method is more accessible to high school?
When I was a grad student, I taught a Calculus I course during the summer. Somehow I came across Robert Moore and I ended up reading his book which I connected with. Rather than being a great student, ...
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What are common mistakes that students will make when solving "What's the original price" percentage problems?
Take this question for an example:
A smartphone is now $\$500$ after a $20\%$ discount. What was its original price?
Now, this is an example of a type of math problem that students face usually in ...
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Topological fun facts for high school students
I'm going to give a class to highschoolers about topology. I've prepared the beginning of the class where I introduce what is topology and give them different ways we use to describe spaces, but ...
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Special topics for introductory probability
I am helping to design a low-level college course whose purpose is to teach critical thinking, logic, finance and probability. I have been tasked with developing the probability section. I am ...
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Speed math appropriate for middle-school students
There are many "rules" for speed arithmetic.
List of some reference links showing speed methods or rules:
https://ofpad.com/multiplication-tricks-for-mental-math/
https://ofpad.com/mental-...
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Is there a standard convention for interpreting ambiguous absolute value expressions?
Consider the expression
$$|x + 2|x + 3|x + 4|.$$
One way to interpret this is that there are two products being added together:
$$|x+2|x \hspace{1cm} + \hspace{1cm} 3|x+4|$$
But you could also ...
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Importance of complex numbers knowledge in real roots
Many students question the importance of complex numbers in real life. We can find many important applications of imaginary numbers in Engineering field and physics. This question is not related to ...
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Educational resources commonly address slant asymptotes. Why not general polynomial asymptotes?
Back in 2018, I wrote a post about asymptotes of rational functions in which I addressed not only horizontal and slant/oblique asymptotes, but also the general case of "polynomial asymptotes.&...
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Basic skill requirement suspension
Oregon appears to have suspended the "basic skills" requirement for graduation; see this. What will be the effect of this on the mathematical proficiency of the graduating class?
Follow-up ...
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How can one lone picture prove the Triangle Inequality, $|x−y|≤|x|+|y|$, $|x|−|y|≤|x−y|$, and the Reverse Triangle Inequality?
I always showcase separate pictures of Triangle Inequality, and Reverse, to 16-years-old students in 1st class. I reshow pictures in 2nd class. I preachify
Please remember these 4 inequalities. ...
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Identifying Trigonometrical proofs
How can we identify trigonometrical proofs from geometrical proofs, do we have purely trigonometrical proof of Pythagoras theorem as claimed by two high school students ? https://www....
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To 17 year olds, how can I explain that two numbers with arbitrarily small difference are equal?
$|a – b| < ε, \forall ε > 0 \iff a = b$ resurfaces on standardized tests to 17 year old (y.o.) students, who can memorize and regurgitate the proof to earn full marks.
But the glut of duplicates ...
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Why not think of derivatives as fractions?
Back in high school—back in the 1900s, as my sons say—when our calculus teacher was introducing the chain rule...
$\frac{dy}{dx} = \frac{dy}{dt} \cdot \frac{dt}{dx}$
...he made a special point of ...
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Geometrical verifications for Algebraic formulae
What is the importance of using approaches related to Geometric Algebra in teaching,is it only useful when introducing Algebra to the students or can it be helpful to improve creative skills in ...
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What benefit is there to obfuscate the geometry with algebra?
Consider:
In a right triangle:
sin(2x + 4) = cos (46)
What is the value of x?
The question above is from standardized tests for a geometry course. If my goal is to have students understand ...
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Seeking References on Deterministic and Stochastic Phenomena Suitable for High School Students
Can anyone recommend good and didactic references that delve into the dualism between deterministic and stochastic phenomena? Ideally, I'm seeking materials that provide a conceptual explanation along ...
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Explaining Sigma-Notation
I attempted to introduce the summation notation $\Sigma$ to my students. The notation was unfamiliar to the students beforehand. I worked through many examples with them, but for most of them, working ...
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Remote Teaching by Video Conferencing
I am in my early 70's and licensed to teach 8-12 math in Texas. I have an advanced degree in the same area. I used to teach in high school decades ago but have since quit because the student's ...
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