Questions tagged [secondary-education]

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

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Tangent line to a curve

How would you define tangent line to a curve at a given point on the curve? I think in secondary education it is not sufficient to say a tangent line is a straight line touching a curve at a given ...
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0 votes
0 answers
61 views

Symmetry of mathematical expressions in problem solving

**How would you use symmetry of mathematical expressions in problem solving in order to save time by minimizing simplifications? This is not related to geometrical symmetry which is very much ...
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5 votes
5 answers
1k views

Explaining difference between improper integrals that converge and diverge

How would you explain the difference in the results given by integration of the two functions $y = \frac{1}{1+x}$ and $y = \frac{1}{1+x^2}$ ? The graphs of these two function look so similar on ...
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6 votes
3 answers
947 views

How can I improve my Retake Policy?

I teach Pre-Calculus at a public high school in the United States. This school year, I allowed my students to retake any assessment regardless of how they performed on their first attempt. However, ...
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1 vote
2 answers
180 views

Importance of exploring skills in mathematics

How can you improve exploring skills in high school mathematics education in order to guide students to get better opportunities to become mathematicians ? Here are my suggestions, Let students to ...
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12 votes
14 answers
3k views

Examples of relations that are not functions

When teaching functions, one key aspect of the definition of a function is the fact that each input is assigned exactly one output. I always felt that the "exactly one" part is confusing to ...
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17 votes
4 answers
5k views

Explaining why volume of cone is a third of cylinder

I came across this video explaining to kids why the volume of a cone is a third of the cylinder of same cross-sectional radius and height. Essentially the explainer presents pre-created cylindrical ...
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  • 273
2 votes
3 answers
608 views

Equation of a straight line on two dimensional Cartesian plane

What is the most appropriate way to write equation of a straight line through a given point $(\alpha,\beta)$? If you write it using the standard form $y- \beta = m (x - \alpha )$ Where m is the ...
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7 votes
7 answers
261 views

Creative problems in 2D vector geometry

What are some "interesting" and creative problems or exercises on specifically 2-dimensional vector geometry that a high school student might find compelling to solve? The class' current ...
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2 votes
2 answers
114 views

Is there a good Animation to explain Rotational Symmetry of Equilateral triangle

I am willing to teach that the Order of rotational Symmetry of Equilateral triangle as $3$ using Animation. Any suggestions of good applet which demonstrates the rotation of equilateral triangle with ...
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3 votes
1 answer
58 views

Resource for International Comparison of Math Education Logistics

Are there resources that compares/lists crunchy facts about the logistics of math education in different regions or countries? I'm talking facts like: Do they use paper homework versus and online ...
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4 votes
1 answer
155 views

Valid Reasons in Two-Column Geometry Proofs

I'm wondering about the relationship between Eculid's work and modern high school geometry. In "two column proofs," certain reasons are considered acceptible for steps in the proof, such as ...
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5 votes
0 answers
154 views

Montessori mathematics for HS/college students

My children attend a Montessori school (as did I when I was a child), and I have visited several other Montessori schools and spoken with their teachers. Numerous times I've had Montessori teachers ...
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4 votes
1 answer
208 views

Math dyslexia is a big problem for me. I lag behind my classmates

I am a 17-year-old secondary school student from India studying math, physics, and other subjects. I lag behind other classmates only because I work slowly when doing addition, subtraction, ...
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24 votes
2 answers
3k views

Are there science-backed effective teaching strategies?

As a math teacher, I am always trying to self-assess my teaching methods. I am trying a lot of different methods but I would like to organize my study on the subject without weighing too much on the ...
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6 votes
0 answers
105 views

Maximize retention

I tutor high school math students. Students often struggle with a problem they had completed few months prior. Like any skill, it's natural to forget what you learned after a while. As high school ...
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3 votes
2 answers
256 views

Is copying working and explanation plagiarism in this context?

In my institution I have a friend who is part of this Math club where they write blog posts and share them online at medium.com. However, there is an issue with my friends post.After they shared it ...
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3 votes
1 answer
162 views

Why is my 8th grade Algebra 1 tutoring student learning mean absolute deviation and standard deviation?

I’m tutoring an 8th grade student in Algebra 1, and he showed me that their class learned how to find standard deviation and mean absolute deviation using the following formulas: $SD=\sqrt{\...
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6 votes
2 answers
3k views

Should proofs include a third “context” column?

Proofs, or any mathematical derivation, appearing in any real setting, such as a book or textbook or talk, or even when we're teaching it in class, includes a great deal of surrounding explanation. ...
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0 answers
70 views

From primary school to higher mathematics all mathematical abstract concept summary

is there any books or articles for summary abstract concepts from primary school to higher mathematics? we know such as mathmatical operations ...
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17 votes
5 answers
4k views

Why is there a disconnect in the usage of "domain" between high school and higher mathematics, and where does it come from?

In high school (in the US, at least), it is common to define the domain of a function as the set of real numbers for which the function is well-defined and returns a real result. Then students are ...
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18 votes
10 answers
6k views

How should I teach logarithms to high school students?

I have some very basic questions about how to teach the logarithm to high school students: First of all, is it better to introduce it as a function with a graph or is it better to treat it like a ...
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  • 307
2 votes
0 answers
61 views

Search for educational articles

I am looking for articles in French preferably (or in English otherwise, but my english is bad..) on the following topics: study of assessments made in class after a problem; phase of conclusion of a ...
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15 votes
3 answers
454 views

How to balance between teaching to the standardized test vs understanding?

For people teaching high school standardized curriculums such as AP, IB, or A-Levels, how do you find the balance between preparing students for the standardized test compared to ensuring they ...
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  • 321
2 votes
1 answer
314 views

Is Stewart Calculus a good book for AP calculus exam prep?

I have some background from completing Silvanus Thompson's book, but I didn't fully grasp the later chapters in it. I'm going to use khan academy and maybe other resources as a supplement. How useful ...
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22 votes
12 answers
8k views

Student asked me if it is necessary to simplify fractions at the end of answering a question. I'm not sure how to respond

I was just tutoring someone and we went through some sort of diagnostic test thing, when the following question came up. Question: Here is some information about $50$ people who took the driving test:...
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6 votes
1 answer
199 views

How to Effectively Implement a "Notice and Wonder" Activity?

I am a first-year Pre-Calculus teacher at a public high school in the United States. The curriculum I am using often contains "Notice and Wonder" activities whenever a new concept is about ...
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6 votes
2 answers
319 views

Effective Strategies for Helping Students Recognize Nonsensical Expressions? (HS - Undergrad Level)

I'm not entirely how best to pose this question, so that it fits within the guidelines (so edits / suggestions for modification are warmly welcome). I'm interested in exploring effective strategies ...
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6 votes
7 answers
1k views

Are these fraction problems different enough to warrant individual consideration?

Consider the following problems: A) You have 20 problems for your math homework this week, and you want to do 1/5 of them today. How many problems do you need to do today? B) You need to read a 20 ...
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4 votes
1 answer
290 views

is it beneficial to encourage high school students to conduct their own 'research' in mathematics?

Is it good idea to encourage students to look up more about particular topics that interest them? The idea is that I don't think they will understand how to read math literature. for example, if a ...
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1 vote
2 answers
242 views

Advice on teaching advanced mathematics to high school students

I am a high school student really into algebra and algebraic geometry. I want to expose this sort of math to other high school students that have the motivation and ability. For a long time, I had no ...
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16 votes
9 answers
3k views

What is the rationale for distinguishing between proper and improper fractions?

I cannot recall ever hearing the terms "improper fraction" and "proper fraction" outside of an elementary and middle school setting. At some point in my mathematics education ...
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3 votes
2 answers
189 views

The value of making students copy your derivations exactly

I have a hypothesis that I have not yet implemented, and am seeking guidance before I do. I have always taught algebra (and above) in such a way that the students understand the derivations. I check ...
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1 vote
3 answers
461 views

Why is highschool math so unrigorous?

I am an highschool student (I'm starting soon the italian equivalent of 12th grade) and I have many problems with the way hs math education works. I don't understand why everything is explained only ...
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5 votes
5 answers
2k views

Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?

Specifically the one updated by Martin Gardner. I'm not studying as part of a high school or college course (I, in the near future, will though) just as a personal project.
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15 votes
17 answers
7k views

How does one tutor an A-level student past the derivative paradox?

Background: I am new to this site, but have 1500 reputation on the main Maths Stack. I am (age-wise) a secondary student of maths, but for a very long time have been informally learning at home and ...
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6 votes
0 answers
183 views

Are there measurements of how much mathematics people remember after high-school?

These days I got curious about something: Are there measurements of how much mathematics people remember after high-school?
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3 votes
2 answers
107 views

Math Modeling search results data set

This year, I will be teaching a Math Modeling course to a group of motivated high school students. One topic we will discuss is providing good search results from an online query. Here's the problem. ...
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5 votes
1 answer
298 views

Research on Waldorf/Steiner mathematics education

I am mildly interested in research on mathematics education in the Waldorf/Steiner educational context, primarily in the upper secondary school setting, but not exclusively. Information about Waldorf/...
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0 votes
1 answer
74 views

Which grade students should be able to solve applied economy / business / profit prediction exercises?

I've designed a few applied problems with business analytics/money calculations. However, I'm not sure which age (or rather, which grade) are those best to introduce. on one hand, solution uses only +...
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7 votes
3 answers
465 views

Resources for mathematics for sustainability

I am looking for resources (books, websites, etc.) for mathematics relevant to or in the context of sustainability, broadly construed, at upper secondary or early undergraduate level - so not ...
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-1 votes
2 answers
81 views

Can anyone help give pointers of Mathematics Story Telling Animated Videos for Age Group 10 - 15?

Ideally, these videos should talk about a real life problem which student can relate to and then showing logically how the problem can be solved. Later bringing in the right mathematical tool to solve ...
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-2 votes
1 answer
334 views

Why are math test scores dropping in America? Lack of student responsibility movement [closed]

Someone asked me this question today. Why do you honestly believe that high school math test scores in America (particularly the United States) are low compared to other countries? I thought about ...
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  • 605
4 votes
2 answers
309 views

Applications of the annihilator from linear algebra

I am currently assisting a course for future teachers at university level for a joint education in maths and physics in Germany and I have a question regarding the use and possible application of the ...
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7 votes
2 answers
241 views

How to get student with ADHD to practice exercises consistently

Background I have recently started tutoring a 14-year-old student who is diagnosed with ADHD and was struggling with passing a basic math course (think basic linear equations systems, first and second ...
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5 votes
1 answer
218 views

Making the leap from Pre-Calculus to Calculus

This question is targeted at teachers who taught both low and high level mathematics. I have a group of students that I'm currently teaching precalculus and they seem to be doing really well in all ...
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7 votes
5 answers
442 views

Creating an Engaging Class Atmosphere

I would like to start out next year by creating a classroom community. This year I noticed a lot of burnout towards the second half of the year. Basically, I want to see what kinds of games/activities ...
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3 votes
2 answers
217 views

Teaching words with multiple meanings in Mathematics and English

We want to teach about words that have multiple meanings, in mathematics and English for middle school children (e.g., function, root, or, volume, angle, constant). This is for students who are ...
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15 votes
7 answers
2k views

An introductory example for Taylor series (12th grade)

I (a student) am doing a presentation on Taylor series in my class (12th grade, in Germany if this is relevant). I am looking for a good example where you can see when Taylor series might be useful. ...
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  • 261
40 votes
22 answers
10k views

Response to Students Who Say "This Is Not Important"

Lately, my students keep telling me why what we are learning is not important. They ask me when will we use this in the real world? I explain how math is important in gambling, cooking, finance, ...
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