Questions tagged [mathematical-pedagogy]
For questions on general considerations and problems of teaching mathematics, such as issues specific to teaching mathematics that are relevant in various contexts or courses.
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Best way to explain the thinking steps from x² = 9 to x=±3
I'm writing four young adult novels with math at the center. The first one is about complex numbers. I'd like to know what good teachers think of the implied pedagogy in the following conversation ...
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Why are volumes of revolution typically taught in Calculus 2 and not Calculus 3?
Solids of revolution are typically taught in Calculus II for most undergraduate students or in AP Calculus BC for most high school students. However, it seems to me that this topic is far more ...
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How to choose a textbook that is pedagogically optimal for oneself?
I am currently using the Russian textbook Mathematical Analysis by Zorich. But the more I use it, the more I feel it is making problems too hard or too advanced for the subject and it is unnecessary. ...
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When Did They Start Using Ohm's Triangle for Arithmetic Topics?
I am here with a historical question about maths education. I hope I have chosen the right SE as there are confusingly three that pertain to historical research into mathematics.
Any quantitative ...
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Mathematics and calmness [closed]
I wanted to ask if in order for someone to be a good mathematician they need to enjoy a relationship, with someone, such as a teacher or a companion, that has a calming effect on them.
Thank you.
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Real-life problems involving solving triangles
Could you advise me where to find real- life or word problems using trigonometry, involving solving triangles, suitable for high-school students? Most of the problems i found were pseudo-real problems ...
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Preparing students to face challenges caused by artificial intelligence
Before the invention of computers, the main objective of teaching was to impart subject-related knowledge and train students in memorization. However, with the advent of computers and their vast and ...
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Truth tables. What does a truth valuation of a formula even mean?
What does a truth table even mean? Does anyone actually spell it out anywhere? (reference please). People feel like the are not taught rigorously like limits are.
Edit: What does it mean for a (non-...
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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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Which cognitive psychology findings are solid, that I can use to help my students?
I read recently on this site that the growth mindset seems not to be real. I did not know that (I admit that I don't follow research into learning as closely as I would like). Can I turn that ...
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Correct notation of a Sample space
From the very beginning I have used the notation $ S = \{ H , T \} $ as the Sample space for tossing a coin once and $ S = \{ HH , HT , TH , TT \} $ in the case of tossing a coin twice.I have several ...
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Math Progress for Year 2 Student?
Have a year 2 student that is years above his peers. Each topic I introduce he has already learnt and understood. I've extended the topics we work on for him but the topics I introduce are rudimentary ...
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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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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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Book or curriculum for teaching base-16 numeral system to elementary, middle, or high school children?
In 1862, John W. Nystrom promoted the base-16 (hexadecimal) number system, which he called the "tonal system": Project of a New System of Arithmetic, Weight, Measure and Coins: Proposed to ...
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Engaging in a puzzle without a guidance of a leader while simultaneously being a component of that puzzle
I have done couple of activities and experienced how interestingly students are engaging. At the end I explained the Mathematical concepts related to the activities. Here I'm suggesting two of those,
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Recreational mathematics to create sense of mathematics
Recreational mathematics serves as a valuable educational tool by enhancing interest, fostering engagement, and refining mathematical thinking. While it often falls outside traditional curricula, ...
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Comparison of two ways to introduce translation to 12-14 year olds
I consider pupils 12-14 years old, who are new to translation. On the other hand, they have been accustomed to placing points in a coordinate system, especially when studying relative numbers. In ...
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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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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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When Interpreting "If A, then B" as "A coupled with B" is rational?
It is known that the meaning of a conditional statement in fuzzy logic can vary depending on the interpretation and context. As we know, some ones interpret "if A, then B" as "A coupled ...
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A good book about mathematical thinking
I am a qualified mathematics teacher but I have left teaching because I could not tolerate the behaviour of students. Now I am a mathematics tutor and I love that I get to teach students who are eager ...
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Alternative approaches in basic mathematical operations
Sometimes awareness of alternative approaches of different origins may be helpful for students to improve their creative skills in mathematics. What would you suggest as alternative methods in basic ...
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Whether to tell students how difficult (you think) a problem is
Background: Most textbooks end a section with a set of questions ranked either by topic or by difficulty. A distinction is often made between "exercises", which are for directly practicing a ...
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Best practices for Proof Revision/ Proof Portfolio?
I'm teaching a class small enough that I'm considering encouraging proof revisions (i.e. students taking a second try on proof based homework problems after getting feedback) for the first time. I'd ...
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"Tools" (literarily) for solving linear or quadratic equations
Since a few weeks, I teach as a tutor (not from that school) a support course in a German 9/10 class. I quickly noticed a horrible lack of basics. (Partly based on just different names - I had to ...
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Bridging the gap between students' intuitive problem-solving abilities and expressing ideas through formal writing
Seeking guidance on how to assist students who possess a solid grasp of problem-solving concepts, allowing them to intuitively arrive at solutions, yet encounter difficulties when it comes to ...
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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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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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Is this a viable Calculus 1 question?
A person is standing next to a hot air balloon. At the same time, the person starts moving away from the balloon at 5 ft/sec and the balloon rises straight into the air at a rate of 12 ft/sec. Is the ...
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What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?
I have helped to TA and taught several courses with mixtures of advanced undergraduate and early graduate students in engineering/STEM. These courses are the classics: signal processing, control, ...
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Role of history of mathematics in contextual teaching and learning
To get a deeper understanding of mathematics conceptual teaching and learning is supposed to be a much better approach than factual teaching and learning processes. Since the conceptual approach is ...
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Better proof for a proposition when a proof is already available [closed]
What is a much better proof in mathematics, is it need to be a much more advanced one compared with the proof already available or a much simpler one?
I think you can challenge a proof in two ...
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Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs
Background
I'm informally helping a few students with college Calc 1. This isn't the first time I've aided people with calculus, and so they've sought me for help, though I don't consider myself to ...
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Is there a resource for learning to read mathematical notation/equations/formulae?
Ideally, I am looking for an online resource. But a book or any other would help already.
Background: I am a senior teaching assistant in the field of business and statistics. Most of my students have ...
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What are some good books on mathematical pedagogy?
I suspect that; just as one must "do" mathematics to learn mathematics, one must have practice teaching mathematics to become a great mathematics instructor.
Still, a good book on ...
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How to teach pure mathematics to a well-educated adult who did badly in maths at school
My partner is a PhD student in philosophy and has recently developed a keen interest in learning pure mathematics. I am doing my best to teach her (I'm a pure maths PhD student myself) and it is ...
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Activities that encourage students to create or evaluate mathematical notations
I'm looking for references about activities that encourage elementary school students to create or evaluate mathematical notations. do you know any?
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Studies on the change in effectiveness of pedagogical practices over time
Are there any studies that have investigated this question?
Why certain pedagogical practices that used to be effective up to a few years ago, may suddenly become less or even no longer effective?
I ...
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A better example of a logical implication
(Updated)
An example of a logical (material) implication that is commonly used is: "If it is raining outside, then the ground is wet." The problem with this example is that it could be ...
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What should I call the "important" values of x?
When analyzing the functions
$f(x) = \sqrt{x-5}$
$g(x) = \frac{1}{x-5}$
$h(x) = 2^{x-5}$
we know that it is useful to think about what happens at $x = 5$.
For the function $f$, this logic will ...
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What to cover on a first ordinary differential equations module?
I will have to teach a first course in differential equations. What should I cover in this module? For example, in most books, have Laplace Transforms which is fine but I would not use LT to solve ...
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Is it possible to learn some basic mathematics using an app?
I am interested in developing an app for students that are starting a grade career involving mathematics. It is a real problem that they start with almost no knowgladge of basic mathematics and there ...
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When dealing with sequences, should we teach students to start at 0 or 1?
The reason I prefer starting at 0 is due to a computer science background and also, I think it helps to start at 0 because there are certain reasons that demand it (in particular, combinatorics) and I ...
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Is this motivation for the concept of a limit a good one?
tldr: There is a simple intuitive definition of a limit for monotone sequences, and I suggest that it can be used to motivate the (more complicated) standard definition. I am asking for feedback on my ...
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How to explain the concept "Without loss of generality" (through examples)?
This is not a precise question. I am curious to know how do you present to your students the (imprecise) concept of "without loss of generality", and how to use it correctly/incorrectly.
I ...
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Geometry in the Community College Curriculum
As many Americans know, the “traditional” high school sequence is:
Algebra 1
Geometry
Algebra 2
PreCalculus
Calculus
For those who take developmental education at the community college level, it ...
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Elementary examples for non-reversible logical steps
While listening to recordings of Calculus $I$ lectures, I noticed that some students get confused between showing that "some object $x$ is a solution", and showing that "every (...
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Does induction really avoid proving an infinite number of claims?
I am teaching calculus $1$ this semester, and I saw the following motivation for using induction by another teacher:
Since we can't go over "manually proving" all claims $1,2,\ldots$ and ...
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