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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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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 ...
Janaka Rodrigo's user avatar
37 votes
5 answers
13k views

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 ...
Jim Hefferon's user avatar
4 votes
2 answers
282 views

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 ...
Janaka Rodrigo's user avatar
0 votes
2 answers
110 views

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 ...
user avatar
0 votes
3 answers
431 views

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
Teacher's user avatar
  • 17
1 vote
1 answer
155 views

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 ...
ryuk's user avatar
  • 131
1 vote
0 answers
113 views

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 ...
Geremia's user avatar
  • 171
0 votes
0 answers
76 views

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, ...
Janaka Rodrigo's user avatar
3 votes
1 answer
224 views

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, ...
Janaka Rodrigo's user avatar
2 votes
2 answers
170 views

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 ...
Stéphane Jaouen's user avatar
3 votes
4 answers
460 views

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 ...
Stéphane Jaouen's user avatar
2 votes
1 answer
221 views

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 ...
Stéphane Jaouen's user avatar
1 vote
0 answers
141 views

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 ...
hasanghaforian's user avatar
14 votes
6 answers
2k views

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 ...
Kristina Dedndreaj's user avatar
5 votes
7 answers
3k views

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 ...
Janaka Rodrigo's user avatar
19 votes
4 answers
3k views

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 ...
Nick C's user avatar
  • 9,639
9 votes
3 answers
569 views

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 ...
Mathprof's user avatar
  • 1,205
2 votes
0 answers
128 views

"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 ...
Hauke Reddmann's user avatar
7 votes
1 answer
678 views

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 ...
user1258481's user avatar
3 votes
12 answers
3k views

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 ...
Janaka Rodrigo's user avatar
5 votes
4 answers
364 views

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.&...
Justin Skycak's user avatar
1 vote
1 answer
207 views

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....
Janaka Rodrigo's user avatar
2 votes
3 answers
297 views

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 ...
Maesumi's user avatar
  • 1,410
25 votes
14 answers
17k views

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, ...
Fraïssé's user avatar
  • 749
5 votes
4 answers
264 views

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 ...
Janaka Rodrigo's user avatar
2 votes
3 answers
954 views

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 ...
Janaka Rodrigo's user avatar
15 votes
15 answers
7k views

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 ...
Krupip's user avatar
  • 291
9 votes
7 answers
2k views

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 ...
Nibood_the_slightly_advanced's user avatar
13 votes
7 answers
1k views

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 ...
Mithrandir's user avatar
26 votes
14 answers
9k views

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 ...
user829347's user avatar
4 votes
0 answers
118 views

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?
Humberto José Bortolossi's user avatar
4 votes
0 answers
168 views

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 ...
Mahdi Majidi-Zolbanin's user avatar
1 vote
4 answers
574 views

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 ...
Dan Christensen's user avatar
8 votes
5 answers
894 views

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 ...
Chris Cunningham's user avatar
1 vote
0 answers
176 views

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 ...
matqkks's user avatar
  • 1,243
5 votes
0 answers
128 views

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 ...
Paula Cardoso's user avatar
4 votes
0 answers
209 views

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 ...
Lenny's user avatar
  • 1,068
3 votes
6 answers
1k views

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 ...
Asaf Shachar's user avatar
10 votes
1 answer
315 views

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 ...
Asaf Shachar's user avatar
6 votes
3 answers
1k views

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 ...
MichaelLink's user avatar
4 votes
1 answer
232 views

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 (...
Asaf Shachar's user avatar
12 votes
7 answers
3k views

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 ...
Asaf Shachar's user avatar
-4 votes
2 answers
174 views

Mathematics and love [closed]

This might seem a bit misplaced, but, is very relevant to mathematics education. The question is, how can I love someone, and teach students to love, or attempt and complete actions of love, through ...
Joselin Jocklingson's user avatar
-3 votes
2 answers
152 views

Best natural language(s) for conveying, conceptualizing, teaching, understanding, and learning Probabilistic & Statistical concepts & theory?

English can be precise but it is rather 'flowery' and easily gets in its' own way. East-Asian natural languages like Mandarin, Cantonese, Korean, and Japanese are notorious for permitting the ...
NoYouNaiveBaye's user avatar
0 votes
3 answers
193 views

The two paradigms of seeing a functions

When we are first taught functions , we are typically taught of them as maps between real numbers and we taught to think of them mainly as a mapping between elements. It seems intuitive to take this ...
Babu's user avatar
  • 595
3 votes
1 answer
86 views

Fitch Style Deduction in Non-Logic Classes

Has anyone experimented with using Fitch-style proofs as a teaching aid in courses outside of logic specifically and if so, how was the technique received by students?
Steve's user avatar
  • 1,604
9 votes
1 answer
362 views

The Interleaving Effect: How widely is this used?

I came across the idea of mixed up practice in Benedict Carey's book, How We Learn, in a chapter on the benefits of interleaving, particularly for learning Maths. For instance, in "blocked ...
Stephen Clement's user avatar
4 votes
0 answers
724 views

What are your experiences with Buck’s Advanced Calculus?

I stumbled across the book when searching for rigorous alternatives to Rudin with some solutions. It’s an “old school” (1965) calculus text but, I think, covers similar material to Rudin in a more ...
akm's user avatar
  • 141
7 votes
2 answers
176 views

Are there pre-printed wall images that might engender understanding in a very young child?

I just read Moebius Noodles. (Thanks for the recommendation Sue). Part of the book talks about keeping images about math around the house. My child's 18 months. But I figure, why not now. It's passive;...
Hal's user avatar
  • 579
3 votes
3 answers
857 views

Walter Warwick Sawyer: How has reading his works changed your learning or teaching? [closed]

I recently worked my way through Walter Warwick Sawyer's book, Mathematician's Delight, which has opened my eyes to Maths. I used to fear maths, feeling I was incapable. Sawyer (among other authors) ...
Stephen Clement's user avatar

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