Questions tagged [mathematical-pedagogy]

for questions on general considerations and problems of teaching mathematics, i.e., issues specific to teaching mathematics yet relevant to various contexts and courses.

Filter by
Sorted by
Tagged with
-2 votes
0 answers
79 views

How do you teach the order of a series of events?

I’m looking for research-backed methods for teaching which order a series of events are in. Notably, ordinality in my case is far more important than cardinality. Even better if the technique allows ...
user avatar
0 votes
6 answers
817 views

Finding an analogy to explain the function of a binary adder

I want to find an intuitive analogy to explain how binary addition (more precise: an adder circuit in a computer) works. The point here is to explain the abstract process of adding something by ...
user avatar
10 votes
6 answers
4k views

What should be memorized in math and what should be reference table?

I can never figure out what should be a memorization concept and what should be in a reference table. For example, in calculus, you are expected to memorize all the derivatives and integrals but in ...
user avatar
  • 769
14 votes
5 answers
2k views

Use of language: "perfect square". is this useful or a hindrance? [closed]

I have recently been noticing the tendency to use the term "perfect square" when "square number" is really what is meant. Usually I have seen it at elementary level: introductory ...
user avatar
13 votes
4 answers
2k views

Why do we use functional composition in the order we do?

Function composition means, roughly, taking the output of a function and applying it to the input of another function. If we define an object C to represent this operation, we could say $C(f,g) = f∘g$ ...
user avatar
4 votes
0 answers
80 views

Word problems written in past tense, present tense, or future tense

Does anyone have extensive classroom experience regarding the best verb tense to use when writing word problems at an elementary or middle school level? I have been writing some lessons recently and I ...
user avatar
  • 349
6 votes
4 answers
736 views

What is the best way to introduce Laplace transforms on an Engineering Mathematics course?

Are there any practical applications of Laplace transform? I would not use Laplace transforms to solve first, second-order ordinary differential equations as it is much easier by other methods even if ...
user avatar
  • 1,225
23 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 ...
user avatar
2 votes
1 answer
182 views

How and what to teach on a second year Engineering Mathematics?

In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things in calculus also changed with the advantage of technology. ...
user avatar
  • 1,225
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 ...
user avatar
  • 321
1 vote
0 answers
367 views

Is it more efficacious, productive to jump to perusing full solutions — before and without attempting to solve problems?

Too many students lack the luxuries of time and effort to mull exercises and problems. They must juggle MULTIPLE jobs to pay exorbitant tuition fees. Single parents or adult learners must prioritize ...
user avatar
9 votes
14 answers
9k views

Why's math way more puzzling, abstruse than law and medicine? [closed]

Most students find math unfathomable, labyrinthine by the time of univariate integration (Reddit). Even overachievers – who ace undergraduate math without studying – will eventually be convoluted by ...
user avatar
15 votes
3 answers
442 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 ...
user avatar
  • 321
3 votes
2 answers
135 views

Teaching Solving Linear Equations before teaching evaluating expressions

Traditionally, I have always taught evaluating expressions before teaching linear equations. But, I was recently given a remedial class of students that have to cover the bare minimums (and we have ...
user avatar
  • 189
15 votes
5 answers
4k views

Why the fear of polynomial long division?

Why do people think long division of polynomials is complicated ? I heard this expressed recently and it seems like an odd sentiment. For me, synthetic division is complicated and totally adhoc ...
user avatar
-6 votes
1 answer
117 views

Which function is more elementary: Constant function or identity function? [closed]

I am not a mathematics teacher, I just want to know which function is more elementary and is more reasonable to be learnt first: Constant function (f(x)=1) ...
user avatar
5 votes
2 answers
234 views

How can I encourage students to show up for exercise classes?

I am doing a maths PhD and naturally that involves leading exercise classes for undergraduate students. The idea is that the students just show up and work through the problem set and I'm there to ...
user avatar
8 votes
4 answers
520 views

Exponential & logarithm in a high school calculus class

So recently I was teaching high school calculus to a high school class and I was wondering about the pedagogically best way to make students actually understand why the derivatives of the exponential &...
user avatar
-4 votes
1 answer
203 views

Can you talk about (the rest of the) field axioms when the operations are not closed? [closed]

Note: Updated based on this. In my course, my instructor posed the following exercise: Let $S$ be the subset of $\mathbb R^n$, $S=\{(a_1,a_2,a_3...a_n) | a_2 = \pm a_1, a_3=...=a_n=0 \}$. Define ...
user avatar
  • 526
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 ...
user avatar
12 votes
0 answers
145 views

What studies exist, comparing the efficacy of exercise sheets with or without worked solutions?

I've been tutoring mathematics at university level for over 10 years, and one of the more common requests from students is worked solutions for sheets of exercises. Most educators I've worked with ...
user avatar
-2 votes
1 answer
333 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 ...
user avatar
  • 605
1 vote
2 answers
233 views

Is there a book or Web site that explains how to use and teach the Singapore math block model?

I have been examining sites that illustrate the use of the block model for solving problems. I am an adult with a degree in math and I have an interest in seeing how math can be taught. From what I ...
user avatar
5 votes
1 answer
217 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 ...
user avatar
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 ...
user avatar
4 votes
2 answers
130 views

Textbooks with solutions and catering to different circumstances

Questions: Are we really taking students into account FULLY when writing textbooks for various areas? Also, are we being unintentionally elitist or dismissive when neglecting to take a more humble ...
user avatar
5 votes
0 answers
89 views

Objectives for group work in undergraduate pure maths

Whether we are preparing undergraduates for research in industry or academia effective collaboration is an important higher skill. I think there are two aspects to this in mathematics - thinking ...
user avatar
  • 151
16 votes
3 answers
3k views

How many of "The Seven Laws of Teaching" are still relevant for teaching maths today?

Wikipedia shows that in 1886 John Milton Gregory outlined his "The Seven Laws of Teaching"; asserting that a teacher should: Know thoroughly and familiarly the lesson you wish to teach; ...
user avatar
7 votes
7 answers
3k views

How do you handle the frustration of having to GRADE student exams / homework?

A math student may write very long and detailed answers, just because he or she does not know what to look for, for example in Geometry proofs. Or - a student may just write an arbitrary step without ...
user avatar
5 votes
2 answers
324 views

Why are most college level math textbooks black and white only?

Why are higher level math textbooks almost completely black and white? I can't think of any math textbooks on a subject more advanced than calculus that uses colors. Edited to add that the comments by ...
user avatar
  • 51
1 vote
2 answers
233 views

Which works better for learning 6 * 7 = 42: saying "six sevens are forty-two", or "six times seven equals forty-two"?

When memorizing and recalling the times table, I learned to say "six sevens are forty-two", and always wondered what it would be like to learn to say "six times seven equals forty-two&...
user avatar
2 votes
3 answers
235 views

Why do we typically only teach high-school students affine transformations of elementary functions?

A standard pre-calculus curriculum consists of the study of elementary functions: Polynomials, rational functions, (circular and hyperbolic) trigonometric functions, exponential functions, their ...
user avatar
9 votes
6 answers
393 views

Worth introducing a mandatory short module on $\LaTeX$ into a mathematics degree?

On Mathematics StackExchange for a particular instance, it is highly recommended that questioners mark up their questions using $\LaTeX$. A surprising number of mathematicians and student ...
user avatar
2 votes
0 answers
312 views

Which areas of maths should underperforming western countries focus on?

I am not sure which StackExchange to ask this question but I am interested in the relative underperformance of Western countries such as Australia, US, UK compared to other higher performing countries ...
user avatar
  • 151
3 votes
1 answer
212 views

Successor to School Mathematics Study Group (SMSG)

From reviews on Amazon of the various high school math texts by Mary Dolciani et al of the SMSG, I assume that there might be a successor to the approach (referred to as “the new math”) taken by the ...
user avatar
2 votes
1 answer
314 views

Are there any university programs that "supersize" calculus courses?

Most differential calculus courses begin with the theory (and analysis) of differentiation, followed by computations, and likewise integral calculus courses. That's a lot for a three credit course, ...
user avatar
  • 1,500
13 votes
3 answers
488 views

How to teach the Pythagorean theorem in a satisfying way to high school students?

I've been pretty dissatisfied with the way the Pythagorean theorem is usually taught, mainly for two reasons: The chosen proof feels like magic and I don't feel like I have a better understanding of ...
user avatar
  • 249
13 votes
3 answers
2k views

Finding the Balance in a Math Question (Teaching)

As we try to work and teach in the midst of this pandemic, some problems arise when making online math exams. My question is simple: What could be an interesting basic differentiation question such ...
user avatar
  • 241
2 votes
2 answers
215 views

How do we explain to a little child that a date in 2020 and a date in 2021 are not necessarily a year apart?

I talked with my friend on December 29 2020. Then I talked with him again on January 03, 2021. Q: What was the year when you last talked with your friend? A: 2021. Q: And what was the year the ...
user avatar
7 votes
2 answers
391 views

Do my students know elementary algebra; do they just use online calculators or external help; and is this ok?

Background I know the question in the title is very broad so I will try to explain it as succinctly as I can. Half my time is spent on as a researcher on didactics, while the other half is devoted to ...
user avatar
8 votes
7 answers
1k views

Advice on teaching abstract algebra and logic to high-school students

NOTE: This question will soon be duplicated, as I didn't make clear that I was a high school sophmore in the beginning. At first I thought it didn't matter, and somewhat arrogant to mention, but in ...
user avatar
11 votes
4 answers
572 views

How do you teach students about the concept of a proof?

I get this question a lot from new students who are taking their first proof-based math class. They are struggling because they don't have that fluency with proofs, to begin with. They don't know ...
user avatar
  • 231
1 vote
1 answer
79 views

Resources for Unit Rates

I am currently mentoring my little brother in mathematics. There is an issue with the pedagogy of unit rates. For example when given the following concept " 11.00 U.S. Dollars to 20 Planet X ...
user avatar
1 vote
0 answers
203 views

Do you avoid examples or test questions that showcase an algorithmic plug'n'chug approach?

If we accept that there's not much learning from doing the "same" questions, like find the derivative of $x^2$, and $x^3$, and $x^4$ due to the algorithmic way of how it's done, then what ...
user avatar
3 votes
2 answers
598 views

Teaching Mathematics to a Younger Sibling

I always wanted to teach my siblings mathematics, and one, ten years of age, is particularly eager. For the purposes of specializing recommendations, I will add he can use arithmetic up to ...
user avatar
0 votes
0 answers
273 views

Prerequisites to study Laplace Transform completely?

Hello to all the professors who read this. I'm an electrical engineering undergrad student. I wanted to ask for advice on what I should learn beforehand to fully grasp the Laplace transform. I also ...
user avatar
-2 votes
1 answer
63 views

Relational understanding for a specific topic

I want to aproach the undertanding of the trigonometric function based on the concept of relacional undertanding, but I have problems to came up with and problemic situation for it. I mean I don´t ...
user avatar
  • 101
1 vote
2 answers
262 views

How can I teach $\frac{300}{200}$ to 10 years old students while s\he knows canceling the zeroes rule?

I am teaching math to a 10 year old student. He learned that $$\frac{300}{100}=\require{cancel}\frac{3\cancel{00}}{1\cancel{00}}=3$$ and $$\frac{6000}{300}=\require{cancel}\frac{60\cancel{00}}{3\...
user avatar
  • 113
2 votes
0 answers
88 views

Math websites/apps for high school students

I am undergraduate math student who is interested in being a high school math teacher. I have been given an assignment to present to my class (for a total of about 20 minutes) a teaching tool or a ...
user avatar
  • 121
9 votes
1 answer
284 views

If a computer could be programmed to do a math test, then should those tests be changed?

Not only do calculators have solving capabilities, but some computer programs or websites also provide step-by-step solutions to questions (here is WolframAlpha's). Although I understand a logical ...
user avatar

1
2 3 4 5
9