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.
432
questions
-4
votes
2
answers
98
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 ...
0
votes
1
answer
76
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 ...
0
votes
3
answers
160
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 ...
3
votes
1
answer
74
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?
- 834
9
votes
1
answer
296
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 ...
- 155
4
votes
0
answers
142
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 ...
- 141
6
votes
2
answers
164
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;...
- 579
3
votes
3
answers
812
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) ...
- 155
4
votes
1
answer
232
views
Is there a widely respected early childhood math curriculum?
If it's a good idea to work on reading and language from early childhood, I'd bet that it's a good idea to work on math and quantities too.
I have an 18 month old. I've pretty much been winging it ...
- 579
0
votes
6
answers
831
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 ...
- 25
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 ...
- 777
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 ...
- 911
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 $C(f,g) = f∘g$ ...
- 363
5
votes
0
answers
105
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 ...
- 359
6
votes
4
answers
752
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 ...
- 1,225
24
votes
2
answers
4k
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 ...
- 653
2
votes
1
answer
187
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.
...
- 1,225
6
votes
0
answers
106
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 ...
- 331
1
vote
0
answers
370
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 ...
user155
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 ...
user155
16
votes
3
answers
462
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 ...
- 331
3
votes
2
answers
148
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 ...
- 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 ...
- 10k
-6
votes
1
answer
122
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)
...
5
votes
2
answers
237
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 ...
- 51
8
votes
4
answers
652
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 &...
- 309
-4
votes
1
answer
212
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 ...
- 564
3
votes
2
answers
197
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 ...
- 474
12
votes
0
answers
153
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 ...
- 221
-2
votes
1
answer
341
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 ...
- 605
1
vote
2
answers
242
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 ...
- 147
5
votes
1
answer
221
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 ...
- 233
7
votes
5
answers
444
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 ...
- 233
4
votes
2
answers
132
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 ...
- 41
5
votes
0
answers
93
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 ...
- 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; ...
- 163
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 ...
- 605
5
votes
2
answers
349
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 ...
- 51
1
vote
2
answers
247
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&...
2
votes
3
answers
243
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 ...
- 121
9
votes
6
answers
406
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 ...
- 911
2
votes
0
answers
313
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 ...
- 151
3
votes
1
answer
241
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 ...
- 51
2
votes
1
answer
349
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, ...
- 1,512
13
votes
3
answers
531
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 ...
- 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 ...
- 241
2
votes
2
answers
218
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 ...
- 1,224
6
votes
2
answers
400
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 ...
- 247
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 ...
- 385
11
votes
4
answers
613
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 ...
- 231