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.
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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 ...
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6
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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 ...
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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 ...
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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 ...
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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 $C(f,g) = f∘g$ ...
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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 ...
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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 ...
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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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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.
...
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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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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 ...
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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 ...
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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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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 ...
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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 ...
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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)
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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 ...
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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 &...
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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 ...
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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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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 ...
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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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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 ...
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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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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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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 ...
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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 ...
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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; ...
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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 ...
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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 ...
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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&...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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\...
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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 ...
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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 ...
user13544