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.
393
questions
7
votes
2answers
447 views
Important topics for first numerical methods course
I will be teaching a one-semester course on numerical methods at a liberal arts college. The students will be primarily math, physics, and engineering majors. Note that there is no computer science ...
4
votes
2answers
452 views
List of math competition problems by topic
I am working with a student who is very interested in math competitions, and I am teaching him Algebra I. I feel like doing competition problems related to a given topic is an excellent way to force ...
23
votes
2answers
1k views
Is Knuth's suggestion on teaching calculus a good idea?
Note: I myself am not a math educator, though I plan to be one someday.
In this letter, Donald Knuth suggests an alternate way of teaching calculus, based on big-O (introduced via a related big-A ...
16
votes
2answers
425 views
Nontraditional calculus recitations
I'm a math grad student, and next semester I start TAing a calculus class for the first time. We all know about the standard recitations: instructor gives short lecture on some more difficult topic ...
4
votes
1answer
941 views
Correct term to say that a number divides another number “evenly”?
This is something that has continued to bother me in general, and recently I had multiple occasions where saying something like "2 divides 14 evenly" has confused students, They expected the result to ...
3
votes
2answers
445 views
What kind of math will be mandatory in the future? [closed]
In mathematics education our primary focus tends to be how to approach the concepts we teach, taking for granted the choice of subjects that enter the syllabus. Traditionally, the way the standards ...
11
votes
8answers
562 views
How best to explain the logarithm to the mathematically naive?
Suppose you need to explain "What is a logarithm?" to an intelligent
but math-phobic adult (or a student well-prior to her introduction to logarithms).1
I have used base-$10$, saying that, essentially,...
14
votes
9answers
2k views
Teaching the History of Mathematics in High School
Is any time being spent on the history of mathematics in high school classes today?
Few observations as a student -
I had to discover Cantor many years after I was introduced to set theory.
I had ...
3
votes
2answers
192 views
How to teach mathematically about Fourier analysis and synthesis? [duplicate]
I have recently started teaching. It gets totally blank in front of the big crowd. Now, I am quite confused about how to start teaching the Fourier transform and Fourier series chapter.
I want ...
31
votes
14answers
8k views
Justifications for: Why learn mathematics?
I wonder how you teachers walk the line between justifying mathematics because of
its many—and sometimes surprising—applications, and justifying it as the study
of one of the great ...
12
votes
3answers
323 views
Resources on interdisciplinary curricula
As I try to incorporate more history, science, language, computing, and art into my math class I keep finding the lessons to be very successful and my students always seem to enjoy them. While I know ...
71
votes
6answers
6k views
Issues with “equals”, where does this come from and how do I combat it?
An issue I see with students a lot is abuse of the equals sign. For example, one problem asked "what is the degree of the polynomial: $\text{polynomial}$?", and I got answers like "$\text{polynomial}=...
8
votes
3answers
288 views
Simple question on radical expressions
Student question to me involved "standard" form of radical expressions. They already know what a radical in simplest form (no perfect square factors, no fractions, no radicals in denominator). My ...
25
votes
1answer
630 views
Is there a Piagetian age at which proofs can be comprehended?
I am wondering if there is literature on the developmental age
(pre-adolescent?, adolescent?) at which the notion of a "proof"
can be understood? I am less interested in mathematical proofs
and more ...
17
votes
3answers
720 views
What teaching strategies can we learn from this logic puzzle going viral?
By now I'm sure everyone has run into the math puzzle where Albert and Bernard try to deduce Cheryl's birthday, which is all over social media, and even traditional media! If you don't know what I'm ...
10
votes
4answers
794 views
Examples of Mathematical Beauty in School Mathematics
Various branches of mathematics have mathematical beauty. Some of this are visual, such as the mandelbrot set, while others are logically sublime, such as the recursive simplicities of peano ...
7
votes
1answer
183 views
Math counterexamples site
Just wanted to share the link to a mathematical counterexamples site that I develop: Math Counterexamples. Any idea for improvement is more than welcome.
On the way the site looks like, on good ideas ...
6
votes
1answer
310 views
Who is E. Kim Nebeuts?
I just learned the name E. Kim Nebeuts from the quote at the beginning of Joseph O'Rourke's answer to this question. Curious, I google searched. All I saw on the first 2 pages of results was things ...
11
votes
0answers
301 views
Books on meta-cognition that would be relevant for those involved in mathematics?
In 1992 Schoenfeld wrote an excellent "review" of (among other things) metacognition as it applies to mathematics: whether from the perspective of a student, or a teacher.
Metacognition, as quoted ...
17
votes
5answers
2k views
How to convince students of the integral identity $\int_0^af(x)dx=\int_0^af(a-x)dx$?
A common identity in integration is $\int_0^af(x)dx=\int_0^af(a-x)dx$.
The steps to prove it (algebraically, ignoring the geometric method) are as follows.
Let $u=a-x$ so $dx=-du$.
$\int_0^af(a-x)...
5
votes
2answers
108 views
Teaching range as a measure of spread
This was originally part of a question on averages but it was suggested to me that it should be a question in itself. If people think the question is too similar it can be deleted.
I'll link the ...
8
votes
3answers
2k views
How to Teach Averages (Arithmetic Mean) to a Teenager?
Suppose you had to teach averages to a teenager. For arguments sake let the question be;
Find the mean of $2, 3, 4, 7$
Of course the simple answer is $\frac{2+3+4+7}{4}=4$ but in my experience the ...
17
votes
3answers
1k views
How to help students bridge the gap between highschool and university mathematics?
Mathematics at highschools is quite different from that in universities.
Instead of calculating numbers and finding solutions to specific problems, freshmen end up proving theorems and figuring out ...
8
votes
0answers
107 views
3-D printing of formulas encoded in LaTex for the visually impaired?
There is software available on the Net for 3-D printing of math expressions encoded in LaTex. What such technology is available off-the-shelf for the visually impaired to learn mathematics? And, ...
7
votes
7answers
3k views
Mathematics in real life
I am interested in examples of use of mathematics in real life situations.
To be more precise, something that could be presented to undergraduate students in order to motivate them for studying maths.
...
11
votes
3answers
508 views
Fighting math phobia with history
After years of experience in some area of expertise, you can easily forget how difficult it can be for the uninitiated to grasp some fundamental concepts, and, indeed, people often edit out of their ...
12
votes
4answers
358 views
How do I get them to appreciate learning a new way of doing that thing?
A typical student mistake
You see this:
$$\frac{15}{4\sqrt{15}}=\frac{15}{4\sqrt{15}}\cdot\frac{\sqrt{15}}{\sqrt{15}}=\frac{15\sqrt{15}}{4\cdot15}=\frac{15\sqrt{15}}{120}.$$
You can see that the ...
13
votes
1answer
373 views
Students blogging on math
Has anyone had their students (high school and beyond) put expositions of math problems/topics/projects on a class blog to be critiqued by other students and revised on-the-fly to provide some ...
2
votes
2answers
144 views
AB 86 Basic Skills Mathematics Courses at the Community College Level [closed]
I am a basic skills community college math instructor here in Los Angeles. This Spring is a very exciting time for our college. There are several campus initiatives taking place. Among them is the ...
11
votes
1answer
368 views
Use of symbolic math apps in teaching
Symbolic math apps, such as Mathcad, are extremely useful in doing exploratory/experimental math. I've frequently used it to run numerical checks on mathematical expressions I've derived; put up quick ...
12
votes
7answers
921 views
Name the heuristic: exploiting the legitimacy of the questioner
As a child, I made frequent use of a particular 'trick' in order to make short work of many different problems. The general form is to be presented a question which wants a definite (numerical) answer,...
11
votes
6answers
1k views
How can I convince students that Fourier series are useful?
Main question: Calculating the coefficients of a Fourier series can be difficult and time-consuming. How might a student be motivated/convinced to go through these (potentially tedious) details? Are ...
9
votes
1answer
174 views
Teaching background skills together with specific concepts
There are a number of skills needed in maths (I'm teaching undergraduate pure maths) that are not really topics on their own, such as interpreting a definition, taking negation, or giving counter-...
11
votes
2answers
589 views
advantage of handwritten materials for course documents
I am curious, is anyone aware of a study which determines the advantage of typed vs. handwritten material in mathematics?
Of course, ideally, we would compare the best of both worlds. Say a ...
8
votes
2answers
230 views
Explaining Closure to “Basic” Algebra 2 Students
I am currently introducing function operations to my basic level Algebra students and it has been semi-disastrous. The biggest problem I have with them is the notation that
$$(f+g)(x)=f(x)+g(x)$$
I ...
8
votes
2answers
541 views
Is non-standard notation useful when teaching new concepts?
I'm learning about groups and $a^n$ suddenly doesn't mean exponentiation anymore, but repetition of $\underbrace{a\circ a\circ \cdots\circ a}_n$. In some sense I think it would be useful to learn $a\!\...
8
votes
5answers
958 views
Teaching students to write the “invisible” ones
some of my students refer to there being an invisible $-1$ in front of the expression $-(x + 4)$ or in the exponent of $x$. While it is not phrased mathematically, I am ok with them saying this ...
12
votes
1answer
573 views
Language to Distinguish Between Variables and Arbitrary Constants
Today in second semester calculus, I found myself stumbling a bit to provide a natural-sounding explanation for all the letters involved in the expression
$$
\lim_{t \rightarrow \infty} \int_1^t \frac{...
9
votes
1answer
223 views
What are the best apps for students to discuss math problems?
I am looking for a good app that enables students to chat with one another in order to work on mathematics problems. The idea is that, in the old days, students would work over the phone to solve ...
5
votes
1answer
242 views
Exam Writing: Combining Topics on Exams in New Ways
The Question: Does combining two or more topics into one question on a mathematics examination when the topics have not notably been combined in the course lecture, homework, or other assessments ...
10
votes
2answers
410 views
How to differentiate between mathematical skills and understanding of mathematical concepts?
How would my Colleagues here on Math Educators differentiate between mathematical skills and understanding of mathematical concepts?
I'm a community college instructor and high school instructor ...
8
votes
5answers
650 views
What are some common fallacies students make when they learn $X$ concept?
What are some common mistakes students often make, which may seem logical at first?
I'm a student myself, but I'm curious of what some of the most frequent mistakes which happens. I'm thinking of ...
12
votes
8answers
2k views
What things should one know in order to enjoy their undergraduate degree?
From looking at undergraduate mathematics programmes it's quite apparent that mathematics degrees are demanding, one could even say the work load is gruelling. However I'm certain that there are ...
13
votes
5answers
453 views
Hands on activities for a college history of mathematics course
I will be teaching a course in history of mathematics to juniors/seniors who are math and math education majors, many future school teachers. It should include highlights from antiquity to early 19-th ...
6
votes
0answers
177 views
Is there a name for 'simple' two-input-one-output word problems?
Andy has 4 apples, and then eats 2. How many does he have left?
Beth drives for 3 hours at 80 km/h. How far did she go?
Carl, Debbie and Earl earned $30 together shoveling driveways. How much does ...
4
votes
2answers
223 views
Mathematics curriculum and book titles to study mathematical analysis for post-grad studies
I am an engineering student trying to study mathematical analysis because it will help me in my post graduate studies.
My problem is that when I searched the internet I found that some university ...
15
votes
1answer
267 views
Order of Topics in Introductory Proofs Class
Beginning next semester I am teaching a course in proofs and mathematical problem solving at my local university. For some background, the university is primarily a commuter university and the ...
12
votes
3answers
4k views
What math courses should be taught to undergrad electrical engineers: a 40 years update
I was browsing IEEE xplore the other day and found this gem called "What Mathematics Courses Should an Electrical Engineer Take? A Report on the National Study of Mathematics Requirements for ...
7
votes
0answers
302 views
Links between mathematical folklore and educational success
I would like to ask if, in the research field of mathematical education, some work has been done to investigate the relationship between 1) and 2):
mathematical education and student motivation
the ...
3
votes
1answer
266 views
I want to learn math from the beginning [closed]
I finished high school 2 years ago and now I'm stuck in a university in Turkey. I am interested in learning precalculus, discrete mathematics, physics and chemistry.
Question: I need to learn math ...
