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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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.
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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,...
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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 ...
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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-...
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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 ...
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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 ...
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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\!\...
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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 ...
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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{...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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How to effectively teach pseudocode
I'm helping with an algorithms course next term. I've taught intro programming courses and seminars, but never intro algorithms. I've spoken with previous TAs and instructors, and one of the biggest ...
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When are non-homogeneous sets first encountered by students?
My 5-year-old son recently brought home (from kindergarten) a worksheet that he had done at school. 6 boxes were given. In one box were 3 kites, in another, 2 bears, in another 8 drums, and so on. ...
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How can inquiry-based learning be used in a college classroom?
I am not an expert on inquiry-based learning, but it seems to be a useful teaching technique to use in smaller classrooms. Since many college math courses are quite huge, I was wondering how inquiry-...
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Statistics Class Held in a Computer Lab
I'm looking into holding my basic statistics class in a computer lab in the future to avoid a lot of the by-hand computing that happens in statistics classes. For example, very few students get ...
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Teaching how to read and translate word problems
High school students have a lot of trouble understanding word problems, and I don't know how to help them.
It's been too long since I've had trouble understanding usual word problems, so when I read ...
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In introductory statistics hypothesis testing, why not always use P-values?
A test statistic is a measure of significance of a data set with respect to a claim.
My statistics textbook is insistent that the students should be able to interpret the test statistic in two ...
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How to read better?
In this semester I've realized that many of the problems (my) students have can be solved by reading better. The most recent example I've encountered was in the last exam; I asked them the following:
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Helping students use constructions in geometry
I work as a teaching assistant in a high school and geometry gives most students headaches.
I emphasize understanding the problem by constructing lines and using elementary properties to arrive at the ...
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How do I help my student understand concepts such as "$x$ divided by $x$"?
I am tutoring a high school level student (who is currently at the level of being introduced to anti derivatives) who has quite some trouble with grasping mathematics.
We have been making good ...
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What is a good answer to the question "Which logic is better?"
In my undergraduate logic courses I introduce several types of logics to my students including propositional, first order, second order, intuitionistic and fuzzy logics and it usually happens that ...
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Real analysis: why usually first limits of sequences and then limits of functions?
I notice that all of the analysis books that I've studied start from dealing with limits of sequences and only then move on to limits of functions.
Does this kind of approach have any particular ...
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Placement tests for middle school math
Our district has changed its approach to placing students in grades 6 and 7 math classes. Students considered for placement above grade level must now take a test composed of problems drawn from the ...
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How to teach addition, subtraction, multiplication and division of binary numbers? Are there any activities that can be recommended?
I want to make the binary class fun for my students, and I would like to apply activities to make it easier.
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Learning Mathematics with the aid of spaced repetition systems
I am currently self-studying, so I learn using a textbook which I work through in a linear fashion. As I am introduced to new concepts I ask myself questions and I attempt to answer these questions ...
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Mathematics and the hermeneutic circle
Many students, teachers and parents view problems as confrontational. Many students develop a self concept in mathematics based on failed attempts to easily win such confrontations.
This leads me to ...
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Calculation versus writing in mathematics
Writing mathematics is an important activity of the mathematician. In trying to write one's mathematics, one finds ways to balance intuition and rigor and to efficiently communicate concepts and ideas ...
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Topics that should be in an undergraduate math programme
According to your experience as students and professors, what are (and why) the courses that should be part of a math undergraduate degree, but that are missing in most institutions?
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Solving problems
I have been telling my students to try to solve the problems on their as much as they can. As I tell them, it will help them be better at solving and understanding problems of Mathematics. This thing ...
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Focusing on definitions for understanding in secondary education
I am a teaching assistant at a school. My job is mostly to help them solve problems given by their teachers. Students are at high school level. I assume the curriculum In Brazil is similar to the one ...
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Promoting intuition (for undergraduate students): visual thinking, geometic approaches, etc. in the classroom
Note: This question is ment to extend the scope of some related questions of mine. I would appreciate very much any suggestion to improve the way the question is posed.
I would like to ask what is -- ...
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Immersive attention when learning mathematics
In Jennifer Roberts' article The Power of Patience: Teaching students the value of deceleration and immersive attention she talks about intentionally slowing down to contemplate deeply a work of art. ...
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Pedagogy, mathematics and Dieudonné's Foundations of Modern Analysis
I've heard from a friend of mine that Dieudonné's Foundations of Modern Analysis is "painful reading" and "a little outdated"; however, my teacher actually suggested it to me, describing it as a "...
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Teaching number theory: geometric approach
Are there any books that are substantially based on a geometric approach to explain topics in number theory (elementary and more advanced)?
If so, is such approach -- judging from your teaching (or ...
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Books that every aspirant mathematician should read
I am a student and I would love to become a research mathematician one day.
So I would like to ask you---experts in mathematics but also in
education---what are some influential ($\star$) books that ...
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