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.
319 questions
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Flow diagrams and summarizing strategies in proof-computation courses: good or bad for learning? Unsuitable for Inquiry-based learning?
For concreteness lets keep our discussion to calculus courses where there is a balance of proof and computations (computing limits but also doing epsilon-delta proofs)
I can understand that in more ...
4
votes
2answers
99 views
What are some suggestions fo teaching statistics concepts to struggling college students?
I'm a private math tutor. I'm fairly new at this, and this semester is the first time I've been tutoring for a statistics class at a community college. I enjoy experimenting and learning about ways to ...
0
votes
0answers
103 views
why did common core remove so many topics from Algebra II?
I don't understand why common core: High School Algebra II (NYC, NY, USA) removed so many topics. I think these ideas are pretty important and useful (especially since a handful of these topics come ...
0
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0answers
79 views
Algebra I common core is too short? [closed]
I feel that the common core: High School Algebra I (NYC, NY, USA) curriculum is too short and tedious. For one, it can be completed in 5 months even with a lot of prolonging. For me, there isn't a ...
0
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1answer
97 views
Verifying Simple Expression Equivalence in a Spreadsheet
For simple expressions with easily derived canonical forms (eg polynomials and simple rational expressions), is there a way to leverage existing tools to verify that two expressions are equal when ...
4
votes
1answer
137 views
Is it feasible to expose undergraduates to a “map”-centric point of view early on?
Question: Would it be feasible to teach undergraduate math students a "map"-centric view early on? If so, how early on?
Now that I'm preparing for a phd program, I'm also reflecting on my ...
2
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1answer
128 views
Existing Tools for Math Expression Equivalence Logic
Note - this question was posted here and garnered some decent replies before it was closed as off-topic in Stack Overflow.
Online systems, such as ALEKS, Cengage's WebAssign, and even Khan Academy ...
6
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2answers
225 views
On fractions and least common multiple
At least in my country, the explanation of the basic operations over rational numbers is done very near to the concept of primer number, prime factorization and calculus of least common multiple. In ...
4
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2answers
155 views
Why bother completing the square to find the minimum/maximum of a quadratic function?
Given a question like
Find the coordinates of the minimum point on the curve $y=3x^2+2x+9$.
students are often taught to solve this by completing the square.
The class I am currently teaching ...
10
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3answers
195 views
Quizzes (with questions known in advance) instead of homework in a graduate mathematics class. Good Idea or Bad Idea? Pros and Cons?
I'm teaching a graduate course in mathematics next semester. I'm planning to have a midterm and a final exam. But I'm thinking about having weekly (or once-every-two-weeks) in-class quizzes instead of ...
4
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0answers
90 views
Why is problem solving important for all of us?
I am looking for academic references related to this questions. In fact, I need to write a paper which shows the importance of problem-solving approach for everyone. Certainly, this should include ...
48
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13answers
8k views
How to get past the “mystique” of Maths
This question is primarily discussing maths education for adult learners, on courses teaching engineering mathematics at an undergraduate level. These students generally never set out specifically to ...
9
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1answer
229 views
How to deal with poor students who don't take notes?
I want to set the context for me asking this question before stating it properly.
I teach at college/university level. This question deals with first-year students, fresh from school. So think ...
4
votes
2answers
101 views
Exposure to Algebra 2/Calculus Under Time Constraints
As part of a free summer enrichment program for highly-motivated high school students, I need to plan eight hour-long lessons for mini-courses titled as "Algebra 2" and "Calculus" separately. Despite ...
2
votes
2answers
118 views
Ideas for high-school proof class?
I have a math degree and have been hired to teach a proof class at a summer program. Our goal is to help the students learn the material they need for school (they take an algebra class separately) ...
14
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3answers
338 views
What to do if all students lack prerequisites?
I am teaching a calculus class for business this summer (6 students) and all of them do not have the math background needed for the class. We are supposed to cover derivatives and integrals, but they ...
5
votes
2answers
159 views
How to explain NP-hardness and NP-completeness to students
Computer science is becoming more and more important for mathematicians nowadays. Terms like big data, algorithm, artificial intelligence and others are frequently on the news. Many mathematical ...
13
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2answers
308 views
Is higher-math pedagogy responding properly to Wolfram Alpha's existence?
Is the current state of math teaching in undergrad college courses struggling with the availability of easy cheap access to Wolfram Alpha?
The homework problem below, one of 40 assigned from one ...
6
votes
2answers
146 views
Effective Assessment that's Easy to Grade
A colleague of mine will be teaching 3 classes (pre-calculus and two sections of calculus, at the university level) next semester with an additional grader in only one of those classes (pre-calculus). ...
15
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13answers
2k views
Mnemonics for some properties in mathematics
I am looking for various mnemonics which help students to remember some important properties or theorems. Very often students confuse signs or relations such as $\leq$ and $\geq$ in some expressions. ...
1
vote
3answers
154 views
when should we teach basic complex algebra?
I am teaching Differential Equations this semester. The pre-req is Calculus II, not even Multivariable Calculus. I made my peace with that, can't fight with the big-shots of the department. So, I have ...
11
votes
4answers
282 views
How would you introduce Frullani integral to students?
Some integration techniques are just "tricks", while some integrals are analytically significant in that they connect different fields of math or they embody higher level concepts.
In the commonly ...
13
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3answers
195 views
Does education research support the idea that answer keys are bad?
I am a physics grad student and several of my professors have stated that they are against the idea of posting answer keys (i.e., worked solutions) for homework and/or tests (after the assignment has ...
67
votes
15answers
18k views
What's a replacement for “married couples” in combinatorics problems?
Many counting problems start with the assumption that we have a certain number of men and women or a certain number of couples, with the assumption (often unstated) being that that gender is binary (...
13
votes
4answers
255 views
Pedagogical advice/articles for graduate student teaching assistants
Are there any good pedagogical resources or articles that you would recommend to math graduate student teaching assistants (TAs)? Is there any sweeping advice that you would give a TA to improve their ...
18
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5answers
636 views
Inability to work with an arbitrary mathematical object
This question is motivated by student responses to homework and quiz problems I have recently posed in an undergraduate real analysis course. I will share some examples and observations first, to ...
12
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1answer
199 views
How to write proofs on the board in the classroom
I'm teaching an introductory analysis course, and I am seeking some feedback on how proofs should be written on the board in class in order to maximize learning. I realize that there is an opinion-...
27
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10answers
8k views
How should a student's inefficient calculation be pointed out?
One time I watched a student solve the equation $0 = (x-2)^2-9$ for $x$ like this.
$$\begin{align*}
0 &= (x-2)^2-9
\\0 &= (x^2-4x+4)-9
\\0 &= x^2-4x-5
\\0 &= (x+1)(x-...
10
votes
3answers
272 views
How to teach a student algebra who misses too much previous knowledge?
I am now tutoring a student in Grade 9, who falls behind in math study. He lacks the basic understanding of operations and inverse operations, and have trouble dealing with negative numbers and ...
10
votes
2answers
119 views
Cognitive demands of a mathematical task
I'm looking for a theoretical framework to classify a task based on its cognitive demand.
I only have the Smith and Stein's (1998) proposal and PISA framework such as my principal references. In ...
4
votes
3answers
209 views
When discussing inverse functions, how can our notation and methods reinforce student understanding?
Yesterday in my precalculus class, I decided to teach students how to find the formula for an inverse function in a new way (to me).
In this curriculum, they have already used the notation $f^{-1}(x)$...
0
votes
3answers
136 views
Advice for Community College Interview Statistics Demonstration
In a few weeks i'll be interviewing at a community college in California for a tenured Mathematics position. They've asked me to present the following in only 12 minutes. I'd appreciate any ...
5
votes
2answers
113 views
Course of action with 13 year old with weak sense of number and operations
One of my private students is a 13year old girl who started school at age 5 (instead of the regular 6, in my country).
Testimony from parents show she had no sense of number at the time, would not ...
3
votes
0answers
62 views
Research on how to teach math to children - what proven approaches are there to teaching math effectively? [closed]
I posted a related question on the Math.SE, but was directed here where I'm asking an similar but different question.
I've been tasked with helping to redesign a math curriculum for an enrichment ...
2
votes
0answers
191 views
Introduction of the power set as a collection of *labels* or *names* for subsets
The way that naïve set theory is usually presented in undergraduate education is via very concrete examples of sets, often involving non-mathematical elements. When power sets are treated, having a ...
4
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0answers
162 views
Mathematics Self-Efficacy Questionnaire
Good Day!
I need help in finding a free validated and reliable tool in assessing (elementary or high school) students' Mathematics Self-Efficacy.
9
votes
4answers
356 views
Surrounding a subject and strangling it to death versus concentrating on the main point
Standard calculus textbooks begin by introducing limits, including
limits of a fraction as the numerator and denominator approach $0,$
limits of a fraction as the numerator and denominator approach $\...
9
votes
4answers
634 views
May we permit identities to be established by equivalent equations?
A trigonometry text like Sullivan's Algebra & Trigonometry often has a prohibition like this (Sec. 7.3):
WARNING: Be careful not to handle identities to be established as if they were ...
6
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1answer
145 views
Easy and good book on combinatorial problems
I am searching for a book on combinatorics and/or mathematical puzzles for very beginners in easy English. The book should not contain detail mathematical expressions, will contain easy understanding ...
13
votes
7answers
680 views
Problem “seeing” the perimeter of a figure
I was helping a home-schooled student with her homework when we came upon several images of figures that we were supposed to find the perimeter of. In several of the figures, some of the lengths were ...
6
votes
3answers
276 views
What is the ULTIMATE Calculus syllabus
After such amazing answers I got here for a related question (link at the end if someone still wants to share with me their views)...
Here is the concept:
If you were to create the ULTIMATE Calculus ...
2
votes
0answers
74 views
what is the standard subdivision or classification of calculus related rates problems?
I am working on a project where I have to group/classify calculus problems. Now with most the calculus topics, it's usually obvious how it's divided in various textbooks, but when it comes to related ...
26
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9answers
7k views
Can mathematics be learned by ONLY solving problems?
Here is the concept:
Student is presented with a problem. He/she may not even understand what is being asked, or may attempt.
Students reads a solution to the problem. In it there may be ...
6
votes
2answers
228 views
How can I improve my problem solving/critical thinking skills and learn higher math?
I'm a rising sophomore in high school. So far, I've taken Algebra One, Two, and Geometry in school. I want to learn higher math such as precalculus/trigonometry, calculus, linear algebra, and more, so ...
7
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0answers
115 views
How can I deal with the time pressure of teaching a short course?
I am an undergraduate applied math student. In about a month, I will be teaching two nine-hour math courses (one precalculus, one calculus) to a small group of motivated high school students. My broad ...
3
votes
3answers
1k views
Difference between whole numbers and decimal numbers
Clearly, whole numbers specify how many elements there are in a collection while decimal numbers specify how much of a substance there is in a lump---but only after a unit of that substance has been ...
18
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3answers
499 views
Constructive refutation of student misconception
Although @Gareth Shepherd recently posted Addressing fundamental math errors close to the issue, I experienced my problem of misunderstanding in class, where two good K10 students were asked to ...
6
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4answers
280 views
Calculus 3 Teaching Demonstration for Community College Teaching Position
Colleagues. In a few weeks I will be interviewed for a position at a community college. I got selected for an interview and the teaching demonstration is as follows:
Assume you are teaching a ...
6
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2answers
156 views
How to introduce Wilson's Theorem?
What is the most motivating way to introduce Wilson’s Theorem?
Why is Wilson’s theorem useful? With Fermat’s little Theorem we can say that working with residue 1 modulo prime p makes life easier ...
6
votes
2answers
190 views
How to catch students from different subjects' interest to math?
I have just started to teach Calculus to freshmans and sophomores who study non-mathematical subjects, e.g., international relations, psychology. They have to take few mathematics classes -including ...
