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for questions on general considerations and problems of teaching mathematics, i.e., issues specific to teaching mathematics yet relevant to various contexts and courses.

2
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1answer
62 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
votes
2answers
206 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
votes
2answers
130 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 ...
9
votes
3answers
185 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
votes
0answers
83 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
votes
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
votes
1answer
216 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
98 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
115 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
votes
3answers
326 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
157 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 ...
12
votes
2answers
303 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
138 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
votes
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
147 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
280 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
votes
3answers
190 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 ...
65
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
250 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
votes
5answers
625 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
votes
1answer
195 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
votes
11answers
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
267 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
118 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
207 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
134 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
61 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
votes
0answers
161 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
353 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
630 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
votes
1answer
144 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
659 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
273 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
73 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
votes
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
218 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
votes
0answers
113 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
votes
3answers
489 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
votes
4answers
278 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
votes
2answers
154 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
189 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 ...
4
votes
1answer
143 views

Erasing students' work - etiquette/guidelines?

What are some guidelines on erasing students' work such as on a chalkboard/whiteboard in a classroom or on paper in a private tutorial class? Usually this is for the parts of maths that involves ...
11
votes
1answer
497 views

How does Project Euler come up with such good problems so rapidly?

Ever since I learned about Project Euler, I have been astonished and wondering about how Colin Hughes (the creator of Project Euler) manages to come up with such problems at such a rapid pace (once a ...
7
votes
1answer
184 views

What is the pedagogical justification and history for using mnemonics to teach order of operations?

There was a recent question/rant about why so many are still using the PEMDAS/BODMAS/BIDMAS/BEDMAS mnemonics to teach order of operations. The question is likely to be deleted at some point, but there ...
3
votes
3answers
404 views

Mathematical difficulty

There exist a large number of reasons why "mathematics is difficult". If one exclude "subjective reasons" such as: "math anxiety, math fear,..." and education factors as: "inadapted math ...
16
votes
3answers
308 views

How to invite humanities students to study mathematics?

This question comes from the perspective of an undergraduate math major who feels that much (although not all) of the mathematical discipline is a liberal art, rather than a science, and should be ...
26
votes
4answers
615 views

The Undergraduate Responsibility Gradient

We tell undergraduate students that they should study two to three hours for every hour they spend in class. We know that many students don't follow through with this nearly to the degree that they ...