Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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1500 questions
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votes
6 answers

Is patching up a student's poor solution better than providing a good solution?

A student benefits from their attempt at a solution or proof being checked by the teacher. My own view is that, if the student's work is poor, it is best just to provide a model solution or proof in its place. In general, I think that bad work is…
John Bentin
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Grading homework problems on completion vs. correctness, and overall grading

I taught Calculus 2 at my institution the past two semesters and several students have left comments in their course evaluations that advocate grading homework problems based on whether they were completed, not whether they were correct. For…
Brendan W. Sullivan
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7 answers

Introductory Books easier than Dover

I'm looking to books introducing different topics of math with fun for my son, to give him a taste of different areas. My son roughly understands A-level topics until single variable calculus (of course, need exercise to get familiar to all the…
athos
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7 answers

Does induction really avoid proving an infinite number of claims?

I am teaching calculus $1$ this semester, and I saw the following motivation for using induction by another teacher: Since we can't go over "manually proving" all claims $1,2,\ldots$ and actually get to the finish line in a finite time, we use…
Asaf Shachar
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6 answers

Why is a Calculus III student more likely to solve this problem?

Consider this elementary problem: Define an operation $*$ between integers as follows: $a*b=ab-a+b$. Solve the equation $4*x=36$. If we give this problem to Pre-Calculus and Calculus III students (assuming that none of them have seen this type of…
Mahdi Majidi-Zolbanin
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10 answers

Can it be defended that $\sqrt 4$ is both $2$ and $-2$ (and likewise for general square roots)?

Over the past one or two years, at least two different teachers have told my children that $\sqrt 4$ is $2$ or $-2.$ I don't think this is useful, but if you want to define $\sqrt x$ as the set of solutions of $y^2 = x$, I guess you could. Of course…
doetoe
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8 answers

Why does math need to be practiced and exercised, when L1 Linguistic Competence is subconscious?

If 'linguistic knowledge is largely subconscious'3, why isn't math? Most math instructors sermonize solving exercises and problems. But a student challenged why students need practice — because most students and adults don't need to know, or…
user20427
12
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14 answers

Examples of relations that are not functions

When teaching functions, one key aspect of the definition of a function is the fact that each input is assigned exactly one output. I always felt that the "exactly one" part is confusing to students because it seems to be "the default", and I have a…
Jasper
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7 answers

What are best practices for building a dedicated space for mathematics majors?

The math department at my institution (a private, four-year college with a total enrollment of about 4000) is in the process of brainstorming about a dedicated study/community space for our math majors (we have about 20-25 total). We would like to…
AegisCruiser
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12 answers

How should I grade true-or-false questions if the student's writing is unclear?

See the attached image: I am having a difficult time grading this paper as I am not sure if the student intentionally wrote the answers in such a way that each answer looks like both "T" (or "t") and "F" (or "f") or if it is just his normal style…
Zuriel
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9 answers

A game that is between Noughts and Crosses and Sprouts for complexity?

I love the game of Sprouts but unfortunately at the moment it seems to be a bit too complex for the young student I have introduced to it. She already knows noughts and crosses (also called Tictactoe). I need a game that is more complex than…
ool
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6 answers

Should my high school students use tablets or conventional calculators?

Background: I'm teaching mathematics at a high school with emphasis on mathematics and natural sciences. Usually, pupils at our school have to buy a calculator (TI-89) and we work with those during class and sometimes they are allowed to use them…
Huy
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2 answers

Assigning students to write solution sets

Next year, I will be teaching a very challenging second year "multivariable calculus and calculus on manifolds" course, and will assign a large number of difficult problem sets. I am thinking of assigning students to go back to problems where they…
David E Speyer
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2 answers

How to encourage students to discuss with themselves in a remote teaching environment?

I am teaching in a hybrid mode (zoom+classroom) this semester. I would like to encourage collaboration between students. So I divided them into pairs and asked them to establish a communication channel between pairs, using whatever apps they…
user11702
12
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6 answers

Dealing with disagreeable students and not compromising

I act as a tutor sometimes for students who are self-studying undergraduate-level math. Most of the students have already earned an undergraduate degree in something and some of the students are PhDs from other STEM fields. How do I deal with…
E2R0NS
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