Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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1500 questions
17
votes
6 answers

Should Eisenstein’s criterion be taught in high-school?

Eisenstein’s criterion: If you have a polynomial with integer coefficients (and a non-zero constant term) and there’s some prime number $p$ such that $p$ goes into every coefficient but not the first (or last) and $p^2$ doesn't go into the last…
msh210
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5 answers

How much memorization should be required in a first-semester calculus course?

To me, first-semester calculus is a "big ideas" course, whereas second-semester calculus is about a certain bag of tricks. How much memorization is it appropriate to require in the first semester? If one gives open-notes and/or open-book exams, then…
user507
17
votes
9 answers

How to convince my student that this is an Identity : $\sec^2x-\tan^2x=1$?

I taught three basic trigonometric identities. One of my 9th grade students asked: How can we say $$\sec^2x-\tan^2x=1$$ is an identity since when we plug in $x=\frac{\pi}{2}$ the identity fails which creates an ambiguity for the definition of an…
Ekaveera Gouribhatla
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17
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3 answers

How to use false theorems or proofs?

I would like students to be critical and not believe that every proof they see is correct. Lecturers make mistakes and students should not think: "That must be a valid argument/proof/syntax because it was given in the lectures/lecture notes/book." I…
Joonas Ilmavirta
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5 answers

SMSG: Did any school districts actual teach the curriculum as planned and what were the results for the teachers and students?

I was introduced to the SMSG math curriculum at Topeka High School between 1965 and 1966. my recollection (somewhat defective for medical reasons) was that the Topeka (KS) school system rolled the curriculum out across all grade levels the same…
user5565
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16
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2 answers

Logic in symbols or words

Making precise logical statements is an important part of teaching and learning mathematics. There are many ways to write such statements, and let me divide them into two main types1: writing in symbols ($\forall,\exists,\iff,\dots$) or writing in…
Joonas Ilmavirta
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16
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2 answers

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 from class, then spends the rest of class solving…
user141592
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16
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7 answers

Where can I find realistic data for college-level elementary statistics problems?

I'm creating a large number of practice problems for my statistics students. These problems are for an elementary stats course where students: measure central tendency measure dispersion use linear regression to extrapolate and interpolate…
futurebird
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16
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5 answers

Is Peer Instruction suited to mathematics classroom?

Peer Instruction is a method developed by Eric Mazur in Harvard, designed with a student-centered approach in mind. In a nutshell, the core of the method is that when presented with a problem, students who readily overcome the obstacles necessary to…
Mark Fantini
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16
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1 answer

How do you fix a broken course plan?

The most terrifying thing about teaching my own class is 'do I actually know enough to effectively teach students?' I know this is anxiety brought on by a lack of experience but finding the tools to deal with crisis moments before they occur is key…
David G
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16
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3 answers

What are good survey questions for statistics students to ask each other in class?

I think this is a nontrivial question, because to avoid embarrassment or singling-out, I cannot ask students about: their age anything about their body (height, weight) anything involving money Ideally I would like some nice questions with…
Chris Cunningham
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16
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4 answers

Policies and practices for supporting students in crisis

I have noticed a common pattern followed by many students in crisis: They experience a crisis or setback (injury, illness, tragedy, etc) This causes them to miss a lot of class. They may stay away from class longer than they "need to" because of…
Steven Gubkin
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16
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6 answers

Fun games for children

I'm looking for fun games for children (from 4 to 12 years) used in learning math concepts. They can be offline or online games.
Filipe Ferminiano
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16
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3 answers

How to balance between teaching to the standardized test vs understanding?

For people teaching high school standardized curriculums such as AP, IB, or A-Levels, how do you find the balance between preparing students for the standardized test compared to ensuring they understand the material? In an ideal world, the two are…
okzoomer
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16
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1 answer

Advice for Tablet/Stylus for Mathematics Teaching

As it stands all of my lectures are presented by me writing on pre-printed acetate sheets (printed with my notes with gaps for pictures, examples, etc.) which are then projected onto a screen using the acetate projector. While I am happy enough with…
JP McCarthy
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