Questions tagged [notation]

For questions about good use of notation, comparison of specific notation, motivation of notation.

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75 votes
6 answers
7k views

Issues with "equals", where does this come from and how do I combat it?

An issue I see with students a lot is abuse of the equals sign. For example, one problem asked "what is the degree of the polynomial: $\text{polynomial}$?", and I got answers like "$\text{polynomial}=...
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20 votes
5 answers
695 views

How students write their work, and learning outcomes

While teaching students mathematics, I have noticed that some seem sloppy in the way that they write down their work. For example, a student is given a question: What is the area of the rectangle? <...
38 votes
10 answers
2k views

Reasons for (not) distinguishing $f$ from $f(x)$

Formally, if $f$ is a function, $f(x)$ is a value. So for instance, $f$ can be continuous, but not $f(x)$. In teaching at school and university, notation is quite often mixed up, e.g. the function is ...
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31 votes
10 answers
2k views

Should students be asked to use more than one notation for the derivative in an introductory calculus class?

There are many, many ways of writing the derivative of a function $y=f(x)$: $$\frac{d}{dx}y, \frac{dy}{dx},\frac{d}{dx}f(x), \frac{df}{dx}, \dot y, D_x f,f',y',f'(x),f_x$$ and so on. Students often ...
31 votes
6 answers
3k views

Allowing nonstandard mathematical language and/or notation

How important is enforcing standard mathematical language and/or notation? Today, I was questioned by a writing instructor as to how vital it is to correct students when they explain something using ...
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14 votes
6 answers
4k views

Explaining the symbols in definite and indefinite integrals

I teach the definite integral before the indefinite for a few reasons, one of which is that I want students to recognize that the definite integral means area (not anti-derivative). If we do ...
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44 votes
21 answers
7k views

How to help new students accept function notation

I am struggling to help some of my new precalculus students accept function notation -- something new to them this term. I am looking for strategies to help them adopt this new notation. Their main ...
  • 7,703
30 votes
6 answers
2k views

What is the rationale for the absent (+) in mixed fractions?

Why are students taught to represent one and a half as $1 \frac{1}{2}$ rather than $1 + \frac{1}{2}$? This mode of expression seems standard at least throughout North America. I believe that it is bad ...
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28 votes
6 answers
6k views

Misuse of parentheses for multiplication

I'd like to raise the issue of constant misuse of parentheses in the U.S., and I'm wondering if anybody else shares the same feelings, has had the same issues, knows any history behind it, and can ...
23 votes
7 answers
5k views

Repeated addition: standard notation?

My daughter showed me the picture below, which came from 9GAG. It shows a question on an exam asking the student to "use the repeated addition strategy to solve: 5 x 3." The student answered "5+5+5" ...
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21 votes
5 answers
3k views

Grating mathematical phrases---How to correct?

As mathematics educators, we all have come across students using mathematical notation incorrectly (looking at you, $\frac{d}{dx}$ vs $\frac{dy}{dx}$ or $\frac{\infty^2}{\infty}$). My question focuses ...
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21 votes
5 answers
1k views

Students using ambiguous notation

I've noticed that many of my calculus students (all college students) will write, e.g., $1/3x$ to mean $(1/3)x$. This is an inherently ambiguous notation which I'd like them to avoid. Is simply ...
19 votes
7 answers
1k views

Notation Conflict between Teachers and Textbooks

In mathematics notation plays an important role in clarifying the subject. A bad notation could be confusing. Recently I use a logic textbook which has a very nice approach and content but an ...
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14 votes
4 answers
989 views

As a TA, how to reduce imprecise notations/statements in students' exams

I'm not a course instructor, just a TA of the first quarter calculus course who lead discussion sections and grade exams. When grading the midterm, I found large number of students showed some ...
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14 votes
2 answers
724 views

The use of "$\therefore$" and "$\because$"

In schools, many students learn the usage of "$\therefore$" and "$\because$" in proofs. Such three-dot notation are popular in many high-school books and exams, but are almost ...
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14 votes
6 answers
606 views

Is using different notations in one course a good idea?

From aesthetical point of view, using two symbols for the same concept during the same course is obviously a very bad idea. However, especially when I teach freshmen, I often deliberately mix ...
  • 1,269
11 votes
1 answer
1k views

How to denote angle?

I'm teaching mathematics on my free time for young pupils. Once I have seen that they denote angles like $\angle ABC$. But sometimes I have difficulties to understand whether they mean an angle or its ...
11 votes
8 answers
12k views

Proof of why BODMAS (or BIDMAS) works?

In my first full-time teaching post, it is very likely that I'll need to be teaching a small amount of GCSE Mathematics to students retaking it. One thing that has been bugging me is that I can't seem ...
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10 votes
3 answers
404 views

Framework for Compound Inequalities

I have been presenting compound inequalities like $3 < x < 7$ as being a shorter way of saying $3 < x$ and $x < 7$. From this point of view, though, I end up having to admit that ...
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10 votes
4 answers
2k views

Notation for change of basis matrix

As far as I can tell, it's only a slight exaggeration to say that every text has a different notation for a change of basis matrix from (say) $\mathcal{B}$ to $\mathcal{C}$. That's not even to talk ...
  • 5,750
7 votes
2 answers
3k views

Is "hat notation" for unit vectors commonly used in mathematics?

As an undergraduate, I clearly remember learning and using "hat notation" to describe unit vectors. That is, if $\vec{v}$ is any vector (in 2 or 3 dimensions) then $\hat{v}$ denotes the unit vector ...
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6 votes
6 answers
795 views

Why do we write $x$ instead of $1x$?

I am currently student teaching for an Integrated Math 1 class (which is similar to Algebra 1) that consists of 9th graders. I have been teaching my students how to solve linear systems using ...
  • 1,067
5 votes
1 answer
224 views

What is the notation for polynomial long division in Norway?

I will be teaching a calculus-type course in Norwegian. Our textbook is unfortunately in English (the curse of a small language), but any custom exercises should be and all exams have to be in ...
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