# Questions tagged [notation]

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

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### 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 ...
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 ...
1k views

### Metonymy in mathematics

Metonymy is a figure of speech where a word or another expression is used to mean something other than its literal meaning. This phenomenon is not restricted to the "usual human languages" (such as ...
1k 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 ...
2k 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 ...
4k 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 ...
1k 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 ...
9k views

### Should we stop differentiating between ln and log?

In many U.S. middle schools and high schools, $\ln$ and $\log$ are treated differently, with the intent that $\log$ is equivalent to $\log_{10}$. However, in undergraduate courses and in the academic ...
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 ...
4k views

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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### 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? <...
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 ...
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 ...
584 views

The slope-intercept form of the equation of a line is often presented in textbooks (in the US) as $$y = mx + b\,,$$ where $m$ is the slope of the line and $b$ is the $y$-intercept. How did $m$ and $... 4answers 582 views ### Do students confuse$\log_ab$and$\log a^b$? I recently observed a group of students being introduced to logarithms for the first time. Some of them had trouble writing$\log_ab$properly, and it looked more like$\log a^b$. All logarithms have ... 5answers 760 views ### Why is multiplication taught using cross notation at first? Alert: I am not a math educator. It seems to me that multiplication is first taught using the cross notation, for example$3\times 5=15$. First question - is that even correct? Maybe not all schools ... 6answers 571 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 ... 6answers 2k 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 ... 5answers 1k views ### Writing Fractions “Correctly” I very often see students writing, for example,$1/3x$when they mean$\frac 13x$. I used to tell them not to write$1/3x$beause it looks like$\frac{1}{3x}$until I realized that, according to ... 4answers 902 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 ... 4answers 453 views ### Using$dx$for$h$in the definition of derivative Is it mathematically correct to write $$f'(x)=\lim_{dx\to0}\frac{f(x+dx)-f(x)}{dx},$$ rather than $$f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}?$$ If not, what is the difference? If so, why isn't this ... 2answers 216 views ### How to teach brackets? I was taught in a school that one has to use different brackets in expressions like$\{[(3+4)\cdot 4]^4\}^{1/2}$to denote the order which subexpression is evaluated first. But can this be recommended ... 1answer 336 views ### Why do some of my, usually international/Indian students, write limits to the left of the integral? I see a lot of my students (I am in the US), usually Indian, write the limits of integration to the LEFT of the integral sign rather than customary top or right. The formula will look for example like ... 8answers 9k 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 ... 5answers 980 views ### A different symbol for the indefinite integral/antiderivative? Examples. An indefinite integral (or antiderivative) of$\cos$is$\sin$: $$\int \cos = \sin.$$ Edit: There has been much unexpected confusion with the above statement. I define the above statement ... 3answers 485 views ### Are there any negative consequences in applying operations/functions to a whole equality? Some of my students solve equations not by applying the same operations on the left and right sides of an equation, but by applying the operation to the whole equality. For example, they may write ... 1answer 557 views ### Language to Distinguish Between Variables and Arbitrary Constants Today in second semester calculus, I found myself stumbling a bit to provide a natural-sounding explanation for all the letters involved in the expression $$\lim_{t \rightarrow \infty} \int_1^t \frac{... 1answer 697 views ### How to denote angle? I'm teaching mathematics on my free time for young pupils. Once I have seen that they denote angles like \angle ABC. But sometimes I have difficulties to understand whether they mean an angle or its ... 1answer 3k views ### When and Why are different division symbols taught? There are 4 division symbols that I have learned/taught. Below is 18 divided by 3, shown with 4 different symbols. This question was sparked by the comments on my answer to the question on examples ... 3answers 290 views ### Framework for Compound Inequalities I have been presenting compound inequalities like 3 < x < 7 as being a shorter way of saying 3 < x and x < 7. From this point of view, though, I end up having to admit that ... 6answers 367 views ### Helping high school students remember inequalities and division Background I sometimes tutor high school students and I have come across various problem types that are best represented by the following two problems. They are unable to keep track of the correct ... 2answers 509 views ### Is this example of Leibniz notation sloppy? In helping a family member who is studying calculus, I was asked about the meaning of the following, which is straight out of a calculus text book (Varberg and Purcell) v'(t) = \frac{{\rm d}\,v}{{\... 2answers 215 views ### Is there a good notation for “ratio” comparable to the use of \Delta for “difference”? It is standard to use the symbol \Delta to indicate a change in a quantity between two points on a curve, two rows on a table, and so forth. For linear functions, we write slope = \Delta y / \... 2answers 3k views ### Notation of points with coordinates At least in Germany, nearly all teachers and textbooks use the notation$$P(x,y)$$for the point P with coordinates x and y. My own math professors at university always cried about this, as the ... 5answers 2k views ### Teaching asymptotic notations at the beginning of calculus [duplicate] I'm thinking about teaching calculus by firstly introducing the asymptotic notations (big-Oh, little-oh, and \sim), secondly explaining their "arithmetic" (things like how to sum little-oh's and ... 3answers 215 views ### What symbol is appropriate to represent a sum modulo N? [closed] I am writing a blog post about cryptography and I need to show some examples that involve sums modulo N. I would like (if possible) to use a different "plus" symbol for these sums. The kind of ... 2answers 1k views ### Is “hat notation” for unit vectors commonly used in mathematics? As an undergraduate, I clearly remember learning and using "hat notation" to describe unit vectors. That is, if \vec{v} is any vector (in 2 or 3 dimensions) then \hat{v} denotes the unit vector ... 3answers 207 views ### Design of a math exam using multiple choice or computer I'm teaching math in first years of university (matrix algebra, differential analysis, etc.) since maybe 5 years, and I usually give written (paper) exams to the students. I'm looking for ideas to ... 1answer 122 views ### Resource about notation for students Others have already here pointed out that students can struggle with notation in mathematics. I can often think that the lack of proper notation gets in the way of solving a problem correctly. ... 0answers 128 views ### Terminology for parts of limit notation When we talk about$$\lim_{x\to{c}}f(x)=L$$is there a formal name for the number$c$? I know of course that it means "$L$is the limit of$f(x)$as$x$approaches$c$". It just would be nice to be ... 3answers 318 views ### In teaching mathematics, should one always follow some international standards such as ISO 80000-2? ISO 80000-2:2009 is a standard describing mathematical signs and symbols developed by the International Organization for Standardization (ISO). In teaching mathematics, should one always follow this ... 3answers 327 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 ... 3answers 286 views ### Wording VS mathematical notations Is it better to write everything in words as the concepts themselves should be known? Or will some teachers in some countries prefer to be able to choose questions which also test the student's ... 3answers 206 views ### Are there standard notations for 'number talks' / ‘math talks?' I’m a homeschool teacher of a nine-year-old, and we sometimes have one-on-one ‘number talks’ (a.k.a. 'math talks') similar to the activity used in primary school classrooms. Part of this process ... 2answers 172 views ### The word “numeral”, is it being taught and does the word exist for it in your language? I am a mathematics educator from Lithuania and I have recently realized that there is no separate word in our language for the word "numeral". To be more precise there is no term to describe the ... 2answers 201 views ### How to reasonably denote lines, line segments and rays? I'm teaching geometry at high school for the first time soon and am struggling to find a reasonable notation for lines, line segments and rays defined by two points$A$,$B$(and a direction). At the ... 5answers 276 views ### Notation for an element in a polynomial ring Let$F$be a field. What is the best notation (in an undergraduate or graduate abstract algebra class) for a generic element of the univariate polynomial ring$F[x]$? The most common notation seems ... 2answers 150 views ### At what educational stage are angles greater than 180 introduced? Prompted by the question, "How to denote angle?," I am interested to learn when students consider and reason with angles$> 180^\circ$. For example, when do they reason with an angle of$270^\...
When matrix multiplication is introduced, it is usually introduced with an additional variable: Given two multiplicable matrices $A$, $B$, one defines the product $C=AB$ to be the matrix given by some ...