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41 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I'm confused. Are you really going to try to make this sort of distinction when teaching geometric figures to students "around 9-13 years old"? Students that age (and engineers my age -- ...
Flydog57's user avatar
  • 595
41 votes

What value is there in requiring students to answer word problems in complete sentences?

Yes, there is mathematical pedagogical value in the usage of complete sentences - but this does not only refer to "answers" and not only to "word problems", but to all parts of the ...
Jochen Glueck's user avatar
38 votes

What value is there in requiring students to answer word problems in complete sentences?

I do think there is value in expecting students to give answers in correct English. It will certainly help when they start to face longer and less structured questions. However, the example you give ...
Especially Lime's user avatar
26 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

One encounters exactly the same issue teaching multivariable calculus when one treats integrals over three-dimensional regions and integrals over the surfaces that are their boundaries. In particular ...
Dan Fox's user avatar
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23 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I think the distinction you are raising is not natural to students at this age. I teach undergraduates and graduate students, not elementary schoolers, but I find that it is not natural for ...
David E Speyer's user avatar
23 votes

What value is there in requiring students to answer word problems in complete sentences?

An example of a problem where phrasing the answer as a sentence might prevent mistakes and encourage understanding is: Alice goes to the store with \$2.00. A gumball costs \$0.80. How many gumballs ...
Tjaden Hess's user avatar
20 votes
Accepted

Do undergraduates struggle with δ-ε definitions because they lack a habit of careful use of their native language?

I wouldn't say so. By studying linguistics on a deep level, this person learned to parse complicated multi-part statements and extract precise meaning from them. This skill--which people in general ...
user22788's user avatar
  • 854
19 votes

Can we save the word "unique"?

I don't see this as a major issue, nor do I believe that the word "unique" is in any particular need of saving. There are a large number of terms in mathematics which correspond to ...
Xander Henderson's user avatar
  • 8,224
17 votes

What value is there in requiring students to declare the dimensions of an answer when it is already clear from context?

In my experience with remedial-level community-college students (USA), it is simply never the case that the units are trivially "clear from context". I can easily see some of my former ...
Daniel R. Collins's user avatar
14 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

Educator here who has worked with many students in the aforementioned age range (9-13) on triangles and squares. In my experience, it has never come up that a confusion between the boundary and the ...
Rivers McForge's user avatar
13 votes

What is it called when terms disappear when reducing fractions?

So German "$b$ kürzt sich weg" becomes in English "$b$ cancels out". We may also say "$b$ is eliminated".
Gerald Edgar's user avatar
  • 7,607
13 votes

How to reduce ambiguity in the following question?

The ambiguous answer is relatively correct (actually you need to know how old they are at the start of the problem). But each fission is an individual splitting, not a generation. Perhaps this: A ...
guest's user avatar
  • 131
12 votes

What's the common word for equations and inequalities?

My phrase has always been math "statement". Equations and inequalities clearly assert/state a relationship between two or more things. My go-to direction using this would be something like: &...
Nick C's user avatar
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12 votes
Accepted

Is 'For all $x$' an abuse of language in math?

No, there is no abuse of language here. $x$ and $y$ are placeholders that stand for individual numbers, and your second suggestion captures this: For each number we can insert in place of $x$ and $y$, ...
Natalie Clarius's user avatar
11 votes

What value is there in requiring students to declare the dimensions of an answer when it is already clear from context?

The legitimate purpose of this is trying to get the student to actually read the question and take note of the fact that there is indeed a context. Many students approach mathematical exercises as &...
Arno's user avatar
  • 966
11 votes

What value is there in requiring students to answer word problems in complete sentences?

Jochen's answer is very good. To add to it, here's the reasoning I was given as a student: answering in full sentences makes students think about the answer in different psychological context. This ...
Omegastick's user avatar
10 votes
Accepted

What is it called when terms disappear when reducing fractions?

If you continue the operations until $$\require{cancel}\frac{x}{b}=\frac{c}{b},\qquad\left(\frac{x}{b}\right)b=\left(\frac{c}{b}\right)b,\qquad x\left(\frac{b}{b}\right)=c\left(\frac{b}{b}\right),\...
JRN's user avatar
  • 10.9k
10 votes

Examples of Mathematical Slang

In Russian, the Squeeze Theorem (a.k.a. The Pinching Theorem) is called "Теорема о двух милиционерах" — "Two Policemen Theorem". The idea is that if two policemen are holding a criminal between ...
zipirovich's user avatar
10 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I confess, when you start talking about 1-D triangles, my own first thought is "how can you have non-colinear points in 1-D?". So, I imagine most students that age will have a far more ...
Brian's user avatar
  • 101
10 votes

What value is there in requiring students to answer word problems in complete sentences?

I do think this has (some) pedagogical value, specifically for word problems. Word problems are designed to give students practice applying math to real-world situations. Doing this effectively means ...
Jonathan Cast's user avatar
9 votes

Is there any research on the impact of dismissive language (e.g., 'it's just...') in mathematics education?

Hypothetically, a study researching the effect of a single word ("just") within a complex educational context would fall under the heading of a psychological priming effect. In some sense, ...
Daniel R. Collins's user avatar
9 votes

What is this symbol called?

That's lowercase Greek phi, pronounced with an initial f sound and rhyming with English pie, lie or sky. That said, some speakers may pronounce it rhyming with English see, key or me. See https://en.m....
J W's user avatar
  • 4,753
9 votes

What is this symbol called?

Please check the entire Greek alphabet, as you can find it in this Wikipedia page: https://en.wikipedia.org/wiki/Greek_alphabet. I must add that there are two ways to write the letter $phi$ in MathJax ...
Dominique's user avatar
  • 2,165
8 votes

What is it called when terms disappear when reducing fractions?

In general, as others have noted, if you have an equation such as $$\frac{x}{b}=\frac{c}b$$ The step to get from there to $$x=c$$ is typically referred to as cancelling the denominator. More generally,...
Milo Brandt's user avatar
8 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I agree with the point that a lot of the answers here are making - some distinctions, while correct and important, are not accessible to the age group you're talking about - I also want to point out ...
Reese Johnston's user avatar
7 votes

Can we save the word "unique"?

To my mind the defintion "Every x has a unique f(x)" of one-to-one is problematic because "has a unique" is neither clear English nor precise. The definition is usually stated as "$f(x) = f(y)$ ...
Dan Fox's user avatar
  • 5,869
7 votes

How to word this exercise about converting "English" into interval notation?

This is my suggestion. Write each set of numbers in interval notation. (a) All real numbers between 5 and 7, including 5 but not including 7. (b) All real numbers between 1 and 10, including both 1 ...
Amy B's user avatar
  • 8,017
7 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

Many of the geometric figures are so elementary that they are deeply rooted in daily language, and there seems to be no great solution. I agree with you here, and I think this is the key point. To me ...
FormerMath's user avatar
7 votes

What value is there in requiring students to declare the dimensions of an answer when it is already clear from context?

Different STEM fields have different conventions about this. These conventions are adapted to the needs of the field, so in general if the work you're doing has the flavor of field X, you will ...
klsjdfhgslfkdjgh's user avatar
7 votes

What value is there in requiring students to answer word problems in complete sentences?

The answer to What is the speed of Anne's car? is simply 45 mph However, math problems such as this follow a very simple pattern of pick up every number and do something with them, so with a simple ...
Ángel's user avatar
  • 171

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