# Tag Info

### 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 -- ...
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### 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 ...
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### 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 ...

### 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 ...
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### 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 ...
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### 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 ...
• 339
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 ...
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### 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 ...
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### 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 ...
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### 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 ...

### 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".
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### 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 ...
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### 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: &...
• 9,639
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 $y$, ...

### 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 &...
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### 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 ...
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Accepted

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### 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 ...
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### 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 "$f(x) = f(y)$ ...
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### 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 ...
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### 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 ...
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