38

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 -- much, much older) think that a triangle is a triangle. It's a polygon formed by three non-colinear points. A triangle has many ways you can think about it. ...


24

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 the word sphere is particularly confusing in this context. (Mathematicians use sphere to mean the the two-dimensional surface; colloquial speech and some ...


21

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 undergraduates who have not had a theoretical math course. In my experience, students do not naturally think of geometric figures as sets of points. If $P = (-1,-1)$, $Q =...


11

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 certain species of bacteria splits into two cells ( a process called fission) every 20 minutes (the "generation" length), assuming proper growth ...


8

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 difficult time with that. Keep in mind age appropriateness. For 9-12 year old children, you are generally looking at a level of psychological development ...


8

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 interior of a plane region was relevant to problem solving at that grade level. For these types of elementary shapes, the boundary and the interior completely ...


7

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 they are clearly well-defined: "Triangle", "square", and polygons in general, are bounded regions on the Euclidean plane, i.e., 2D figures. ...


5

I have seen the phrase "make a ten" in wide circulation. Example: https://www.mathcoachscorner.com/2020/11/make-a-ten-strategy-for-addition/


5

Programmers consider the naming of things to be one of the three leading problems in our field. For the cases you describe, we do already have a well-established and widely-used set of terms that even non-computer users should recognize and be familiar with. A circle can be called a solid or filled circle, contrasted with wireframe or outlined circle. ...


5

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 an important benefit of not making the distinction for them. While it is crucial in higher mathematics to be able to be extremely precise, it's also important to ...


4

If the domain was the real numbers, I would say that it raises two to the power of its input. If the domain was positive integers, I would break your model and say that it multiplied together $x$ copies of $2$ because I think it is more intuitive to describe what exponentiation actually does that to imply that it is as natural as addition and multiplication.


4

A triangle is born from three non-collinear points and the axiom that two points determine a line. In the context of neutral geometry, a triangle has no structure other than three lines and three points. In particular, there is no notion of the interior of a triangle without more axioms. In the real projective plane, one cannot define the "interior"...


2

Neither of your sample answers are correct. You ask :"At what time does the tenth fission occur?" The problem is that "Fission" is the incorrect word, as that would relate to individual fissions of individual bacteria. If 5 bacteria reproduce at the same instant, then in that instant 5 fissions occurred. I believe you intend to ask when ...


2

Use the word "generation" instead of "fission" as also suggested in @guest answer above. Also I couldn't understand the use of this sentence fragment, "Let n be the number of fissions that have occurred since 10:00."


2

"The function $h$ raises $2$ to the $x$, where $x$ is the input" and "The function $h$ raises $2$ to the $x$th power, where $x$ is the input" both ape the structure of $f$ and $g$ and, despite containing a clause, sound less awkward/contrived than the alternatives.


1

In German, the word is "Zehnerzerlegung".


1

I don't really know what's the big problem. Terms need not be ambiguous; it's up to you to define and use them in clear and unambiguous manner. For example you can use "triangular region" or "cylindrical volume" to clearly differentiate from "triangle" and "cylindrical surface", and of course you have to define whether ...


1

In Mandarin Chinese, numeral: 数字 number: 号码


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