They probably are, especially since at the basic and intermediate levels of maths, formal definitions are generally not important, and people are just ‘doing sums’, so to speak, which is certainly the 算 aspect of maths.
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Wow, looking up all these math terms just resulted in a moderate mind-blown for Japanese in general. Several math words start with 被. Probably the most useful would be 被除数, which means dividend, but there’s also less common (in English) words like 被減数 (minuend), 被乗数 (multiplicand), etc. This led me to discover that 被 is a general Japanese prefix to indicate the target of an activity (similar to the suffix -ee in English, plus other uses). This helps explain non-math words like 被害者, 被疑者, and a lot more. This could be really helpful for picking up unknown words in context.
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Yeah, it’s actually the passive voice particle in Chinese, though it’s not always necessary when expressing that an action is received rather than done. I kinda took it for granted, but I guess it’s true that it’s rarely made clear in Japanese textbooks or other Japanese learning resources. I thought that it would be fairly clear for anyone who’s seen the term for victims of the atomic bombings: they’re 被爆者. However, I guess that isn’t that common a word unless you’re talking about remembering World War II.
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I’m not denying you’re right about the technical meaning of ‘calculation’, but I’m coming at it from the ‘not necessarily technical audience’ POV. The word ‘calculation’ has a lot of baggage due to its association with Calculus, which most of the population, even those with a moderate amount of university-level math courses under their belt, would consider ‘definitely not mindlessly straightforward’. Even the idea of a calculator, which ostensibly ‘just’ does all the ‘mindless’ calculation for you (I mean, it really does, don’t get me wrong) is perceived by many as basically performing magic when it gives the square root of 2. (Arthur C. Clarke’s third law comes to mind: “Any sufficiently advanced technology is indistinguishable from magic.” And we’re not even talking about super-advanced technology here, just a pocket calculator!)
So, that’s where I perceive the word-association ‘impedance mismatch’ would probably come in. However, enough people have done enough homework questions where they’re asked to ‘calculate blah blah blah’ where ‘calculation’ on its own still has a pretty strong connection to ‘just grinding the numbers’ via the traditional hand-arithmetic algorithms, so that’s why I agree that 足し算 could be labeled Addition (Calculation).
My point about ‘computation’ was simply that modern computers (machines) literally replaced the computers (humans) of the previous era, who performed all the calculations/computations prior to the first computing machines. Thus, if it’s so ‘mechanical’ a machine can do it, I mean… that’s what computations literally are!
But anyway, it’s a nitpicky semantic point. I think we actually agree on more than we seem to. Language is funny, eh? 
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I’m using it the same way you are, in the non-technical, ‘can have variables’ meaning. And, actually, I wonder, does 加法 really only apply to arithmetic? I have a feeling it’s more general than that, that it literally is the algebraic kind of addition. Indeed, maybe that’s the actual distinction underlying everything here. 加算 might be arithmetical addition, and 加法 might be the slightly more general algebraic addition? Again, just speculating! Could be way off in the woods.
I think that would be a totally fair move, especially if you really just want to get a ‘first version’ out there that’s ‘good enough’. You can always add extra cards later, especially if people request them, or if you later learn more about how the various words are actually used. The 算 words seem like very safe bets; the 法 words more speculative.
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Yeah, I was actually agreeing on how most people would probably take ‘computation’. All the associations you mentioned make etymological sense, but in common usage, I think ‘calculation’ is a bit more common than ‘computation’ for the sorts of operations we’re talking about. Both are correct, and I think ‘computation’ has the more precise sense, but because of modern usage and the ubiquity of (electronic) computers, people are more likely to associate it with everything you mentioned earlier. On the other hand, like you said, ‘calculate’ seems to be a common word in homework problems with a very general mathematical sense of ‘work this out and find the result’.
Perhaps I’m wrong though, but I can’t think of a non-technical sense of ‘calculation’ in common usage, because even the sense of ‘working out something for predictive purposes’ is based on the mathematical sense, in my opinion. Is there actually a non-technical equivalent of ‘calculation’? I guess ‘reckoning’ might work, and it’s probably the only word in the discussion with native English roots, but its usage isn’t limited to mathematics.
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A relatively common non-technical – even non-mathematical – usage of calculation is when describing someone who makes cold-hearted (not necessarily evil, tho) decisions, or who comes up with dastardly schemes (usually evil! ), such as 'He made a calculated decision to order his unit to defend the breach at all costs. His poor momma should be proud!" Or, “By her calculation, those rascally Dalmatian pups wouldn’t be able to resist the squeaky chew-toy bait in the centre of her trap!”
Prior to mathematical prediction, we all have an innate ability to make intuitive predictions. They are still referred to as ‘calculating’, though, even though it’s understood that no numbers appear anywhere in the person’s mind. The connotation is more about the person ‘thinking like an unfeeling/unemotional machine’ or ‘plotting in a clever, yet uncaring, or even cruel way’.
I’m aware that a non-mathematical sense exists, but what I meant was that, since you raised this
and then mentioned the connection between ‘calculation’ and ‘calculus’, I figured that you were implying that there’s a sense of ‘calculation’ in common usage in mathematics (and by this, I’m talking about language linked to what mathematics is to the layman, which is to say numbers and basic operations) that doesn’t relate to the mechanical aspect of working something out. That’s why I wondered whether there was a non-technical word that wouldn’t have that double meaning when used to describe basic mathematics.
As for the origin of the non-mathematical sense of ‘calculate’, while I agree that the phenomenon it describes is something innately human that likely even predates mathematics, as you said here
Oxford confirms my guess that ‘calculate’ is first and foremost a mathematical word:
The mathematical definition is the first one, suggesting it is the most common sense, and etymologically, it stems from a Latin word that refers to an object used as part of a device for… well, calculations, or basic mathematical operations. In other words, the other definitions are an extension of the mathematical sense, and not completely unrelated. For that matter, this particular connotation
is clearly a result of the fact that such calculations can occur entirely mechanically, or at least with only mathematical reasoning, which does not need to account for emotions or other strictly human factors.
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By the way, here is my list of math words so far. If you guys have any suggestions I’m all ears.
(I started writing this post like 40 minutes ago, and then I went on a very long tangent expanding my geometry section! )
General:
- 数
- 算術
- 演算
Addition:
- 足す
- 加法 (might skip)
- 加算
- 足し算
- 和
Subtraction:
- 引く
- 減法 (might skip)
- 減算
- 引き算
- 差
Multiplication:
- 掛ける
- 乗法 (might skip)
- 乗算
- 掛け算
- 積
- 九九
Division:
- 割る
- 除法 (might skip)
- 除算
- 割り算
- 被除数
- 除数
- 商
- 余り
- 剰余 (formal of 余り)
- 割り切れる
- 割り切れない
Exponenents and Roots:
- 冪 (best term for exponent?)
- 二乗根
- 平方根 (which is better?)
- 三乗根
- 立方根 (which is better?)
Fractions:
- 分数
- 分子
- 分母
Decimals:
- 小数点
Number Sets / Types of Numbers:
- 集合
- 整数
- 偶数
- 奇数
- 素数
- 負数・負の数 (the latter was used in the Addition wikipedia page)
- 正数・正の数
- 自然数
- 実数
- 虚数
- 有理数
- 無理数
- 複素数
Symbols:
- 括弧
- 等号
Algebra:
- 変数
- 定数
Geometry (general):
- 幾何学
Geometry Lines:
- 直線
- 曲線
- 角度
- 鋭角
- 直角
- 鈍角
- 内角
- 外角
Geometry 2D Shapes:
- 円
- 直径
- 半径
- 多角形
- 正多角形
- 三角形
- 二等辺三角形
- 正三角形
- 正方形
- 長方形
- 四辺形
- 平行四辺形
- 台形
- 六角形 (to give a shape using the “normal” pattern)
- 八角形 (to give a shape using the “normal” pattern)
- 平面
- 面積
Geometry 3D Shapes:
- 球体
- 多面体
- 立方体
- 角錐 (general term for “pyrimid”)
- 三角錐
- 四角錐
- 円錐
- 表面積
- 体積
Other:
- 行列
- 比 (ratio - doesn’t quite belong with the division section)
- 総和
- 二進法 (maybe not relevant?)
- 十進法 (maybe not relevant?)
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Still not 100% sure where we disagree, if we even do – this might be a case of ‘violent agreement’. Anyway, I’ll give one last go at finding a mutual understanding of what each other of us meant by this or that, just in case. 
“I figured that you were implying that there’s a sense of ‘calculation’ in common usage in mathematics (and by this, I’m talking about language linked to what mathematics is to the layman, which is to say numbers and basic operations) that doesn’t relate to the mechanical aspect of working something out.”
Re: ‘calculation’, in common usage, among laypeople, but definitely related to math, that is not related to ‘the mechanical aspect of working something out’.
- I do believe there is/are at least one meaning of calculation that is math related that is not about the mechanics, and that would be just ‘general mathematical problem solving.’ Homework questions – especially in later years, say in high school, where math is still compulsory and many students find it more and more ‘out of touch’ with their lives and thus more boring and more difficult – you will often find such questions phrased like, “An 8m ladder is leaning against a telephone pole which has a shadow of 29 m at 3:00pm on Winter Solstice in Denver Colarado. The phone technician fixing the phone lines from 3 rungs down doesn’t notice that the bottom of the ladder is on a patch of black ice, and it takes him 3.4 seconds to fall and break his 5th cervical vertebra, paralyzing him for life. The ambulance arrives 3 hours later. Calculate the initial angle of the ladder against the pole.”
These are clearly not simple mechanical computations, but require deciphering what the problem is, what facts are relevant, etc. etc., all to come up with a single numerical ‘calculation’ that at the end of the day is either correct or incorrect. So, the word ‘calculate’ is being used in this way as a euphemism for a rather complex problem-solving task that many students find (as the years of this go on) rather esoteric and ‘meaningless’. So, in that way, it can retain its ‘mindless’ connotation (since the students feel themselves ‘mindlessly lost’ trying to figure out what they’re supposed to do) yet not actually being primarily about the ‘mindless’/mechanical aspects of performing some computation (except near the end of the problem-solving process, once the problem has finally been correctly identified and prepared).
This also connects with the other non-technical meanings of ‘calculate’, particularly the idea of coming up with some clever scheme to serve some sinister purpose (who knows why these textbook authors want to figure out the proper angle to cripple a poor telephone technician!?!!? What is their master plan???).
Well, IMO, you put the bold on the ‘wrong’ word(s), as I was trying to emphasize this aspect of the situation:
‘thinking like an unfeeling/unemotional machine ’
Sure, it’s because of the connection with ‘machine’ that the ‘unfeeling/unemotional’ aspect arises, but it’s that aspect that I was intending to highlight. As a counter-example, there are plenty of things that people do ‘mechanically’, like ‘machines’, that are in fact very thoughtful, caring, empathic. Example: A nurse mechanically, yet gently cleaning the area around a painful wound. She has done it so many times and is so good at it that she can do it efficiently and without thinking or worrying about how to do it, yet she is doing so from a place of compassion and care for another person. She may even be ‘mechanical’ in how gently she moves the wounded limb around and how carefully she avoids irritating or aggravating the sore spots around the wound. Being mechanical or machine-like does not necessarily imply unfeelingness or lack of any emotion at all.
Whereas when one uses the word ‘calculating’ or ‘calculated’ (or ‘by their calculation’), there is an implication/connotation of unfeelingness or lack of emotion. (Not always, there are always exceptions, but usually, I would say.)
Again, I don’t think we actually disagree on much (if anything?), I’m just clarifying what I meant and the point(s) of view I was trying to represent.
I’m not too sure myself, but I guess my impression was that you felt that ‘calculation’ wouldn’t be very clearly mechanical because of its links to calculus, and I was just pointing out that I don’t think many people immediately think of calculus when they see the word ‘calculation’. However, yes, it’s true that many things that are referred to as ‘calculation’ are not simply mechanical, so you have a fair point.
That aside, I was suggesting that ‘calculation’ would nonetheless probably be the more intuitive word since, like you said, ‘computation’ tends to be associated with computers nowadays, even if its stricter (and likely original) sense is much closer to the ‘performing mathematical operations’ sense of ‘calculation’, and so it might be the better word to choose. That’s all I’m getting at or contesting (the appropriate word to use depending on whether or not there’s actually disagreement, which I’m not sure of myself).
And yeah, OK, fair enough: in my own analysis, I mentioned the unemotional nature of mathematical reasoning. I guess I highlighted ‘machine’ just because the word ‘mechanical’ came up earlier and I felt that machines are the epitome (or at least a favoured illustration) of unfeelingness.
In short, however,
perhaps this is what we’re looking at. All the potential points of contention I’m aware of, I’ve raised above. That aside, I don’t think I particularly disagree with anything you’ve said.
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You might be interested in this Youtuber I’ve been watching who makes study aids on various topics. I’ve been watching him for his 国語 videos (like how to divide sentences into phrases and such), but he has lots of other subjects as well, including arithmetic and more advanced math.
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Don’t think I can offer much help, as the words/items I picked up were more for ‘personal use’, some quite obscure, and probably wouldn’t serve very well to add to a curated list for a more general mathy audience. E.g. several of the words I was looking up were related to probabilities, and in particular Bayesian probability terms like ‘log likelihood’ and ‘likelihood ratio test’ etc. Others were just terms for certain linear algebra concepts I was familiar enough with that I thought they would make good ‘bridge’ items to link the more obscure terms to a more general (but still rather specific to my own interests) vocabulary.
Gotcha, that makes sense. As you could probably see from the sections in my list, I’m mostly focused on arithmetic, geometry, and sets so far. Some of the set terms I picked are already beyond basic math, but I definite don’t plan to go beyond this in terms of complexity.
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Maybe not really basic arithmetic anymore, but 関数 = function and 値 = value (also very useful for programming)
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Since you mentioned being interested in more advanced terms as well (pulling from this combinatorial game theory paper). I’m going to include non math terms just to be clear what ones are used in math contexts.
This list will probably overlap with your own but I’m too tired to crosscheck right now
組み合わせ - combinatorics/combinatorial. For example, combinatorial game theory is 組み合わせゲーム理論
代数 - Algebra (and 代数的 for algebraic)
定式化 - Formulation
解析 - (mathematical) analysis
アルゴリズム - Algorithm
再帰 - recursion (再帰的 being recursively)
値 - value (ie: variable value, Sprague Grundy Value, etc. )
整数 - integer
定義 - (mathematical) definiton
有理数 - rational number
2進有理数 - Dyadic rational (I haven’t heard this one outside CGT)
奇数 - odd number
具体例 - concrete example
I’m sure that paper has more but I just did some skimming
Edit more I missed:
図 and 表 appear to both be used for “figure” and “diagram” in the math paper sense as well as the other meanings
有限 - finite
有限個 - countable
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I think most of those are probably too advanced or not direct math terms (I don’t think I want things like 解析 and 再起). I already added 代数 and I already had 整数, 有理数, and 奇数. 有限個 might fit into the section on Sets though, so maybe I’ll add that one. I’ll add that one to my list at least so I don’t forget about it.
Actually, I think I’d probably have to make it 有限集合 to fit into the Sets section. But then skimming through the Wikipedia article on that, it’s getting into actual set theory, which is probably too advanced for this deck. Hmm… 
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再起 and 再帰 are two different terms. The first is more like "comeback (from a bad/worse state) while the latter is recursion/recurrence
That was just bad typing on my part.
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If someone ask me I would just say
いくつか数学物しているだけど
Im just doing some math stuff.
Solution 