matamataig---àireamheachd

[Tha_Mi_Sgìth]

Here is my understanding how how arithmetic (àireamheachd) works in Gaelic.
I’ve given statements, commands, and questions.
I’d be very grateful for any and all comments and corrections!

To say “What does…make?”, use “Dè tha…a’ dèanamh?”
To say “What does…equal?”, or “What is…equal to?”, use “Cò ris a tha…co-ionnan?”
To say “…equals…” or “…is equal to…”, use “Tha…co-ionnan ri…"

Addition/Plus = Cur ris, agus
agus = and
air a chur ri... = plus, added to (NB, ri does not lenite, e.g. co-ionnan ri trì = equal to 3)
Tha aon agus dhà a’ dèanamh (co-ionnan ri) trì = 1 and 2 makes (equals/is equal to) 3.
(NB I prefer to avoid using adjacent numbers in "Tha aon agus dhà trì" = 1 and 2 is 3)
Tha aon air a chur ri dhà a’ dèanamh (co-ionnan ri) trì = 1 added to 2 makes (equals/is equal to) 3.
Aon agus dhà! = One and two!
Cuir aon ri dhà! = Add 1 and 2!
Dè tha aon agus (air a chur ri) dhà a’ dèanamh? = What does 1 and (plus, added to) 2 make?
Cò ris a tha aon agus (air a chur ri) dhà co-ionnan? = What does 1 and (plus, added to) 2 equal?

Subtraction/Minus = Toirt air Falbh (bho), bho
bho = from (does lenite, e.g. bho thrì = from 3)
air a thoirt air falbh bho... = subtracted from, taken away from...
àicheil trì = negative (minus) 3 (i.e. less than zero)
(mìonas exists but seems a fudge to me, and grammatically strange: trì mìonas dhà---is it a verb or preposition?)
(maybe mìonas is used in algebra: x - y spoken as “x mìonas y”?)
Tha dhà bho thrì a’ dèanamh (co-ionnan ri) aon. = 2 from 3 makes (is equal to) 1.
Tha dhà air a thoirt air falbh bho thrì a’ dèanamh (co-ionnan ri) aon = 2 subtracted from 3 makes (is equal to) 1.
Thoir dhà air falbh bho thrì! = Take away/subtract 2 from 3! (I think “air falbh” is riatanach here, so can’t just use bho)
Dè tha trì air a thoirt air falbh bho thrì a’ dèanamh aon = What does 2 subtracted from 3 make?
Cò ris a tha dhà air a thoirt air falbh bho thrì co-ionnan? = What does 2 subtracted from 3 equal?

Multiplication/Times = Iomadachadh (le)
air iomadachadh le... = multiplied by (le does not lenite)
uiread = times, as in “trì uiread cho mòr ri sin” = three times as big as that
Tha dhà air iomadachadh le trì a’ dèanamh (co-ionnan ri) sia = 2 multiplied by 3 makes (equals/is equal to) 6.
Iomadaich dhà le trì! = Multiply 2 and 3!
Dè tha dhà air iomadachahd le trì a’ dèanamh? = What does 2 multiplied by 3 make?
Cò leis a tha dhà air iomadachadh le trì co-ionnan? = What does 2 mutiplied by 3 equal?

Division = Roinn (le)
air a roinn le... = divided by (le does not lenite)
Tha sia air a roinn le trì a’ dèanamh (co-ionnan ri) dhà = 6 divided by 2 makes (is equal to) 2.
Roinn sia le trì! = Divide 6 by 3!
Dè tha sia air a roinn le trì a’ dèanamh? = What does 6 divided by 3 make?
Cò ris a tha sia air a roinn le trì co-ionnan? = What does 6 divided by 3 equal?

I think that covers about everything. Any improvements, additions, comments, corrections….welcome!

[Tha_Mi_Sgìth]

Could somebody please proofread my posting above?

[Níall Beag]

'Fraid I'm not really able to help as I never did any Gaelic maths terminology. Never had need of it, and I'd already heard criticism that the standard school stuff was idiomatically rather tr*nsl*t**n-y anyway, so didn't really dare to look.

Tha aon agus dhà a’ dèanamh (co-ionnan ri) trì = 1 and 2 makes (equals/is equal to) 3.
(NB I prefer to avoid using adjacent numbers in "Tha aon agus dhà trì" = 1 and 2 is 3)

Strictly neither of those are right, but I've got little doubt that they're used in schools.

"1 + 2 makes 3" in English is a universal rule. "1 and 2 are making 3" would be something different. One of my (many) pet peeves is how people keep repeating the lie that "tha X a' Yadh" is both "X is Ying" and "X Ys" in English. I think they're getting their Gaelic confused with French and German.

"1 + 2 is 3" is also a universal rule, and it's also covering two noun phrases, so is a 's e ... a th' ann an ... situation rather than tha.

I will now exit this thread before I get trapped in a never-ending rant about bilingual education policy.

[Tha_Mi_Sgìth]

Hi Níall,

Thanks for posting. I'm very interested in your comments. First, I'm very keen to be using grammatically correct phrases to express basic arithmetic. I do find this is a neglected part of the language, due to the historical lack of maths being taught in Gaelic. I think maths is an important aspect of human thought, and deserves to be expressed in Gaelic.

In English we use the terms "is", "makes", and "is equal to", to express equality (or the outcome of an operation), and conveniently these terms separate the subject from the object. So we have "1 plus 2" makes "3", or "7 times 3" is equal to "21". In Gaelic, the language structure is very different. I think you have correctly identified a language error in the use of the progressive "tha .... a' dèanamh ..." to express "is/makes" in maths. I'm not so sure that is also the case with "co-ionann ri", as that is an adjective.

So, if it's correct that we need the copula to express 1+2 = 3, then what is the correct form?
How about: "Is a h-aon agus (no 'air a chur ri') a dhà trì"---putting the trì right after the a dhà seems confusing.
Should it be "'S e a trì a th' ann a h-aon agus a dhà", with the output of the operation coming first in the sentence?

I would be grateful for any opinions on this.

[akerbeltz]

The basic pattern the schools use is
X cuir ris/thoir air falbh/iomadaich le/roinn le Y a' dèanamh Z

Love or hate it, I think that particular die has been cast.

[Tha_Mi_Sgìth]

Oh dear. Oh crikey. No, no, no...That is just...wrong.

[faoileag]

Like primary school maths in English:

10 take away 4 makes/equals 6. (You have 10, now take away 4, that makes 6).

As a non-arithmetical person, I find most ways of expressing sums illogical or slippery, so I'm all for simple commands.

10 minus 4 is 6 is to me not true; it gives 6 / produces 6 etc, but it isn't identical to the number 6.
So I wouldn't want an Is/ 'S e version in Gaelic either.

Like a lot of us here, maybe most of us, I didn't go through school in Gaelic medium, so haven't got first hand experience. But I've come across the "cuir ris" pattern before, and have used it in teaching Gaelic numbers.

[Níall Beag]

The basic pattern the schools use is
X cuir ris/thoir air falbh/iomadaich le/roinn le Y a' dèanamh Z

Love or hate it, I think that particular die has been cast.

It would be trivial to switch from tha... a' dèanamh... to bidh... a' dèanamh..., though, and the schools then wouldn't be actively exposing kids to a misleading model on a daily basis.

[Tha_Mi_Sgìth]

There is a song used in cròileaganan:
Bidh cù ag ràdh, ùf ùf ùf
Bidh cù ag ràdh, ùf ùf ùf
Bidh cù ag ràdh, ùf ùf ùf
Dè bhios tunnag ag ràdh?
etc.
So GME kids are very familiar with that pattern.

[Tha_Mi_Sgìth]

As someone with a degree in mathematics, I can reassure you that "10 minus 4" is indeed 6, in the sense that they are equal and identical to each other, in the sense that the expression "10 minus 4" is interpreted the *result* of the operation of subtraction of 4 from 10, rather than the action itself.

My concerns are 1) There are actually many ways to express arithmetic expressions in English (add, added to, plus, is, makes, equals, is equal to, times, multiply, multiplied by, etc.); so I'm try to fathom a range of Gaelic expression, rather than be fixed to one form. 2) As Gaelic is VSO, it seems strange to me to be forming as phrase with the 'action' coming second (1 cur ri 2).

By the way, I'm not just concerned with primary maths. I want to become familiar with how maths is expressed in Gaelic all the way to the Advanced Higher exams.

[Níall Beag]

There is a song used in cròileaganan:
Bidh cù ag ràdh, ùf ùf ùf
Bidh cù ag ràdh, ùf ùf ùf
Bidh cù ag ràdh, ùf ùf ùf
Dè bhios tunnag ag ràdh?
etc.
So GME kids are very familiar with that pattern.

Exposure to the correct pattern doesn't necessarily compensate for exposure to the incorrect one -- it may even further the confusion.

[akerbeltz]

The dog says af af in Gaelic, incidentally, ùf ùf is just a respelling of woof.

It would be trivial to switch from tha... a' dèanamh... to bidh... a' dèanamh..., though, and the schools then wouldn't be actively exposing kids to a misleading model on a daily basis.

The use of tha here is hardly paradigm shattering. Even if you read really old stuff, bidh is used a lot less for the present habitual than grammar books say. Sure, it does cover the present habitual but its use isn't anywhere near as rigid as, say, the conditional for conditional stuff.

[Tha_Mi_Sgìth]

In Cròileaganan and any materials I've seen, children are given "Bidh cù ag ràdh ùf, ùf, ùf" (woof) and not "af, af, af", so I think there's a big job to change the existing practice of using English animal sounds. It would appear that most Gaelic speakers generally don't care or know about Gaelic animal sounds. They say pigs "oink" and even that hedgehogs "snuffle" (yes). It's as if they believe the language never had it's own way to say these sounds. Such a pity.

Returning to my issues with arithmetic, I am in a quandry about the use of "tha/Dè tha" vs "bidh/Dè bhios". I have learnt that both "Will you live here? and "Do you live here?" = "Am fuirich thu an-seo?" and that "Are you living here?" = "A bheil thu a' fuireach an-seo?" But is this another lost cause, lost to language erosion, or was it never really so strict anyway?

Arithmetic statements are not just for "today", they are enduring. To me, that suggests that "bidh" would be more appropriate. But when I suggested this recently, someone told me that using "bidh/dè bhios" would be harder for the little ones than just using "tha/dè tha". So it seems to be there are various forces at play (i.e. not just the principal of using of present habitual or not, but a desire to be "dumbing down" grammar for children, which will just become how the adult speaks), and I have grave concerns for the current state of Gaelic standards in GME. Nobody ever dumbed down English grammar for me in school, and I didn't suffer any hardship because of it!

[GunChleoc]

My brain understands "Am fuirich thu an-seo?" as "Will you stay here", and not as "Do you live/stay here?" at all.

[Tha_Mi_Sgìth]

OK, if that's the case for your brain, then could you please tell me how you would say the following:
"Do you live (stay) here, permanently?"
"Are you living here, just now?"

In "Gaelic in 12 Weeks" it has on page 110:
'The future forms of tha may also be used to denote habitual actions, particularly when adverbs implying habit are present, e.g.:
Bidb mi ann an Glaschu a h-uile latha. I am in Glasgow every day.
Bidh mi a' snàmh a h-uile madainn. I swim every morning.'

Also in section 64c on page 113: Habitual Present:
'Ceannaichidh lain am pàipear a h-uile latha. John buys the paper every day.
Falbhaidh iad gach seachdain. They go away every week.
Bidh mi an Glaschu gu math tric. I am in Glasgow fairly frequently.'

I think the question forms of the first two of these would use "do":
An ceannaich Iain am pàipear a h-uile latha? Does John buy a paper every day?
Am falbh iad gach seachdain? Do they go away every week?

That's why I thought "Am Fuirich thu..." could mean "Do you stay/live ..."

For a learner, the examples in books like Gaelic in 12 Weeks form important illustrations of usage. It is the case that they are not reliable?

Returning to arithmetic, how do I say "What does one plus two make/equal?"?
Is it the same as "What is one plus two?" ??
In other words, in Gaelic, should I use the present with "Tha/Dè tha?", or the future habitual with "Bidh/Dè bhios?"
Or are both perfectly acceptable?

A separate question: in these arithmetic sentences, should I use "a h-aon, a dhà, a trì", or just "aon, dhà, trì"??

Thanks for any opinion or advice anyone can offer.