Street math and diglossia

In "Mathematics in the streets and in schools" (Carraher et al. 1985), child street vendors were given a paper and pencil and asked to calculate multiplications that they had, in fact, already done in their heads in the course of selling their wares. The results were often sobering, as in the following case:

Informal test
Customer: OK, I'll take three coconuts (at the price of Cr$ 40.00 each). How much is that?
Child: (Without gestures, calculates out loud) 40, 80, 120.

Formal test
Child solves the item 40 x 3 and obtains 70. She then explains the procedure 'Lower the zero; 4 and 3 is 7'.

As you can see, the children were perfectly capable of doing (some!) multiplication their own way, but when faced with school-style problems, this ability frequently deserted them. Confronted with a piece of paper, they attempted to apply the algorithm they had learned at school, without so much as checking their answers against the algorithm they had mastered as part of their daily life. In daily life, conversely, they presumably weren't getting much out of the multiplication algorithm they had learnt at school, even though it would let them tackle a much wider range of multiplication problems. School-learning that stays at school, and never affects real life despite having an obvious potential to be useful there: it's an educator's nightmare.

What this immediately reminded me of is diglossia. In a schoolroom or an essay, you obediently attempt to use Standard Arabic, and all the grammatical rules and vocabulary you learned for it. Almost anywhere else, you carefully avoid it, even while claiming to accept that Standard Arabic is correct and that what you actually make very sure to speak is wrong. To me, that seems to send a fundamentally problematic message: that what you learn in school is not supposed to be useful outside of some limited institutional contexts. I hope that's not the message most people get from it, but it would be great to know for sure. I don't suppose anyone knows of a study addressing the question?

*-min-: an Algonquian morpheme that went global

American English was born in the clearing of the eastern woodlands, where British settlers encountered native Americans mostly speaking Algonquian languages. The same is true, mutatis mutandis, of Canadian French. If either language can be said to have a native American substratum at all, it's Algonquian. This substratum is hardly conspicuous, manifesting itself almost exclusively in loanwords. If the Algonquian languages had vanished without record, as most of the pre-Indo-European languages of Europe did, could anything at all be said about their morphology on the basis of this influence?

It turns out that there's at least one bound morpheme that shows up in quite a few loanwords: *-min- "berry, fruit". But it manifests itself more clearly in French than in English, where it has been obscured by a number of irregular developments.

Today, French barely survives in the upper Midwest; but before Jefferson's purchase of the Louisiana Territory, France claimed the whole of this vast area, and attempted to back up its ambitions with a handful of missionaries and settlers. There, up among the Illinois near Peoria, French speakers encountered two quite unfamiliar fruits, and adopted their names from the Myaamia-Illinois language:

• plaquemine (persimmon), first recorded as piakimina by de la Salle in 1682. Cp. Myaamia pyaakimini pl. pyaakimina "persimmon fruit", with corresponding pyaakimišaahkwi "persimmon tree". In modern Paris, you are far more likely to hear the Japanese word kaki; but in Dellys, if you find a persimmon at all, it'll still be called plakmina پلاكمينة...
• asimine / assimine / (Louisiana) jasmine (pawpaw). Cp. Myaamia ahsiimini "pawpaw fruit", corresponding to ahsiimišaahkwi "pawpaw tree" (but this seems to be a reconstruction, and the source might actually be Virginia Algonquian).

English missed the chance to borrow a local term for the pawpaw - the English word derives from papaya, a fruit originating much further south - but adopted a reflex of the same word for "persimmon", along with several other terms containing this. Unfortunately, most are fairly obscure (although no more so than "asimine"), and no two show the same form of the morpheme:

• persimmon; cf. Virginia Algonquian putchamins (Smith), pushenims (Strachey), apparently reconstructed by Siebert as pessi:min (cf. Skeat 1908; although that looks rather implausible given the Illinois form).
• hominy (because it's made from corn); cf. Virginia Algonquian ustatahamen (Smith), vshvccohomen (Strachey) and other forms.
• chinquapin (a kind of chestnut); cf. Virginia Algonquian chechinquamins (Smith), checinqwamins (Strachey).
• saskatoon (a berry); cf. Cree misâskwatômin ᒥᓵᐢᑲᐧᑑᒥᐣ.
• pembina (a kind of cranberry); cf. Cree nîpiniminân ᓃᐱᓂᒥᓈᐣ.

The prospects are not that encouraging, but combining the English and French evidence, an alert etymologist just might be able to spot the *-min- morpheme, and hence guess that Algonquian had head-final compounds. Thankfully, in North America, such hyper-speculative substrate chasing is hardly necessary; Algonquian is a fairly well-documented family. In other parts of the world, though, such approaches may occasionally prove effective.

What's wrong with the obvious analysis of waš bih واش بيه?

In the Algerian Arabic dialect I grew up speaking, "what's wrong with him?" is waš bi-h? واش بيه. (Further west, in Oran and in Morocco, it's the more classical sounding ma-leh? ما له.) When the object is a pronoun, as it usually is, waš bi-h? can readily be understood as waš "what?" and bi-, the form of "with" (otherwise b) used before pronominal suffixes (in this case, -h "him"). But substitute a noun, and this historically correct interpretation becomes synchronically untenable: we say waš bi jedd-ek? "what's wrong with you (lit. your grandfather)?" واش بي جدّك, whereas "with your grandfather" would be b-jedd-ek بجدّك. Nor can we cleft it with the relative/focus marker lli اللي: *waš lli bi jedd-ek? (*"what is it that's wrong with you?") is totally ungrammatical, while *waš lli b-jedd-ek? does not have the appropriate meaning (in fact, out of context, it makes no sense at all). This tells us that, whatever its origins, waš bi- can no longer be analysed as "what?" plus a preposition "with"; it has to be treated as a morphosyntactic unit in its own right. In particular, this bi- cannot be used to form an adverbial - it only forms a predicate - so it can hardly be treated as a preposition. Nevertheless, it continues to take the prepositional pronominal suffixes: "what's wrong with me?" is waš bi-yya? واش بيَّ, not *waš bi-ni.

The independent unity of waš bi-? becomes a lot clearer when the construction is borrowed into another language, as has happened in the Berber variety of Tamezret in southern Tunisia. The stories recorded there by Hans Stumme shortly before 1900 are a bit hard to read, but provide probably the single most extensive published corpus of material in Tunisian Berber. These texts furnish many examples of aš bi-, although Tamezret Berber neither has aš to mean "what?" (that would be matta) nor bi- to mean "with" (that would be s). Many of these look just like Arabic: aš bi-k "what's wrong with you? (m.)" (p. 14, l. 11); aš bi-kum "what's wrong with you (pl.)?" (p. 27, l. 26), aš bi-h "what's wrong with him?" (p. 14, l. 3); and even, with a noun, aš bi iryazen "what's wrong with men?" (p. 41, l. 5). But the similarity is somewhat deceptive; in some cases, this construction takes Berber rather than Arabic pronominal suffixes, as illustrated by aš bi-ṯ "what's wrong with her?" (p. 25, l. 21) instead of Arabic aš bi-ha, aš bi-m "what's wrong with you (f.)?" (p. 10, l. 5). Unfortunately, the texts do not provide a complete paradigm - further documentation is needed! But judging by the available data, all cells but 3m.sg. match well with the Berber paradigm:

	Algerian Arabic	Tamezret	Tamezret, direct objects	Tamezret, objects of prepositions
2m.sg.	waš bi-k	aš bi-k	-ak	-k
2f.sg.	waš bi-k	aš bi-m	-am	-m
2m.pl.	waš bi-kum	aš bi-kum	-akum / -awem	-kum
3m.sg.	waš bi-h	aš bi-h	-ṯ	-s
3f.sg.	waš bi-ha	aš bi-ṯ	-ṯ	-s

The 2m.sg. and 2m.pl. suffixes are quasi-identical between Tamezret Berber and Arabic, facilitating the borrowing; for the second person, neither language clearly distinguishes direct object forms from objects of prepositions. The third person, however, distinguishes the two in Berber but not in Arabic, and 3f.sg. suggests that the object in this construction is treated as a direct object, not as the object of a preposition, contrary to the situation seen for Arabic. This fits Berber-internal patterns; throughout Berber, nonverbal predicators (Aikhenvald's "semi-verbs") typically take the direct object pronominal paradigm, and assign absolutive case to their arguments. The perfect agreement of the most frequently used cells in this paradigm between Arabic and Berber surely facilitated the borrowing of this item, but within Berber the paradigm got rebuilt on a largely Berber basis. In morphology, etymology is not destiny!