Wednesday, March 23, 2011

language of portraying negative #s

Numbers can be seen metaphorically as quantities, points, distances or operations, as constructed objects and as relations.

"But no individual metaphor for numbers can make negative numbers fully comprehensible," continues Kilhamn. "It is therefore important that the deficiencies and limitations of these metaphors are also made clear in teaching, and that logical mathematical reasoning is used in parallel with concretised models."

Her study also highlights a number of problems relating to the fact that the mathematical language used in Swedish schools is a little ambiguous or inadequate. For example, no distinction is made between subtracting the number x and the negative number x if both are referred to as "minus x." There is also no word in the Swedish language corresponding to the English term "signed number."

"Swedish textbooks introduce negative numbers without making it clear that all the natural numbers change at the same time and become positive numbers," she adds. "Another difficulty is the size of negative numbers, which have two contradictory properties that are distinguished in mathematics by separating absolute value (magnitude) from real value (position). A large negative number has a smaller value than a small negative number. This distinction also needs to be made clear to pupils."


D (short for my name. And for duh! if you didn't get that) - some languages may be better able to express math concepts, giving that group a competitive advantage.

We've already mentioned the importance of # names themselves.
I have yet to procure a copy of the book "Outliers" (I think it is called that).

I was looking at typical # naming conventions.
English - zero, one, two, three...
Espo - ?, unu, du, tri...
Visemese - (2-4) ba, cha, da...
Comments - The English # names are challenging to spell for newbies. They are also often long, and so require more working memory.
Espo- ses and sep (6 and 7) have only 1 minimal pair difference, so would be easy to confuse with each other. Both 4 and 5, kvar, and kvin, begin with kv-.
Visemese- even though there is a regular method to the naming (simply listing the consonants, which are each linked to a # concept thereby), they too suffer from the minimal pair issue noted above.

I think the musical note naming convention provides a useful guideline.
Do re mi fa sol la ti...
Both the consonant and (often) the vowel vary.
They are typically of short C-V construction.
By drawing a diagonal line through a chart showing C-V combinations,
we have clear-sounding, short and methodical # names.
In CVN, this seems the ideal trade-off.
This insight can be extended to naming other basic concepts.

I still hope to apply various AUI and syllabary notions to this jumbled mess.
I hope sufficient planning can make for some sort of obvious inherent shorthand system. For example, each letter (small and capital?), #, and so on can be named after, sound like, and stand in for a basic syllable.

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