Math Forum Discussions

Ladnor Geissinger

Posts: 313
From: University of North Carolina at Chapel Hill
Registered: 12/4/04

Re: Numeracy and literacy as analogs
Posted: Jul 7, 2006 12:05 AM

Plain Text

I am unclear how Mark expects his students to work out the problem he
mentions -- but I think I roughly agree that 'it's not fractions but
mostly notation'. But just where in the problem solving is a search for
meaning occurring, and when should they ask "what's the problem
asking me to do?"?
And what is being decoded or encoded and why in the following possible
path to a solution? Is this what you hope the students will do?

1. Abbreviate and name for clarity and instant apprehension the facts
that are given:
AgeJ = (1/2)*AgeT hence 2*AgeJ = AgeT
AgeM = (2/3)*AgeT hence 3*AgeM = 2*AgeT or (3/2)*AgeM = AgeT

2. Now note connections - relations between facts, guided by question
which asks for a relation between the ages of Mary and Jane:
4*AgeJ = 3*AgeM or 2*AgeJ = (3/2)*AgeM

3. So AgeJ = (3/4)*AgeM or AgeJ = (1/2)*(3/2)*AgeM

Finally, if you wish to using fractions and division one could do
something like this for another version:
AgeJ/AgeM = [(1/2)*AgeT] /[(2/3)*AgeT] = (1/2) / (2/3)
=(3/6) / (4/6) = 3/4

Would one of these seem more agreeable to your students than another?

David Rosen wrote:

> Mark, Milo, and others,
>
> Thanks, Milo, for this clear description of what you have learned from
> your students.
>
> Numeracy and literacy are in many ways analogous. In literacy we must
> "decode" the text symbols and also "get meaning" from them. Getting
> meaning requires making a connection between what we are trying to
> understanding and something(s) we already know. Metaphors, examples,
> and drawings and other visualizations are all good tools for
> understanding (getting meaning from) both text and notation. I wonder
> if vocabulary, background knowledge, fluency, and interpretation are as
> relevant to numeracy as they are to literacy. Do you think so? And
> would you agree that numeracy which uses a compact, precise set of
> symbols for meanings, is more like poetry than prose? Is unpacking the
> meaning of the relationships of two fractions like unpacking the
> meaning of a poem by T.S. Eliot ? Or is that pushing the analogy too far?
>
> And I wonder if teaching math might make more sense to adult literacy
> teachers (who too often teach math without any training at all) if they
> were introduced to numeracy teaching with analogies to literacy.
>
> David J. Rosen
> djrosen@comcast.net
>
>
>
> On Jul 2, 2006, at 8:09 PM, Mark wrote:
>
>> Interesting discussion about fractions; let me tell you what my students
>> have taught me.
>>
>> What they say is "It's not about fractions; it's notation". Those aren't
>> their exact words, but whether doing operations with fractions, or using
>> them in equations, or word problems, or any time they appear,
>> students have
>> trained me to explain carefully what the problem means. For example (a
>> simple one), when you have 1/2 divided by 2/3, this can be expressed
>> many
>> ways. What I found is that typically the first thing they do is
>> search for
>> the rule. I've learned to ask them to put down their pencils and pens
>> and
>> stare at the problem and converse with themselves -- "what's the problem
>> asking me to do?" In essence, know what the notation (think about how
>> many
>> ways this problem can be written, directly and indirectly) is
>> specifying;
>> what is the relationship; can you visualize the problem; can you
>> maybe draw
>> a picture? Then, pick up your tools and go to work. The notation: (I
>> don't
>> have the capacity to produce all the characters, but ... one-half
>> divided by
>> two-thirds; 1/2 / 2/3; one stick is 1/2 foot long, a second one is
>> 2/3 of a
>> foot long; if you lay them end to end, what length have you? Jane is
>> 1/2 as
>> old as Tom; Mary is 2/3 as old as Tom. How old is Jane compared to
>> Mary? and
>> on and on.
>>
>> The point isn't fractions (or equations or integers or ...); it's
>> notation
>> and understanding what it's asking you to do ... mark
>> ----- Original Message -----
>> From: "Milo Schield" <milo@pro-ns.net>
>> To: <numeracy@europe.std.com>
>> Sent: Tuesday, June 27, 2006 11:03 PM
>> Subject: Fractions and Statistics
>>
>>
>>> The concepts of fractions, decimals and percents are important
>>> in statistics where they can reflect conditional probabilities.
>>>
>>> Consider these phrases:
>>> 1. The percentage of men who are smokers
>>> 2. The percentage of men among smokers
>>> This is the difference between P(Smoker|Man) and P(Man|Smoker)
>>> where the vertical bar means "given that."
>>>
>>> Consider these two statements:
>>> 3. Widows are more likely among suicides than widowers.
>>> 4. Widows are more likely to commit suicide than widowers.
>>> The first compares P(Widow|Suicide) with P(Widower|Suicide).
>>> The second compares P(Suicide|Widow) with P(Suicide|Widower).
>>>
>>> In both cases, small differences in syntax can reflect big
>>> differences in
>>> semantics. This focus on ordinary English to express these algebraic
>>> relationships is the basis for statistical literacy. And since
>>> students
>>> will encounter these ordinary English statements in the everyday news,
>>> they must understand these differences if they are to be numerate.
>>>
>>> Milo Schield
>>> www.StatLit.org
>>>
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>
>
>
>
>
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--
Ladnor Geissinger
Prof. of Mathematics
Dept. of Mathematics
Univ. of North Carolina
Chapel Hill, NC 27599 USA

ladnor@email.unc.edu

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