Hi David et al,

I wanted to comment on some of the issues you raised about the differences
between children's and adults' experiences learning math/numeracy. To me,
one of the primary differences is the whole idea of learning math vs.
learning numeracy.

In school, children are generally learning math so that they can go on to
and be successful in higher levels of math. Children are full time
students; that's pretty much what they do. While there is an assumption
that the math children learn will be available for other, everyday
purposes, meeting those purposes (usually expected to be in the future) is
not generally the goal of school.  Thus, our statement about the exclusion
of societal contexts in school math. I know that's a gross generalization,
but I think it's often true. Just think about "word problems" that have
sometimes been promoted as "real world applications." Word problems are
virtually always contrived, pretty formulaic, and function as
computational examples with words, and usually aren't very
realistic/meaningful to the learner (When was the last time a teenager
really needed to figure out when the two trains would meet? For that
matter, when was the last time you needed to figure that out?). Most of us
noticed pretty quickly that the word problems following the pages on
multiplying fractions could all be solved by multiplying the fractions
between the words.

On the other hand, we have been thinking of "numeracy" as being integrally
connected with real world activity, continuously crossing the
school/everyday life chasm. Adult learners have one foot in the classroom
and the other in the outside world. They bring that world into the
classroom with their experiences, and they should be able to bring their
classroom-based learning out to their real lives. Tasks and problems in
real life are messy, call for judgements, estimations, and assumptions.
Math becomes a tool, not an end in itself.

Without getting into the whole "math wars" thing, the K-12 math reform
movement has tried to shift the emphasis of school math learning from a
focus on acquiring and mastering decontextualized computation skills to a
focus on developing conceptual understanding. To me, this is a shift
towards my vision of numeracy.

Getting back to your question about the teacher training videos that show
children exploring, talking about math concepts, struggling with making
meaning of the math -- I agree these are similar to what I would like to
see in adult ed classes. The few existing videos of adult ed math
instruction are also in this vein (from the TIAN/EMPower projects, from
NCAL's PDK, others?) Generally all these videos are from reform classes,
often from National Science Foundation curriculum projects. I think these
video tapes have been created from the need for teachers (K-12 & adult ed)
to be able to see what a different kind of instruction might look like,
especially since most teachers didn't experience this kind of schooling
themselves. [I know that this was the rationale behind "Captured Wisdom"
which focused on using technology in the classroom].

That said, I am sure there are also some videos out there promoting rote
learning of math facts, but we all already know what that looks like.

Sorry to be rambling,
Lynda


David J. Rosen wrote:

> Colleagues,

>

> I do hope our guest authors might address the three questions I posed

> yesterday, and here are  three more:

>

> 4. One difference, that you point out in the study on page 15,

> between how children and adults learn numeracy is “The inclusion of

> societal contexts in adult-focused frameworks stands in marked

> contrast to the exclusion of such contexts in school-based

> frameworks.”  Are there other differences?

>

> 5. I have been looking at some numeracy teaching/teacher training

> videos, for example:

>

> http://mlots.org (“Ratio and Proportion”)

> http://www.teachersnetwork.org/media/index.cfm (“Real Math”)

>

> Most of the videos I have found are focused on children; very few are

> focused on adults; but the approaches are similar: getting teachers

> comfortable in the language and use of numeracy thinking, organizing

> classrooms so students are actively engaged in discovery of numeracy

> concepts, and helping learners make those concepts and related skills

> their own. What do you see as the similarities between how children

> and adults ideally should learn numeracy?

>

> 6. On pages 16-17 of the study you describe a continuum of

> contextualization and give examples of two very different word

> problem learning activities, the opposite ends of the spectrum. The

> first is a decontextualized opportunity to practice some recently-

> taught skills – an activity that is “realistic”, not “real”. The

> second grows from a real-life context where students do not have

> clues, other that the context of the problem itself, for what

> numeracy is needed. I wonder if you have other examples along the

> continuum that you could share.

>

> David J. Rosen

> Special Topics Discussion Moderator

> djrosen at comcast.net

>

>

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-- 
Lynda Ginsburg
Senior Research Associate, MetroMath
Rutgers University
tel: 732-445-1409