From: bh@anarres.CS.Berkeley.EDU (Brian Harvey)
Newsgroups: k12.ed.math
Subject: Re: DOING HOMEWORK IN SCH
Date: 16 Dec 1992 16:51:20 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: anarres.cs.berkeley.edu

Carol.Hooper@f64.n381.z1.fidonet.org (Carol Hooper) writes:
>  Can you address the frustration idea though?  For instance, 
>let's assume (I'll use my grade level students 7/8th) that the student 
>is lost...no idea as it is new material so they become frustrated and 
>sit for the 10 minutes gazing into the sky despite repeated prompts 
>from the instructor....how would you motivate the student to give it 
>the ole' school try?

It's not 100% clear from the context which message this is a response to,
but it sounds like mine about starting the class day with activities that
lead into new ideas.

Kids who've been in school for years often have the idea that they are
supposed to *know already* whatever the topic is; the purpose of school
is to determine which are the smart kids who know it and which are the
dumb kids who don't.  The first thing to do is address this idea
explicitly and tell them they are expected not to know the stuff.
Another idea is to give them problems expressed in a way that makes
it clear they're not supposed to know the answer:  "When the astronauts
land on Mars they discover a tablet that says..." with some arithmetic
problem in made-up notation, and the kids are supposed to figure out
the translation.

This style of work is itself something that has to be learned.  And certainly
it's especially hard for students who have a history of failure at math.
I think I'd start by explaining the method clearly.  Tell them that math is
about problem-solving, not about problem solutions.  Tell them that they're
expected not to know the answers to these problems and that they aren't
graded on them.  (Each day, clearly mark the problems that are review vs. the
problems that are new stuff.)  Then, spend some time on material that's
really easy, even if it's not the official curriculum.  I like the pool-table
trajectory stuff in _Mathematics A Human Endeavor_ for example.  Or some
logic puzzles ("who lives in the yellow house?").  Also, do some activities
that focus on cooperative learning -- there is a whole literature about this.
One that I remember requires a group of five people to put cardboard shapes
together to produce five squares, one in front of each person.  The rules
are that no talking is allowed, and you can't ask another person for a piece
by gesture either.  All you can do is (silently) *offer* a piece that you
have to someone else if you think it'll help them.  Another good one is
that NASA lost-on-the-moon game, where first everyone chooses answers
individually and then they redo it in groups, and it always turns out that
the groups do better than even the best individual answer within the group.

I think that a lot of the fear in math class is grade-related.  The ideal
would be if you can get permission not to give any grades at all; then
the students' learning would jump dramatically.  If you can't get away
with that, see if you can arrange some sort of grade cushion; that is,
anyone who keeps up a serious effort all semester (or whatever the grading
period is) and learns a specified bare minimum of stuff gets a C; the hard
things that require creativity get you higher grades.

(I once saw a high school computer programming class that worked this
way.  There were tests, and you had to get some percentage, like 60%,
to get a C.  But getting more test questions right didn't get you
higher grades; for that you had to do projects.  There were a slew of
projects you could choose, ranging in difficulty all the way from
"make a collage of magazine stuff about computers" to serious programming
projects.  You had to negotiate with the teacher about which projects you
chould choose, so the more able kids couldn't get by on collages.  And the
projects were divided into B-level ones and A-level ones, so if you want
an A you have to pick some hard ones.)

(I know that most people believe the opposite of what I said about grades
and learning -- that kids wouldn't learn anything were it not for grade
pressure.  The past few summers I taught an inservice program for high
school teachers at Kent State University; the participants came for six
weeks in each of two consecutive summers, and worked very hard indeed.
There were no grades.  Participants were asked to take on very difficult
new ideas in mathematics and computer science.  We also talked about
pedagogy, and I said this about grades and met a lot of skepticism.  But
it was completely clear to everyone that *they* were able to take on
these frightening intellectual challenges only because they weren't getting
grades; if we graded them they'd have gotten all defensive and whiny and
only taken on the required minimum, just like the kids.)

If you are dealing with a group of kids with a history of failure in math,
part of their fear may be not just the grade but also worry about looking
stupid in front of their peers.  You may need to spend some time in
trust-building activities -- the sort of thing where you climb up on a
table and then jump off into everyone's waiting arms.  (You have to do it,
too, not just the kids.)

Let me reiterate that if homework is a problem I think you could just
forget about homework altogether.  15 minutes of highly-focused group
work at the beginning of class will teach them more than two hours of
unsupervised work done unwillingly later.  Perhaps once they get the
idea of learning by attacking problems you could gradually introduce
homework, to be done *in groups* after school.