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Q&A #3982


Math homework

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From: Gail (for Teacher2Teacher Service)
Date: May 21, 2000 at 05:19:40
Subject: Re: Math homework

I agree with Suzanne that homework can be a useful tool.   When I assign
homework in mathematics I try to make sure it is to REVIEW content we have
already learned, to provide some independent practice.  Because it is
practice, I don't grade it for correctness (even though we DO correct the
work the next day).  I want my students to be able to take some risks, and I
find they are much more likely to do that if they aren't penalized for being
wrong, so the homework grade is mostly an effort grade.  (In my school system
homework counts for only 10% of the total grade, so this isn't a problem for
me...)

I try to assign something that will make them think, and will help them
review more than one thing at a time.  If we are doing some computation work,
maybe I will ask them to use their estimation skills to select 5 problems on
the page that will have answers over 5 (since I HAVE all the answers it isn't
too hard to figure out a limit) and then just solve those.  Or I might ask
them to do the first 4 and then write new problems that have the same answers
as the first four.

To grade the homework I have groups of students talk together about the
answers they worked out, justifying their ideas with proof (rather than with
loud voices -- we spend some time discussing how to do this!)  They are just
fifth graders, so this is a great was to give them ownership of their work,
and empower them to be math "experts".  Then we talk about the problems the
small groups couldn't come to a consensus on...

I should also say that I rarely assign more than 10 problems, usually less
than that, actually.  I believe that if they know how to do they work, it is
a waste of time to do a whole page worth, and if they don't know how to do
it, they are practicing mistakes, and imprinting THEM instead of correct
procedures.

Often, the work I assign can be completed quite easily, too, but with a bit
more effort, could be a challenge.  For example, last week the homework was
to write an addition, subtraction, multiplication and division problem that
all had the answer 2.46.    When we checked the work in small groups, I found
(as I listened) that several students had used 1 and 0 to achieve their
answers (1 X 2.46 = 2.46,   2.46 - 0 = 2.46  etc.).  I used the whole group
time to ask students what they thought was necessary to earn an "outstanding"
on the assignment, then, when they said the answers should all be correct, I
put the four equations on the board and asked them to decide what grade they
would give the work...

To my delight, most decided the work was correct, but didn't show them much
about what the student knew, since the identity elements were something they
had learned in earlier grades.  They said it didn't take much effort to do
that work, so it shouldn't get more than a satisfactory grade.  I then
countered with the question, "How many of you were able to choose answers
that worked on the very first try?"  and many hands went up.  I reminded them
that if they could "do it quickly in their heads, it wasn't very challenging,
either, so that wouldn't be worth more than a satisfactory grade either...
and we spent some time discussing how to show effort.

Mind you, this is just a 10 - 15 minute time period during my total math
time.  I find I learn a lot about what my students are thinking as I listen
to their discussions, though, so it is well-spent time.

So, to sum it up briefly, I think homework is an opportunity to reinforce
what is learned in the classroom, and can be more than busy work, if the
problems are chosen to help students think about the mathematics they are
doing, and they are required to justify their responses.

 -Gail, for the Teacher2Teacher service

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