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Math Training Module: Using the Internet in Support
of GED Math Instruction
Session Two: Problem Solving
1. Exploring Websites
Procedure
1. Ask participants to think individually about their own school math
experiences. Ask them to focus on how information was presented to them,
what they were expected to do with that information, and what happened
after that. Give them 3-5 minutes to jot down some ideas.
2. After five minutes, ask them share their recollections. Try to find
common experiences and relate them to the process of problem solving.
The scenario you are most likely to hear will be something
like, “The teacher lectured and put problems on the board, we had
to solve the problems, and whoever got the right answer first told how
s/he got it.”
3. Ask if they ever heard “You got the right answer but you did
it the wrong way.” If you get affirmative responses, ask them what
message that conveyed to them.
You’re looking for something like “it told
me that there was only one right way to get one right answer.”
4. Finally, ask, “What learning occurred in this situation for
those who couldn’t do it the ‘right’ way?”
You will probably get several answers, e.g., they learned
that they weren’t good at math; they didn’t learn anything;
they had to learn on their own.
5. Make the following points:
- Adults who come to our programs often were the ones who felt that
they couldn’t do math because they couldn’t do it he “right”
way.
- In the math classes they knew—and in too many adult classes
today—no opportunity existed for exploring “other”
ways to a solution. In this kind of class, the focus is often on memorizing
rules that would allow students to get answers the “right”
way. If you couldn’t remember the rules, you couldn’t be
“good” at math.
- The challenge for adult educators is to change the structure of the
math classroom so that the focus is less on getting the answer and more
on the process of solving the problem.
- Math as problem solving rather than answer getting is much closer
to the way we “do” math in real life.
- In everyday use, we frequently learn from our mistakes—so the
process of problem solving must assume that mistakes will be made and
it must articulate a way of dealing with them.
- In practicing the process of problem solving, we develop an assortment
of problem solving strategies that we choose from, trying and selecting
strategies until we find one that works. The most successful problem
solvers are those that have experience with a wide range of strategies.
- Problem solving usually involves communication of some kind—in
small groups, pairs, triads, or even “self-talk” where we
“talk out” what we’re trying to do and how we’re
trying to do it. This is one good way to learn about different strategies.
- On-line math lessons and activities may support either the classroom
that emphasizes getting the answer, or the classroom that emphasizes
the process of solving the problem.
6. Ask participants to explore the websites listed on Handout 2a from
the perspective of a teacher planning a lesson. Ask them to select three
(3) websites to review and answer the questions that follow. Tell them
that once their exploration is complete you will take a break, and then
groups will share their impressions. Allow 60 minutes.
7. After 60 minutes, take a 10-minute break.
If possible get a discussion going as different individuals
share what they found on the websites. How did their concept of a “good”
lesson change as they considered shifting to the process of problem solving
instead of just getting the answer? This is an opportunity to communicate
about mathematics.
8. Tell everyone that for the next 40 minutes they will be sharing impressions
of websites. If possible, project each website so that everyone can see
it during the presentations. Begin with the Figure This website. Ask anyone
who chose to review that site to share their impressions with the group.
Invite others who also reviewed it to add their comments, to agree or
disagree with the first speaker, or to give a different perspective.
9. Continue in this way through all of the websites. Because you can
allow only 40 minutes for this debriefing and sharing activity, you will
need to watch your time to ensure that you get to cover all the websites.
10. Wrap up this section by asking for any questions or final impressions.
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