|Q: Regarding your classroom environment, I assume you used two
different rooms? Is that right? How did you organize this?
A: I organized this out of necessity. My classroom is
a computer lab with twenty computers. I teach all of my classes in it and
I have talked another teacher, who also teaches 7th grade math, into trading
with me one day a week. It was going to be two days a week but she can't
handle that so my class goes to her "regular" classroom one day a week
and the rest of the time we are in my computer classroom. Yes, I think
it is better to have two rooms at your disposal at any time when you teach
this way so that you can go back and forth, however, the reality of a school
is that you have to make do with what you have.
Q: Where did you learn about this puzzle?
A: I first learned about it during a professional development
technology workshop. It was introduced as an ice-breaker activity and we
used our bodies and tiles on a porch. After that experience I did not have
a full mathematical understanding of the problem. During another workshop
the instructor demonstrated a Java applet that let you do this puzzle on
a computer. I later discovered that the same puzzle was in my Glencoe textbook
as a warm-up exercise but did not get into any of the math. I used it with
adults in a workshop and with those adults I learned the algebraic solution.
So I decided to build on that lesson, put in the math, and use it as a
more complete lesson with my students.
Q: You say it took you five days to do this lesson sequence?
A: Actually six, I started the activity in the lab (but
I would have preferred to have been in a classroom) but the students didn't
use the computers. We read the problem aloud from the textbook; the students
had the baskets and plastic people and they interacted with them. At the
end of that period I was going to have the students interact with the applet
but I ran into a java glitch (because of the age of the computers in my
room) and we did something else instead the last ten minutes of class.
Q: Regarding resources, describe your computer classroom.
The second day we were in the classroom and I displayed the applet on
the screen (using a video projector). One student interacted as the other
students watched or gave suggestions and we started looking at the pattern.
(This was not the only task that day but that is the only part of what
we did on Traffic Jam.)
(There were some days in between here when we did something else.) The
third day (I had fixed the computer glitch) we reviewed the problem and
then went to the Java applet. We started discussing the problem putting
the chart on the whiteboard and looking at the pattern.
The fourth day we were in the classroom again and this time we reviewed
all of the information and worked through the pattern and the algebraic
The fifth day the students took a quiz. The sixth day the students practiced
in groups to perform the activity with their bodies and near the end of
the period I videotaped the results. If I had time tonight I would replay
the video and maybe my memory would return better.....we did this activity
the end of September....but... I know I spent about a week and a half of
class time with this activity overall and I feel that it was time well
Two years ago I taught in two-hour blocks. One hour we were in a classroom
and the second hour we were in my computer classroom. This was a great
arrangement to do Traffic Jam because if you start in the classroom and
then go to the applet in the lab and then the next day you're back in the
classroom again. Fun!
A: My computer room usually has twenty LC580s running
System 8 with 40MB of RAM. We had to use Netscape 3 with the Java applet
but usually run Netscape 4.05. All computers are connected to the Internet
Q: For software you used a Java applet (Traffic Jam) along with
an overhead projector displaying on a whiteboard. You also use a computer
projection device. For this lesson you decided not to use the projection
device. In retrospect, how would you have improved your lesson?
A: Every time I do this lesson I change something, either
the order of using plastic people, using the Java applet, and/or using
student bodies or when I jump in and have the group discuss. Trying to
assess where the students are in their learning is important and sometimes
I assess correctly and other times I do not. So, I could list a variety
of things that I might change but then the next time with a different set
of students, those things might not apply. To answer your question honestly
I would say I wouldn't change anything because I was happy with the results.
My students were engaged and more importantly they were challenged. Some
students thoroughly understand the algebraic formula that we finally developed
and others still don't have a complete knowledge of it but they are much
closer to understanding it than they were when we first started.
Q: Given your students' background, what did you hope to accomplish?
A: I didn't assume anything. I rarely do. :) It's a
weird quirk of mine. My students usually come to me so lacking that if
I worried about background mathematical knowledge all I would ever do is
drill them in their basic facts. So, I just dive in and see what happens.
Q: It appears that you were encouraging them to focus on finding
patterns horizontally. Were you looking for any patterns or did you have
a game plan for horizontal and vertical approaches? I note your focus on
your horizontal method in part 3.
A: Actually, I had no game plan. I was waiting to see
how they would go. It seemed at one point that they were looking horizontally
and I tried to follow that, but I had no way that I was guiding them (that
I was aware of).
Q: What are your thoughts on the debriefing phase, how might have
you done it differently? What do you think the kids learned?
A: One thing that I distinctly remember cringing about
was some of the notation that I used. Also, the overhead was not placed
close enough to the wall - changing that would be an easy adjustment.
Q: I know you are a big fan of multiple representations of activities
(i.e. using a variety of resources to solve problems). In this activity,
doing the computer activity certainly enhances their computer experience,
but how does the computer enhance the learning of math here?
A: This Java applet that Mike Morton wrote gives the
students immediate feedback. I only have the students use the "easy" and
the "medium" settings which are two pairs and three pairs of people. Until
the time that the students use the Java applet they are not certain that
they have reached the minimum number of moves. Interestingly, once they
do it once they can't always duplicate their success. At that point continuing
to try using the applet reinforces their knowledge. Then it is important
to have them return to using the plastic people and show me they understand
Q: After you had your students come up with the rule for predicting
the moves for any given number of people, what did you do?
A: In the following lesson, I had the students do a
human puzzle. I had three students on one side and three on the other and
they walked through the puzzle.
Q: Why did you do this activity last, rather than earlier in the
A: I tried doing it that way a couple of years ago.
It was a disaster! The students had no idea what was going on. Even using
the people pieces posed problems. What worked the best was the Java applet.
Q: Really? Actually your response leads to my next question. It
seems to me that the computer played only a minor role in this activity.
Could you have just as easily done this activity with the people puzzle
A: No. Using the computer made it easier for them to
do the puzzle AND keep track of the number of moves at the same time. That
was the big problem with the people pieces - not only was the puzzle hard
for them, but they also had trouble keeping track of the number of moves.
On the computer, it was much easier for them to experiment with different
moves. They were able to focus more on the patterns and problem solving.