Not quite a video game

Computer-based simulations for inquiry-based teaching of best-

practice pedagogy

Larry Copes, ISEM

The Experience

Problem

Simulation

Reflection

You’re the teacher!

CatchupI am helping my friend move by driving his car across country behind the rental truck he is driving.

As we start, he points out that the car needs gasoline. He says he’ll go on ahead because the truck will go only 55 mph and I can catch up with him.

After filling the tank I leave the gas station 15 minutes behind him. If I drive 60 mph, how long will it take me to catch up with him?

The Experience

Problem

Simulation

Reflection

The Experience

Problem

Simulation

Reflection

Reflection questionsAsked in a methods course last month (Kay Shager, Augsburg College):

1. a) Where would the Catchup problem fit into a math curriculum?

b) Which NCTM standards are addressed by the Catchup problem? (Be sure to check the objectives.) Write out the complete standard and benchmark.

Was the Catchup problem represented effectively? Which representations were used?

b) Can more than one representation be legitimate?

c) What other representations might have arisen, legitimate or not?

a) Which of the students in this class are “good at math”?

b) Can all students learn mathematics?

c) Was this lesson taught the way you were taught mathematics?

a) What made it possible for Yiscah to ask the question about closing speed?

b) Which of these questions had you thought of before seeing them here?

c) Which if any of these questions are important for teachers to think about?

Asked in a professional development course (Larry Copes)

Are the Catchup problem and the other problems of this simulation real math problems?

Are problems different from exercises?

Were the students engaged in problem solving?

Is Yiscah’s idea valid mathematically?

What’s your response to Terry’s question about Yiscah’s idea?

Did any of the solutions to these problems constitute a proof? Please explain.

Write a lesson plan for the most successful choices in this lesson.

What choices do you think would have been better?

At one point you as a teacher said,

An elegant approach can lead to feelings of exhilaration that overcome the many feelings of frustration along the way.

Have you ever experienced that exhilaration in doing mathematics? If so, please describe your experience.

Now you’re the educator/supervisor

How will you describe your simulation experience to someone who isn’t here?

What questions can you ask about the simulations?

c) Is it ever OK to discuss mistakes rather than just correct them and move on?

In this simulation it worked best to discuss mistakes rather than correct them. Learning can happen best from mistakes sometimes. Then they will really understand why they have to be careful when setting up a table or graph and why they have to define their axes and charts. New ways of looking at a problem can also come out of a mistake, though I cannot think of an good example for this situation.

Pre-service teacher responses

I found a number of [NCTM] standards that were met but none of them completely. For organization, the benchmarks that are crossed out were not satisfied, in my opinion, by this activity. I tried to explain as well why I thought some were fulfilled.

[There follows a page and a half of single-spaced analysis of four standards and substrands.]

When [Yiscah’s] idea was presented in our small group in class [before doing the simulation], I didn’t understand it. It was explained verbally several times, but I still struggled to comprehend. However, when it was explained in the simulation it finally made sense.

I was intrigued by [virtual student] Sean’s insight in seeing the 1/3, 2/3 split. I am often befuddled when students come up with a solution that’s foreign to me. Sometimes I have to tell them that I need time to think about it because I don’t want to shut them down, but I also don't want to verify a method that is just coincidental.

Inservice teacher responses

about various simulations

At first, I tried doing what I thought that I would do in the situation and I kept getting scores in the 6000's. Then I thought that it would be a good idea to try something different and see where that would lead. I learned so much by doing that. I kept trying new things and seeing how that changed my score. I really stepped out of my comfort zone and it helped so much. I think that I really learned a lot about how to improve on my teaching by doing this simulation.

One insight that I have gained is that I really need to work on strategies for group work. I do not use group work a lot because it has not really worked for me or other teacher who work with the same students. I need to research strategies.

The multiple approach to find the answer is very interesting. I have worked for some heavy-handed managers and with bull-headed coworkers outside of teaching who did not appreciate the multiple approach method of finding a solution. They wanted everyone to think and do as they did. It makes for a very unfriendly and stilted work environment. I will have to pay closer attention to how I use this in my classroom.

Methods class discussion

Rose Chu, Metropolitan State Univeristy,Urban Teacher Program

How might simulations like these be used?

After a year of teaching

I do recall the simulations...i haven't thought of them consciously since then, but i found them quite helpful.

though canned, they helped me to think of how students may respond to what i say or don't say, regardless of whether or not i would really say what my options were

in this age of video gaming, this and maybe only things like simulations can hold our interests and keep us engaged.

Not quite a video game

To use in a course or workshop, contact Larry Copes, ISEM, copes@edmath.org

www.edmath.org/MATtours/simulations

sample simulation: