The Math Forum: 2000 Summer Institute - sum2000

July 25 - August 11, 2000 - Swarthmore, Pennsylvania

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2000 Summer Institute || Agenda || List of Participants
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Participants' Comments about ESCOT PoWs

Matt: Scale and Bowl reinforces the relationships between fractions and decimals. I Iiked that you could see the changes in the fraction as you changed the numbers.

Shirley: I think the kids would like these kinds of problems because they like video games. Personally I wasn't stimulated.

Jo: I love Search and Rescue. It's so visual and really teaches kids.

Jeanne: I would use S&R in AlgII/Pre-Calc class. It's a nice jump off for teaching vectors.

Dave: In the future, I would like to see some problems with equations and basic integers. Also ratio/proportion.

Jeanne: I would also like to see probability as a topic. It is part of the Standards and teachers need more ideas/resources for teaching this. Most of the activities available are at lower or higher levels than what I and other secondary teachers need. Many activities include dice and cards, which are not appropriate in some schools because of people's religious beliefs. She wants more varied approaches.

Jo: Key Curriculum has a probability and statistics book that uses graphing calculator activities. It would be great to have simulation models to go with them. For example, there are probability problems centered on the likelihood of people getting on and off elevators under certain circumstances, which could be visually modeled.

Suzanne: Which concepts are difficult to visualize? These would be important for the ESCOT PoW to address. What about a problem that combines Algebra and Geometry. For example, the question could be focused on a graphic image that shows a spatial relationship, and the students must represent it symbolically.

Jeanne: Like area, volume, ...

Matt: Or scale factor, changing triangles, ...

Jody: Is there any feedback on specific problem sets?

Danielle: The size of the text is too small. For the earthquake problem, the gray line that represents time passing gets lost in the gray grid of the coordinate plane, because of the color. For the llama problem, the blue and yellow representations parts of the fence on the description page are confusing. In the Sketchpad parts of the problem, the question mark was confusing because it looked like it might be interactive.

Group: Yes, it looked like a link.

Shelly: The earthquake thing made more sense to me by the time I got to the third problem. It was a great way to represent that the greater the distance, the greater the time difference. In the figure in the first activity it was unclear why rate was fixed but I could manipulate the parameters of time and distance. An explanation in a teacher page would have helped make things clearer through the problem.

Dave: Be careful. You don't want to give too much away to middle school students.

Jody: Suzanne wants to write teacher pages to help clarify the questions. They could also give background for the math and or content.

Jeanne: ESL kids get stuck on interpreting language. If a house can be 3, 7 or 10 miles away, it doesn't mean that the house is moving.

Suzanne: Middle school students with lower reading achievement have trouble too. Nathalie and I are thinking of making support pages that could include video clips, etc to help.

Shelly: I would like the program to keep a trail of data you have already tried. Keeping a record could be very helpful. The llama had a slider to show the change in scale. This would be helpful in the decimal/fraction problem.

Suzanne: The teacher can teach kids to take their own notes. They can be responsible for their "trail". Including this in the program would slow it down and perhaps make the screen confusing.

Jeanne: The best learning for me is when I have to struggle a little to understand. I need some challenge to keep going. As for the "slider", I prefer the idea of students entering different numbers that they choose so that they can see that 1.75 is less than 1.8. The slider won't give them the "pause" to think about this.

Suzanne: Agree, it may be better not to put "too" much on the page.

Jody: Future steps: Would you be interested testing problems on browsers with an honorarium? Would you be interested in using them in the classroom? (Dave and Danielle both showed interest in using them in class.)

Jody: They should be ready to run on other browsers in October.



Susan who is now participating online offered the following comments:
What are some strengths and weaknesses of the EPoWs?
  1. I love the interactivity of the problems. I think this is the strongest point that the web has to offer for instructional purposes. If you look at my web page, you can see that almost all my sites are built around this principle.
  2. I don't think that the student should have their responses "tracked" for them. Part of data collection is learning how to collect and organize data! I see this as a strength rather than a weakness. Students need to create their own format for collection of data.
  3. I think it would be a good idea to survey teachers who use these with a class to ask them what kinds of questions they asked the students to guide them through the process. These questions probably need to be included with the problem.
  4. I thought some of these problems would be difficult for "regular" middle school students. Have they been tested with gifted and talented and "regular" kids. I think my high school students would find these at their level.
The helicopter problem
A weakness: I think you have to be careful about how the problems are constructed. I loved the helicopter problem, but I did it just by trial and error, without any mathematics at all.
Here are the directions for the first part: Experiment with how the directional arrow on the compass affects the direction of the helicopter.
That was easy enough--just move the arrow, and it redirects the helicopter. I didn't notice myself that the degrees were in negative numbers in the box until I played with it some more. Since the hospital is in a positive degree direction, the students probably didn't even pick up on any negative headings.
How would I change this?
  1. Experiment with how the directional arrow on the compass affects the direction of the helicopter. Try making it fly Northeast, SouthWest, Northwest and observe the degrees on the compass and the headings. What is the relationship between degrees and headings?
  2. See if you can figure out how far it is from one concentric circle to the next. What is the radius of the largest circle?
Part Two is ok, but again, the heading is a positive degree measure and can be found by trial and error. I think I would have put the hospital over to the left, to make the bearing negative, so that in step three, they weren't learning two things, both changing direction and a negative heading.

Part Three--If you changed part Two so that they understood negative headings, I would remove the compass in Part three so that they would have to input the headings by understanding, not by trial and error.

Part Four--I think if the changes above were made, the students would be able to do Part Four.

What other simulations/visualizations do you wish would be available? What math concepts should be addressed?
One of our geometry standards that is very difficult for the kids to visualize are stacked cubes, from 3-d to 2-d. On almost every one of their tests, they are given a three-d view of cubes, and told to figure out which 2-d picture matches the 3-d views. This is hard to explain without a diagram. In the 2-d views, a bold line means there's a break in elevation. Anything you can do with spatial visualization would be greatly appreciated by all of us in the trenches. Another concept that was very difficult for students to grasp this year was the relationship between linear measure, surface area and volume of similar figures. (Surface area is squared, volume is cubed). They would get the concept, but they couldn't apply it to a problem involving a scale model of a car! I thought this would be great for visualization--you could scale something up and down and see the actual change in surface area and volume, and then apply it.

How would you use it in class?
I think I would have the students begin work on these during the class period and then send them home to work on it some more. I would use this as a continual discussion point throughout a unit, and refer back to it often. I would keep the link on their link list so they could get to it easily.

Would you want to customize the activity?
I would customize it only if I felt that the students weren't getting it. I wouldn't want to tell them how to do it, but I might want to add some more questions to help them get to the resolution of the problem.


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