ESCOT Summer Workshop 2000
ESCOT Summer Workshop 20000 || Math Forum Workshops

Day 2 Summary

New ESCOT Interface
Chris shared the new ESCOT interface. The plan is to use applets this year instead of the ESCOT Runner.

Proposed changes:
Students will identify themselves before using the applet by logging in, or they can register as a guest. Only if they login, can they save their work on the applet. They won't have to describe as much of their work in text. As a guest they can only use the applet.

The explanation and directions will appear at the top of the page. Then the activity loads while you wait. When you click on the button, the applet will appear in a new window. This way, you will have one window to work in and one window to write answers/responses. There is some concern about students needing to juggle multiple windows. Other concerns include machines being able to run JAVA and the size of the monitor. This new format prints well. Suzanne likes having the activity as a separate window. It allows them to concentrate on the activity without getting caught up in the print. A computer need to have Swing in order to run the activities on the browser. This setup only happens once.
The Escot Catalog is also new.

The catalog contains components, description of the activities, background information, and a link to the Math Forum.
Components include Sketchpad, graphing, box plots, histograms, world, tables, a spinner (for probability problems), a calculator, Image/J, widgets, a recorder, and Scripting.

Each strand in the NCTM Standards is described and linked to specific problems that address the Standard.
The project will use Bean Builder 2000 to create the ePOWs. It lists the components and allows developers to modify the components. If you click on "sample", the program will record data from the activity like a snapshot.
Ideas for New Problems:
Individual participants contributed ideas for the problems list. Some conversation ensued to clarify the problems. Ten of the problems were discussed in two break-out sessions.
Session 1: Choosing problems for collaborative teams to elaborate.
1. Fraction Tetras -- Nathalie, Bill, Gerri, Seth, Alex

The group brainstormed many ideas. Two ideas that we like:
  1. The first is kind of freeform. Students build a mosaic by coloring pieces and setting fraction parts. They can build a wall or stained glass window with the shapes. This may be something like tile by number.
  2. The computer would seed a row with a number of tiles. Then kids would be given a format for their answer (percentage, fraction or decimal). Maybe they would want to get as many rows as possible. Rows could be numbered, you'd be told the pattern (1 block, 2 block, etc.) They might choose blocks from a "box". (Leslie might have ideas to add since she had the original seed idea.) Instead of working with the time component of the original Tetras game, set a challenge to see how high a wall can be built with different rows -- combinatorics.
2. 3-D -- Steve, Chris
  1. The group spent a fair amount of time defining the problem and making sketches.
  2. It can be 2-D or 3-D. What happens if you double or triple the dimensions. What happens to surface area? Three main directions:
  3. Try making it a unique problem by having students work on the screen and then print out the net. Compare volume change to surface area. They would actually build the shapes. Perhaps use Poly for this.
  4. Do it more graphically. Would we provide a GSP opportunity? Could plot data to show changes in area, perimeter, etc.
  5. A 2-D question would be: How does the perimeter change when you change the configuration of tiles? How many different "perimeters" can you get with a certain number of tiles? This could be a fixed area problem. Ex. take a set area, how does the perimeter change? Or set a fixed perimeter and investigate different areas.
3. Chances of making a triangle from a stick -- Dave, Vicki, Mark, Orit

The group quickly realized how difficult this problem was. Combining math and standards: first they needed to figure out where to make the breaks. There is a site on the Math Forum with ideas for this. Nathalie showed some programs that could already help with this. To define the problem, they used counting numbers as lengths (up to 12) and listed the possibilities.

4. Taxi Cabs and Euclidian Circle Geometry -- Nick, Jim, Wenming

They want to do more research, need more time and a computer. Jim found a Math Forum site that already addresses this problem. This could be a reason to discount it from the project. Nick: However, many problems students get in class are available somewhere else. Instead we should think about the on-line experiences. Can the technology add something to problem.

5. Zooming the graphs -- Jeremy, Holly

They brainstormed many approaches to the problem and then worked to narrow their focus to two questions. This was difficult due to the richness of the possibilities. They have two leads.
  1. Make a line look like y=x by changing the scaling. The students won't need to know a lot about equations to work with this. They could do this with a line and with a parabola.
  2. Use two functions. You have to change m in one, and b in the other. Make them intercect within the zoom, make them not intercect within the zoom.
  • What math question(s)?
  • What technology?
  • What Standards and topics will this cover?
Question to the group: Nick asked, What kind of questions do we want to ask? Should they all have a specific right answer? Or should they be more open-ended?

  • A child should be able to state an answer and support it with a full explanation.
  • Mentors have to work harder when questions lead to multiple answers.
  • In a sense all of our problems are open-ended. Our real questions should be: How can we use technology to teach concepts like pi?
Session 2: Choosing problems for collaborative teams to elaborate.
6. Spinner -- Mark, Gerri, Seth, Holly, Alex

Task: Design a spinner for a carnival game. The company pays $10 each time they hit the CD. They pay out $1 every time they hit the yo-yo. The company can't keep more than 10% of what it earns. Students can change number of wedges, color of wedges, and location of wedges. Perhaps students can define their own functions using a spread sheet or data table.

Concern: implications of gambling. Perhaps use chores in a family instead of raffle. Or could use a grid where people move around and then the caller yells stop; "players" see what color square they are on.

Lots of ideas without focusing on one best question.

7. Marbles -- Seth, Holly

They generated a lot of ideas without exactly seeing how to put it into a problem. 1. Two bags of marbles, compare the probability between them. 2. Make a bag match the probability of another bag set. Look at probability as fractions. 3. We have a bag and do not know what is in it. What kind of sampling can you do to figure out what is in the bag? Can you make several bags of marbles that would have the same probability ofgetting a "green".

8. Rational/Irrational -- Chris, Jim, Suzanne, Nathalie, Vicki

There were a few issues we tried to address. How can we show the distinction between rationals and irrationals? How can technology help us deal with that? Also, how do we show students what makes numbers like sqrt(2) special?

On the issue of getting sqrt(2) to have meaning, we could approximate it and see a visible representation of the difference between our estimates and the actual number. Can we zoom in on the number line where each interval is broken into 10 pieces and each successive decimal amounts to finer and finer break outs. We could color code the intervals, and zoom in by orders of ten to get closer to the irrational number. Problem: We weren't convinced that students at the end of the period wouldn't believe that if they just had more time they would be able to "get there".

Another possibility is to create the area of a circle square so that the radius or diagonal of it is a rational number.

9. Sprinkler -- Jody, Orit, Steve (Nick - this is related to a parking lot problem I received yesterday)

Task: Watering the lawn. It can be any size. Cover the lawn with sprinklers, selecting from 45's 90's and 180's. Minimize water (overlap) and cost of sprinklers. They could change the radii and figure out the best way to cover the yard. This problem addresses the Standards. It does not need to be a specific mathematical skill, but focus more on real world understanding. This is like the Grazing Goat problem.
Vocabulary to include: Transformations, rotations and translations

10. Pool Table -- Jeremy, Nick, Bill, Wenming

Pool tables and angles were too easy/boring. This led to other ideas. Question: What if there were a round pool table. Using GSP, what are the angles so that when you hit the ball it will come back to you. Questions for middle school are appropriate because they will use common angle measurments (90, 60, 45) and look for patterns. The group has an intuitive feeling that there is a good question in there. What are the shapes? There are three kinds of shapes that are formed: lines, polygons, stars. What is the measure of the angles for the polygons? 180/s. Is there a relation between the star and the polygons. Standards? observing number of interior angles of polygons, interior/exterior angles, sequences.
Birds of a Feather
Alex led a workshop using AgentSheets
Others played with math.
Tuesday, August 15, 2000
Written by Kristina Lasher

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