NSN 96 Home Page || Agenda || Daily Summaries || Bounce

Bounce is a piece of software developed at BBN. Basically, it's a simple program that can be used to explore patterns in geometry. The set-up includes a gridded square, with labelled x and y axes. The user selects a trajectory for a ball starting at the origin, and watches path that it takes as it bounces around the square, until returning to the origin. The idea is to notice numerical and visual patterns.

Fadia explained that the goal of this week's Bounce sessions is to use this real, face to face environment in order to test inquiry-based classroom experience. How can one sustain a true inquiry on the Internet? That involves, first, settling on a language for inquiry in class, but our focus is trying that on Net.

An outline of our goals looked like this:

1. Math investigation
   
2. Reflections on inquiry
   
3. communication
   
4. communication on the Net
   

Throughout these three days of Bounce sessions, we're planning to use the lab and the classroom next door to simulate two seperate classes, in different schools. Each group is going to do internal communication, and then eventually, we'll share across the two classes using the Internet.
Before splitting into two groups, we did exercise about "What's purpose of sharing in a math environment?" Here are some of our ideas:

• hearing others' difficulties gives insight into their thinking and person
  
• to encourage your partner
  
• to reaffirm understanding
  
• (Vicky felt strongly that ...) asking questions carries stigma of being intelligent and thus NERDY. How do we convince them that sharing and learning is the most important thing, not playing sports, etc. It's good to be intelligent. Before coming up w/ what sharing's good for, how do we first convince them that sharing is important? Fadia answered by pointing out 2 threads from vicky's comments. One: what if they know but don't share? Let's look at our experience this week and keep this in mind. Two: how does the group influence what we share and what we don't share. That's crucial for every group anywhere. So ...
  
• How am I influenced by the whole group.
  
• Sharing by DOING vs. talking. To avoid leaning on more vocal group members, teachers need to establish environment ...
  
• environment est'd over time
  
• sharing in pieces. don't coopt other people's discoveries. entice them to want to work w/ it, go check it out, etc, but don't tell them what it is.
  
• learning diff. methods to approach the same problem. (related to last one: not spilling all the beans)
  
• LISTENING
  

We'll revisit these ideas throughout the week. We finally split into two groups. One went with Fadia and one with Ricky.
Exploration in pairs. Sharing findings, on public forum. Discussion here. Repost on forum. Then write brief note on shared forum (same as other group). Put in numbers.

The ball leaves the origin, bounces around box, leaving trail, until it returns home. We, as math scientists, asked to explore the relationship twixt number put in a trail left. The numbers that get input are into the fields "Over" and "Up"

One question that arose during the initial exploration period was "does this thing take negative numbers?" Ricky answered "good question". (The answer was yes.)

After about 1/2 hour, we stopped work on the computers and gathered our findings as best as possible. We then went to the Forum News Gateway, where we've started local discussion groups for Group 1, Group 2 and nsn. You can find all of these comments at:

http://mathforum.org:2222/

Findings:

• multiples give you same pattern
  
• prime pairs give fewer bounces
  
• prime and composite numbers give many bounces
  
• Angles?
  
• Effect of negatives?
  
• mirror images
  ++ quad 1
  +- quad 4
  -+ quad 2
  -- quad 3
  
  
• Can you pick numbers such that it never returns to middle? Asymmetry
  
• if hits corner, it comes back on same path
  
  
• If over is a factor of up, quads 1 &4 (w/ pos. numbers)
  
• If up is a factor of over, quads 1 & 2 (again, pos. numbers)
  
• Relationship of slope to number of hits. (**)
  

We ran out of time at this point. We plan to begin the Bounce session tomorrow with our second round of posting, this time to the discussion group "nsn".

Eric Sasson

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