All posts by Jonas Reitz

OpenLab #7: Proof Journal

OpenLab Assignments, Project, , ,

Your assignment for the next week is to try to prove the conjecture that your group created in class on Tuesday, 10/22/15.  You must spend at least 90 minutes working on this.  Trying to prove something can consist of many different activities, such as the following (you do NOT have to do all of these things – you can choose how to spend your time – they are provided for inspiration only).

  • coming up with ideas, and testing them out (for example, by creating puzzles and trying to solve them)
  • trying to understand what the conjecture says
  • trying to solve puzzles that other people created
  • trying to create puzzles (and solve them yourself)
  • communicating with other members of your group (talking, emailing, etc.)
  • trying to write down a proof
  • other stuff…

As you work, keep track of what you are doing, thinking, and feeling (this is metacognition – an idea that discussed way back in OpenLab #2).  What did you do during the time you spent?  Did you create any puzzles?  Did you solve puzzles?  Did you change your mind about whether the conjecture is true or false?   Did you have any new ideas about how to prove the conjecture?  Did you have any ideas that you gave up on?  How did you feel as you worked – were you frustrated/confused/happy/depressed? Why? Did your mood change along the way?

Assignment (Due Thursday, 10/29/15):  Submit a journal of your efforts in the comments below.  Your response should be at least 300 words.  Describe what you did during the 90 minutes you worked, and express in some way what you were thinking and feeling during the process.  Your response can include puzzles or other work you did along the way.

In-Class Group Project Activity 10/20/15 – Make and Test Conjectures

Assignments, Project

NOTE: As a component of OpenLab #6, each person should bring to class a conjecture or question about the Bridges and Walking Tours game.

Group Activity (30 min).  Get into your groups, arrange your chairs in a circle, and take 30 minutes to:

1. Each person should share their conjecture with the group.  For each conjecture, the group should decide if they think it is true or false (or don’t know).  The group should record their conclusion for each conjecture.

2. Choose one conjecture (or create a new one) to focus on as a group.  Your goal for the next few weeks will be to try to prove or disprove this conjecture.  Come up with several ideas about how you might prove it.

Group work due after 30 minutes:  Each group will hand in a sheet of paper with the names of the group members, the date, and the following:
– Each member’s conjecture, along with a brief description of what the group thinks – is it true or false?
– Be sure to clearly indicate which of the conjectures the group has chosen to work on – or, if you have created a new conjecture to work on as a group, include that as well.
– Two different ideas about how you might try to prove the chosen conjecture.

Reflection:  To be completed individually after group work is complete, and submitted on paper with your names and the date.  Take 5 minutes to write on the following prompt:

Briefly reflect on the process of working in a group by responding to each of these points:
1.  Describe something you learned.
2.  Describe something you contributed to the group.
3.  How did today’s work change your understanding of your assigned game?

Week 9 Assignments

Assignments, , , , ,

Written work, Due Tuesday, November 3rd, in class:
Chapter 6 p.116: 3,4,5,8,9
      **NOTE: this assignment is not due until November 3rd, HOWEVER I strongly recommend that you spend some time working on the first problem before Tuesday October 27 – this is a tricky topic and tends to give people some trouble, so early preparation will help you!
WeBWorK – none
OpenLab – OpenLab #7 due Thursday, October 29th at the start of class

Class work: There will be group & individual work completed & submitted in class on Tuesday 10/20/15, which will count towards your “Project” grade.