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Week 12 Assignments

Written work, due Tuesday, November 19th, in class:
Chapter 8: 3, 4, 7, 18, 19, 20
Chapter 9: 3, 4, 5
WeBWorK Рnone
OpenLab – none

Project РInitial Draft of paper due in class next Thursday, 11/21 (feedback will be sent by email to group members).
Final Draft of paper due in class on Thursday 12/5.
Group Presentations on Thursday, 12/5.

Semester Project – Group Process Paper

In his essay A Mathematician‚Äôs Lament, Paul Lockhart says ‚ÄúA good problem is something you don‚Äôt know how to solve.‚ÄĚ This is quite different from most of the ‚Äúproblems‚ÄĚ that appear in our mathematics education. ¬†In the past weeks, you‚Äôve all spent some time individually and in groups working on such problems, in the context of graph theory (“Bridges and Walking Tours”).

As a group, write an account of your experiences working on your puzzle/problem.  You should include the following elements:

  • Description of the Bridges and Walking Tours problem, in your own words.
  • An account of working on your problem¬†as a group, from playing with the problem¬†to formulating and perhaps proving a conjecture. ¬†What did your group do/think/feel? ¬†You can include examples of puzzles and solutions if you wish, as well as work by individual group members completed outside the group (both optional). ¬†Your goal is not to go over every detail, but to tell a story that your readers will enjoy – ‚Äúwhat was it like‚ÄĚ?.
  • A statement of your group‚Äôs chosen conjecture, and a proof (or disproof) of the conjecture.
  • At least three images (more if you wish). ¬†They can include images of puzzles you‚Äôve created or solutions, but you can also be creative with images or photos related to your puzzle, your group or your story in some way. ¬†Each image should have a caption describing. ¬†NOTE: You may freely use your own drawings, images or photos. ¬†If you wish to use photos from another source, they must be from a legal source (for example, Creative Commons licensed, with proper attribution – the library or your professor can help with this).
  • Basic details: the names of all group members, the date, course and section numbers, and your professor’s name.

I will be meeting with each group next Tuesday, November 14th, in class.  Please be in touch with your other group members before then!  Be prepared to discuss your progress so far Рat the very least, you should be able to describe how you are dividing up the work of the paper among your group.

The first draft of this assignment is due in class on Thursday, November 21.  Each group should submit one paper, of no less than 1500 words.  You may decide as a group how to divide up the work.  Be aware that you will be asked at a later time to describe your own specific contributions as well as those of each group member.

The final draft of this assignment is due in class on Tuesday, December 5.

REGARDING SEMESTER PROJECT:  As you may recall from the Course Description, the semester project is worth 10% of your overall grade.  The project consists of a number of interrelated activities (many of which have already been completed) Рcomplete details can be found on the Project Overview & Deliverables page.  The group paper assigned here forms a significant portion of the project.

Group 1: Song Yu, Randy, Aurkaw

A diagram is solvable when a diagram has a greater than or equal to a number of vertices with an even number of adjacent lines than the number of vertices with an odd number of adjacent lines. And a line graph is solvable by choosing either of the endpoints of a line.

Group 2: Youshmanie, Dylan:

A puzzle is solvable with a bit string where the length is the total number of points and the elements are the amount of bridges connected to each point in descending order then the pattern is solvable for any other puzzle with the same bit string.

In-Class Group Project Activity 11/7 ‚Äď Refine Your Group Conjecture

Assignment.  Your goal for today is to refine the conjecture you decided on during your last class meeting.  Some things to consider:

  • Specificity: The conjecture should be stated clearly. ¬†It should include all information necessary to be understood by someone who is familiar with graph theory terms (vertex, edges, paths) and familiar with the assignment (walking tours). ¬†A reader should be able to tell from the statement¬†whether a conjecture applies to a given drawing or not.
  • Generality: Your conjecture should apply to more than just a single specific graph (it can apply to a collection of similar graphs, for example, as long as you describe exactly what types of graphs you are considering).
  • Drawing:¬†You can create a drawing to accompany your conjecture, but your conjecture should be understandable without the picture.
  • You can revise your conjecture as a group if you wish – but try to come up with something similar.
  • You can add additional clarification to your conjecture.
  • You can extend your conjecture to include more types of graphs.

 

GROUP CONJECTURES SUBMITTED AT END OF CLASS TODAY:

 

Week 11 Assignments

Written work – Due Tuesday, November 12, in class:
Chapter 7: 5, 6, 7, 9, 12
WeBWorK – none
OpenLab – none

Project –¬†First draft of your group paper is due in class on Thursday, 11/21.

EXAM #3 will take place on Tuesday, 11/26 (right before Thanksgiving break).

Exam and Midsemester Grades are posted on the OpenLab

Hi everyone,

Your Midsemester Grades (including your grades for Exam #2) are posted on the OpenLab Gradebook  (Dashboard / OpenLab Gradebook). You will see that your grades for Exam #2 as well as your current Homework, OpenLab, and Project grades have been posted.

Your Midsemester grade is based on the following work completed so far:
Homework 30%, OpenLab 25%, Exams 45%

Midterm grade key:
P: passing/satisfactory progress; likely to complete course requirements.
U: failing/unsatisfactory progress; not likely to complete course requirements.
BL: borderline; barely passing or just below passing; there is a reasonable expectation that the student will pass the course
SA: stopped attending; for students who were attending (at least once) and have now have stopped attending your class.
WN grade:¬†Student never attended. Do not assign this grade.¬† This information was based on the ‚Äú verification¬†of attendance‚ÄĚ (VOA) roster you submitted at the 3rd week of the semester.

Let me know if you have any questions.

Regards,
Prof. Reitz

OpenLab #6: Proof Journal

Your assignment for the coming week+ is to try to prove the conjecture that your group created in class on Thursday, 10/24.¬† You may need to refine/expand your conjecture first (let’s discuss this in class).¬† ¬†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 Рan 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 Рwere you frustrated/confused/happy/depressed? Why? Did your mood change along the way?

Assignment (Due Thursday, 11/7):  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 (use sketchtoy.com) or other work you did along the way.

Extra Credit. ¬†Respond to a fellow student’s comment. ¬†Did you do similar things? Different things? Do you have any suggestions for them? Be kind.

 

 

GROUP CONJECTURES (created in class 10/24):

Group 1: Song Yu, Randy, Aurkaw

Group 1 Conjecture

 

 

Group 2: Youshmanie, Dylan

Group 2 Conjecture

Week 10 Assignments

Written work, Due Tuesday, November 5th, in class:
From last week: Chapter 4: 27, 28, Chapter 5: 29, 31
Chapter 6 p.116: 3, 4, 5, 8, 9
WeBWorK¬†–¬†none
OpenLab РOpenLab #6 due Thursday, November 7th

 

In-Class Group Project Activity 10/24 – Make and Test Conjectures

NOTE: As a component of OpenLab #5, 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 complete the following:

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‚Äôs work¬†change your understanding of the “bridges and walking tours” game?

Week 9 Assignments

Written work, Due Tuesday, October 29, in class: Chapter 5: 1, 4, 9

GCD Problems: Because of the exam, these problems will not be due until Tuesday, November 5:
Chapter 4 p.101: 27, 28
Chapter 5 p.110: 29, 31

WeBWorK¬†–¬†none
OpenLab Рnone

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