We’ll use this page to keep track of what has happened each day in class. It won’t contain any of the nitty-gritty details, but will instead serve to summarize what has transpired each day.

Week 1

  • Monday, August 28: First day! The first few minutes of class were devoted to me attempting to learn names. Next, I summarized the first few homework assignments, which was followed by a whirlwind tour of the course webpage. After this, the students engaged in an exercise aimed at understanding "productive struggle". This exercise is the second half of the Setting the Stage activity. The remaining portion of class was devoted to highlighting some key items on the syllabus.
  • Wednesday, August 30: The first few minutes of class were devoted to learning names and making sure there weren't any questions about the syllabus. Next, we had a quick discuss about writing code to solve some of the problems. For the record, I'm totally fine with students occasionally taking this approach. However, it is important to reflect on the meaning of the output. We also discussed trying to avoid "legal battles" when interpreting the wording of problems. This was followed by a quick discussion of Problem 1 involving taxi fares. We then split the class up into 6 small groups, where each group was responsible for one of Problems 3, 4, 5, 6(a), 6(b), and 6(c). After a few minutes we came back together to discuss the problems. Our very first presentation was given by OW. She presented Problem 3 (1000 doors in a hallway) and did an excellent job! With the time we had left had EB and HR present Problem 5 (sticks in a bag) and Problem 4 (triangles with toothpicks), respectively. Both of these presentations were also great. I'm very happy with how things went today. Unfortunately, we didn't get to Problem 6. The plan is tackle the 3 parts of this problem during the next class.
  • Friday, September 1: Another busy but productive day. After I lead a discussion about Problem 6(a) (Variation 1 of pebbles on a chessboard), we started tackling Problems 6(c), 6(c), 7, and 8, all of which deal with pebbles on a chessboard. DC and MF presented solutions to Problems 6(b) and 6(c). I took the lead on discussing Problems 7 and 8 and along the way, MG provided some key insights. Next, JG presented a proposed solution to Problem 9 and KC verified the solution was optimal.

Week 2

  • Monday, September 4: Labor Day, no class!
  • Wednesday, September 6: I was surprised how much we accomplished today. After a quick discussion of the upcoming quiz, we split the class up into 8 small groups, where each group was tasked with discussing their proposed solution to one of Problems 10-13. When all was said and done, we had AT, MF, HR, and QS present solutions to Problems 10, 11, 12, and 13, respectively. Our discussion of Problem 13 (ants on a log) was a bit rushed, so I hope to return to that one on Monday (since we have a quiz on Friday).
  • Friday, September 8: The students took Quiz 1.

Week 3

  • Monday, September 11: The week is off to a good start. After a few quick announcement, we split the class up into 5 small groups. After a few minutes, we had YS, OW, VM, AG, and KR present solutions for Problems 14, 15(algebraic), 15(visual), 16, and 17, respectively (but not in that order as KR actually went first). I meant to revisit Problem 11, but I completely forgot, so we'll have to do that at another time. We had some time left at the end, which we devoted to discussing the upcoming problems.
  • Wednesday, September 13: While I was out today, Monika Keindl covered for me. My understanding is that JK, KS/DO, VM, and MG presented their proposed solutions to Problems 18, 19,20, and 21, respectively. There was also some preliminary discussion of Problem 22.
  • Friday, September 15: Nandor Sieben covered for me today. It appears that EB, KW/KR, VM, and HR presented Problems 22, 23, 24, and 25, respectively.

Week 4

  • Monday, September 18: After some discussion about Problems 22 and 23, we started discussing Problem 27, which is a lot more involved than it looks at first glance. As a class, we discussed the cases of 2, 3, 4, and 5 orbs. We also got most of the way through discussing the cases involving 6 orbs. Along the way, we heard from QS, EB, TN, JR, AT, MG, HR, and KW. The goal is for the students to wrap up the cases involving 6, 7, 8, 9, and 10 orbs.
  • Wednesday, September 20: After a few announcements, the students formed 8 small groups with 3 students each. Each group was tasked with discussing 2 of the 4 problems that were currently outstanding. After 10 minutes or so, we started having students share out. We had MQ, JL/JK, JR, and SS present solutions or ideas for Problems 26, 27, 28, and 29, respectively. Problems 26 and 27 are still outstanding. VM conjectured a solution to Problem 26 and students were asked to prove this for Monday.
  • Friday, September 22: Coming soon.

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 220: Math Reasoning
  MAT 411: Abstract Algebra

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