Week 2 Group 4: Problem Debates

Held our math circle this evening, two groups of two students ages 8 to 10. All but one of the children I would consider "mathy". My first thought reading through the activities was that they might be too easy and that not all the kids would enjoy the competition format. This proved to be true. I had hoped to add some difficulty to the puzzles but did not have time to do so. I also thought that one group (NN) would enjoy the activities more than the other group (ST). That proved to be the opposite. Group ST was reluctant to participate but their initial success spurred them on. Group NN, expecting something more and initially excited, did not enjoy it.

Chairs at the Wall: I expected this to take about 10 minutes and that was accurate. I gave the kids unifix cubes as chairs and trays as rooms. Both teams enjoyed this activity and had different solutions. Both teams built on an idea for each subsequent part of the problem, rather than approaching it anew each time. I pointed out to them that I thought that was clever of both teams. There was not much debate because both sides agreed all the solutions were valid and essentially the same, when you simply slid the cubes around a little.

True Expression: I expected this to be quick and it was. Both teams saw the answer immediately. No need for debate.

Which is Correct: There was some debate with this but both teams agreed that using IS or ARE were appropriate. None caught the joke of the addition error. I'm not sure how I feel about these kinds of problems in a math setting. I wonder if they make people feel like they've been tricked. Not so much a math problem in my opinion, though I understand the value in analyzing what you read.

Cavity Conundrum: Team ST came up with the solution quickly that the dentist was the boy's grandfather, equally valid to the dentist being the mother! Team NN agreed. It was around this point that team NN deteriorated. One of the participants did not like the kind of questions being asked and no longer wanted to participate. She was expecting something more mathematical than logical. Though I tried to engage her, she was simply done. Her partner, feeling frustrated by her partner, stopped participating as well. I encouraged the two to try working together again while group ST wanted to continue with the activities.

How Many Triangles: Team ST got this quickly. No one to debate at this point so I simply had them explain their solution.

Mr. and Mrs. Boo: I expected some initial confusion with this one but thought everyone would get it. All participants said the answer was 4, except for my 4 year old, who correctly answered 3! Once she blurted that out, they quickly saw their error. Again, no debate but an interesting discussion followed. If the answer is 4, each boy has two sisters. By original logic, there are now six children, with each boy having 4 sisters, and so on. This would have been a good one to draw out on a white board, as was suggested, but we were still spending energy trying to regroup the other team and team ST was anxious to move on.

Matches and Triangles: I thought this one would be a little tricky but it was not. Perhaps following the counting triangles puzzle, this became more obvious. Again, no debate.

Overall, the math circle took about 25 minutes. Team ST said it was fun and wanted to do more. Team NN thought it was far too easy and will likely not want to participate in something similar again. I feel like I should have adjusted the questions to meet everyone's level a little better, therefore this probably wasn't a good test of these math circle ideas. I feel like the competition style as well could have been left out for better success. As it was, I eliminated using points and just held debates. All the children working together might have had more success, maybe not.

I feel many of these activities would be good in a math circle book as they are, with the exception of True Expression and perhaps Which is Correct. I think the latter frustrated the kids. They didn't see the humor and were all somewhat disappointed with the answer. True Expression could be more difficult and perhaps be a series of expressions. Some advice on how to encourage children with competition would be helpful. Various levels of the activities, as you have in Moebius Noodles, would also be useful.

Thanks so much! I hope this helps somewhat. I plan to try some of the other math circle ideas in the near future!

Leanne

Our math circle is tomorrow (actually today, it is after midnight I just noticed). If everybody shows up there will be 8 children ages 6 to 10, plus their younger siblings (hopefully quietly playing and not distracting the older ones). I think the chairs activity will keep them busy for a while and I think we will have some great discussions and arguments. The "true expression" activity seems very simple, so if they get it right away, I'm thinking of using an easy hexa-trex to supplement and hopefully spark some discussion, activity number 3 "Which is correct?" tricked even me!, so I think we will all have a good laugh with that one. The dentist and siblings activities seem very simple to me, so I think the kids will fly through those. As for the triangle ones I am still debating what to do about those. My oldest son (8 year old) has already done both of those in the past, so it seems his team will have an unfair advantage there. I might ask him to try to let the other kids on his team deal with those activities without him. I also don't know whether to keep score or not. It seems if I do the team that doesn't win might be dissapointed, but if I don't, they I wonder if they will be motivated to give it their best anyway.

I am a bit confused about the first activity regarding the chairs and the walls. The intro says that the room is triangular, but then a) says to place the chairs along of the walls of a rectangular room. So what do we need the triangular room for? Also, b), c) and d) do not mention the shape of the room at all. Is it triangular, rectangular or what? Or is the problem ill-defined on purpose, so that the kids can debate over the number of walls in the room and pick whatever number of walls they want their room to have?