Week 2 Group 1 - Introduction Problems: A Sampler

Hello all!

Today we started the activities for the math circle! We currently do not have much of a "circle" but waited for a day my husband would be around to make it one more. The participants were myself, my husband, 7 yr old boy and 5 yr old boy. I will work towards finding some kids for a more official circle, but for now, being so new with this material and new to our city I feel more comfortable getting a feel for it before introducing to others. After going through the activities it is easy to see how several kids in the same age range can be beneficial and even required to reap all the benefits of Bright, Brave, Open Minds.

We started with the human survival activity and my 7yr old had many specific answers particularly for the saber tooth tiger since he read a Magic Treehouse book about them. He was confident and we talked about how there can be many examples.

Then we did the stock/flow diagram and I was inclined to give some examples to point him in the right direction. Once we started the following activities we did come back to this and added some and it became a lot more relevant.

When we moved on to the count the square activity my 7yr old was convinced of the nine squares for quite sometime. I eventually used the phrase "there are nine SMALL squares" to guide him since he had stopped really thinking about it, totally convinced that 9 was the answer. Eventually I drew the large square very slowly on the wipe board before adding the smaller squares he caught on and then quickly came up with the solution. I think as he starts to understand more about tricky questions I can use less guidance, but for the first time, he really had no idea what I was looking for as an answer. I hesitated giving too many hints too quickly, but didn't want to get stuck so early on in trying this new perspective on math. He enjoyed eventually seeing the 14 squares.

We skipped the Game of Nim.

For "Without an Umbrella" 7yr old answered the Samuel was under shelter, we talked about how there could be many answers and he came up with many more. I suggested maybe there wasn't even any rain at all and he thought it was neat that the question was tricky like that.

In "What doesn't Belong" he quickly shared multiple answers. It seemed his awareness of this type of problem solving was really starting to click.

In "Matchstick Puzzle" he did exactly as suggested in the student reactions and came up with building various types of houses. We played with the sticks for a while and he eventually thought it was neat how moving just the two could turn the house. A lot of distraction here due to his desire to just play and create his own designs.

In "Continue the Pattern" we left up the Fibonacci numbers all day. Even though at the very beginning he noted the adding pattern in 3,5,8, he didn't quite relate it with the rest. It was REALLY hard not to guide him he was so close so many different times! He used the wipe board and we added "Messy" to the stock/flow chart because his notes and attempts were starting to interfere with being able to see the pattern. Man, he kept getting so close and was frustrated many times, but also dedicated. He knew there was an answer in there and wanted to get it. He finally got it during a moment when he was really frustrated. We talked about frustration being a part of problem solving. I then wrote the two interlacing sequences problem up on the board and said he didn't need to work on it - we would get to it tomorrow, but though the frustration was still fresh, he really wanted to see if he could solve it and then did in about 2 minutes or less. We were really excited. This manner of thinking is starting to click on for him and he is pretty into it now. I erased the board and again said, don't work on it now, take a break, but here is the next one... and drew the Paskal Triangle. He started to work on it and quickly got part of it right, but also some wrong so decided to break for dinner and come back to it tomorrow.

I think he is feeling interested and confident, but weary of the brain power and work needed to put into solving some things. It is really neat to see him thinking like this after the memorization and 'word problem' heavy math curriculum at the public school (we now homeschool). My recently turned 5 year old stays pretty quiet, but is listening and creating patterns with stickers was a good activity for him!

I am currently looking for a 2nd grade curriculum and intend on incorporating the Open Minds philosophy in our Math futures. Also, @julkabro , it really helps that you worked at NASA! I get to tell my space obsessed sons that a NASA astronaut instructor is instructing me on how to teach them and they are really interested in THAT! Thank you @julkabro and @MariaDroujkova for this opportunity!

I had a first session on Monday. I started the class with a discussion about mathematics and got the children to introduce themselves one after the other and then tell us one thing that came to mind when they thought about mathematics. As they were sharing ideas I drew a map of their input on the board (will share picture later). Then we focused more on problem solving and I used the cave men examples to emphasize the importance of problem solving. Apparently cave men invented wheels... We then discussed inventions that continue happening nowadays. The squares problems was fun for them, one child took a long time to think about it although everybody else had their hand up right away ready to volunteers their answer. I gave him the time to think it through, and after most students shouted out the answer "9" I asked if everybody agreed, at which point the one students said he did not. I asked him what his answer was and he said 14, so I turned to the rest of the class and asked them how they thought he might have seen 14 squares in there. Several suggested that maybe he had counted some squares several times without noticing (especially the ones in the corners). Eventually I had him come to the board and demonstrate his solution, still some students were not seeing it, so I had another students come and tell us what she understood his solution was... finally they all came on board and we had a discussion about assumptions which we expanded with the raincoat riddle (I'll share responses for that one too in pictures later). A couple kids shared their own riddles afterwards. We skipped the game of Nim because I thought it would take them a good amount of time to begin thinking about strategies, and we did not have that kind of time. We finished with the matchstick problem, which really involves two types of difficulties, the first one being how to make the house in the first place, and the second one how to modify it given the restrictions of moving only 2 matchsticks. Kids really enjoyed that one, as it was very hands-on. With a bit more time I would have liked to discuss how they saw the house and figured out how to build it (i.e. decompose the shape into a square, a rhombus... etc), but I was under time constraints and I wanted to give each group enough of a chance to practice with moving the manipulatives around so we finished the session with a class sharing of their strategy. When I came back on Wednesday several of them said that matchstick activity was really fun. One of them also mentioned the riddle as fun.

On Wednesday we looked back at the math map and noticed that somebody had suggested "Patterns" as a part of mathematics, so we looked at the two numerical patterns from the last problem solving activity (Fibonacci + alternate sequences). This occurred as a think-pair-share, and students were very engaged in sharing their thoughts. More than one way to explain the alternate sequence was provided (I will share picture later). Then students wanted to make their own sequences so we had some sharing time for that as well. Because this is a 20 students class and I could not have everybody share (I use popsicle sticks with their names to pick volunteers), I asked them to bring them to me by Friday as homework. Since there was a good amount of argumentation regarding whether a rule worked for the whole sequence or not, this allowed me to move into what I had intended for the day, which was discussing Logic. I found the Logic activities much harder to engage kids with, that is with sustained attention. They were interested in them, but clearly the cognitive demands were higher and some of them started losing focus faster than in the problem solving activities. However that is a discussion for another group.

If I were to use this experience to change the way I teach I would live in an ideal world were time does not get in the way of free exploration. Possibly I should have chosen to use fewer activities, but there is a fine line between students losing focus and having enough time to tackle a problem in depth.

Our first circle is tomorrow - I am nervous and excited. We have anywhere from 1-10 other kids that will be showing up other then my two. One of the kids coming I know I can count on, all the others are a little iffy just because I don't really know the families so well, and it being so close to the holidays. No matter who shows up, I'm hoping it will work out well. And thank goodness it seems like the activities are easily scaleable at the last minute.

I am expecting the kids to not really want to talk and share much at first.

I have a feeling that my kids are going to get the answer to the square problem pretty quickly, I just did this a few weeks ago with my 8 year old, I guess it will be good to see if she remembers it or not.

I think they are going to like to play the Nim game, and I think this might get them interacting with each other. This is when I really see the kids starting to work on problem solving and trying out different ideas.

I have no idea how they are going to react to the problem solving, what does not belong. My 6 year old is in love with finding and making up patterns and things like that. I think he will really like this.

House matchstick problem - I think they will enjoy, most kids like doing things with manipulatives in my experience.

I am not planning on 'assigning' homework, since this is not an on-going circle and it is most likely that I might not see some of the kids in the near future. I will give the website out to the parents however in case they want to look into it.