This week, after you run your Math Circle with family or friends, tell us how it went. Your reply will help parents and teachers all over the world, and contribute to the citizen science study.
You can just write your major impressions in a couple of sentences. In case you want to tell a story, here are some prompts:
Photos are always welcome.
Answer by Denise Gaskins · Sep 28, 2013 at 06:44 PM
I've tried three times to post an update with pictures, and it always seems to upload just fine, until I click "Post Answer"---and then everything disappears. Grrr! I gave up and wrote it up in Word, so here's hoping that will go through:
Denise, we updated to the new version of the platform, so the Explorer glitch you encountered should go away.
It was interesting to read your comments on how the settings change what math kids do. For example, individual large whiteboards invite the kids even when they are tired. It takes them a while to start using the mirror that is a bit too far from their seats, so they build on the table instead. Having only little boys in the group sometimes makes for more chaos.
The tree and shirt discussion illustrates how kids can "embody" their math. A lot of activities in math only require our eyes (looking) or fingers (writing, making). If the whole body is involved, it's a whole different story!
I think your comment in the summary article (that Making needs to come before Searching) was a problem for us. In retrospect, I think I would omit the scavenger hunt and try to do more Making activities. It would be nice to have several sessions in a row, so we could focus on only one or two multiplication models each session, and then let the scavenger hunt be the big culmination.
But with only meeting once a month, we really don't have continuity from one session to the next, so it's harder to plan a long-term series. I'll be puzzling over that between now and our next session...
Answer by keetgi · Sep 19, 2013 at 04:19 PM
Both of my kids (8 and 6) enjoyed the scavenger hunt concept. We walked around our neighbourhood and they tried to outdo each other by pointing out the various examples of multiplication. They carried the multiplication models sheet around with them and the goal was to try to find one example of each model. We took pictures of their examples. The biggest challenge for me was to stop myself from imposing my own ideas onto those of my kids. For example, my 6 yo asked me to take a picture which illustrated scale and I kept trying to get her to stand next to the ivy (which had leaves of increasing size) but what she was actually pointing out was the brick steps (each consecutive step was taller than the one before it). The next step if for them to put their finding together into a mini-presentation for their math groups at school.
@keetgi, if you do make this mini-presentation, please share it here! What helped you, in the end, to "not impose"? Sometimes I recommend the simple tool of taking turns when speaking or doing things. When it's your turn, you do things your way and others help. When it's the kid's turn, they rule and you follow. So you can ask your 6 yo to pose with different ivy leaves on your turn, but she gets to pose with the stairs on her turn.
Hi Maria, Here is the mini-presentation that my 6yo put together. She shared it with her teachers (one of whom had never heard of fractals before!) So it was educational for all involved.
@keetgi This is a nice way to keep your findings! Thank you for sharing. I like how you made some models (array, folding) and found other models out there. Fractals are beautiful - glad everyone is learning.
Answer by hdongen · Sep 19, 2013 at 01:50 PM
All participants just left, so I thought I might as well give you an update at once.
One of the most important observations I made is: the parents. I sent the parental roles to all participating parents but they had a hard time fulfilling this roles. Some observations:
Another observation that I made where the mindsets and how a fixed mindset can be really disturbing in the process. There where two girls of about the same age. One was afraid to answer a question wrong, answered it like everybody else and could not explain why, because it wasn't her own answer. The other stayed much closer to herself and wanted to tell about her findings and was really proud of them.
The good thing was, that this girl, I will call her Claire, infected the other girl, who I will call Violet. Violet wasn't afraid to tell her findings to Claire, which was a real win. And I worked with Claire myself and praised her as much as I could and her mother and I noticed how she loosened up. We gained something there, but there still lies a road ahead to move her away from this fixed mindset.
Violet's mother was also enthusiastic, because she also noticed how safe Violet felt and how she liked being able to find all these patterns. She even found the table of seven!
The drawing activity, where everybody had to design there own poster, didn't work well. The smaller children did feel like drawing, but didn't stick to the assignment and the older children just didn't feel like drawing and didn't put in an effort. One of the boys, I was really counting on, didn't feel like drawing at all.
Figuring out the posters was a favorite activity, especially with the eldest girl and the grownups. It was much the same with the construction activity.
I hoped the playfulness of the activities would motivate everybody to participate, but they did not. I am asking myself now: Did I choose the wrong activities?
The eldest girl liked the construction activity, but she is a lot like me, very visual and tactile in her learning. So I gave her a bag of matchsticks and some tube to continue working with it at home.
My son only participated to humor me. Will I do this again? I don't know. Because homeschooling is at risk in the Netherlands, it won't be my priority for the next few months, but maybe afterwards ... who knows.
I think it is important to work with the same group, so I can educate the parents too. That's the most important thing I learned today: that this is a learning process for parents too and you need them on board.
@hdongen, I greatly appreciate your description of the process. It will help others in the future. For example, I already see we need to simplify parent roles a whole lot! Sometimes I get carried away with fancy descriptions - it's the roleplaying legacy.
The story about Claire and Violet is a huge part of what Math Circles are all about. The benefits to Violet, who was at first afraid, are obvious. But think of what it gives to Claire - the feeling of math power, not OVER other people, but WITH other people.
The poster-making activity may work better over several weeks, or with a large group. Everybody contributes a few minutes of their time at any given time.
I hope homeschooling survives in the Netherlands!
@MariaDroujkova, I hope so too, Maria. If you want to help, there is an international petition to sign, but I am not going to post this unless you allow me to. I fully understand when you don't want that.
@hdongen, email it to me droujkova@gmail.com and I can make your message go to on-topic groups. If you find more multiplication models, post them here!
Answer by cjmarchis · Sep 20, 2013 at 05:01 PM
We started by looking a some pictorial representations of the times table (http://thegriddle.net/handouts/mult_color.pdf) and factors (http://mathinyourfeet.blogspot.com/2012/11/new-math-game-factor-dominoes.html). They couldn't believe there really were 100 squares at the bottom of the times table chart, so they counted to make sure. We were all amazed. As we looked at the factor dominoes, some pearler beads were lying around that they had been playing with earlier in the morning (http://www.michaels.com/Perler-Beads®/products-kidsteachers-brands-perlerbeads,default,sc.html). They immediately connected the dot shape of the pearler beads to the dots of the factor dominoes, and wanted to make their own. This was not my plan or idea, and I thought it sounded great, so we went for it. We decided to make models for all even numbers to 32, or the 2 times table. We immediately noticed that due to the constraints of the foundations for the pearler bead art, we could not arrange the dots however we wanted. Symmetry was going to be a bit more challenging. We found that the circle shape worked better for some, the square for others. We noticed that some were really difficult to make a pretty shape with--14, 26, 28, 22, 30... 22 and 26 were especially hard. Why? We could only divide them evenly into 2 groups, which were odd. Our circle shape had limited options for how many could fit around, and neither 11 or 13 were options. So we did the best we could, and allowed some to look "funky." After ironing our shapes, we threaded them like Christmas ornaments and made a mobile. This was my son's favorite part--figuring out how to get two sticks tied into a "t" shape to hang parallel to the floor. We decided to spiral the smaller to the larger starting from the middle. We began to notice that the shapes on one bar were "prettier", and the other bar were more "funky." The "prettier" ones were also multiples of 4. It was interesting to discover. After that we went to a park/children's garden to look for patterns, but their attention had run out. I was the primary one looking for multiplication at that point, and I was obsessed. They were having fun climbing and running. I think it was too much for them in one day, but not for me! I'm still playing. And they did make a few more observations as the day went on. The thing I have learned the most is how to incorporate just a bit of math vocabulary and conversation into things we are already doing. They love to color Mancalas. We did that all morning, noticing which ones reminded us of what numbers. They also love Kirigami (Japanese paper cutting). It is very symmetrical, offering more 4, 8, 6, 5, and 10 sided figures (probably more that we haven't done), which can show us a lot about multiplication. Who knew we were doing so much math? I wonder what the next step is. Is there a next step? Is there a time when we need to make it more formal? How can we take what we've learned and apply it to long division without memorizing the tables? Is that even important? If so, when does it become important?
I will post our mobile, but the picture does not do it justice with my camera phone. The pieces are just too small for the detail to show, but you get the idea.
Ah, this is so funny. I wanted to make our own beads poster, but couldn't make it happen and with you it just emerged. That's how I felt, afterwards. That it is so much more important to have a whole vocabulary of maths and to have a lot of tools to share when the moment comes, but not to push anything, because then the thing that surfaces is only mine and not the children's.
@cjmarchis, that whole bead exploration is an amazing piece of math! You play around, then you notice patterns, then you ask the all-important WHY! This leads to problem-posing and conjecturing. Before you can solve a problem, it needs to be discovered - and you discovered several interesting ones!
"We found that the circle shape worked better for some, the square for others. We noticed that some were really difficult to make a pretty shape with--14, 26, 28, 22, 30... 22 and 26 were especially hard. Why?"
I put the numbers you found into the Online Encyclopedia of Integer Sequences search, and found several patterns - but not those you found. If you are interested, you can describe them a bit more formally and submit to the Encyclopedia.
"I was the primary one looking for multiplication at that point, and I was obsessed" - I can believe that. I've seen it happen, and it also happened to me. That's why these activities are for all ages!
Answer by hdongen · Sep 25, 2013 at 06:51 PM
I wanted to thank you, Maria, for this wonderful learning experience. If you organize something like this again, I would like to be informed.
All the best, Henny
@hdongen, thank you for your kind words. I added course participants to the general email list for Moebius Noodles, where we announce new courses. Our goal is to run them every few weeks.
Answer by Silina · Sep 26, 2013 at 04:18 PM
We were noticing multiplication models while we were out and about last two weeks. I mostly notices symmetry models, like flowers, birds, bees and even cars and planes. My son notices skip counting (elevators), sets (people in the room sitting at the tables), stretching (pictures on the expanding balloons he blew for his sister), number line (manometer, speedometer,etc), combinations.
My 2 year old noticed the splitting tree (with two trunks) and immediately pointed that she had two arms herself, she posed and I took a picture of her showing her discovery.
We also did folding and cutting activity with her (she loved how her beloved dogs multiplied :) I also did the good old family tree drawing with her.
We will definitely are going to continue look for different models. Thank you very much, Maria, for your outstanding course! Through this class you also reminded us that we DO have freedom to choose the model we like and we DO have power to change the way we want to learn something.
@Silina, amazing how toddlers sometimes have the eye for the similarities! Under one definition, math is noticing similarities in different things, and differences in similar things.
You noticed quite a few models. I wonder if making things such as trees and dog snowflakes helps you to notice these models later on. I am thinking of our discussion with @dendari during the live meeting on Friday, about being "stuck" on one model as you go on scavenger hunts. We need to suggest making 3-4 models before hunting for them!
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