Inspired by Calculus: Thursday Math Circle Week 1

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This Math Circle report has three parts. The first part summarizes “whys” behind club activities, and gives ideas on what to do at home. The second part has samples of what the group said and done, from Yelena McManaman. The third part has links to resources.

I will keep adding our pictures to a set on Flickr. Thank you for the photos, Lynna Mattia!

The main three principles:
1 – Make math your own, to make your own math
2 – Have adventures
3 – Do it with friends

Whys and home ideas

  1. Who are you? What do you like to do? This activity helps kids feel confident and secure. It’s a value affirmation: here is who I am and here is what’s important for me. It gives a safe home base.  At home: whenever kids mention what they like to do, note it in a journal, a bulletin board, or a shared file. When the going gets tough, look there. Mix math with those activities.
  2. Draw or Make Infinity. This is a scavenger hunt of sorts: a gentle step from “this is all about me” to “this is about my ideas in math.” It supports learner agency while focusing on one a math concept. At home: keep looking for infinity everywhere – in books, in games, in the nature, in people’s cyclic behaviors, in the arts and sciences.
  3. Knots and loops. One of the main goals is to get up and move around, while doing some relevant math. At home: look for loops, cycles and iterations as special examples of infinity. Say, day-night cycles and the corresponding human routines: get up, have breakfast… go to sleep.
  4. Fractal drawings. Making fractals (self-similar pictures) took us to a particular, highly useful implementation of infinity. We will start there next time to go toward limits. At home: look at fractal pictures and videos online. Go on scavenger hunts for fractals in nature (ferns, feathers) and culture (designs). Draw fractal pictures.
  5. Videos. Watching good videos together helps kids to make friends (by sharing their appreciation), and to add energy and focus to the activities – or finish on a high note. Kids are likely to seek more math videos at home, since YouTube has a good “relational” search. Children also see themselves as makers (of their fractal pictures) among other makers (of more polished, but clearly home-made media). It can inspire them to the higher quality and the higher interest in math projects. At home: watch short YouTube videos about fractals, infinity, and dimensions. Invite kids to make up scenarios of fractal videos.
  6. Hotel Infinity story. Telling stories together is another friendship-building activity. Classic math stories, such as Hotel Infinity, ground advanced ideas in everyday objects – with some sci-fi, playful twists. Math is about creating new worlds, so fairy tales and science fiction are very appropriate. At home: read or tell other math stories, such as “The wise man, the king, and the chessboard.”


Circle Leader: Maria Droujkova
Participants: Gray, Jeremy, Mark, Elena, Chloe, Roman, Luca

1. Who are you? What do you like to do?

Kids introduced themselves. Most knew each other from other activities and some previously met Maria, but everyone still seemed to be a bit shy and uncertain. Some kids want to talk about what they like for a long while, and others are silent. Friends: “Your t-shirt has Angry Birds, so you must like that!’

Maria got Gray, the oldest of the kids, in charge of writing the word “infinity” on a 3×5 card. It took some doing: infity… inffinn… infinity! Then Elena pinned the card to the board.

2 – Draw or Make Infinity

Jeremy drew the symbol for infinity and said he was done.
Gray: Do we have to write the word “infinity”?
Maria: Is the symbol the same as the thing itself? Is your name the same as you?

Kids laughed and said “no”.

Maria: Let’s think of what is infinity and where it is.

Mark: It’s in the Universe (draws a big round universe with lots of stars)
Gray: A mirror behind a mirror (draws mirrors)
Luca: It is something that’s far far away (draws a small dot in the middle of his paper)

Maria gets everyone’s attention and points to Elena’s drawing (numbers 1, 2, 3… in order and then an arrow).

Elena: I made numbers because infinity is just a really big number, so I couldn’t go on forever, so I drew an arrow.
Maria: Who thinks infinity is the largest number there is?

Some kids say infinity is a number, some say it is not.

Maria: What are numbers?
Kids begin counting.
Elena: It is something you use to say how many of things are there.
Maria: Ok, let’s play a little game.

3 – Knots and loops

Kids stand in a circle holding hands.
Maria: we can walk round and round in a circle because infinity goes on and on. But now let’s make it interesting. Let’s make knots.

Kids giggle as they move over and under while holding hands.

Mark: Oh, it’s getting complicated!

After a while Maria suggest to untangle, but the kids had to release each other’s hands. Maria pointed out that no matter how much we tangle/untangle, as long as we hold hands together, we will come to the circle we started with.

Next, Maria directs kids to hold hands in a circle a certain way, then untangle. Now they end up with 2 circles and in the larger one (4 kids and Maria) the kids are facing both in and out of the circle while the smaller one (2 kids) they face each other.

Maria: How come we ended up with 2 circles this time?

This is when Chloe joins the group.

4 – Fractal Drawings

Maria directs the kids to draw something they like in the middle of a blank sheet of paper. Then to place 2-3 points on the object and, using different color marker, draw the same, but smaller object at each of these points.

Gray: What if I have a point inside a shape?

Maria goes around and makes sure the kids are on track, briefly discusses with each kid what s/he is drawing, suggests to Chloe to simplify her model for the next levels.

After the kids draw 2-3 levels of their fractals:

Gray: How many are we going to do?
Elena: We can do infinity!
Maria: Can you see the idea of infinity in these pictures?
Jeremy and Gray decide to “draw an infinity, a ton, of points” and make a “point cloud” on their papers.

Maria, holding one of the fractal drawings: What math do you see here?
Mark: Symmetry
Others remain quiet.
Elena continues drawing, the idea of a “too many cats” fractal seems to be very appealing to her. Boys are still discussing their dot pictures. Making lots and lots of dots happens in almost every group where infinity is discussed. Papert wrote about similar behaviors in computer-based learning systems, as well. It’s meditative. Maria says they will watch a little movie next.

5 – Fractal Hand Video

Maria introduces the term “fractal”.
Luca: It sounds like “pterodactyl”
Gray: It sounds like “hats” (Maria: I know how it is when you like something! I see math everywhere, just as you see hats everywhere.)

Kids watch “Fractal Hand” and agree it’s not scary.
Gray: It’s hypnotic.
Luca: It’s infinity. It keeps going on and on.
Chloe: It’s a pattern.

Fractal videos rock

6 – Hotel Infinity story

Maria tells a version of Hotel Infinity story. Once she gets to the part where a new guest arrives and everyone moves 1 room and there are enough rooms for all and all rooms are occupied:

Elena: There were enough rooms because there were infinite number of rooms!

Maria tells how next day 2 more guests arrive and need 2 rooms. What is Bob, the hotel owner, to do? Kids suggest moving everyone 1 room over, but quickly correct themselves and agree that the guests will have to move 2 rooms over. Someone brings up a question why can’t 2 guests share one room instead, or build more rooms. There is some in-universe discussion of Bob’s skills, alien conflicts, and other pretend-play.

Maria: Guess what happens on the next day. Kids: 3 guests arrive! 10 guests arrive!

Roman: eagerly counts by 10 to 100

Kids throw out different ideas – the guests will need to move over 1 room, 3 rooms, 10 rooms, 11 rooms. There’s a brief discussion, but no decision is made.

Luca and Roman come up with ideas to count to infinity, such as 100+100+1, 100+100infinity+1.

Maria: Can you make infinity like this?
Gray, Luca and Roman think “yes”. Elena thinks “no”.

7 – Fractal Cows video

Kids are very excited and agree that this video is “creepy”. Yet they want to watch it again. Maria shows them the 3×5 card with the word “fractal” on it; they read the word and the card goes onto the cork board. But the kids want to continue discussing the cows video. Luca moves around to show how cows were stretching and shrinking. Boys suggest all sorts of objects that could be made with cows, like a balloon, the Creeper from Minecraft, etc.

Maria announces that the meeting is over for today. Several kids seem surprised at how fast it went and seem to want to continue. Then everyone goes to play outside before heading home.


Fractal hand video.

Cows & cows & cows video.

Living Math lists of math readers and math stories – book references.

Several full Young Math stories online.

Vi Hart tells a math story: Wind and Mr. Ug.

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