# Math Club writeup - 2nd-ish grade

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### Laura Combs

Jan 28, 2011, 9:23:47 AM1/28/11

Today’s second-ish grade math club was the biggest club we attended in three years! We kicked the semester off with 10 happy kids. Prior to that (three years we have been coming to Maria’s clubs) we hadn’t exceeded six in our age group. We were very glad to be starting the new semester!

SHOW AND TELL

The club started with five of the kids presenting their math inspirations/show and tell and the group finding math in them. The items were as follows:

1.    Origami – symmetrical, 3-D and 2 wings

2.    Nautilus fossil – textures. Textures are mathematical and can be measured. A texture measuring instrument was passed around (Maria has everything!) Some kids began drawing nautiluses.

3.    Abacus – Different ways of using an abacus were discussed.

4.    Action figure – 3-D, lego, combinations. This led to a discussion of colors and are they mathematical? YES. Hue, Brightness and Saturation are all assigned numbers.

5.    Koala bear – 3D, colors, FLUFF. The FLUFF became the mystery of the day. How is FLUFF mathematical?

INFINITY ACTIVITY

Maria next asked the kids to draw a portrait of infinity. What does infinity mean? Kids started drawing the symbol for infinity, but Maria asked again, what does infinity look like, and not the symbol?

·         One kid, who assigns color to numbers consistently and regularly (ok, he is mine) says that infinity is gray.

·         Infinity goes on and on and on

·         Mirror books show infinity.

·         On kid drew a butterfly/person-like infinity mascot

·         Blank paper

·         Nautilus shell

·         Visible light spectrum

OUTDOOR EXPERIENTIAL ACTIVITY

We went outside and did an experiential activity. The kids and parents got in a circle and held hands. They the put their right hands in the circle and grabbed another person’s right hand. The same happened with the left hands. Somehow they goofed and there was one extra, unheld hand, so they started again. The second time there were no unheld hands. The kids and parents had to untangle themselves from this human knot without letting go. The did it successfully, with two people having their back to the group. This was a great thinking and teambuilding activity, but I am not certain how it is related to infinity, other than it is a circle with no start or end, and infinity exists even when it is tangled up. MARIA – THOUGHTS PLEASE!

BREAK AND GREEN PEPPER MATH

We  took a break and did some green pepper math, focusing on edges and holes when the peppers are cut. An edge is a section of pepper that has been cut and the cut continues unbroken.

Maria cut off the top and asked how many edges? 2

She cut again and asked how many edges? The possible answers shouted out were 2, 3, 4, and 6. The correct answer was 4. Some forgot that the edge had to be continuous, so even if the edge formed a right angle, it was still one edge and not two for example. Other kids remembered this rule.

She cut again and the possible answers were 5, 6 and 7. The answer was 6.

She cut again and the answer was 8.

Then we did some similar banana math.

STORY

After break Maria told a paradox story about aliens and hotels to encourage more exploration about infinity, and she drew the story on a whiteboard. It was brilliant! It went something like this:

The hotel was named Hotel Infinity. It had infinity number of rooms and infinity number of aliens staying in the rooms. They really liked it there and never left. A new spacewalker person showed up and wanted a room. How should he be put in a room? The kids ideas were:

1.    Kick out an alien

2.    Build a room

3.    Find another shelter

4.    Share a room with another alien

5.    Continue his journey

6.    Make a spaceship

Freddy the desk clerk gets on the speaker system and announces that each alien should go to the room with the next number, so Alien 1 goes to room 2, Alien 2 goes to room 3 and so forth. Room 1 is now empty for the new visitor. If there are infinity rooms and infinity aliens and there is now one more alien in a room, then the equation is ∞ + 1 = ∞. The kids clearly got it.

Two more aliens showed up in need of rooms and all aliens had to move two rooms over from where they were staying, thus freeing rooms 1 and 2 for the newcomers. One kid liked the visual pattern of each alien shifting 2 rooms that Maria drew on the whiteboard. The kids realized that the new equation is ∞ + 2 = ∞. Infinity always equals infinity.

Then the lesson ended and everyone had a ball. Very wonderful class today, Maria!

Laura Combs

The older I get, the better I feel!

### Maria Droujkova

Feb 3, 2011, 7:34:51 AM2/3/11
Laura, thank you very much for the write-up! This is a very good example of noticing things kids do. And it is nice to write the story on the same day, when everything is fresh in your mind. At grad school, we were very strongly urged to write field notes within hours of observations, because of how memory works. Otherwise, details escape.

A few of my comments are below. You can see photos from the club here:
http://www.flickr.com/photos/26208371@N06/tags/naturalmathclub01272011/show/

I know several more parents took photos. Please email them to me or put them online where we can find them and send the link to this group!

On Fri, Jan 28, 2011 at 9:23 AM, Laura Combs wrote:

SHOW AND TELL

The club started with five of the kids presenting their math inspirations/show and tell and the group finding math in them. The items were as follows:

1.    Origami – symmetrical, 3-D and 2 wings

2.    Nautilus fossil – textures. Textures are mathematical and can be measured. A texture measuring instrument was passed around (Maria has everything!) Some kids began drawing nautiluses.

3.    Abacus – Different ways of using an abacus were discussed.

4.    Action figure – 3-D, lego, combinations. This led to a discussion of colors and are they mathematical? YES. Hue, Brightness and Saturation are all assigned numbers.

5.    Koala bear – 3D, colors, FLUFF. The FLUFF became the mystery of the day. How is FLUFF mathematical?

This is a very good example of "growing math eyes." Once a kid mentioned 3d, several chimed in with "3d" for every next object. Eventually, they explained everything is 3d - a strong idea about this world.

I will start a poster of math ideas we notice in the club. Consider starting such a poster at home and keeping it up on a wall where people can be reminded of ideas.

OUTDOOR EXPERIENTIAL ACTIVITY

We went outside and did an experiential activity. The kids and parents got in a circle and held hands. They the put their right hands in the circle and grabbed another person’s right hand. The same happened with the left hands. Somehow they goofed and there was one extra, unheld hand, so they started again. The second time there were no unheld hands.

Hint: even-odd

The kids and parents had to untangle themselves from this human knot without letting go. The did it successfully, with two people having their back to the group. This was a great thinking and teambuilding activity, but I am not certain how it is related to infinity, other than it is a circle with no start or end, and infinity exists even when it is tangled up. MARIA – THOUGHTS PLEASE!

I don't know how it relates to infinity, either. "Human knots" is just something we always play when there are enough people. Let's ask kids today what their thoughts are on relationships. They found the relationship to fluff eventually, after all!

BREAK AND GREEN PEPPER MATH

We  took a break and did some green pepper math, focusing on edges and holes when the peppers are cut. An edge is a section of pepper that has been cut and the cut continues unbroken.

In geometry, we usually focus on SIDES - lines that connect two corners. In topology ("pepper math") we focus on EDGES, which are notably different from sides - as kids discovered, and discussed. An edge can contain a lot of sides.

STORY

After break Maria told a paradox story about aliens and hotels to encourage more exploration about infinity, and she drew the story on a whiteboard. It was brilliant! It went something like this:

The hotel was named Hotel Infinity. It had infinity number of rooms and infinity number of aliens staying in the rooms. They really liked it there and never left. A new spacewalker person showed up and wanted a room. How should he be put in a room? The kids ideas were:

1.    Kick out an alien

2.    Build a room

3.    Find another shelter

4.    Share a room with another alien

5.    Continue his journey

6.    Make a spaceship

The vast majority of kids test at genius levels on divergent thinking. Many educational methods discourage divergent thinking, and as a result, most adults are quite mediocre at it. Here's a cool animation made out of TED lecture that mentions it: http://www.youtube.com/watch?v=zDZFcDGpL4U

Carol Cross, an old time Math Club member, is leading a discussion about convergent vs. divergent thinking at her Peer To Peer University parent course on learning psychology that I am taking: http://p2pu.org/math-future/node/15191/forums So far, people think it's important to develop both convergent and divergent thinking.

You will see a lot of Math Club activities asking kids for a variety - a large collection - of ideas and answers. Drawing infinity is another divergent activity. This is hugely important for problem solving, where you need to generate many different ideas, try and try again before a solution emerges.

If a group of kids has a good flow, more divergent and more convergent thinkers help one another. Seeing a few examples of other people drawing infinity helped convergent thinkers to make up some ideas too. But seeing convergent thinkers organize different types of drawing, others started to organize their collections as well. We will do more organizing of infinity representations today.

When you design group activity, there is a need for a rhythm inviting kids to be divergent and to be convergent. I am adding this topic to the list of "mathematical balances" required for a good flow experience: http://naturalmath.wikispaces.com/Flow+Channels

Cheers,
Maria Droujkova

### Brendan Murphy

Feb 3, 2011, 8:11:58 AM2/3/11
Divergent thinking got me thinking about a common practice in TV writing (or so I'm told). When stuck on a plot solution try an obviously wrong solution to get the creative juices flowing.

Brendan Murphy

The Blogs:
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http://berkleyjmurphy.blogspot.com/
http://philosophywithoutahome.blogspot.com

"The question is not will he be a doctor, but what kind of doctor will he be"
paraphrase from Harry Wong

"I can't define a hero. All I know is that it's someone you probably don't notice, but when you find out what they did and how modestly they did it, you can never shake off the feeling that you're cut from a lesser cloth, and you find that braggarts suddenly offend you a great deal more than usual."

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### Maria Droujkova

Feb 3, 2011, 8:29:22 AM2/3/11
On Thu, Feb 3, 2011 at 8:11 AM, Brendan Murphy wrote:
Divergent thinking got me thinking about a common practice in TV writing (or so I'm told). When stuck on a plot solution try an obviously wrong solution to get the creative juices flowing.

Brendan Murphy

Brendan,

Thanks for bringing this technique up!

Something similar can also be hugely therapeutic for math anxious people! When a kid is feel bad about being stuck with a problem, or just very anxious, I sometimes ask to make as many mistakes as he can, and as outrageous as he can. Laughter happens (which is valuable by itself, and not only for the mood - deep breathing brings oxygen to the brain). Then the kid starts making mistakes. In the process, features of the problem become much clearer, and in many cases a way to a solution presents itself.

Cheers,
Maria Droujkova

### Laura Combs

Feb 3, 2011, 8:49:08 AM2/3/11

Thanks for the additions and explanations, Maria! You make math more exciting and illuminating than I would have ever known.

Laura

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### Maria Droujkova

Feb 3, 2011, 9:51:32 AM2/3/11
On Thu, Feb 3, 2011 at 7:34 AM, Maria Droujkova wrote:
A few of my comments are below. You can see photos from the club here:
http://www.flickr.com/photos/26208371@N06/tags/naturalmathclub01272011/show/

I just added a big batch of photos Ali Rosselle emailed me this morning. They are under the same tag, so the link above works.

Our club parents ROCK!

Cheers,

### Laura Combs

Feb 3, 2011, 4:01:28 PM2/3/11

This is not the official write up, but I have to share a moment from today’s awesome class that was especially awesome. The kids were sitting on the blanket for show and tell. They were making straw sculptures while math discussions around show and tell were occurring. The group was a little rambunctious until about ¾ of the way through. Then Delta said that the body was infinity, which caused kids and adults to pause and think, and then MaryAnn (maybe – maybe it was someone else?) said that time was infinity. At that point in the discussion the group became noticeably calm and a very organic, non-facilitated discussion grew around time being infinity, with five or so kids externally sharing their “ah-ha” moments around time and infinity. I sat back in awe  and watched them, realizing that at ages 6 – 8 they were having this really profound discussion around a concept that I didn’t explore until well into my 30s. It was such a natural and gorgeous moment.

Thank you, Maria, for your time and energy to create the opportunities that you do! Simply amazing.

Laura

### Laura Combs

Feb 3, 2011, 4:55:05 PM2/3/11

I was wrong on who began the Time is Infinity discussion. It was Delta. Thanks, Delta!

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### Jen

Feb 3, 2011, 10:50:32 PM2/3/11
to NaturalMath
What an incredible story! Thank you for sharing! Sounds like Bohmian
Dialogue where conversation rises from the silence rather than to fill
the silence.

### Annette

Feb 5, 2011, 10:12:13 AM2/5/11
Laura;

Thank you for sharing this.ï¿½ :)ï¿½ Makes me feel very grateful that we are a part of this group.ï¿½ I had the same experience and was completely humbled by how infinitely wise our children are.ï¿½ How they can be rambunctious one moment and be a channel for profound truth/genius the next.ï¿½ For sure it only re-emphasizes the fact that we are each students and teachers to each other....no matter the age.

I cannot remember the little girls name that was sitting next to Delta (she has also sat next to my boys at the table) but after Delta said that her little fluffy kitty's eyes had infinity in them, this little girl said, "Hey, we all have infinity in our eyes" which led to her projection of her inner aha of "I am infinity" followed by "we all have infinity inside us." The progression of the discussion was amazing and yes, very organic (great word for the moment) along with the shift in attention.

I second your sentiment to Maria as well.ï¿½ Hope everyone has a "warm" and amazing weekend.

Annette

ï¿½

On 2/3/2011 10:50 PM, Jen wrote:
```What an incredible story!  Thank you for sharing!  Sounds like Bohmian
Dialogue where conversation rises from the silence rather than to fill
the silence.

On Feb 3, 2:01ï¿½pm, "Laura Combs" <laura_co...@bellsouth.net> wrote:
```
```This is not the official write up, but I have to share a moment from todayï¿½s
awesome class that was especially awesome. The kids were sitting on the
blanket for show and tell. They were making straw sculptures while math
discussions around show and tell were occurring. The group was a little
rambunctious until about ï¿½ of the way through. Then Delta said that the body
was infinity, which caused kids and adults to pause and think, and then
MaryAnn (maybe ï¿½ maybe it was someone else?) said that time was infinity. At
that point in the discussion the group became noticeably calm and a very
organic, non-facilitated discussion grew around time being infinity, with
five or so kids externally sharing their ï¿½ah-haï¿½ moments around time and
infinity. I sat back in awe ï¿½and watched them, realizing that at ages 6 ï¿½ 8
they were having this really profound discussion around a concept that I
didnï¿½t explore until well into my 30s. It was such a natural and gorgeous
moment.

Thank you, Maria, for your time and energy to create the opportunities that
you do! Simply amazing.

Laura
```

### Laura Combs

Feb 5, 2011, 1:54:05 PM2/5/11

Wow, Annette, thanks for filling in some more of the story. I was so mesmerized by the discussion, and I was not the note taker, that much of it escaped me. I remember the infinity in our eyes part – that was AMAZING! I think that was MaryAnn who said that. I know she said something that blew me away.

Smiles,

Laura

Sent: Saturday, February 05, 2011 10:12 AM

Subject: Re: [NaturalMath] Re: Math Club 2nd gradish class today

Laura;

Thank you for sharing this.  :)  Makes me feel very grateful that we are a part of this group.  I had the same experience and was completely humbled by how infinitely wise our children are.  How they can be rambunctious one moment and be a channel for profound truth/genius the next.  For sure it only re-emphasizes the fact that we are each students and teachers to each other....no matter the age.

I cannot remember the little girls name that was sitting next to Delta (she has also sat next to my boys at the table) but after Delta said that her little fluffy kitty's eyes had infinity in them, this little girl said, "Hey, we all have infinity in our eyes" which led to her projection of her inner aha of "I am infinity" followed by "we all have infinity inside us." The progression of the discussion was amazing and yes, very organic (great word for the moment) along with the shift in attention.

I second your sentiment to Maria as well.  Hope everyone has a "warm" and amazing weekend.

Annette

On 2/3/2011 10:50 PM, Jen wrote:

`What an incredible story!  Thank you for sharing!  Sounds like Bohmian`
`Dialogue where conversation rises from the silence rather than to fill`
`the silence.`
` `
`On Feb 3, 2:01 pm, "Laura Combs" <laura_co...@bellsouth.net> wrote:`
`This is not the official write up, but I have to share a moment from today’s`
`awesome class that was especially awesome. The kids were sitting on the`
`blanket for show and tell. They were making straw sculptures while math`
`discussions around show and tell were occurring. The group was a little`
`rambunctious until about ¾ of the way through. Then Delta said that the body`
`was infinity, which caused kids and adults to pause and think, and then`
`MaryAnn (maybe – maybe it was someone else?) said that time was infinity. At`
`that point in the discussion the group became noticeably calm and a very`
`organic, non-facilitated discussion grew around time being infinity, with`
`five or so kids externally sharing their “ah-ha” moments around time and`
`infinity. I sat back in awe  and watched them, realizing that at ages 6 – 8`
`they were having this really profound discussion around a concept that I`
`didn’t explore until well into my 30s. It was such a natural and gorgeous`
`moment.`
` `
`Thank you, Maria, for your time and energy to create the opportunities that`
`you do! Simply amazing.`
` `
`Laura`
` `

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### Maria Droujkova

Feb 6, 2011, 5:52:40 AM2/6/11
Our photo correspondence, Ali and Annette, sent excellent club photos. Here is the slide show: http://www.flickr.com/photos/26208371@N06/tags/naturalmathclub02032011/show/

Cheers,
Maria Droujkova