Wednesday, July 16, 2014

Trip Math {or} You Can't Get There From Here [#tmwyk]

You know that alphabet game you play on long car trips? You can play it a bunch of ways -- look for a word on a sign that starts with A, then B, etc. or just look out the window and look for things whose names start with A, B, C...

Today my kid and I were driving to the Indianapolis Zoo. It takes over an hour to get there. Near the end she suggested playing the sign version of the alphabet game and I said, "What if we did a math version?!"

She was all for it. Right away she said, "I see angles!"  I don't remember everything but here are some highlights:

[C] Congruent shapes: I found this one and a nice way to introduce that language.

[C] Curves: This was hers. She saw curves in the telephone wires.

[D] Degrees: I saw a 90 degree angle in a roof

[E] Equal: She used this word in relation to the shapes she saw. I mentioned the word congruent again in relation to this idea.

[H] Height: Some trees were higher than others.

[I] Interval: The telephone pole were spaced in equal intervals. In this game I don't think it matters if the adult ends up identifying more things than the child.  It's engaging for everyone to be looking out the window and a great opportunity for talking math with your kids in a low-pressure, (hopefully) highly enjoyable context.

[P] Parallel lines

You get the picture, right? Math talk can be about numbers but also about relationships (higher, smaller, faster) and other ways we describe our physical world.  Next time it would be fun to look for [A] Arrays, [M] Multiples, [N] Numbers or even the math version of "Are we there yet?"

[Z] Zeno's can't get there from here.

Thursday, July 10, 2014

That time my kid made me a math book while I was away

One of the best things about going out of town to work is coming home to discover some new math treasure my kid has created during my absence. One of my favorites was a couple years ago when she embellished a piece of fabric with a beaded freeze pattern. Here's what I got this morning after returning from a fabulous day-long Math in Your Feet intensive with some amazing educators in Connecticut.

The first page says: "Shapes can be found in everything! Especially a cat. Make a graph."

I think I'm supposed to put an X for every shape I see in the cat.

The second page says: "A cat running across a baseball rhombus! [!!!] Half of a rhombus is another triangle! There are ____ triangles. How many triangles. Answer on the back."

How many do you see?

Her answer was 6.

Apparently she went downstairs (where all *my* math making materials are kept, even though she has plenty of making supplies upstairs) when she wasn't supposed to.  But the call of the scissors and glue sticks were just to great, I suppose!

I was supposed to discover this on my desk at some point, but she was too excited to wait.  What a treasure!

Sunday, July 6, 2014

The Magnetizing Pencil Lead Experiment [#dswyk]

My (newly 9yo) daughter is a sensory girl who likes to mix things and ask questions while doing so. Over the course of her short life she has created all sorts of goopy, colorful, muddy, tasty inside and outside concoctions out of food, paint, mud, sidewalk chalk, bubbles...all the while narrating non-stop about what she's going to do and how and why.

This is great but she is very messy and I am, in all honesty, sometimes low on tolerance for daily messes (and for long-running verbal narrative) but I know this is the kind of thing that lights her up. So when she asked:

"Can I take salt and pepper and pencil leads and try to magnetize them in water?"

I said:

"Yes, as long as you clean up after you're done. And make sure to record your findings."

And she said:


She put water, salt, pepper and magnets from our fridge into a bowl along with the pencil leads. Her essential question was: "Can I magnetize these pencil leads?"  Here is what she wrote down about her experimenting (edited only for spelling):
If I put a pencil lead in water with pepper and salt and rub it to the non magnetized side: 
Will it still work if it's just water and pepper? YES
Will it work with just water? YES 
Will it work without water? NO. It does not work if both are not in water. It only works if one is rubbed! 
Will it work with a different magnet? YES 
When it's wet it sticks to me! Will it work when I don't rub it on the magnet? YES, but it does not stick for long.
Her ultimate conclusion was that she could "magnetize the pencil leads but they could not stick to other magnets beside themselves" and that "water has something to do with it."

I recently picked up a book at our public library used book store called Curious Minds: How a Child Becomes a Scientist.  The book is a collection of essays from interesting scientists who were asked to write about how and when in their childhoods they became interested in an idea that led them to go into the sciences.  My favorite essay is from Mary Catherine Bateson who is the daughter of Gregory Bateson and Margaret Mead. She talks about how she grew up in a household where "the how" of science was the focus. "The what" her father and mother studied changed over time, but it was her childhood experiences of looking for patterns and asking questions that really brought her into her field.

So, when my husband pointed out that the leads stuck together because they were wet, not magnetized as she had concluded, I agreed.  We did not succeed in convincing her otherwise, which is just fine with me.  What is most important about her sequence of question asking is that she was engaged in THE PROCESS (the how) of science.  To me, at this point in her life, the feel for the process is what we want her to have -- the curiosity, the personal agency, the flow of question asking.

After all, if you talk to real scientists and mathematicians they will tell you their work is about days and months and years and decades of wrong turns and the resulting new questions. In today's fast paced world it's hard to muster patience for this idea of building understanding over time but the truth is this: Coming to know often means you may not have all the answers you want or need right away but as long as you have new questions to ask you can be sure you are heading in the right direction.

Saturday, June 28, 2014

Do ducks count as amphibians? Do penguins count as birds?

It wouldn't be an exaggeration to say that I have learned the most about how my child thinks and what she knows by watching what she does (while making things, while at play, while talking to others) and then initiating conversations based on what I notice. The more I do this the more accustomed she's become to me asking "How do you know?" or "Can you tell me how you thought to do it that way?" And I have become much better at staying present in the conversation and really listening to her answers. For the most part they are often surprising and delightful.

My approach to having (usually math-related) conversations has generally been to keep my eyes and ears open and jumping on any opportunities. But not all the time. Here's the story of what happened when I set out something I truly hoped she'd interact with in a mathematical way.


I recently found all these animals in a basket for $5.00 at a garage sale. She was with me but, at the time, wasn't really interested.

I took them home. Later in the afternoon I washed them. I waited to see if she'd notice them. SHE DID!!

The minute she saw them she was FULL of ideas. A mile a minute, the ideas gushed out of her:  "Let's sort them into categories! I'm going to make a zoo! I'm going to make a pile of cats and a pile of dogs. And we'll give all the horses to Alice..."

" I'm going to put them into lines. The darker colors here, the lighter colors here. See? Take a picture of the cats, too. But make sure NO other animals are in the picture."

And here I'll pause to say that her inclination to sort, classify, arrange, and organize by attribute seems to me to be the essence of mathematical activity, and a thinking skill useful and applicable at all levels of mathematics. Over the course of the next hour she narrated what she was thinking and what she was going to do next. During this time I had ample opportunity to listen to her reasoning, ask her questions to challenge her thinking and clarify my understanding of the choices she was making as she physically and mentally sorted the animals within the framework of her elaborate narrative.

She had decided to make a zoo. Each category (her words) of animal would be in its own area and assigned a color. Here's where things got interesting.  Green was the color for all the cats, but the "tame cats" got a second color as well (purple). Wildcats were in a different pen but still in the green category.  The lone mouse got put into the cat pen "so the cats can play with it."

Orange was for giraffes. Elephants were light blue. Dinosaurs "will need a big area because they're, well...dinosaurs.  Birds will go with dinosaurs because they're part of the same family." 

Her plans were big: "We'll record how many of each and make a graph.  I'll put them in arrays of fives if possible." (I love that in addition to the sorting and classifying she also thought of them as potential data and that they could be organized in arrays to help the counting process).

For the most part she stuck with the arrays (except for a few categories). In the picture above she sorted the dinosaurs into lines of small and big, but not the rhinos. When asked about this, she didn't really want to talk about it. Too busy with the next thing, I think.

Then came the sea creatures. She put them in a bucket of water because "they just need a place to swim."  She started to put the crocodiles and turtles in too. "Wait a minute!" I said. "Those are amphibians. They live in water and on land. Do they belong with the sea creatures?" She decided she'd sort the amphibians out another way, but decided to add a yellow mark to the sea creatures "so they don't get confused for the amphibians. And, they might wander off." 

She had more questions as she sorted:

Do ducks count as amphibians? [Why do you ask that?] Well, they are on land and in water.
Do penguins count as birds?
Are hippos amphibians?
[Why?] Cause they go in water too. I always thought they were amphibians.

As she continued she built an extension for the zoo to make room for the 30 horses.

Earlier, as I washed and sorted the animals into loose categories (that's just how my brain rolls) I had wondered what she might do with all these creatures and, if it was sorting, what kinds of categories she might choose.  I started my sort by grouping by animal type (zebras, horses, cats, dogs, dinosaurs, etc.) but pretty soon created categories to include a wider definition. So, in addition to cats and dogs I also had "farm animals," "sea creatures," "animals from Australia," etc.

That's how it went for her too, although our categories differed. What I called sea creatures ended up as "water animals" and "amphibians" for her. There was also a fascinating category she initially called "under three" which was a catch all for any small animal group. All creatures with "under three" members would be put in a pen together. I got confused and thought it meant "three and under" but she was clear "under three" meant TWO. I asked her why she hadn't called it "two and under" but I got the brush off.

It took an HOUR of sorting, arranging, categorizing, planning and organizing for her (and about a million mosquito bites for me) before her zoo was complete. I was exhausted. The kid, on the other hand?

"And now!? We need to organize the tours!"

And here I'll make a pitch for Talking Math with Your Kids and Doing Science with Your Kids ('cause you know we did both, right?). Both sites (and conversations via Twitter hastags - #tmwyk and #dswyk) provide incredibly strong, real-life models for how to have mathy and science-y conversations with your kids just by listening to what they have to say and going from there.  Don't delay, talk science and math with your kids today!

Monday, June 23, 2014

Math in Your Feet Educator Intensive

It's official!

Math in Your Feet is back in Connecticut this July!


Join physical educators, classroom teachers, music teachers and math specialists who would like to insure physically active schools in a professional learning workshop sponsored by the Connecticut Association for Health, Physical Education, Recreation and Dance (CAHPERD) and presented by Malke Rosenfeld.

In this active, six-hour workshop for educators, participants will:
  • be introduced to the concept of rhythm making with the feet (percussive dance)
  • experiment with an educational tool designed for non-dancers to create, sequence, and record their own rhythm- and foot-based dance patterns
  • discuss the math learning inherent in these activities
  • have an opportunity to reflect on their experience and learning and think forward toward implementation of the ideas and lessons presented
  • leave with comprehensive resource lists, classroom materials, and lesson plans for the Math in Your Feet program for use in individual classrooms
Wednesday, July 9th, 2014
9:00am - 4:00pm
Central CT State University, Detrick
615 Stanley Street, New Britain, CT 06050

Visit the CAHPERD website for more details and to REGISTER for the event.

Sign up soon, space is limited!


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