So...who likes bedtime? I, for one, am not generally enamored with detours from the normal bedtime routine.
But when my kid said, "Hey Mama! Want to hear this song I made up that helps you with your three times table?!" I decided to give her a little leeway so I could capture the moment. What can I say, I'm a sucker for math!
The song starts: "There were three ice cream trucks at the corner of Circle Drive..."
My favorite part is 'on the corner of Circle Drive' since, of course, circles have no corners! But, I'm pretty sure this was not intentional on her part.
Did see her looking off to her right to silently skip count the answers in her head? We've been doing a lot with conceptualization of multiplication/division (arrays, multiplication towers, factor dominoes, scale, re-imagined factor trees, exploring the concept of units) but almost nothing with memorization.
I'm happy to have this unexpected piece of evidence that she is thinking about and internalizing these concepts. I'm also pleased to report a happy conclusion to bedtime!
Saturday, March 30, 2013
Thursday, March 28, 2013
Full to the Brim
I've got so many amazing things happening these days. Not only am I facilitating my daughter's path to math and bringing the Math in Your Feet program to students and teachers, but I've got a lot of other fun projects going on as well, all related to the theme of math and making. Take a look!
My TEDxBloomington Talk: Jump into Math!
It was an amazing process and, finally, an amazing day at TEDxBloomington. (There I am in the green/yellow shirt at the end of the day when all the speakers, crew and organizers made their way onto the stage.)
My talk will be online in the next couple months alongside the talks from Drew Ramsey, MD (one of psychiatry’s leading proponents of dietary change to balance mood, sharpen brain function and improve mental health), Ryan Germick (Google Doodle team lead), Eric Deggans (TV/Media Critic for the Tampa Bay Times and author of Race-Baiter: How the Media Wields Dangerous Words to Divide a Nation), Robert Einterz, MD (whose efforts have literally saved thousands of AIDS inflicted people in Kenya) and many other incredible people with incredible stories. I was in fine company and it was an honor to share my my work in this way.
The Tape Chronicles Project
Oh Happy Day! The Tape Chronicles Project has finally launched! I've had this idea for a couple years and am so excited to see what we can build. Here's the basic description:
Tape! The ultimate open-ended, the world is your oyster, creative, hands-on learning and making supply. Check out the endless ways tape can be employed in the interest of math, art, kinesthetic exploration, invention and education.
Check out the Tape Chronicles page on my website and please consider submitting examples of your own!!
Teaching Artist Tool Shop
As part of my participation in the new collective, Teaching Artist Tool Shop, I created a video about what success looks like in my teaching of dance and math and in a moving classroom. You can watch the video What Success Looks Like in My Teaching on my website. From the feedback I've received, the ideas in this video can be applied across disciplines.
Moebius Noodles
In January I was invited to contribute to the Moebius Noodles blog! I'm so honored! Read my first two contributions Thinking in Threes and Hidden Math: Book Edition and then spend some time over there in math adventure land!
Math in Your Feet Facebook Page
Oh, we're having so much fun over there. It's the place where I share all sorts of cool percussive dance videos, incredible visual math art, links to interesting ideas about teaching and learning math....all of which would never really make a great blog post on their own. We all hope you'll join us!
My TEDxBloomington Talk: Jump into Math!
It was an amazing process and, finally, an amazing day at TEDxBloomington. (There I am in the green/yellow shirt at the end of the day when all the speakers, crew and organizers made their way onto the stage.)
My talk will be online in the next couple months alongside the talks from Drew Ramsey, MD (one of psychiatry’s leading proponents of dietary change to balance mood, sharpen brain function and improve mental health), Ryan Germick (Google Doodle team lead), Eric Deggans (TV/Media Critic for the Tampa Bay Times and author of Race-Baiter: How the Media Wields Dangerous Words to Divide a Nation), Robert Einterz, MD (whose efforts have literally saved thousands of AIDS inflicted people in Kenya) and many other incredible people with incredible stories. I was in fine company and it was an honor to share my my work in this way.
The Tape Chronicles Project
Oh Happy Day! The Tape Chronicles Project has finally launched! I've had this idea for a couple years and am so excited to see what we can build. Here's the basic description:
Tape! The ultimate open-ended, the world is your oyster, creative, hands-on learning and making supply. Check out the endless ways tape can be employed in the interest of math, art, kinesthetic exploration, invention and education.
Check out the Tape Chronicles page on my website and please consider submitting examples of your own!!
Teaching Artist Tool Shop
As part of my participation in the new collective, Teaching Artist Tool Shop, I created a video about what success looks like in my teaching of dance and math and in a moving classroom. You can watch the video What Success Looks Like in My Teaching on my website. From the feedback I've received, the ideas in this video can be applied across disciplines.
Moebius Noodles
In January I was invited to contribute to the Moebius Noodles blog! I'm so honored! Read my first two contributions Thinking in Threes and Hidden Math: Book Edition and then spend some time over there in math adventure land!
Math in Your Feet Facebook Page
Oh, we're having so much fun over there. It's the place where I share all sorts of cool percussive dance videos, incredible visual math art, links to interesting ideas about teaching and learning math....all of which would never really make a great blog post on their own. We all hope you'll join us!
Tuesday, March 26, 2013
Math: In, Out, Through, Between and All Around...Everything
I really do think that the way to make math more enjoyable for everyone is to find a million tiny examples of how math plays into our interests and daily lives. Because then? Then it's OURS. And, as any math teacher will tell you, math isn't really that hard, but you do have to be motivated to take it on.
I get re-motivated every time my daughter and I enter a new cycle of discovery and exploration. I've determined that even though I can't always predict when it will happen I do know for sure that it'll come around again...
The latest cycle started Saturday with a trip to the Lotus Education and Arts Foundation's annual spring outreach program, the Lotus Blossoms Family Day Bazaar.
Cultural traditions from all over the world were represented there and my seven-year-old jumped for joy when she discovered a table with Native American activities, specifically Navaho. She got to make a beaded cord by twisting fiber in a specific way and then finished it with her own beads at home. Her final product is below:
The other part of the booth was learning a basic traditional string figure of a Navaho rug design, which I did while my kid was working on her cord. On Sunday she found the string I had brought home and played around with it. "Hey look! A triangle!"
Lucky for me I had been sitting on a Cat's Cradle book, ready to pull out at just the right moment, and now she knows three basic figures. It reminded me of James Murphy's work; he used Native American string figures (all of which he learned as a child) to teach reluctant high school math students a few decades ago in New York City. His book is on my wish list now and I can't wait to read more about his work, but I did notice that, among other things, string figures require the ability to follow an algorithm/sequence/recipe which was the perfect challenge for my second grader.
More than anything the Native American booth reminded my daughter that she knows a lot about that subject and she decided to create her own Native American museum. She wanted to start right in on a mural but I encouraged her to do a draft first. On Monday she got started on the real thing:
While she was drawing she pointed out the color patterns she was using in the bead and quill work detail on the person's clothing. The ability to create pattern units and be conscious of the patterns she designs as specific entities is something that popped into view just about the time her reading really took off this past December. Based on my work last summer I'm convinced that the development of this kind of "chunking" skill in both math and reading is completely related. I'm even more sure about this after her facility with multiplication and division concepts (understanding units and groups) really zoomed ahead this January and February.
Also on Monday I chose a book to read at lunch which I had found at the local library's book sale for a quarter: Fun With Numbers by Massin. The girl often rolls her eyes when I bring out a book like this outside our normal math time, but the first page had some fun stories about the Mayans and base 20 and she was way more open when I pointed out that the Mayans are native peoples. Then came the Sumerians and base 60 which, as the book says, is how we tell time today.
"Go get me the clock!" the girl commanded, "so I can count like a Sumerian!" She was eager to show, yet again, that waiting until the learner is ready makes learning easy -- last week she learned how to tell analog time in one day.
Culture, math, art, math, stories about math history, culture, math. And that is our story of how math is in and out and all around us for the moment. I'm excited to see how it all connects when it comes around again!
I get re-motivated every time my daughter and I enter a new cycle of discovery and exploration. I've determined that even though I can't always predict when it will happen I do know for sure that it'll come around again...
The latest cycle started Saturday with a trip to the Lotus Education and Arts Foundation's annual spring outreach program, the Lotus Blossoms Family Day Bazaar.
Cultural traditions from all over the world were represented there and my seven-year-old jumped for joy when she discovered a table with Native American activities, specifically Navaho. She got to make a beaded cord by twisting fiber in a specific way and then finished it with her own beads at home. Her final product is below:
The other part of the booth was learning a basic traditional string figure of a Navaho rug design, which I did while my kid was working on her cord. On Sunday she found the string I had brought home and played around with it. "Hey look! A triangle!"
Lucky for me I had been sitting on a Cat's Cradle book, ready to pull out at just the right moment, and now she knows three basic figures. It reminded me of James Murphy's work; he used Native American string figures (all of which he learned as a child) to teach reluctant high school math students a few decades ago in New York City. His book is on my wish list now and I can't wait to read more about his work, but I did notice that, among other things, string figures require the ability to follow an algorithm/sequence/recipe which was the perfect challenge for my second grader.
More than anything the Native American booth reminded my daughter that she knows a lot about that subject and she decided to create her own Native American museum. She wanted to start right in on a mural but I encouraged her to do a draft first. On Monday she got started on the real thing:
While she was drawing she pointed out the color patterns she was using in the bead and quill work detail on the person's clothing. The ability to create pattern units and be conscious of the patterns she designs as specific entities is something that popped into view just about the time her reading really took off this past December. Based on my work last summer I'm convinced that the development of this kind of "chunking" skill in both math and reading is completely related. I'm even more sure about this after her facility with multiplication and division concepts (understanding units and groups) really zoomed ahead this January and February.
Also on Monday I chose a book to read at lunch which I had found at the local library's book sale for a quarter: Fun With Numbers by Massin. The girl often rolls her eyes when I bring out a book like this outside our normal math time, but the first page had some fun stories about the Mayans and base 20 and she was way more open when I pointed out that the Mayans are native peoples. Then came the Sumerians and base 60 which, as the book says, is how we tell time today.
"Go get me the clock!" the girl commanded, "so I can count like a Sumerian!" She was eager to show, yet again, that waiting until the learner is ready makes learning easy -- last week she learned how to tell analog time in one day.
Culture, math, art, math, stories about math history, culture, math. And that is our story of how math is in and out and all around us for the moment. I'm excited to see how it all connects when it comes around again!
Tuesday, March 19, 2013
Quality, Quantity and the Commutative Process
My puzzlement first began while I was building multiplication towers. What's the difference between two 3s and three 2s? The commutative property says, essentially, no difference. But I say, take another look:
3x2 | 2x3
What's the difference between...
#1: 3 green-3 red
#2: 2 green-2 red-2 blue?
Quantitatively, nothing. Qualitatively, everything. These are two of the multiplication towers I built. They both have exactly the same number of beads in exactly the same places, but they are qualitatively different from each other in some interesting ways. You can read the full post here.
1x2 | 2x1
Here's another example: We were out to breakfast one Saturday morning. The kid wanted more sausage and bacon. I told her she could have two more pieces of protein. Fair enough, right? But is it going too far to argue that 2 sausages do not equal 1 bacon + 1 sausage? If you're seven years old, it's a tricky choice. [Edit: Re-reading this, I realize this is not necessarily mathematically sound, but I think my defense is to say that if we focus on the value of '2', 2 means different things if you have 2 of 1 thing or two different things. Make sense?]
3x4 | 4x3
And, consider a job I have coming up. I have work in the city, which is a 3 hour drive round trip. I am working 4 days with 3 workshops each day for a total of 12 workshops. I inquired about doing 4 workshops a day for 3 days since that would mean I would have one less day of driving and incur less child care costs.
Just like in the sausage/bacon example it's important to compare units. Sure, 3x4=12 and 4x3=12, but when you factor in the driving time, gas consumption, and child care costs...
3 days of 4 workshops per day is qualitatively better than 4 days of 3 workshops per day, wouldn't you say?
Quality vs. Quantity: An Alternate Perspective
These ideas have been in the back of my mind for a month or more. As I was thinking about it again today the subject spontaneously came up as my daughter told me about her new invention. She had figured out a way to mechanize the production of what she calls "tape rope". A month or so ago she twisted it manually with her fingers for hours and got some big blisters. Today she harnessed the turning action of the electric pencil sharpener to help her twist.
Here's what she had to say about quality vs. quantity as she spun her tape rope. If you listen closely all the way to the end, I'm pretty sure her final conclusion does not support my argument here, but in the service of a balancing my own view point, here it is:
"The quality [tape] is tighter, the quantity [tape] is looser...but it still works as rope," she says.
I think she's on the side of the commutative property, but me? I'm still not sure what I think.
3x2 | 2x3
What's the difference between...
#1: 3 green-3 red
#2: 2 green-2 red-2 blue?
Quantitatively, nothing. Qualitatively, everything. These are two of the multiplication towers I built. They both have exactly the same number of beads in exactly the same places, but they are qualitatively different from each other in some interesting ways. You can read the full post here.
1x2 | 2x1
Here's another example: We were out to breakfast one Saturday morning. The kid wanted more sausage and bacon. I told her she could have two more pieces of protein. Fair enough, right? But is it going too far to argue that 2 sausages do not equal 1 bacon + 1 sausage? If you're seven years old, it's a tricky choice. [Edit: Re-reading this, I realize this is not necessarily mathematically sound, but I think my defense is to say that if we focus on the value of '2', 2 means different things if you have 2 of 1 thing or two different things. Make sense?]
3x4 | 4x3
And, consider a job I have coming up. I have work in the city, which is a 3 hour drive round trip. I am working 4 days with 3 workshops each day for a total of 12 workshops. I inquired about doing 4 workshops a day for 3 days since that would mean I would have one less day of driving and incur less child care costs.
Just like in the sausage/bacon example it's important to compare units. Sure, 3x4=12 and 4x3=12, but when you factor in the driving time, gas consumption, and child care costs...
3 days of 4 workshops per day is qualitatively better than 4 days of 3 workshops per day, wouldn't you say?
Quality vs. Quantity: An Alternate Perspective
These ideas have been in the back of my mind for a month or more. As I was thinking about it again today the subject spontaneously came up as my daughter told me about her new invention. She had figured out a way to mechanize the production of what she calls "tape rope". A month or so ago she twisted it manually with her fingers for hours and got some big blisters. Today she harnessed the turning action of the electric pencil sharpener to help her twist.
Here's what she had to say about quality vs. quantity as she spun her tape rope. If you listen closely all the way to the end, I'm pretty sure her final conclusion does not support my argument here, but in the service of a balancing my own view point, here it is:
"The quality [tape] is tighter, the quantity [tape] is looser...but it still works as rope," she says.
I think she's on the side of the commutative property, but me? I'm still not sure what I think.
Sunday, March 10, 2013
A Flood of Self-Initiated Math
So, the seven-year-old has been having a spate of self-initiated math lately. First there was her 'map of angles' and then having her dolly write an essay on 'What Infinity Means to Me'. So, I guess I wasn't too surprised to hear her from the other room giving her dolly another math lesson:
In her most patient, teacherly voice:
"I'm drawing a simple house, Amelia. Everything in the house is mostly 90 degrees...you don't have to be exactly accurate but it just has to be good...a triangle window and here's the front porch....compare these two houses. Can you fix this one? Good job!"
[Her explanation to me when I asked her later what she was doing: "I drew a house without angles and with angles and Amelia had to fix the house without angles up!"]
After Amelia's success, she continued the lesson with this explanation:
"There are even angles in nature -- straight up and down trees, but some are even 80 degrees, slanting. The old ones are 50 or 40 degrees."
Later, I got a look at her drawings:
In the larger house I see her thinking through the angles all starting from the bottom left vertex/corner of the house, which is forward movement from her original representations in the Map of Angles post. Below the big house is the 'house with angles' at the bottom and what I think is the 'house without angles' (all wonky looking) above that (I thought I saw a different drawing with the same ideas but that, apparently, has gotten lost in the shuffle.)
Another quiet moment found her exploring the structure of an isosceles triangle.
"See, there are eight of these triangles on each edge [above] and fifteen squares on the bottom edge," she told me. She also called the line she drew from the top vertex to the center of the bottom edge a "diameter" which she knows is how you divide a circle in half.
In addition to all our sidewalk math adventures over the last year, we've learned more about identifying and classifying geometric shapes in the Beast Academy 3A series but it's been a while since we did the polygons chapter. We got through skip counting which was perfect and, after entering the perimeter chapter decided to take a break. This drawing really shows me she's thinking very specifically about the length of each edge.
And, finally, although this may seem more in the 'art' category, I know for sure that drawing three-dimensionally has all kinds of math involved in it, I just don't know what kind, lol! Six or nine months ago she tried to sketch Platonic solids and really didn't do it very successfully. I think her eye has come a long way:
Her milk box:
An Asian ceramic bowl with some paper flowers in it:
Her electric pencil sharpener:
I love seeing (and hearing) the world through her eyes.
In her most patient, teacherly voice:
"I'm drawing a simple house, Amelia. Everything in the house is mostly 90 degrees...you don't have to be exactly accurate but it just has to be good...a triangle window and here's the front porch....compare these two houses. Can you fix this one? Good job!"
[Her explanation to me when I asked her later what she was doing: "I drew a house without angles and with angles and Amelia had to fix the house without angles up!"]
After Amelia's success, she continued the lesson with this explanation:
"There are even angles in nature -- straight up and down trees, but some are even 80 degrees, slanting. The old ones are 50 or 40 degrees."
Later, I got a look at her drawings:
In the larger house I see her thinking through the angles all starting from the bottom left vertex/corner of the house, which is forward movement from her original representations in the Map of Angles post. Below the big house is the 'house with angles' at the bottom and what I think is the 'house without angles' (all wonky looking) above that (I thought I saw a different drawing with the same ideas but that, apparently, has gotten lost in the shuffle.)
Another quiet moment found her exploring the structure of an isosceles triangle.
"See, there are eight of these triangles on each edge [above] and fifteen squares on the bottom edge," she told me. She also called the line she drew from the top vertex to the center of the bottom edge a "diameter" which she knows is how you divide a circle in half.
In addition to all our sidewalk math adventures over the last year, we've learned more about identifying and classifying geometric shapes in the Beast Academy 3A series but it's been a while since we did the polygons chapter. We got through skip counting which was perfect and, after entering the perimeter chapter decided to take a break. This drawing really shows me she's thinking very specifically about the length of each edge.
And, finally, although this may seem more in the 'art' category, I know for sure that drawing three-dimensionally has all kinds of math involved in it, I just don't know what kind, lol! Six or nine months ago she tried to sketch Platonic solids and really didn't do it very successfully. I think her eye has come a long way:
Her milk box:
An Asian ceramic bowl with some paper flowers in it:
Her electric pencil sharpener:
I love seeing (and hearing) the world through her eyes.
Saturday, March 2, 2013
"What Infinity Means to Me"
From the other room came:
"C'mon Amelia, time to write!"
"No, you're right handed!"
"Don't scribble!"
Curious, I checked it out. "What's going on in here?" I inquired.
To which my seven year old replied, "Amelia [the doll she sewed] is writing an essay called 'what infinity means to me.'"
"Oh cool, what did she write?"
"It is sewing that has never been done [finished]. It is also a cloth that can never be done [finished]. And a mountain that reaches on forever."
"Wow, that's cool! But, I'm curious why Amelia is thinking about infinity on a Saturday morning..."
"Well, she was in math class and this was her assignment."
Now there's a math class I'd love to attend! Lucky dolly.
"C'mon Amelia, time to write!"
"No, you're right handed!"
"Don't scribble!"
To which my seven year old replied, "Amelia [the doll she sewed] is writing an essay called 'what infinity means to me.'"
"Oh cool, what did she write?"
"It is sewing that has never been done [finished]. It is also a cloth that can never be done [finished]. And a mountain that reaches on forever."
"Wow, that's cool! But, I'm curious why Amelia is thinking about infinity on a Saturday morning..."
"Well, she was in math class and this was her assignment."
Now there's a math class I'd love to attend! Lucky dolly.