February 6, 2012: Week 4 tasks
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Maria Droujkova
Feb 6, 2012, 6:41:16 PM2/6/12
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Welcome to Week 4 of the course!
WEEK 4 TASKS
Live meetings throughout the week - pick one or more! Course discussion Monday 7pm ET. Next week it's on Wednesday 7pm ET. http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-4-live-meetings-february-6-12/
Some people object to object patterns as a math task. Express your opinion: http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-4-patterns-dont-go-anywhere-february-6-12/
Edit our Wikipedia article: http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-4-wikipedians-reloaded-february-6-12/
SOME WEEK 3 HIGHLIGHTS
Carolyn wonders why working backwards is such a powerful method:
http://thesingaporemaths.com/stratf.html
I thought this description on how to solve math problems combined the idea of this weeks theme of art by drawing but also involved my theme of finding patterns. I skimmed through the strategies they posted a d I found that I have used almost all of them, especially the working backwards method that I mentioned in my bio. I am interested in finding different articles that explain why kids choose a certain method because although I have used all of the methods, working backwards seems to be the one that works the best for me. Is this familiar to anyone else?
Amanda Graf shares a story from her childhood:
I remember that my teacher taught me this concept in 2nd grade by "betting" me that he could draw a line longer than me and handing me a piece of chalk. I didn't fully understand the task, so I went to the chalk board and drew a line about 4 feet long. My teacher took the chalk back and drew a circle on the board with bout a 3 foot diameter and asked if his line was longer. Half the class raised their hand yes and half raised their hand no. He explained that if he were to stretch his circle out into a straight line that his line would, in fact, be longer. I was perplexed...he had drawn a circle, I didn't understand how this was the same thing as a line. Another student raised their hand and asked to draw a line on the board. This student drew a zig-zag line from one side of the board to the opposite side of the board. The teacher then took a marker and, drawing on the wall (because the student had drawn perfectly to the edge of the chalk board), added an inche to the zig-zag line that had been drawn on the board. We slowly began to understand two concepts: one, that a line is never-ending and two, the concept of infinety.
Julia Brodsky posts questions from her 6-9yo math club:
Who invented numbers?
Who invented math?
When was math first used?
Are there any unsolved math problems?
Do figures with rotational symmetry have central symmetry? (To answer the question that came up in our discussion, this was an 8yo who is very much into construction kits)
Laura Haeberle poses a philosophical question:
Do we base our understanding of art and nature off of math? Or do we frame our understanding of math on the laws of nature and observable physical properties?
I thought of this question from my prior research and interest in the Fibonnacci sequence and it's applications in nature. In learning the sequence, I realized how deeply math and nature fit together, and how the world supports both. My math question is rather philosophical, yet I have a few different ways that I could adjust this for children.
How to open up a closed question? SandyG has an example.
Closed question: How many blue (red, yellow) squares are in this pattern?
Open question: I could ask the children to rearrange the colors to make a pattern. Each child might come up with a unique pattern, but the concept of patterning would still be taught.
And another story example:
For the 3 Bears story, I could ask number questions that aren't directly answered in the story such as "How many bites did Goldilocks take from Papa's bowl, mama's bowl, & baby's bowl? How many all together? How did you come up with that number?" Because it isn't in the story, each child might have their own idea.
Kathy Cianciola follows up on an idea:
I really like your quilt idea. If each child designed their own unique hexagon you could eventually join them together creating a huge wall hanging for the classroom. This is using the child's inner sense of creativity in making their own original designs.
SOME COLLECTIONS IN PROGRESS
Movie channel http://www.youtube.com/playlist?list=PL84E80E3C18F033D9
Wikipedia article http://en.wikipedia.org/wiki/Modern_elementary_mathematics_(mathematics_education)
Cheers,
Maria Droujkova
919-388-1721
Make math your own, to make your own math
WEEK 4 TASKS
Live meetings throughout the week - pick one or more! Course discussion Monday 7pm ET. Next week it's on Wednesday 7pm ET. http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-4-live-meetings-february-6-12/
Some people object to object patterns as a math task. Express your opinion: http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-4-patterns-dont-go-anywhere-february-6-12/
Edit our Wikipedia article: http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-4-wikipedians-reloaded-february-6-12/
SOME WEEK 3 HIGHLIGHTS
Carolyn wonders why working backwards is such a powerful method:
http://thesingaporemaths.com/stratf.html
I thought this description on how to solve math problems combined the idea of this weeks theme of art by drawing but also involved my theme of finding patterns. I skimmed through the strategies they posted a d I found that I have used almost all of them, especially the working backwards method that I mentioned in my bio. I am interested in finding different articles that explain why kids choose a certain method because although I have used all of the methods, working backwards seems to be the one that works the best for me. Is this familiar to anyone else?
Amanda Graf shares a story from her childhood:
I remember that my teacher taught me this concept in 2nd grade by "betting" me that he could draw a line longer than me and handing me a piece of chalk. I didn't fully understand the task, so I went to the chalk board and drew a line about 4 feet long. My teacher took the chalk back and drew a circle on the board with bout a 3 foot diameter and asked if his line was longer. Half the class raised their hand yes and half raised their hand no. He explained that if he were to stretch his circle out into a straight line that his line would, in fact, be longer. I was perplexed...he had drawn a circle, I didn't understand how this was the same thing as a line. Another student raised their hand and asked to draw a line on the board. This student drew a zig-zag line from one side of the board to the opposite side of the board. The teacher then took a marker and, drawing on the wall (because the student had drawn perfectly to the edge of the chalk board), added an inche to the zig-zag line that had been drawn on the board. We slowly began to understand two concepts: one, that a line is never-ending and two, the concept of infinety.
Julia Brodsky posts questions from her 6-9yo math club:
Who invented numbers?
Who invented math?
When was math first used?
Are there any unsolved math problems?
Do figures with rotational symmetry have central symmetry? (To answer the question that came up in our discussion, this was an 8yo who is very much into construction kits)
Laura Haeberle poses a philosophical question:
Do we base our understanding of art and nature off of math? Or do we frame our understanding of math on the laws of nature and observable physical properties?
I thought of this question from my prior research and interest in the Fibonnacci sequence and it's applications in nature. In learning the sequence, I realized how deeply math and nature fit together, and how the world supports both. My math question is rather philosophical, yet I have a few different ways that I could adjust this for children.
How to open up a closed question? SandyG has an example.
Closed question: How many blue (red, yellow) squares are in this pattern?
Open question: I could ask the children to rearrange the colors to make a pattern. Each child might come up with a unique pattern, but the concept of patterning would still be taught.
And another story example:
For the 3 Bears story, I could ask number questions that aren't directly answered in the story such as "How many bites did Goldilocks take from Papa's bowl, mama's bowl, & baby's bowl? How many all together? How did you come up with that number?" Because it isn't in the story, each child might have their own idea.
Kathy Cianciola follows up on an idea:
I really like your quilt idea. If each child designed their own unique hexagon you could eventually join them together creating a huge wall hanging for the classroom. This is using the child's inner sense of creativity in making their own original designs.
SOME COLLECTIONS IN PROGRESS
Movie channel http://www.youtube.com/playlist?list=PL84E80E3C18F033D9
Wikipedia article http://en.wikipedia.org/wiki/Modern_elementary_mathematics_(mathematics_education)
Cheers,
Maria Droujkova
919-388-1721
Make math your own, to make your own math
Garrett, Sandra
Feb 7, 2012, 3:45:08 PM2/7/12
to ed218a...@googlegroups.com
Have you posted the recording of last night's discussion? I can't locate it.
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Maria Droujkova
Feb 7, 2012, 3:50:38 PM2/7/12
to ed218a...@googlegroups.com
On Tue, Feb 7, 2012 at 3:45 PM, Garrett, Sandra <sgar...@arcadia.edu> wrote:
Have you posted the recording of last night's discussion? I can't locate it.
Thank you, Sandra - I thought I did! It's up now at http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-4-live-meetings-february-6-12/
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