About this time last year, I didn't know much about blogs, Twitter or PLN's. I did, however, have questions about why we do what we do and how to make it matter. This blog was born because there are a lot of great teachers having great conversations and I thought 14 years of going it alone was enough. It continues to boggle my mind that many of you have a better idea of what takes place in my classroom than many of the teachers in my own school; it matters to you what is happening in classrooms of others. I hope that in the next year, the questions asked here will be more honest and continue to challenge.
I am humbled and honored that Sam and Kate found this blog worthy of a Best New Blog nomination. If you feel so inclined, you may cast your vote here.
Monday, December 14, 2009
Thursday, December 10, 2009
Triangle Centers Lab
The other day I made up a triangle centers lab for my 8th graders.
Here is how it went:
Day 0: Homework for tonight is to make a triangle larger than your hand out of some material heavier than paper. Cardstock or cardboard are ideal.
Day 1: Open GeoGebra and get to work. Kids got after it. Some slowed themselves down by not reading directions very well. The nice thing about GeoGebra is that it's easy to erase.
Day 2: Most finished the lab and went onto extension activity. Those who didn't finish had a difficult time managing time. They could do the work, but staying focused was the issue.
Extension: Now that you know how to find the circumcenter and incenter, construct an inscribed and circumscribed circle using only compass and straight edge. These students haven't done anything with a compass, so I offered a 6th point (assignment was worth 5) for those who could figure out how to do the constructions on their own. If they chose to look up the "how to" of constructions, they then would have to prove that the method of angle bisecting works.
David came up with his own extension. He asked, "why does the centroid allow you to balance the triangle?"
"Nice question. Now go away and come back with an answer." He's figured out that the three medians divide the triangles into six smaller triangles with equal area and that would account for equal weight distribution from the centroid. He can see it in GeoGebra, but is working on a formal proof. Brandon tried to backdoor me with a proof by contradiction, "well the six triangles have to have equivalent areas because if they weren't, the large triangle wouldn't balance."
Don't try to beat me at my own game, son.
Chris' reflection: "Hey Mr. Cox, you just kinda gave us a test without giving us instructions."
"Yeeeeaah kinda, huh?
For Next Time: Stamp each page after students have demonstrated the correct constructions. Then allow them to go to the next page. Take a little more time discussing the difference between "drawing" and "constructing."
Here is how it went:
Day 0: Homework for tonight is to make a triangle larger than your hand out of some material heavier than paper. Cardstock or cardboard are ideal.
Day 1: Open GeoGebra and get to work. Kids got after it. Some slowed themselves down by not reading directions very well. The nice thing about GeoGebra is that it's easy to erase.
Day 2: Most finished the lab and went onto extension activity. Those who didn't finish had a difficult time managing time. They could do the work, but staying focused was the issue.
Extension: Now that you know how to find the circumcenter and incenter, construct an inscribed and circumscribed circle using only compass and straight edge. These students haven't done anything with a compass, so I offered a 6th point (assignment was worth 5) for those who could figure out how to do the constructions on their own. If they chose to look up the "how to" of constructions, they then would have to prove that the method of angle bisecting works.
David came up with his own extension. He asked, "why does the centroid allow you to balance the triangle?"
"Nice question. Now go away and come back with an answer." He's figured out that the three medians divide the triangles into six smaller triangles with equal area and that would account for equal weight distribution from the centroid. He can see it in GeoGebra, but is working on a formal proof. Brandon tried to backdoor me with a proof by contradiction, "well the six triangles have to have equivalent areas because if they weren't, the large triangle wouldn't balance."
Don't try to beat me at my own game, son.
Chris' reflection: "Hey Mr. Cox, you just kinda gave us a test without giving us instructions."
"Yeeeeaah kinda, huh?
For Next Time: Stamp each page after students have demonstrated the correct constructions. Then allow them to go to the next page. Take a little more time discussing the difference between "drawing" and "constructing."
Friday, December 4, 2009
To Wiki or Not to Wiki
I know, I know:
"Using a tool for it's own sake is bad pedagogy."
"Have an objective and then find the tool that will help you best meet that objective."
"If your favorite tool is a hammer, everything looks like a nail."
Blah, blah, blah.
What if you didn't know if your objective was even possible until you tried out the tool? Then what?
I completely understand Kate's frustration when it comes to the speed bumps caused when we try to rely on certain tools. But what about just making the tool available and allowing kids to come and go as they see fit? Why can't we do that? Does everything have to have a lesson plan attached to it?
I originally created this wiki just because I could. I let kids take some class time to familiarize themselves with how to use it--in fact, we learned how to use it together. But the space has taken on a life of it's own. I have kids who are now in high school coming back to access the resources they created last year.
That's a good thing, no?
"Using a tool for it's own sake is bad pedagogy."
"Have an objective and then find the tool that will help you best meet that objective."
"If your favorite tool is a hammer, everything looks like a nail."
Blah, blah, blah.
What if you didn't know if your objective was even possible until you tried out the tool? Then what?
I completely understand Kate's frustration when it comes to the speed bumps caused when we try to rely on certain tools. But what about just making the tool available and allowing kids to come and go as they see fit? Why can't we do that? Does everything have to have a lesson plan attached to it?
I originally created this wiki just because I could. I let kids take some class time to familiarize themselves with how to use it--in fact, we learned how to use it together. But the space has taken on a life of it's own. I have kids who are now in high school coming back to access the resources they created last year.
That's a good thing, no?
Speaking Mathanese
Kids butcher the Mathanese language. I'm just sayin'. We have all these kids who speak text just fine. It seems to me that Mathanese should be right up their alley. All we are doing is taking a bunch of words and converting it to symbols. Should be easy, right? Not so much.
I find that kids have a tough time translating algebraic expressions to English and vice versa. Am I alone?
Yeah, didn't think so.
One of the things that I have been trying to focus on this year is to convey to students the universality of the things they are learning. For example, cause/effect in language arts becomes input/output in math. Conflict resolution is the same as problem solving. Language arts has expressions and sentences, so does math. Scientific method can compare to making a conjecture in geometry, testing it out and then using inductive logic to arrive at a conclusion (read: rule).
So what happens when you tell them to translate: the product of 3 and the sum of x and 2?
You get: 3x+2, right?
Not quite.
Well I figured we needed to develop a mashup of English and Mathanese; Mathglish, if you will. Here is what we came up with:
English to Mathanese:
[caption id="attachment_458" align="aligncenter" width="500" caption="This should read: The product of 2 and the sum of the product of 4 and x and 3. "]
[/caption]
Mathanese to English:
The key this time was to allow the mashup. I live in a rural area where the Spanish speaking population is very large. Many of my kids speak and understand Spanglish. I have never done it this way before and the kids nailed it.
How do you do it?
Update: Just did a quick check for understanding 2nd period and 26/28 kids circled the bases.
I find that kids have a tough time translating algebraic expressions to English and vice versa. Am I alone?
Yeah, didn't think so.
One of the things that I have been trying to focus on this year is to convey to students the universality of the things they are learning. For example, cause/effect in language arts becomes input/output in math. Conflict resolution is the same as problem solving. Language arts has expressions and sentences, so does math. Scientific method can compare to making a conjecture in geometry, testing it out and then using inductive logic to arrive at a conclusion (read: rule).
So what happens when you tell them to translate: the product of 3 and the sum of x and 2?
You get: 3x+2, right?
Not quite.
Well I figured we needed to develop a mashup of English and Mathanese; Mathglish, if you will. Here is what we came up with:
English to Mathanese:
[caption id="attachment_458" align="aligncenter" width="500" caption="This should read: The product of 2 and the sum of the product of 4 and x and 3. "]
[/caption]Mathanese to English:
The key this time was to allow the mashup. I live in a rural area where the Spanish speaking population is very large. Many of my kids speak and understand Spanglish. I have never done it this way before and the kids nailed it.
How do you do it?
Update: Just did a quick check for understanding 2nd period and 26/28 kids circled the bases.
Wednesday, December 2, 2009
Joining the Fray
I'm sorry, I couldn't help myself. I can't let Sean Sweeney have all the fun in class (see here and here). I do, however, have to credit Sean with giving me the push I needed to actually do this with my class. Thanks!
The Setup
I told my students that before the Fray was "The Fray", they were called The Phray and their lead singer was a math teacher. He wrote a song called "Solve to Save Your Life" but when they were signed they changed the name of the band and made some adjustments to the song on account of "math songs don't make the top 40, baby." It took some searching to find the archive of the old song, but I did it. I also told them that OneRepublic had a song called "Rationalize." We'll see if that one surfaces.
So with no further ado: The Phray performing their hit single, "Solve to Save Your Life."
If you want the lyrics.
We'll be releasing the official video soon.
Reflection: This really isn't my thing. I was debating whether or not to scrap the whole thing even though my 4 yr. old can now solve equations. The thing that really hit me was that me leaving my comfort zone allowed some of my students the freedom to do the same. I made some connections with kids where I may not have otherwise been able to. I also learned that playing guitar for 1.5 hours over 3 periods may cause tendonitis. Advil anyone?
The Setup
I told my students that before the Fray was "The Fray", they were called The Phray and their lead singer was a math teacher. He wrote a song called "Solve to Save Your Life" but when they were signed they changed the name of the band and made some adjustments to the song on account of "math songs don't make the top 40, baby." It took some searching to find the archive of the old song, but I did it. I also told them that OneRepublic had a song called "Rationalize." We'll see if that one surfaces.
So with no further ado: The Phray performing their hit single, "Solve to Save Your Life."
If you want the lyrics.
We'll be releasing the official video soon.
Reflection: This really isn't my thing. I was debating whether or not to scrap the whole thing even though my 4 yr. old can now solve equations. The thing that really hit me was that me leaving my comfort zone allowed some of my students the freedom to do the same. I made some connections with kids where I may not have otherwise been able to. I also learned that playing guitar for 1.5 hours over 3 periods may cause tendonitis. Advil anyone?
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