Sorry, guys, I gave WordPress a try, but it just isn’t working out. I’m moving. New address is http://coxmath.blogspot.com. I hope you don’t mind making the adjustment in your reader.
Yesterday I had a few students absent and we did a lot of examples involving multiplying binomials, factoring and solving quadratics by completing the square. It was one of those lessons that “just happened.” I had one idea I wanted to nail down and it kinda morphed into a bunch of examples. I made up most of the examples on the fly because I was just gauging their reaction and taking what they gave me. So believe me when I say, “they wasn’t the pertiest lookin’ notes ya ever did see.”
Apparently, they were effective, though. The countenance of the class went from chin-on-hand-it’s-Friday-I’m-tired-here-we-are-now-entertain-us to thank-you-sir-may-we-try-another-cuz-this-is-some-cool-stuff-and-I’m-gettin’-it.
Its tough to reproduce lessons like that so I exported the notes to .pdf and emailed them to the absent students.
I just received this email from one of the recipients:
“Thanks for the notes! They will really help. I do have one question though; did you have to take time specifically out of the lesson to take the pictures or some other program that did them for you? I’m asking this because I think that if you did this every time we learned something new and posted it on your website[s], it would be a good resource.”
So I told him I slaved over my computer all of 30 seconds to export and email as an attachment. Which leads me to my question:
I have always taken a “students gotta take responsibility for their notes and review them regularly” kind of approach which has prevented my from exporting and posting the chicken-scratch covered slides from class. But if posting them is going to help them learn, should I care about the personal responsibility they take on (or don’t take on) in regards to their own note taking?
Note: if you’re interested in what a spur-of-the-moment-ugly-as-heck-yet-equally-effective lesson in my class looks like on static slides, hit me up in the comments and I’ll update the post with a link. I’m posting this from my phone and won’t have access to the notes until Monday.
Tags: easter egg, row game, worksheets
Gotta thank Kate for introducing me to the Row Game. I also like the idea of using box.net as a way for teachers to upload and share them. But, me being me, I couldn’t leave well enough alone. I like the fact that these activities are self checking and that if students find that they have different answers, then there is a mistake. The problem with that is if I create two sets of 10 problems, I would like my students to work as many of them as possible.
So I introduced the “Easter Egg.” I have used this concept in the past when doing test review. Basically, I hide wrong answers so students need are a little more alert when looking at the solution to a problem.
How does this work for row games? Well, in the row game, if the partners have different answers, then someone messed up. This opens the door for discussion. But what if they never disagree? Then there was no real need to discuss anything. With the Easter Egg, I will make a couple of the problems diverge, that way agreement doesn’t necessarily equal correctness. Now they have to talk even if they get the same answer.
Today I rolled out this row game on slope with my 7th graders. Once they got used to the concept, the did pretty well. I look forward to doing more of these.
I don’t know, maybe this defeats the purpose of the row game. Maybe not. What say you?
The move to middle school has really allowed me to consider not only why we do what we do, but why students do what they do. I had one such opportunity the other day during my introduction to quadratics.
I gave my students the “magic number” worksheet where they choose a number and then select integer pairs whose sum is the magic number and place them in a table. The third column of the table is the product of the integers.
Plotting the relationship between columns 1 & 3 went very smoothly as well. So smoothly that students were very nonchcalont about the symmetry of the resulting parabolas.
Things got interesting when I asked them to give me an equation that represented the relationship between column 1 and column 3. It was interesting to me when I asked them what was happening in column 2.
Most students saw column 2 through the lense of addition. For example, if the magic number was 12 and the number in column 1 was 4, students would mentally figure,
“4 + what = 12?”
The answer’s 8. Obvious. And they got this answer as if it were a thoughtless reflex.
As long as column 1 contained an integer, there was no problem. However, this was no help when it came to generalizing an equation. As a result, many students struggled with going from the concrete to the abstract.
“What’s happening in column 2?”
“Look again. Is it really addition?”
“No, subtraction. You’re subtracting in column 2.”
“OK, so what happens if we write column 2 like this…
Recognizing what was happening in column 2 made finding the equation simple. The real problem was that there was a disconnect between what they thought they were doing and what they actually were doing.
This led to a nice discussion on what I like to call “taking thoughts captive.” Teachers call it metacognition. Students call it…well, they don’t call it anything, because they don’t usually realize they’re doing it.
Somewhere in there is the reason we get a shoulder shrug and an “I don’t know” when we ask questions.
But once they realize that they ask themselves questions hundreds (maybe thousands) of times each day, it’s impossible for them to not think about it.
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.
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.”
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?
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?
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:
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’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!
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.”
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?