It Was Fun While It Lasted

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.

Personal Responsibility vs. Learning?

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?

Whatdaya think?

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.

The Easter Egg

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?

Metacog…what?

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.


Filling out the table took all of 30 seconds because my students are very good at following directions.

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?”
“Addition.”
“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…


…and then let column 1 be x?”


“Ooooh, column 2 is 12-x.”

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.

Why I Love Twitter: Reason #247

11:47am: I ask @rjallain if he has an effective way to demonstrate to students how the horizontal velocity of a projectile is not affected by gravity.

12:00pm: He sends me this link.

Yeah, that pretty much sums it up.

Thanks, Rhett.

Really?

 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.

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.”



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