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.

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? 

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:

This should read: The product of 2 and the sum of the product of 4 and x and 3.

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!

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?

I’ve kind of been off the grid lately-save following a few conversations via Twitter- due to  the birth of my son.  Thanks again to everyone for all the well wishes.  Mommy and baby are doing great.  Sleep is a precious commodity but I am blessed to be able to take a few days off to enjoy the adjustment to our little one.  I always seem to compare my approach to teaching with my approach to parenting and vice versa.  Here’s the top 10:

10.  The clientele will expose your bad habits. 

9.  You can read as many “how to” books as you want, but nothing prepares you for your first real life encounter.

8.  They like it when you act goofy.

7.  Sometimes you just have to wing it. 

6.  They get grumpy before lunch time.

5.  They get sleepy after lunch time.

4. You’re gonna lose some sleep.

3. Working at one makes you better at the other.

2.  Balance is crucial.

1.  If it stinks, change it.

Man, I am horrible right now.  No, not the tell-people-that-I’m-bad-so-they-tell-me-I’m-good kind of horrible.  I mean really horrible. I am way behind in planning, grading and have way too many ideas and no way to implement them.  Or if I do try to implement them, they’re half-baked.  It may have a little to do with a certain visitor we are expecting.  But at the end of the day I have been feeling way scattered.  It’s not a good feeling but I know it’ll pass.  I have been doing this long enough to know better.

There, I said it!  Let the healing begin.

During the warm up today, I asked the question:

When does the absolute value of r equal r?

I liked the way the students handled themselves during the discussion so I took out my phone and recorded the following. After a little prodding, Jose jumped in.  I’m thinking of changing his name to Q.E.D.

For the past two years I have had a classroom Voicethread account.  It has been really difficult to set up the accounts for the students, though.  So much so, that I have put it on the back-burner until today.  I saw that I could import multiple accounts as long as I had a Name, UserName, Email and Password in a .csv I could import. 

Piece of cake.  I set up a Google Form, embedded it on our wiki and had the kids fill it out.  Done.  Now I’m gonna eat lunch.

Today, my 7th graders were dealing with a problem that eventually they will solve by setting up a system of equations.   Right now, they don’t have that in the tool kit, so guess-and-check would  be the strategy of choice.  Here is the problem and our first step:

One student was able to come up with the equation: 1.50 a + 2.00 d = 360, but another was quick to point out that there would be many different solutions, so we couldn’t use it…yet.  So the first guess is 20 and we recognize that the total is too high.  Usually that indicates that the first guess is too high, so we normally go with a lower second guess.  However, this time, Aaron pointed out that it didn’t make sense to decrease the guess on advanced tickets because they are cheaper.  In fact we want to increase that one.  This is right about the time I almost lost my poker face:

Aaron: “So if we add to the advanced tickets our total will actually go down.”

“Why?”

“Because for every $1.50 we add, we lose $2.00.  So every time we change the tickets by one, we drop $.50.  Since we need to drop $30, we need to sell 60 more tickets in advance.”

At this point, I almost blew it.  Nearly jumped right in and said something stupid like, “That’s right Aaron.  You guys get it?”   To which they would have all nodded “uh-huh” and we would have moved on.  But I caught myself, gave him the “eh, I am not sure about that” and removed myself from the conversation.  So Aaron had to try to re-explain to his classmates what he was saying.  I could tell that a couple of them got it, but many were still perplexed.  After a couple of minutes I asked Jose if he could explain what Aaron was saying.  Jose nailed it and a bunch of  kids have an “a-ha” moment.  Good stuff. 

Later I asked Jose why he didn’t speak up a little sooner.  He said that he didn’t figure that he needed to ask any questions because he understood it.  I asked for a show of hands on how many understood after Jose’s explanation and that’s when about 15 hands shoot up. 

We have been talking a lot in my classes about how important it is to join the conversation.  Some kids still think that it’s just about them.  They don’t realize that if they offer something to the conversation, not only do they benefit from explaining something they already understand, but there is no telling how many other kids benefit too. 

Today, I think Jose gets it.