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.”

Thanks, G-Docs

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.

Almost Blew This One

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.

Calculator : Arithmetic :: GeoGebra: ?

To tell you the truth, I don’t really have a problem with my state’s math standards (here and here).  I do, however,  have a serious problem when the standards become the target rather than the scope through which we aim at the target.  So what’s the target?  What should be the point of math education today?  It has become very clear to me that it has never been easier to find correct answers to anything rooted in computation.  With WolframAlpha,  GeoGebra and all the other resources available, there probably isn’t a question we could ask a student where they couldn’t quickly look up an answer.   When I first started teaching, the big question was whether or not we should let our algebra students use a calculator.  A lot of the “veteran” teachers were dead set against it because they “gotta add, subtract, multiply and divide, for cryin’ out loud.”  But the calculator would allow a student to speed up all the calculations (read arithmetic)  and get to the “math.”  Well can’t the same be said for WolframAlpha or GeoGebra?  Don’t these tools give students access to certain problems where previously they would have been bogged down by calculations they couldn’t complete?

I remember when basic skills were being able to perform the four operations over the Real Number system.  What’s a basic skill look like today?  Is algebra the arithmetic of the 21st century?

SHOW YOUR WORK!

I’ve been getting real tired of having to sift through my students chicken scratch to find the few nuggets of information they have hidden in their “work.”  It kind of came to a head the other night as I was grading our most recent geometry test.  It became clear that many of these students really have not been taught what it means to show work in a clear and organized manner.  I have modeled it many times, pointing out how one should line up the equal signs, how arithemetic isn’t necessarily showing work, etc.  However, I think that when I’ve tried to explain this, all they hear is Charlie Brown’s teacher. “Wha wha wha…wha wha whaa.”

I decided to give them a taste of their own medicine. I took the warm up I had planned and dumped it into Wordle (I figured Wordle must be good for something). Yesterday’s warm up:

 

 ”But Mr. Cox, what are we supposed to do?”

“The directions are all there.  It’s worth 100 pts. you know, so ya better make it snappy.”

“It’s hard to understand.”

“Ok, you don’t like this one; how about this?”

 

“That’s no better.”

“No?”

They’re on to me by now. 

“Yeah, of course I’m proving a point; but what is it?”

 The conversation went something like this:

“You think this is confusing?  Well that’s what you do to me whenever you show your work.  Why is it that in your Language Arts classes you all understand that we start writing in the top left, we work left to right and top down, but in your math class, you seem to think that starting right in the center of your workspace and then going any which way is a good idea?  How in the world am I supposed to understand what you’re telling me?”

So I threw up some examples of what to do…

 and what not to do…

 and we discussed what made one student’s work acceptable and the other’s unacceptable.  We also discussed the difference between “showing your work” or “showing your steps” and that which belongs on scratch paper.

Oh, we also agreed that starting in the upper left hand corner of the workspace is acceptable in a math class as well.

I’m Lovin’ This!

A couple of weeks ago, I posted a question regarding how I should handle my advanced 8th grade class.  I got a bunch of great responses which cemented my opinion that these PLN’s are no joke.  In a matter of hours, I got a responses from Kate Nowak (telling me to pull my head out and quit encouraging this “jump through hoops” mentality), Darren Kuropatwa (detailing some great extension lessons as well as some online resources), a tweet from Jackie Ballarini (suggesting that I go with an analytical approach to geometry) and an email from Alison Blank(offering a problem based analytical geometry curriculum).  By the end of the weekend, I was in conversation with Alison and Jim Wysocki regarding the geometry curriculum. 

This problem based geometry is good stuff.  It is rigorous, but the skills the kids need are all review.  We may only get through 10-12 problems every day or two, but they are really causing them to think.  That’s good, right?

Anyway, this allows me to try to implement something I have been working on for a while.  Chris Lehmann called it “inverting the classroom.”  I like the idea because it allows me to have kids work on the skills review outside of class while we spend the class time discussing the meaty stuff; the problems that make our heads explode only to find out that if I would have just stepped back and taken a different look at the problem, there is a simple yet elegant way to solve it.   

I can see two camps evolving in the class.  Those who embrace the problem solving and those who feel like they can’t do it.  I’ll keep you posted on how it goes.  But, so far, so good. 

Thanks again.

Is This Wrong?

In a 6-1 vote, the Los Angeles City Board of Education decided to turn over 250 of its schools over to charter and other private operators.  I’ll definitely watch this story unfold with tremendous interest.  Although I don’t really understand all the ramifications of such a decision.  I have to ask: Is This Wrong?

Is turning schools to charter groups and/or private operators going to foster competition and if so, is that a bad thing?

Will this help turn teaching into a profession where innovation is rewarded?

Do the teachers’ unions actually have students’ best interests at heart?

Who stands to profit from this? And do these folks care about education as much as they care about making money?

Some have said that this is a direct result of high stakes testing and the one-size-fits-all philosophy of education that inevitibly Leaves Children Behind. 

But were we doing such a good job before NCLB and the high stakes test?

I don’t know, but I’m curious.

The Evolution of the Mathcast

Two years ago my principal approached me about getting a SmartBoard for each of the math teachers in my department.  I had no idea what he was talking about.  Heck, before I came here, my daily tech decision was: Vis-a-Vis or Expo?  So when he starts talking about this board that lets you interact with the computer whose screen is projected back on the board, I think my head almost exploded.  Didn’t have a clue how I’d use it.  Against my better judgement, he ordered them anyway.  They came in a couple of weeks before school started, I helped him install one on my wall and off I went.  No training, no direction.  Just me and my computer. 

I particularly appreciated the ease by which I could do the drawings and graphs which were such a drag with an overhead.  I hated to give up my vintage set of chalk board drawing tools, but it had to happen.  A guy’s gotta grow up some time.  As I was toying around with some of the features, I noticed that there was what looked like a record button.  We played around with the thing and figured out how to record the annotations but had a tough time getting the sound to record.  I played with the settings and in walks a wireless lapel mic.  Got it up and running and away I went. 

At first the recordings were a train wreck (I’m still not completely pleased with the quality of some of the examples).  The default file was .avi and I would post the lessons through the school website.  The problem was a student would click the link, go make a sandwich, do the dishes and come back just in time for the recording to play.  One of our district IT guys suggested I compress the .avi in MovieMaker to allow it to open faster.  Keep in mind, I really had no idea what I was doing.  I was basically swinging at pitches in the dirt hoping to connect.  Anyway, I had my first examples online ready to view by Christmas. 

Man, we thought we were cutting edge.  Then last year, I stumbled upon Tim Fahlberg’s wiki. Turns out this guy has been doing mathcasts since I was in high school.  He practically invented this stuff.  I contacted Tim and he turned me on to Camtasia Studio.  It’s a bit pricey, but it allows one to render the videos in many different formats.  It’s also very easy to use.  Eventually this led to a channel on blip.tv as well as a podcast through iTunes.

The learning curve has been pretty steep but has started to level off a bit.  I am now passed the point of wondering how much can be done with this technology, but now I am wondering how to best use the ability to create dynamic notes for my students.  The nice thing about the channel on blip.tv as well as being on iTunes is that kids can subscribe and download the examples so they can take them wherever they go.  It’s amazing to think that I have kids watching these things on their iPhone’s and PSP’s.  But they are.  So the question is how do we best use this tool?  Chris Lehmann suggests inversions.  What say you?

Hom-asse-ferentiation

All the new schools come with cafegymatoriums so I figure I’ll go with a 3-in-1 post.

Homework

 For 12 years I had assigned it but it always bugged me that we would spend 15+ minutes the next day going over something that many of the students didn’t complete.  And if they did bring it in, how did I know if it was actually their work?  Now that I have children of my own in school, I am even more bothered by the amount of busywork that imposes itself on family time.   

My question isn’t regarding the validity of homework.  My question revolves around the idea of how to make homework matter.  How do we make it meaningful to our students?  Can we tie it to assessment and/or differentiate it so that kids can work on what they need at any given point in time? And further, can homework become part of a meaningful dialogue between teacher and student rather than a box to be checked on the daily “to do” list? 

Assessment

Quiz, Quiz, Test.  Quiz, Quiz, Test. Quiz, Quiz, Test. 

Isn’t that how the pattern goes?  Followed that one too.  But again, over the past few years, my view of assessment has changed.  When do we assess?  How often?  How many times should a student have to show us he can do something?   How many different ways should he have to show it? Multiple choice or free response?  Where does writing come into play? 

For the past three years, we have been dealing with pacing guides and benchmarks due to the fact that my district is in program improvement.  I am in favor of it.  Pacing guides and benchmarks  have allowed us to begin with the end in mind, check for understanding along the way and then find ways to intervene with students who are struggling to grasp the concepts/skills.  However, I have noticed that teachers have a tendency to become very procedure oriented and lose sight of all the great thinking that can be provoked in a math classroom.  I don’t blame this on pacing and benchmarks any more than I blame bad lessons on the tools being used in the classroom.  It has become obvious that the textbook pacing isn’t the way we want to go, so we have started to teach one standard at a time.  But I think that many of our standards need to be deconstructed even more in order to ensure that when we assess, we get a grip on where a student is really struggling.  For example, in California, Algebra Standard 15.0 deals with mixture, rate and work problems.  It isn’t enough to say that a kid is struggling with 15.0, we need to be a bit more specific in order to fix the problem.  I know that Dan has done a nice job of explaining the need to break the curriculum down into skills and he has a great assessment plan.  The part we have struggled with is what to do in between the initial assessment and the re-assessment(s).  Which leads us to…

Differentiation

Is it enough to throw some review problems up on the board for warmups and call it “intervention?”  Do we give students different assignments based on their need — and when we give  these assignments, how do we grade them?  How much weight do they carry in relation to the final grade? Can I actually have 30 kids working on 30 different things?  If so, does that mean that I have to come up with 30 different assignments for each skill I want to remediate?  My head hurts just thinking about it. 

Until recently. 

Why can’t we tie them all together? Why can’t homework/classwork be prescribed based on the results of an initial assessment becomming a prerequesite for the re-assessment; a key to unlock the assessment box.  A student can be placed into one of two paths: the road to proficiency or the road to advanced status. Once a student reaches proficiency in a certain standard/skill, he earns a B.  He then has the choice to move towards advanced status in that skill (for an A) or work towards proficiency in another skill. If he never moves onto the advanced path, the score for that skill remains a B.  I am not sure if we should go with a 1-5 grading system or attach a percentage to the rubric score. (ie. 5 = 90%, 4 = 85%, 3 = 75%, 2 = 65%, 1 = 50%)

  Over the past month, I have had some release days and have come up with a template.  The challenging part has been to decide which “tasks” a student must complete before being allowed to re-assess.  These tasks are very minimal in that they merely show what I would like a student be able to show before he is allowed to re-assess.  Could a student take these tasks and “create” their own problems based on the template, or would the teacher need to be more hands on in helping direct the student?  Are there skills I am missing?  Are there ways to demonstrate the skill that I am leaving out?  How can this be adapted for student interest and/or modality?  And most importantly: does this idea stand a chance? I would really appreciate any feedback that I can get on this.

Note: Our math classes are in 94 minute daily blocks, so time for intervention/enrichment is built in.  We will go with a sort of 60-30 model next year where we do regular instruction for the first 60 minutes and leave the last 30 minutes for students to work on their choice of previous skills. 

The proficiency tasks for each skill will be followed by the student doing an exemplar.  My working definition of “exemplar” is a problem that exemplifies the given skill worked by the student with written and/or verbal explanation of the process used.  I have found these to be very good authentic assessments.  The student has the option to do this via paper and pencil or mathcast.