Wednesday, November 7, 2012

More Fraction Multiplication

My 7th grade students are in the middle of exploring fractions.  They are currently researching the question:

What are fractions and how can I add, subtract, multiply and divide them?

I'm not sure how much instruction I want to give here. Is this intuitive? What can I do to make this more usable?

 Applet with more instruction is here.

John Golden:

Good idea.  Updated version.

Saturday, November 3, 2012

Please Wu, Don't Hurt 'Em

Yes, this is a mission that Wu's on—taking out the weak.

Hung-Hsi Wu
[Textbook School Math] gives students (and teachers) a gimmick; the CCSMS require that students actually learn mathematics.

You can't touch this.

Friday, October 26, 2012

Integrated Teaching

For the past six years, our middle school science and social studies departments have kinda been given the short end of the stick.  The minutes given to math and ELA doubled at the expense of these two departments.  I don't know what the teachers were worried about, though, because only the 8th graders are tested and the test only covered, I don't know, three years worth of standards.  (And besides, Jason says teaching science in CA is easy.)
This year we decided to give some relief by reducing the minutes to math and ELA and adding a semester of integrated math/science and a semester of integrated ELA/social studies to each student's schedule.
My assignment this year is to teach one section of 7th grade math and four sections of the integrated class.  It's been tough because we are really creating this class as we go.
So far, this is what I've learned:

  1. Students will do exactly what you tell them to do.  

  2. Students have trouble breaking large (essential) questions down into smaller (guiding questions) questions. 

  3. Students think "try harder" is a plan. 

  4. Polya and the guys who invented this were life coaches.   

  5. Establishing protocols is essential. 

  6. Scaffolding doesn't just refer to content. 

  7. Changing "Why?" into "Tell me more about that" is magic. 

  8. "Common knowledge" isn't so common.  

  9. We need to do a better job of helping students distinguish between opinion and argument. 

  10. After 16 years of teaching, I still get excited when students realize that thinking is better than memorizing. 

  11. Any list worth reading stops at 10.  

Wednesday, October 24, 2012

The Best Thing

I'm overwhelmed.  I'm tired.  I have pockets of excellence in a sea of mediocrity. My wife deserves more than I'm giving. My two-year-old is challenging every thing I ever thought I knew about parenting--we have put child locks on the freaking upper cupboards, for crying out loud. My other boys need more of me.  Four of my five periods are spent teaching a class we are inventing as we go.  I'm convinced that everything revolves around the scientific method or some variation of it.  Questions still are way more satisfying than statements.  My planning is always weaker than the adjustments I make in the middle of the period.  A good problem is more engaging than engagement strategies, but I don't know enough good problems.  Expo markers dry out way too fast.  Some of my students have bigger problems than I'll ever encounter and somehow I have to make what we do matter. 

And yet, my students keep showing up, my boys still greet me with "I love you, Daddy" and my wife still loves me.  

And tomorrow, I get to be better.  

Friday, July 27, 2012

A Closer Look at Why

David Coffey:
For years I taught as others taught and I do not want to go back to those times. I am comfortable and confident in my teaching but that is not to say complacent. Thanks to all of you, I continue to find ideas that inspire me.

This is what makes Dan's most recent series of posts so important. Posts outlining specific classroom activities are important as they give us insight as to how we do what we do. As David alludes to in his post, these ideas are important, but they're limited in the I'm-not-you-and-you're-not-me kind of way. The Ladder of Abstraction is bigger than any specific activity as it get to the heart of why we do what we do. It's not limited by the skill set of the teacher. In fact, it's the one thing we all have in common, but until now, has been a bit nebulous. As this unfolds, I think we will see more great ideas come out of the mathtweet-o-blogosphere.
- Posted using BlogPress from my iPad

Sunday, July 15, 2012

When Engagement Strategies Attack

Just watch this.
h/t @mpershan

We have to be really careful here. Total physical response is great. Having common responses to things in class can be very effective (and fun). But to call this "whole brain teaching" is troubling when many students are mindlessly following mirroring.

I've had a problem with the use of "engagement strategies" for a while. It's as if we are buying into rhetoric sans argument; looking at the accidents and ignoring the essence.

Stop it, already.

Sign below.

I was warned.

x ________________________

- Posted using BlogPress from my iPhone

Saturday, July 14, 2012

Creating Audiences

I've tried to stay out of the Khanversation, at least here. Occasionally, I'll throw a tweet or two out there, but no official statement. However, the latest Vi Hart video has me confused. So confused, in fact, that after my first view, I thought she had just called out Khan Academy.

Vi's video posits that true artists tend to break the previously held rules of maximizing one's known audience by clearly addressing them via existing channels. In essence, an artist creates her audience. I originally thought she was taking aim at Khan Academy with this video until it was pointed out to me that right around the 2:07 mark  she says,

"There's a reason that people prefer my videos which ramble through my thought process or Sal's Khan Academy videos which he makes in real time..." 

Vi actually aligns herself with Sal as if what they do are Khansubstantial.

I Khan't disagree more.

I don't think I have to argue that Vi Hart creates her own audience, but to say Khan Academy does the same thing is, well, just wrong.

Let's take these three points one at a time.

1. Know your audience and address yourself directly to it.
Sal's audience is every student who ever asked the question, "Can you show me how to do ?" This is a prevalent view of education. Give kids enough knowable things and they'll sort out which ones they'll need at a later date and which ones they can discard. Unfortunately, the real point that gets missed is that this approach actually robs students of the opportunity to learn how to discern between what's important and what's unnecessary noise within the actual learning process. There is no co-production between Sal and his audience (at least in the videos I've seen) as his audience is the consumer.

2. Know what you want to say and say it clearly and fully.
Though his videos may not be scripted, Sal knows exactly what he wants to say. The fact that he makes his videos in "real time" doesn't hide the fact that he's taking a message that's highly glossed and falsely making it seem rough around the edges. He's basically taking a belt sander to a new pair of jeans and telling us he's worn them for years. Taking an "aw, shucks" attitude into the videos is really no different than a politician putting on a hard hat with the good ol' boys down at the factory and saying, "see, I'm one of you."

The message is very clear: Here's what you need to know, now know it

3. Reach the maximum audience by utilizing existing channels.

I believe Vi when she says she's making videos for the only person she truly knows: herself. As a result, she's come to know and be known by many. Sal, on the other hand, is playing to an audience and adjusts to feedback.

As for the suggestion that those of us who criticize should make our own videos, here you go, I have an entire library of real time videos, many of which were recorded before a live studio audience group of students. These videos were inspired by their questions. They aren't anything special, but for the kids who asked the questions, they meant a lot.  For those of you who prefer to follow the textbook, I've got you covered.[1]

[1] Keep in mind that these videos were not intended to be initial instruction.  They were intended to be a resource for students who needed a reminder or an archive of past conversations.  

Wednesday, May 23, 2012

On Chapters vs. Lessons

Phil Daro:

"Manage chapters; don't manage lessons.  As soon as you shift the focus to lessons, you shift it away from mathematics." 

As a baseball coach, I always taught things from a whole-part-whole point of view. The game has a lot of moving parts.  If a ball is hit to the right-center field gap, everyone on the field has a job to do: RF and CF go after the ball, LF backs up 3B, 2B and SS line up for the relay to 3B [1], 1B covers 2B, P runs straight towards the 3B dugout and  reads the play and finally the C directs traffic.  If we look at everyone's job in isolation, it makes no sense.  However, if we see each responsibility within the context of the overall goal of keeping the runner off of third base, then it all fits.

In math, Daro argues, each concept has a proper "grain size."  If it's too large (strands), the math becomes fuzzy and incoherent.  If it's too small (lessons), the math becomes fragmented and incoherent.  It is important for us to understand the parts that make up a concept.  It may even be important for us to offer feedback on the parts.  It is never a good idea to teach the parts in isolation.

[1] Bonus points if you can explain why both the SS and 2B line up for the relay to third base.

Tuesday, May 22, 2012

On Problem Solving

Phil Daro:
The American teacher looks at a problem they're going to use in a lesson and asks themselves, "how can I teach my kids to get the answer to this problem?"  The Japanese teacher asks, "What's the mathematics they're supposed to learn from working on this problem? How can I get them to learn that mathematics?"

If you want better answers, ask better questions.

Monday, May 21, 2012

Classroom in Crisis

From the recent issue of California Educator:

“My pacing guide doesn’t fit these students, and it’s almost inhumane to do it this way,” says the El Monte Union Educators Association (EMUEA) member. “The rigor is really too much for these kids.

 I'm not gonna lie, things are tough.  With the budget situation in California looking as bleak as ever, Special Education services are being cut.  Many students with special needs are being mainstreamed without the support they need to succeed.  And "despite [teachers'] best efforts, most students with disabilities are flunking algebra."

I mean, how else are they going to be able to learn about the 10-16-18 right triangle?  It's difficult enough for students to grasp the 5-8-9 Pythagorean Triple, though we may be able to do it with limited resources.  But, to use similarity to derive 10-16-18?  No, it takes a fully funded program to pull that off.

Please, Governor Brown, give these people their money.  Otherwise, they're going to have to cancel their biology field trip to the unicorn zoo.

Friday, May 11, 2012

Did I Get It?

The Prompt

Given: The green, red and blue points are collinear. What is the dimension of the blue square if the green and red squares are 4x4 and 7x7 respectively?

After a few minutes, B comes up and says, "Mr. Cox, can you check this out. I think I've got something."

She shows me her diagram.

And her results.

Yep, kid.  You've got something.

Thursday, April 19, 2012

Common Opener

I really like where we are going here.  Our video production class has been broadcasting daily announcements live for a while and now we are really starting to take advantage of this time to establish some campus habits of mind. Recently, we started a series of "Common Opener" segments airing on Tuesdays and Thursdays focused on Flexible Thinking.  Math was up first and we used the Number Talk as the vehicle.

Basically, we are asking students to deconstruct and reconstruct numbers by looking for ways to find the answer that may be different than what they're used to.  We want them to leave their comfort zones just a bit.

Once the announcements are finished, teachers send their "exit slips" up to the office (or a student aide will pick them up) and I end up with a delivery of ~500 index cards/half slips of paper with student responses.  I quickly go through them and look for patterns.  It's been interesting to say the least.  Many students have started to look for new ways to work with numbers while a large majority still stick with the standard algorithms, but I'm optimistic that students will become more comfortable with the uncomfortable.

Hopefully, this acts as a vehicle to further the student/student, student/teacher and teacher/teacher conversations about learning on our campus.  What really encourages me is the opportunity we have to show how big ideas show up in all over the place.  Once the other content areas have a chance to interpret Flexible Thinking, we may see some real aha moments with our students.

You can find the announcements here.

Tuesday, April 17, 2012


What if we could design a project-based class for middle school students that integrated math and science-- that provided context for math and gave instructional minutes back to science?  What if this class capitalized on the natural correlation between the Practices For K-12 Science Classroom and the Standards for Mathematical Practice.  What if students were asked to design investigations, used modeling to move from the concrete to the abstract and then presented their findings for peer review?  What if they used technology to take snapshots of their learning along the way and kept a running journal of the process?

What if...

Wednesday, April 11, 2012

The Comma

If [this], then [that].  We talk a lot about [this] and [that] in the math classroom. Teacher supplies [this], student responds with [that]. They even have names:  hypothesis and conclusion.  But, what about the comma?   All the power of the entire process is summed up with a tiny little "," that is all too often ignored.

No more.  It's time to give the comma a voice.

We were getting ready to add rational expressions and I wanted my students do have a workable rule for adding fractions with like and unlike denominators.  My goal was to develop the idea that when adding fractions with unlike denominators:

A lot of students don't see this very clearly.  They do what they do to jump from [this] to [that].  And most of the problems end up looking a lot like
with no real understanding of what's taken place between the hypothesis and conclusion.  And up to this point, no one has really cared because Johnny was able to find the correct answer on multiple choice scavenger hunts with a great deal of accuracy added fractions like a champ in 6th and 7th grade. However, when Johnny gets to algebra, and sees

for the first time, you'd think he's never worked with fractions before.

Time to talk about the comma.  It was actually a pretty simple adjustment to a simple question, but the conversations it generated made all the difference in the world.

This quickly became

See, the beauty here is that the process became the outcome.  The numbers become the variables and we get a good grip on how one-third plus two-sevenths becomes thirteen-twentyfirsts.  The abstract isn't so abstract and the easy part is swapping out the 1, 2, 3, and 7 for a, b, c, and d.

Mission accomplished.  Now, lets hope they remember it tomorrow.

Wednesday, February 1, 2012

On Teaching By Learning

One of the things that I have learned over the years is to let go of any preconceptions I have about how a problem should be solved.  I have methods I prefer, but my students need to develop their own.  Never has this been more obvious than it was today.

We are beginning to play around with non-linear functions and so I gave my class the following problem:

You're going  to build a garden and need to build a fence around it.  If you have 120' of fencing, how would you set it up in order to have the biggest garden?

...or something like that.

I didn't specify rectangle although I figured most kids would default to that.  I didn't mention the barn in the back of the property that could be used as one of the sides.  I just kept the prompt as simple as possible so I could see where they took it.

Many assumed a square right off the bat. And one group felt pretty ambitious and looked up some shapes in their school planner only to settle on the typical decagon.  (Good luck calculating the area of that one, fellas.)

So, I'm walking around and seeing groups all proud of themselves by defining x as one side and y as the other and they're arguing about whether 2x + 2y = 120 or x + y = 60 is the better equation.  I ask a few questions like, "so how will that equation help you determine the largest garden" to which they reply, "we'll find the maximum."

"Mmm-kay," I say as I mutter to myself, "I'll be back..."

Then I walk up to a group of three boys who usually push the envelope when it comes to creative problem solving and I see the equation x + y = 60.  I think to myself, "oh, no not you too."

Then I look a little closer and I see this other thing they're working on.

xy > 900

I double take.

"Wait, what?"

Before any of them even address my incredulous look, one of them says, "let's go put it in GeoGebra."

"So how'd you come up with that?"

"Well we figured that x + y = 60 tells us how much fencing we have.  And since a square would give us 900 ft2, we want to know if there is an area out there that's greater than 900."

"Uh, yeah.  That's, uh, yeah, that's exactly how I'd do it."

Not really.  This is what I really said.

These kids used a system.  Not in a million years would I have ever considered using a system to solve this problem and three 13 year-olds set me straight.

Man, I love this job.

Wednesday, January 25, 2012

Something's Wrong Here

Search Institute [1] has compiled a list of 40 Developmental Assets that may protect youth from high-risk behaviors while promoting positive attitudes and behaviors.  I don't know how valid the research is, but I found the list to be interesting and the data to be fascinating.

Each of the 40 assets remain the same for each developmental stage while the application of assets change based on the age of the child.  They're worth a look. 

I took a particular interest as I have a son in each of these developmental stages.  Suffice it to say, I have some reading to do.  

When I first saw this chart, I thought, "Man, I gotta get my kids 31 of these assets."

But then, when I saw this chart I thought, "Holy, crap.  We're doing something really wrong."

Figure it out in the comments, will ya?

[1] I have no idea if this is even a credible organization.  I learned about this today at a meeting I attended and it was the one thing that didn't make me want to stab myself in the eye with a pencil.