For the start of this school year, I am excited about…

It’s Labor Day and in Michigan that means that school starts tomorrow. Every school year comes with its own challenges. It also comes with a great deal of excitement.

I am excited to be getting a second try teaching Algebra II (which is coming in two different versions: Algebra II, the one-year version and Algebra IIA, the first year of a two-year version). The first try was clunky and unorganized. Having three sections will help as it is nice to have multiple tries at the same lesson, which wasn’t the case the first time around.

I am excited to be starting geometry again. Last year’s course got really backed up because of the incredibly intense winter that easily cost us a month’s instruction.

I am excited to (finally) make Desmos and Geogebra a regular part of my instruction. I am glad that teacher.desmos.com exists. (Does anything like that exist for Geogebra?)

I am excited about the chance to explore the possibilities for student math blogging. My school’s one-to-one program makes that possible. I am very thankful for that.

I am excited to meet a new group of young people. I am also excited to get a chance to work with some students for a second year, as we worked together to learn geometry last year.

I am excited about the new teachers that we brought into our community this off-season. So far they have brought a lot of energy. Energy is nice to have around, I’ll tell ya.

I am excited for a couple of my colleagues who accepted new positions for this school year. I’d say both moved upward and in a direction that will serve them and their educational communities very well.

I am excited to roll out the math club this year at our school. Our first task will be to design and test the m&m’s project.

There is a lot to be excited about. What are you excited about? I hope to hear back from you. Drop me a comment (or a link to your own blog post).

My Most Recent Thoughts About Student Blogging

I have spent the last few months processing this temptation to integrate student blogging into my instructional practice. I have some medium-rare ideas. And some Iron Chef colleagues who do a nice job of focusing my thoughts and cooking medium-rare ideas. Like this very evening in a conversation with two such colleagues:

 

 

Like… bingo. That’s it.

 

So, here’s are my goals. Here’s what I’d like to accomplish:

A. I want to give the students a meaningful way to explore math topics, or think mathematically when they aren’t in my classroom. I don’t trust traditional homework problems to achieve this goal. I think there is value in understanding that in class we spend an hour exploring thoughts and ideas that have real value during that hour and the other 23 hours of the day. I’d like to create SOME mechanism that enforces that.

B. I want to give the students a chance to develop their own voice when talking, writing, and reasoning mathematically. Too often, I use gimmicky phrases, memorized lingo, and rigid vocabulary to guide student language. There are wonderful reasons for this. But, I want them to develop their own voice, too. I’d like to see them develop their own ability to verbalize a mathematical idea and…

C. I want to open the students’ ideas up to each other and to the greater math and educational community. I feel like this will offer a level of authenticity that simply having the students submit their work to me wouldn’t. Also, I want them to be able to think about the mathematical statements of another student and respond. I want to break away from this idea that the students produce work simply for my review. A mathematical statement isn’t good and valuable simply because I say so.

I think blogging can do that. I am sure other things can do that. Perhaps other things that are easier. Or less risky. Or have undergone better battle-testing. Or…

 

And as for the second question. The evidence would be a gradual improvement in the math discourse in class. More people talking, and talking better. Explorations becoming richer. Questions becoming an increasingly regular occurrence. Students trusting each other, and themselves, and not looking at me as the lone mathematical authority in the room. We would begin to talk and explore together, and sense-making would become a bigger and bigger part of what we do.

I told you. Medium-rare ideas.

I’m hoping that some more of my Iron Chef colleagues will take my ideas, season them, finish cooking them, and help me turn them into an action plan.

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My advice to the newly “en-Twitter-Blogged” (reflection on #edcampmm )

Today I got to meet a lot of folks at EdCamp Mid-Michigan in Charlotte, MI. Some of them are seasoned tweeters and bloggers (Elizabeth Wellfare – @ealfoster or Tara Becker-Utess @t_becker10, for example) and some are just starting out. A couple of people got set up with their very first Twitter handles today. Welcome. I talked to a couple folks who are interested in starting their own blogs (or rethinking the way they use the blog they already have).

Now, that EdCamp is over, we start the “now what?” stage of all the new stuff we learned.

What are we going to do with it?

How intensely do we want to attack it?

How is it going to be useful to us in the practice of constantly improving as educators?

All of these are fantastic questions. We discussed some of these issues already, but I want to offer a bit of encouragement and advice.

First, don’t be afraid to be selfish. (I believe Dan Meyer – @ddmeyer gave this same advice a few weeks back). By that, I mean that you are likely going to take a WHOLE LOT more than you give for a while as you start out in the world of twitter and blogging. That’s okay.

The first major idea is trying to decide what you want the Twitter feed or the blog to do for you and your professional practice. Sometimes the first step in that is seeing what other people are doing. How do they tweet? What do they tweet about? How do they use #hashtags? What do they blog about? What types of blogs/tweets are interesting for you to read?

Tweet and blog about the stuff you find interesting. Your blog and your tweets should AT LEAST be interesting to you.

Second, keep at it. When you first start tweeting/blogging, chances are that you (and a very few other people) are going to be the only ones reading. That’s okay. That changes over time. The more you write/tweet/interact/question/comment/favorite the more you will find people who are trying to do the same things you are doing. And THAT is what you want. You want to begin to form a network of people who are all trying to support each other in common goals.

Now, if you are brand new to this, follow me at @hs_math_phys. When you start your blog, tweet me the link to your blog. I look forward to reading your ideas and thoughts.

Finally, if you want a nice network of people who want to read your thoughts, check out The MathTwitterBlogoSphere homepage for a ton of GREAT bloggers and tweeters. Don’t let the name fool you, it’s not just for math teachers. There are takeaways for educators of all makes and models. They are good people.

Welcome to our world. Please don’t be a stranger. And Please, let me know what I can do to be helpful.

The M&M Project

 

 

So, here's my next project...

So, here’s my next project…

 

So, I’m standing in the checkout line at Meijer looking around at the various distractions. And there, hidden among the Kardashian magazine covers and “Buy One, Get One” packs of gummy worms, I see candy… and math.

Apparently M&M’s have two sizes the “milk chocolate” ones (known ’round these parts as “regular” M&M’s) but also the “MEGA” sized ones that, according to the package are “3x the chocolate per piece” as the regular M&M’s.

Oh yeah. This is just ASKING for a classroom full of students to test this claim.

But, it’s one thing to have an idea. It’s another thing entirely to design the teacher and students moves that will do what we need to do.

I unleashed this conversation on my Facebook page and here’s what happened:

MMChat MMChat2

 

 

So, we couldn’t decide on a couple of issues: A. mass vs. volume, B. What to do with those colorful candy shells? (3x the chocolate was the claim, after all…)

So, now I ask you: Help me design a lab to test this claim with a classroom of high school students. The school year is coming up soon and activities like these help to not only help students apply their problem-solving procedures to something a bit more tangible, but also, it is activities like these that make the math class something students can look forward to.

I look forward to your input.

Why I’m not THAT worried about the future of math education…

A New York Times article by Elizabeth Green has made its social media rounds lately. “Why Do Americans Stink At Math?” has been tweeted/shared a couple million times by now, with good reason.

It’s actually a really good article with some good story-telling and relevant history, and all the data and examples to back up the title. It’s worth a read. (It isn’t a quick read, mind you, but a good read.)

As far as I can tell, the thesis of the article is in the middle of the piece:

The new math of the ‘60s, the new new math of the ‘80s and today’s Common Core math all stem from the idea that the traditional way of teaching math simply does not work.”

The “traditional way” that Ms. Green speaks of is summed up a bit later in the piece.

Most American math classes follow the same pattern, a ritualistic series of steps so ingrained that one researcher termed it a cultural script. Some teachers call the pattern “I, We, You.” After checking homework, teachers announce the day’s topic, demonstrating a new procedure: “Today, I’m going to show you how to divide a three-digit number by a two-digit number” (I). Then they lead the class in trying out a sample problem: “Let’s try out the steps for 242 ÷ 16” (We). Finally they let students work through similar problems on their own, usually by silently making their way through a work sheet: “Keep your eyes on your own paper!” (You).

Green goes on to say that quite often teachers recognize the limitations of the traditional model, but have a hard time reforming it largely because of poor resources and ineffective training. From later in the piece:

Sometimes trainers offered patently bad information — failing to clarify, for example, that even though teachers were to elicit wrong answers from students, they still needed, eventually, to get to correct ones. Textbooks, too, barely changed, despite publishers’ claims to the contrary.

So, here we go. Sounds like a big problem, right?

Well…

I’m not that concerned. Ya know why?

First off, I don’t want to give the impression that I think that Green is writing untruths or is exaggerating. That isn’t where I’m taking this. American math education needs some serious work. But see, that’s where I get encouraged.

Let’s look at a specific bit of content. How about volume and surface area of prisms?

So, my textbook provides this:

Prism Clip

taken from Holt’s Geometry, 2009 Edition, Pg 684

 

These practice problems fit in with the “I, We, You” model that Ms. Green described in her article. Right on cue, the textbook appears to be pitching to our education system’s weaknesses.

But those weaknesses have entered a brave new world where teachers who have found models that work are not only willing, but also able to share them freely for anyone and everyone who might be looking.

For example:

Andrew Stadel’s “Filing Cabinent” is, by content standards, just another prism surface area problem. But, the situation he sets up is anything but ordinary.

Timon Piccini’s “Pop Box Design” asks a relatively simple question in a context that is approachable by practically everyone.

Dan Meyer’s “Dandy Candies” pushes the envelope on video quality, pushes the same content, and includes it in a blog post that discusses a competitor to “I, We, You.”

All those fantastic resources are available… for free. And the creators can be reached if you have a question about them.

A movement has begun. An (ever-growing) group of math teachers decided that it was one thing to discuss reforming math education and it was quite another to effectively reform math education. The group is getting larger. It’s inclusive. It’s welcoming. It’s free to join. And it doesn’t expect anything from those who join. Everyone does what they are able. Some share lots. Some steal lots. Some do both. The bank of resources is growing.

And this isn’t legislated reform. There is a genuine desire for this. I spoke in Grand Rapids, MI this past spring and was amazed that the crowd that was willing to gather to hear someone talk about reforming math education. Nearly 100 folks crammed into a room to have, what ended up being a rather lively, discussion about how to engage all learners, push all learners, and keep as many learners as possible interested in meaningful mathematical tasks.

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They had to turn people away from a talk on effective math lesson planning.

So, Ms. Green is certainly right. Americans stink at math. But there is a growing group of teachers who are aware of the problem, interested in seeing it solved, and now, more than ever, there are places they can turn to, people they can reach out to (and who are reaching out to them). And it is all available for free on technology that practically everyone already has.

So, forgive me, but I am quite optimistic about where this might take us.

 

We math teachers need to trust each other

I have had a great time working with 5th and 6th graders for two weeks this month. Kids College makes up some of the favorite weeks of my summer. I mean, after all, when a giant trebuchet is involved, it’s hard not to get excited.

But an interesting moment occurred when I looked over a student’s shoulder to see what was in their lab notebook. Here’s what I saw.

Student Work Big

See it? It’s significant… You know what? I’ll zoom in.

Student work

 

There we go! See that? That is a  straight-up attempt at long division. This might seem mundane and ordinary, but let me tell you why this grabbed my attention.

That student is trying long division. What does that mean?

That means that student was TAUGHT long division by someone. (While acknowledging that this student might be learning long division from a parent, tutor, pastor, or babysitter, I feel like the highest-percentage guess is that the “someone” is a teacher.)

This is important to me because I know several fifth grade teachers who have confirmed that it is common practice for each student to leave elementary school having had the opportunity to learn long division. (I promise, I have a point coming…)

Fast forward that fifth-grader about… mmm… 6 years. Now suppose they are learning this.

Polynomial long division

Taken from Holt Rinehart Winston’s Algebra II book, 2009 Edition, Page 423

This is, give or take, halfway through Algebra II. Now, I have seen firsthand that this isn’t the easiest skill for a lot of students to master, especially just as it is introduced. In fact, I would go so far as to say that there are plenty of student’s who successfully complete Algebra II while never mastering this particular skill.

There are a lot of reasons that students might not master this skill, one of which might be that THIS is typically the type of situational math problems that this skill gets applied to.

 

Applied Polynomial Division

Taken from Holt Rinehart Winston’s Algebra II, 2009 Edition, Page 426

But the one that I have heard mentioned to me with the most enthusiasm is that schools are starting to move away from teaching long division. And that division of polynomials is much more difficult to teach to students who haven’t been exposed to long division. Fair enough, except I have a couple of thoughts.

First, (and I’ll admit that this is a little off-topic) even if we assume that the struggling Algebra II students weren’t ever taught long division, what grade do you suspect they should have been? 4th or 5th grade, maybe? It just seems to me that any essential skill that was academically appropriate for 10-year-olds could very well be taught to 17-year-olds. I don’t see any reason to believe that long division is a skill with a window of opportunity to teach that is open to 10-year-olds, but has closed by the time students reach upper adolescence.

However, my second thought is that the evidence I gathered this week confirms what I suspect was true. They WERE taught long division. They fact that they can’t USE long division regularly in their junior year of high school requires a completely separate explanation. There are plenty of potential reasons why, but we shouldn’t allow ourselves to think that the explanation is as simple as “they were never taught that.”

This is a dangerous way to address academic deficiency. This has been a social complaint of schools for a while now. Jay Leno made a regular segment out of it. Every time a clerk has a hard time making change, or a young person appears to struggle balancing his or her checkbook, the question largely becomes “what the heck are they teaching these kids in schools?”

Well, I assure you all, that practically every American middle schooler has been in a math class that has covered the necessary skills to make change or balance a checkbook.

Just like we teach European geography, basic grammar, and the names of the Great Lakes.

But not every student learns it. And whose to blame?

I don’t know, but as a teacher, there aren’t a ton of folks giving me the benefit-of-the-doubt these days. We should, at least, be able to expect it from the person who teaches down the hall, down stairs, or in the building next door.

Common core is trying to deal with the “when to students get taught this” conundrum because there is a lot of social pressure that assumes that the problems with missing knowledge is missing instruction. I’m not sure if Common Core has what it takes to address that issue…

… especially if that isn’t the issue. Because what happens when we make sure that every fifth grader coast-to-coast is taught long division and 6 years later, coast-to-coast, the 17-year-olds are still unfamiliar with it?

I’m pretty sure I’m going to be writing about Algebra II A LOT this year.

So, I’ve began thinking about the school year that begins in about 5 weeks, and about the Algebra II course that I am going to be teaching this year. Algebra II? I’ve taught 1 section EVER.

This year I teach three sections. Our school does Algebra II over one year, which we call “Algebra II” and Algebra II over two years which we call “Algebra IIA” for the first year, and “Algebra IIB” for the second year. I will be teaching one section of Algebra II and two sections of Algebra IIA.

So, as has become my habit, I am posting the Algebra II class that I will be teaching the year here. It is a work in progress. I am hoping to get a TON of feedback from all of you. Please help me out here. Links of great activities in the comments would be fantastic.

Also, if you know of any math teachers (#MTBoS or otherwise) who are especially killer at teaching Algebra II, I would love to be in touch with those people.

Thank you in advance.