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.

There is one thing that never seems to fail…

2014-07-08 10.23.03

This is going to be a short blog post, but it comes with a request.

2014-07-08 10.23.47

I was reminded today that there is nothing quite as powerful the department of meaningful student engagement as allowing students to set things on fire.

 

2014-07-08 10.24.23

 

But I’m a science teacher these next two weeks and come fall, I’m a math teacher again. This begs the question: What opportunities are there to allow students to set things on fire meaningfully in a math classroom? (Think Geometry or Algebra II)

 

I need ideas people! Let me know what you got!

Testing at the speed of… change.

I have a question:

Will the problems the public education system be solved by employing standards-based solutions like Common Core (or some other standard-based curriculum)?

This seems like an interesting question. A lot of follow-up questions would be needed.

1. What are public education’s problems?

2. What’s causing the problems?

3. What do we do about problems that aren’t solvable under current law?

4. Are certain standards-based solutions better than others?

5. What will education look like when all its problems are solved?

 

I don’t want to sound like a skeptic, but, here in Michigan, we’ve been at this for a while.

In Novemeber 2005, the National Governor’s Conference decided that high schools weren’t rigorous enough to prepare students “for an increasingly competitive global economy.” In Michigan, this led directly to the development of the Michigan Merit Curriculum.

The results weren’t good. By 2011, the state set the proficiency “cut scores” at 39% of the MEAP Test questions correct. (Got that? The Michigan Department of Education was cool writing a test, giving to every student in the state, and calling “proficient” any student who could get 40% of the test right.) This, of course, showed that 90% of 3rd graders were proficient in mathematics statewide. By 2012, when the cut score was raised to 65%, statewide proficiency dropped to closer to 40%.

So, after all this, apparently, the people of Michigan wanted Common Core. So, along with that, we passed some other laws to try to get Arne Duncan’s Race to the Top money (We failed, by the way. Then we failed again. Then we failed for a third time.)

After all that, we’d changed a number of laws, including approving the Common Core standards. However, a lot of those laws were designed to appeal to Arne Duncan and his several billion dollars, which never came.

So, we have a department of education that has approved Common Core. By January of 2012, the state was gearing up for the Smarter Balance Test. We even had school districts running trials and pilot testing situations (my district included), even as the state legislature determined that it didn’t have the funds to support Common Core.

Bear in mind, these changes had all come quite quickly. If this upcoming junior class (class of 2016) is to take the Smarter Balance Assessment, it would have done so after an education that included no standards (from kindergarten to 2nd grade), Michigan Merit Standards (3rd grade until 7th grade), and Common Core Standards (since 8th grade). Keeping in mind the implementation dip that is going to accompany the transition periods, it’s really any wonder why we have any expectations for this group beyond simply finishing the test.

And the speed of change wasn’t being lost on people. Common Core dissent is gaining publicity and some think that is makes for some pretty compelling television. So, Michigan is stuck having blazed a trail that isn’t exactly popular and isn’t exactly funded.

Moreover, in the past month, a new set of questions is brewing in Michigan: What test will those students be taking next year? The public pressure is mounting. Business leaders and education groups support it, but there is a lot of apprehension over the online nature of the test. (And Bill Gates suddenly isn’t a huge fan of high-stakes testing anyway.)

So, it looks like we’ll stick with MEAP another year, except we might steal some of the Smarter Balance questions. We currently don’t have a test written, or dates to plan on. The only certainty we have is that we can rest assured, there will be some test we will have to give.

I started teaching in 2006. This has been my experience for the entirety of my career. All of this flurry over which standards, which test, which questions. For what? People are yelling, negotiating, quitting their jobs over all of this. But we still don’t have an answer to the original question.

Will the problems the public education system be solved by employing standards-based solutions like Common Core (or some other standard-based curriculum)?

Oh, and don’t forget. We need to grow consensus on those five questions BEFORE we get to the original, bigger question. Here’s the problem. We aren’t prepared to try to build consensus on those five questions, at least not in the right way. Discussions like these require cooler heads. (Every been in a meeting when people start to get worked up? All progress stops until everyone calms down.)

Oh, and there’s these other questions that are going to come into play.

6. Should kids who fail to meet a proficiency standard move on with support and accommodations? or be held back to start the program all over again?

7. What are the academic grounds on which a student should be eligible to be a varsity athlete? What level of participation is acceptable if the student doesn’t meet all the standards?

8. What is the acceptable age at which a young person, or their family, should be able to freely opt a student out of the state’s preferred education program without penalty? What are the conditions on which an opt-out application is accepted?

All of these questions I have seen people yell and scream in disagreement with each other. Yelling. Over athletic eligibility and the disagreement over social promotion vs. retention.

Education is filled with passionate people. We don’t need any more passion. We need more wisdom. We need calmness. Patience.

I would love to see the State of Michigan (or any state) just stop all of this madness until it can issue a research-based negotiated document answering those 8 questions with rationales, just so that we know that those answers have been factored into any plan to move forward.

I hate to sound like a skeptic, but until we are prepared to clearly build consensus on those eight questions, all of our “fixes” are much more likely to make the problems worse, not better.

 

My (imaginary) conversation with a baseball sabermatrician

Baseball’s gets most of the benefits of a very talented group of statisticians. They spend their times trying to figure out the value that each action of a baseball player adds to their team’s chance of winning a game. Every possible action. In fact, ESPN just issued an article regarding the value of a catcher who frames pitches well.

So, I’ve been wondering why education can’t get in on a little bit of that action. A while back, I appealed to Sabermetricians hoping to get some of that talent to play for our team.

Today, through some Twitter conversation with school data aficionado Andrew Cox (@acox) I got an idea of what the conversation might look like if a Sabermatrician responded to my appeal.

We’ll call our statistician Timmy. I’ll play the part of Andrew.

Andrew: Thank you for calling. I have been looking forward to this conversation for a while now.

Timmy: It’s no problem. I’ll do whatever I can to help. But first, I need some information from you.

Andrew: Anything. Just name it.

Timmy: Well, I need to know the goal of the education system?

Andrew: The goal?

Timmy: Yeah, the goal. You know, like baseball’s goal is to win games. The most successful team is the team that wins the most games.

Andrew: Yeah, well, that sort of depends on who you talk to. This article lays out 11 goals (some more explicit than others). President Obama says this. Thomas Jefferson says this. These folks say we should teach entrepreneurship

Timmy: Well… okay. So, you’re saying that education as a whole doesn’t have an agreed upon goal?  Who makes the decision of what a school goal is?

Andrew: Well, school boards make a lot of decisions. Increasingly, it seems like legislators are getting a larger say.

Timmy: I see, well, Okay, okay. So, are schools doing anything to measure how strong the long-term retention is for it’s students?

Andrew: um… while I can’t speak for schools nationwide, I am not aware of any K-12 school districts that are doing anything to measure the long-term retention of the content.

Timmy: Well, that makes it tricky to figure out the practices that contribute to that.

Andrew: I agree.

Timmy: Well, okay. Goals might be tough to define. I understand. It’s a diverse system. What about the means?

Andrew: The means?

Timmy: Yeah, like, in baseball, the means of reaching your goal of winning is to maximize the runs you score and minimize the runs your opponent scores. So, what are the means of reaching the goals of the educational system?

Andrew: Yeah… the means.

Timmy: Yep.

Andrew: Well, it kind of depends on which goal the school has.

Timmy: I’m sorry, I know I come from the baseball field, but isn’t learning the goal?

Andrew: Yes, absolutely.

Timmy: So, what practices maximize that?

Andrew: Well, these people say effective use of formative assessment and differentiated instruction. These folks have all kinds of advice. Some of that advice matches these folks’ advice.

Timmy: Okay, there some things to work with there. Some of that’s teacher stuff. Some of that is student stuff. Some of that is parent stuff. Some of that is administrator stuff.

Andrew: Yup. That is pretty much true.

Timmy: How can you tell if those things are actually happening in a classroom or in a student’s home?

Andrew: That can be tricky business. Principals have a hard time get into the classrooms to support instructors. And you can’t really ask to do walkthroughs on students’ homes. 

Timmy: So, what data do you have?

Andrew: We have TONS of demographic data. We have attendance and behavioral data. We have test scores.

Timmy: I’m sorry, do you really need to contract me so that I can tell you that there is value added to a kid’s experience by showing up to school and not getting in trouble?

Andrew: No… no, we knew that one.

Timmy: One thing that helps baseball statisticians is that every play is recorded from at least 3 camera angles. So, why don’t you just put cameras in each classroom to get a real sense of what teachers and students are doing?

Andrew: Some think that would be usefulLawyers say that’s risky. 

Timmy: Well, Andrew. If you don’t have a goal, you can’t really isolate the means, and we can’t really observe any of the practitioners in any real detail, then what do you expect do get done with your statistics?

 

Doggone it, Timmy. That’s a great question.

How many baseball are in this bucket?

2014-06-24 16.15.21

 

Dan Meyer (@ddmeyer) asked me for this picture somewhat relating to this post from a year or so ago. Once I tweeted the picture, it got the attention of a few others who simply wanted to guess how many baseballs were in it. I had forgotten how engaging a “who can guess the closest amount of…” questions can be.

So? How many you think?

Also, how can we use this in a math classroom? it’s tricky to use as a spheres-inside-of-a-cylinder problem simply because of the non-uniform amount of empty space between the baseballs. It makes the answer of actual baseballs less than the theoretical “volume of bucket divided by volume of baseballs” solution.

But does that mean it can’t be used? What do you think? Chime in.

 

Also, if you want to see how many baseball are in the bucket, then see for yourself.

Student blogging has me thinking… (reaching out for help once again.)

I think I want to try student blogging next year in my Algebra II classes. I’ve only ever taught Algebra II once and I didn’t do a particularly wonderful job.

It was the sense-making that really got to me. My students were pretty good at learn procedures and algorithms, but the long-term retention was remarkably low. I have seen several examples of student blogging and feel like if I framed the discussion questions properly and encouraged the students to read each other’s posts, and comment. That could… COULD… open up a different mathematical thinking experience for the students.

If that were used to supplement the number-crunching practice, and the group problem-solving and exploration, that could potentially act as a way to deepen (or at least broaden) the thinking that the students were being asked to do. In addition, the opportunity for the entire internet to read and respond can add an extra-level of interaction. The students wouldn’t have to apply their real name if they didn’t want to. There is a chance for creative anonymity.

All of that being said, if you have your students blog, will you please comment on this so that I can pick your brain on what’s worked, what hasn’t, what to watch out for and what to definitely do! Links to other blog post would be much appreciated. E-mail this post to people you know who do this. I would love a rich, challenging comment section on this one. And trust me, if you don’t help me, I will make my own idea and learn this the hard way!