Reflections of a teacher who taught alongside Jim Boehmer

By the time I got hired at Pennfield, Jim Boehmer had been working there for quite a few years. He was a math teacher, like me. I was a 25-year-old novice. He wasn’t any of that. He was an experienced educator. And that was the perfect word to describe Jim… educator. I knew him almost 5 years and he embodied the label “educator” as well as anyone.

It’s easy for me to say nice things about Jim. He and I saw eye-to-eye on a lot of things. School things, home things, life things.

Jim and I were part of the District Math Team which included he and I and several of our administrators. One year, the group would meet monthly at a different school in Battle Creek with some other groups from the county. Jim and I would ride together. He would always drive because I get lost in Battle Creek. For that whole school year, once a month, Jim and I got 30 minutes to talk. Jim and I got to know each other well during that time. We talked about all sorts of stuff: school, sure, but also sports, politics, God, our similar faiths, singing, technology, theatre. It was enjoyable. We could disagree peacefully, but that didn’t happen very often.

What I did find out about him was that he was a thoughtful man who desired excellence. In the time I knew him, he never quit tinkering with his teaching style trying to find the formula that would maximize authentic student learning. He didn’t want to see his students simply pass tests. He wanted them to learn. He wanted them to enjoy real success. He knew his role in that. He was always trying to find activities that would engage the students. If you want, you can read about one of my favorite of his activities.

One more story: When the time came to reform the Algebra I classes to align with the Common Core, he and I sat down together and set out to realign the entire course. We began to review the literature and our resources and decided that we needed to create quite a lot of material… not only because we wanted them to align, but because our textbook didn’t impress us… and he wasn’t interested in a good-enough Algebra class. If it wasn’t excellent, he wasn’t done with it.

And yesterday he passed away.

And we have a giant hole to fill. But I’m sure my story isn’t unique. Jim was authentic and I’m not special. Who Jim was to me he was to so many others. And isn’t that all you can ask? Within my faith, we have a phrase that we use to honor someone special who has passed. We say, “Memory Eternal!”

If Jim was to so many what he was to me, the memories of him won’t be fading anytime soon.

Multiple Approaches to The Lake Superior Problem

Today we did The Lake Superior Problem. In keeping with the basic theme of my previous post, this problem has a very easy to understand task. What’s the area of the lake?

Then the fun begins as you watch the students explore the different options for taking a rather bizarre shape and inject familiarity to it. There isn’t a formula for the area of Lake Superior. So, what can we do?

Strategic Grid on the image

Strategic Grid on the image

Above was the most accurate response and also the least used method.

Strategic tracing of image onto grid paper

Strategic tracing of image onto grid paper

This was a similar approach. Still seldom used. Still quite accurate.

Perhaps tracing it onto patty paper will help

Perhaps tracing it onto patty paper will help

This group found it useful to have an image they could manipulate better. A see through sheet of patty paper helped them.

String to get an accurate perimeter

String to get an accurate perimeter

This group asked for string so they could get an accurate perimeter measurement. They found that the perimeter was not an incredibly helpful measurement, but better they explore than I shut down ideas.

Recreate the area of the lake with polygons...

Recreate the area of the lake with polygons…

Many students saw the lake as a “sort-of triangle” and measured and calculated accordingly.

Recreate the lake are with circles...

Recreate the lake are with circles…

Said this team, “There’s only five different circles. Once you know the area of each of them, you just count, multiply, and add them up.”

I continue to find it fascinating that these students, who struggle with scale, area formulas, identifying polygons, and other mathematical skills in isolation struggle less with them in the context of an approachable task.

Designing Engagement and Collaboration

Collaboration and engagement are the goals. Learning comes through these.

Collaboration and engagement are the goals. Learning comes through these.

High school students can be capricious. Especially here in the nether regions of school-after-Memorial-Day. It can be hard to predict what type of assignment will engage the students. Something that has worked in years past might flop this year. But today, something worked.

Mind you, when I say that it “worked,” what I mean is:

A. It engaged more than 90% of the students.

B. It challenged more than 75% of the students.

C. Almost all of the students who were challenged persisted through the challenge.

D. It inspired honest and effective student-led collaboration.

That something is a handout that I like to call Wrap Battle.

(Now, fair warning: I didn’t write the handout and I don’t remember who did. I edited it a bit, that’s all. If you who wrote the handout are reading this and want your credit, I will be more than happy to provide it. Please let me know and I will make sure and give you all the credit.)

So, why did this handout contain work so well?

Well, first (and I feel like this is the most important), the situation in which the problem exists is easy to understand. Practically everyone has either wrapped a present or opened a wrapped present. So, there isn’t any students lost in the context of the problem.

Second, the actual number crunching isn’t overly complicated. This problem consists of adding, subtract, multiplying, and dividing of positive, whole numbers. You aren’t going to lose any students who have an idea of what to do, but get lost crunching the numbers.

Third, this problem has high predictability. The always important question, “Does your answer seem reasonable?” is a great turnaround when the students inevitably come to you with their paper and ask, “Is this right?”

Finally, that leaves us with the meat of the energy being designing the solution and testing/comparing results, which, at this point in the year, is exactly what they should be doing.

So, just a like a workout that is designed to isolate a certain muscle group, this problem approaches the students so that all of them can play, contribute and analyze the result. When they feel like they can, then that increases the chance that they will try.

What’s the Opposite of Success?

I want to explore two very important questions: How? and Why?

These questions tend are at the heart of the talk over how to “reform” America’s schools. Everyone from Sir Ken Robinson and Dan Carlin to Sal Khan and President Obama has an ideas. Some I agree with (the first two), some I’m not completely sold on (the last two). Either way, they all agree on this: something’s wrong and we need to fix it.

How do we go about fixing things? Bush’s No Child Left Behind, with it’s younger brother Race to the Top has something of a logical plan for creating success. Except that is isn’t really working very well. When it doesn’t work, then you have to move past the why-it-should-work-explanations and move toward a new set of discoveries.

What if there was a place where education is working well and we could explore HOW the system works. We can deal with WHY later. We have theorists and researchers who love to publish papers. They can work on the WHY. I am a practitioner. I am entertained and engaged by the WHY question, but find the answer to the HOW question more fulfilling.

One place has found success by doing the following things:

  • Narrative grades only until Grade 5
  • After that, teachers stress grade “as little as possible”
  • Not comparing schools or students by standardized testing
  • Teacher training programs resulting in each teacher having a master’s degree with the expectation that they will be “experts of their own work.”
  • Allow high levels of teacher autonomy by not mandating curriculum from the top down
  • Highly emphasizing “soft skills” like analysis, creativity, collaboration, and communication.

By doing this, they’ve created a national school system that is among the very best in the world.

That place: Finland.

Now, before I get labeled a “Finn-o-phile,” I want to state up front that I have no particular affinity for the Finnish culture (although, full-disclosure, I am partially of Finnish descent). I am focusing on Finland’s system because it is working better than ours.

To explain, I am going to let two articles most of the heavy lifting on this one. One from the Globe and Mail out of Toronto and the other from The Huffington Post.

I want to isolate some quotes from these articles:

The First from the Globe and Mail:

One of the ways the Finnish education system accomplishes [its success] is by giving individual teachers greater autonomy in teaching to the needs of their classes, rather than a top-down, test-based system.

America is currently moving away from this model. You can think good things or bad things about the content of Common Core, but the message is clear: Across the country, we want everyone doing the same thing. The Finnish system does have a National Core Curriculum which are defined  as “the legal norm for educational institutions” (sincere thanks to Dan Meyer (@ddmeyer) for fact-checking me on that) although discussions of assessment are much different than those of NCLB(which mandate statewide testing) and instead focus on assements “guiding and motivating” students as well as developing “their abilities in self-assessment.” (Quotes from the Finnish National Board of Education)

Also from the Globe and Mail:

The reality in Canada, which is unfortunate in Dr. Sahlberg’s view, is that students are rewarded for competing against their peers, teachers are held accountable by their class’s performance on exams, and schools are compared through widely published standardized test results. Finland takes an alternative approach.

The story is the same below the Canadian border as well. Standardized testing is THE evaluation tool for most schools and teachers. Real estate agents love it because it is so ingrained in our culture that parents will move into communities with good test scores because we’ve been conditioned to think that those are measures that tell the whole story. The Finnish system does the opposite.

Also from the Globe and Mail:

In addition to emphasizing collaborative work, Finnish schools have a different conception of knowledge than the traditional one. Teachers don’t think of knowledge as a cumulative store of objective information. “It is not primarily what individuals know or do not know, but more what are their skills in acquiring, utilizing, diffusing and creating knowledge that are important for economic progress and social change.”

Perhaps exposing a bit why standardized testing is avoided in Finland, these “soft” skills that are difficult to assess off a bubble sheet. According to Finnish National Board of Education, the National Core Curriculum includes options for on-the-job training with flexible assessments in which student can earn credits through “set of work assignments, a written paper, report, project assignment, product or equivalent” completed “performed individually, in a group or as a more extensive project.” American policy-makers are starting to appreciate these skills. Indeed, have you read about the Smarter Balanced Assessment? Leave it to us Americans to try to find a way to create such a standardized test.

From the Huffington Post (quoting Finland’s Minister of Education, Ms. Henna Virkkunen)

Our students spend less time in class than students in other OECD countries. We don’t think it helps students learn if they spend seven hours per day at school because they also need time for hobbies…

We seem to think that if students are struggling, they need more time in school. The Finnish system does the opposite.

So, let’s recap: Less time in school. Less testing. Less competition. More success. Could you imagine an American Politician standing on that platform?

The Finns have produced a system based on trust. They trust the teachers, they trust the local districts, they trust the students. The American system is based on a lack of trust. We call it accountability. We mandate curriculum because we don’t trust local districts. We over-rely on standardized tests because we don’t trust the teachers. We want longer school days because we don’t trust the students.

There is a nation that is excelling at education. They are, in many ways, doing the exact opposite of the things that we are doing. We, who are eagerly seeking to improve our system, are putting our hopes in standardized testing and state and federal manipulation of school districts through funding incentives. Perhaps it’s too early to state boldly that American reform efforts will fail, but we can say boldly that there are places where real excellence is happening and those people are moving in the opposite direction.

We could spend weeks arguing/discussing/explaining about WHY the Finnish system works. Don’t get me wrong, that is important. But, what matters most to me is this: It works. We could be doing what they do. We’re not… and it appears we won’t be for the foreseeable future.

Double Stuf Oreos: Are they really double the Stuf?

Double Stuf: A factual statement or clever marketing trick?

Double Stuf: A factual statement or clever marketing trick?

I was inspired by this post by Nathan Kraft (@nathankraft1) in which he engages his staff in a question about Oreo cookies. (Mr. Kraft was quick to inform me that Christopher Danielson (@Trianglemancsd) was the inspiration for his post. I do want to give credit where it’s due.)

I decided to see what my third hour students would do with it. So, last week Friday I showed them the picture and we started discussing the a variety of aspects of Oreos (some of which were more useful than others). Then, it happened. One students asked:

“Is the stuff of a Double Stuf really double of the stuff in a single stuff?”

The beauty of this activity is that the students were able to become involved in the formation of the solution process. They practically all had a prediction. First idea, would double the stuff be twice as tall?

It didn't appear to be double by height.

It didn’t appear to be double by height.

The above image represents what multiple students observed. It was an awesome opportunity to discuss conclusions. What conclusion can we draw from the observation we just made?

Either it was double the stuff and it wasn’t manifesting itself in its height, or it wasn’t double the stuf. (Often, the student’s original predictions colored their conclusion to these observation.)

Double by what measure? Mass?

Double by what measure? Mass?

Next idea was mass. Gave in impromptu call to Mr. Corcoran, the chemistry teacher, who loaned us some scales. But what do we measure? The whole cookie? That opened up another important question? Is the same wafer used for both the standard and the double-stuff?

After some quick diameter and mass measurements, it seemed like there was no meaningful difference between the two. But, just to be safe, each student scraped the Stuf from a standard and a Double Stuf and set to the scale to get a mass measurement.

What math class looked like today.

What math class looked like today.

Then we compiled the results.

The mass of the stuff scraped off a sample of standard and Double Stuf Oreos.

The mass of the Stuf scraped off a sample of standard and Double Stuf Oreos.

Each group took a moment to deliberate and concluded that, for the most part, it seems that the Double Stuf is appropriately named. Some groups seemed to think that, if anything, the Double Stuf contained more than double the Stuf.

This activity contained so much of what makes contextual, collaborative learning valuable. Authenticity, source of error, conclusions that were not clear, but needed to be discussed. Students needed to listen, speak and rephrase when others didn’t understand.

It also had the beautiful feature of me not knowing the answer and they knew it. So, there wasn’t the temptation to treat me like the math authority, as though all math learning begins and ends with the Teacher’s Edition.

And for an added bonus, the AP Stats class meets next door at the same time and so, we were able to strike a deal to rerun the trial with the guidance of the stats class for a broader, students-teaching-students experience.

I’ll report back with our findings.

Isn’t Geometry an Art?

The things I do to get the students to learn geometry...

The things I do to get the students to learn geometry…

By the time most students arrive in my classroom to take geometry, they have seen Math 7 and Math 8 (which are two sides of the same pre-Algebra coin) and Algebra I. The stated goals of this sequencing is to “prepare the students with the necessary algebra skills to be successful in Algebra I (and later on in Algebra II) and also to be successful on the state tests (currently the Michigan Merit Exam, soon to be replaced by the Smarter Balanced Assessment).

And then there’s geometry…

And our textbook decides that it wants to teach this class right in line with the sequencing pattern: right between Algebra I and Algebra II comes “Algebra G” or Geometric Algebra. I’ll admit it makes some sense. We have spent several years training our students to “do algebra.” Typically that includes plotting points, graphing lines, solving equations and systems, and manipulating functions. If that has been the environment for the last three math classes, then, for the sake of the students, it would make sense to keep the model the same, right? Consistency and predictability breed success, right?

But what’s the risk? Well, as I’ve talked about before on this blog, the Algebra taught in most places is significantly lacking in it’s ability to engage students. So, while the theory is that our students come in well-prepared and well-trained, the reality is that most students come in with sensitive pressure points and calluses similar to someone who has walked for three years in the same pair of shoes. While the shoes are certainly familiar, they might also be smelly and worn out. The ankle support might be gone and the students have learned how to walk funny in them to avoid the blisters and shin splints that have plagued them in the past.

Is this any less geometry then having the student solve equations?

Is this any less geometry then having the student solve equations?

Perhaps what some of them need is a new pair of shoes.

Today’s learning target is getting students to be able to visualize cross-sections and 3D shapes made when 2D shapes are rotated around specific lines.

To approach that, I started with this activity and I noticed very quickly that the students started “walking funny.” I had asked them to put on their old Algebra shoes and the predictable disengagement started setting in very quickly. I wasn’t going well. Following the Dan Meyer Model, I could find at least three indicators that I was doing math education wrong.

Then something dawned on me: Why do we insist that students do algebra all the time? Geometry is the measuring of the earth, a true down-to-earth, visual math. Why can’t it be art?

So, we changed things up. I had them all get a piece of paper and I acted like an art teacher. I put stuff on a stool and had them draw what they saw.

Engagement hit 100% fairly quickly, especially once I struck a pose and asked them to draw me (see the pic at the top).

If 100% are willing to do this, and 40% are willing to graph lines, which is a better math activity?

If 100% are willing to do this, and 40% are willing to graph lines, which is a better math activity?

Apparently, the new shoes I gave them to wear were a lot more comfortable and many more of them were willing to follow along the path. Content-based discussion and collaboration began to happen without me telling them to do so. As a result, when we had to discuss how the activity supported the learning targets, the connections were much better.

Then I gave them back the original handout (which, for the record, I still think is a good handout), and the students did much better with it the second time.

So, I ask again: why do we insist on turning Geometry into an Algebra course? It doesn’t seem like it has to be. Our current textbook says it has to be, but the textbook only has the authority we choose to give it. (See The Blessed Textbook Conflict if you want my take on the authority of textbooks.)

Today’s activity would suggest that if we are willing to consider what a class would look like if we really wanted the students to simply learn geometry, perhaps it would look more like an art class instead of a math class.