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.


Making over another typical geometry problem

It’s time to look at another typical geometry problem to make over. This time Dan Meyer (@ddmeyer) presented this problem for revision.

Dan decided to go in this direction for the revision, which, for the record I really like. I would encourage you to check it out.

I took a try at it, too. I’ll let you decide which you like better.

I like this problem’s basic core idea. Looking at the volume of a sphere (the meatball) and the volume of the cylinder (the cooking pot), in general, this is a pretty tasty set-up (pun intended). Especially considering that I am always a fan of problems that make use of food.


For this problem, food and cooking were actually more of a problem that a support.

First, the cooking pot is sitting on a hot burner and I’ll be the first to tell you, a cooking pot doesn’t have to be full to spill over. So, the question of whether or not sauce will spill over is a bit more complicated that it might seem at first.

Second, meatballs aren’t spheres. They are irregular and rarely are two of them congruent.

So, my first thought was to choose spherical objects that are all congruent: for example, baseballs. Coaches regularly carry baseballs around in 5-gallon buckets, so there is our cylindrical container.

And I figured I’d deliver the task in a video simply because videos tend to improve engagement on their own.

Now, once I made the video (and some meaningful conversation was had among those who are better at this than I am) I found that my task had one glaring drawback. When you put baseballs in a bucket, they don’t pack tightly. There is air between them. A lot of it, in fact.

So, now it seems like if we are to use this video for instruction, we would need to change the question in to multiple parts.

1. How many baseballs can we fit into the bucket? (This would likely end up being a demo or a lab where we collect data. Tricky to calculate this.)

But then we supplement the question above by…

2. How much volume is wasted by packing that many baseballs in the 5-gallon bucket.

This would get back to the original content. Likely the cylindrical volume would need to a unit conversion, and then some analysis of the collective volume of the collection of baseballs.

Now, if we could ind a way to check it. The first thought I had was to fill the bucket with water. Put the baseballs in to displace the water out of the bucket. Take the soggy baseballs back out of the bucket. Find the volume of the water that’s left.

Problems with this idea: 1. Baseballs float which is going to effect the manner in which the water is displaced. 2. Baseballs absorb water. This means that some of the none displaced water would get removed with the baseballs and not counted.

Hmm… I thought of filling the bucket with baseballs and then topping the bucket off with sand. Which would solve both of the above problems, it would also give me an opportunity to make a beach trip.

Any other ideas out there?

Reflecting on the Common Core, Part II

Creativity, flexibility, are were on the rise this year.

Creativity, flexibility, are were on the rise this year.

Around Halloween of 2011, we began to prepare to rewrite our geometry class to align with the Common Core. This enabled us to do a couple of things that I had been wanting to do for a while. First, we ditched the textbook. Then we began to move toward Standards-Based Grading (Shawn Cornally (@thinkthankthunk) has some great stuff on this). We also decided to reconsider Algebra as the backbone as had been the previous practice in favor of a more visual, experiential approach.

We made the decision to embrace the CCSS’s Standards of Mathematical Practice because they made so much sense. We imagined building a class around patient problem-solving with strategic use of a variety of materials, student-to-student geometric arguments making use of geometric modeling and repeated reasoning. We imagined a course that drew the student into an experience. We didn’t want to see student memorize facts. We wanted them to experience the relationships, explore the different figures and circumstances, and draw conclusions about the significance of their observations. The Common Core enabled us to do that.

It was a lofty goal. I thought we tried our best this year. We didn’t do all that we were hoping. Our course didn’t live up to my standards. The students still memorized. The students didn’t explore enough. I told my students too many things. They told me too few. (Dan Meyer (@ddmeyer) would say that I was “too helpful.”) Needless to say, we have some work to do and I look forward to all of you coming along side of me for year two. Your support has been unbelievable so far.

Common Core puts a premium on student-to-student discussion

Common Core puts a premium on student-to-student discussion

So that’s that. The 2012-2013 school year is over and with it, the first try at creating a geometry class filled with patient problem-solving with strategic use of a variety of materials, student-to-student geometric arguments making use of geometric modeling and repeated reasoning. Those are our targets. I get 12 weeks to catch my breath and version 2.0 gets released to another collection of eager young minds.

And to me, that’s the essence of Common Core.

I understand the political conflict that exists when a single set of educational expectations are being enforced coast-to-coast. There are a lot of different ideologies, a lot of different beliefs, a lot of different communities. There isn’t much hope of finding something that everyone is excited about.

But, Common Core or not, a class depending heavily on patient problem-solving with strategic use of a variety of materials, student-to-student geometric arguments making use of geometric modeling and repeated reasoning, is something that I suspect most people can get excited about.

Reflecting on the Common Core…

photo credit: flickr user "Irargerich" - Used under Creative Commons

photo credit: flickr user “Irargerich” – Used under Creative Commons

A lot has been said about the Common Core State Standards in the last year. Some of it has been by me. Some has been by guys like Glenn Beck who is not a big fanMost (if not all) states have some sort of a “Stop Common Core” group. There is even a #stopcommoncore hashtag on Twitter that turns up quite a few results (although some use that hashtag as a means of highlighting objections in the arguments of CCSS opponents.)

The pub isn’t all negative. Some groups, The NEA among them, have come out in favor. Phil Valentine has some good things to say in support.

It is possible that both sides are probably overstating the impact that the CCSS will have. That being said, I will admit that I have some opinions on the CCSS. This year is our first year introducing a new geometry curriculum that we designed around the CCSS. I’ve written a few pieces before this one that have chronicled my journey through a CCSS-aligned geometry class. For example, I’ve documented that the CCSS places a greater emphasis on the use of specific vocabulary that I was used to in the past. I have also discussed (both here AND here) that the CCSS has present the idea of mathematical proof in a different light that I have found to be much more engaging to the students.

As I read the different articles that are being written, it seems like the beliefs about the inherent goodness or badness of CCSS has a lot to do with how you view the most beneficial actions of the teacher and the student in the process of learning. It’s about labels. Proponents call it “creativity” or “open-ended”. Opponents call it “wishy-washy” or “fuzzy”.

I suspect they are seeing and describing the same thing and disagreeing on whether or not those things are good or bad.

To illustrate this point further, a “Stop Common Core” website in Oregon posted a condemned CCSS math lesson because the students “must come to consensus on whether or not the answer is correct” and “convince others of their opinion on the matter.” The piece ends with “What do opinions and consensus have to do with math?”

The authors of this website are objecting to a teaching style. They are objecting to the value of a student’s opinion in the process of learning mathematics. Fair enough, but that was an argument long before the CCSS came around. I can remember heated discussions during my undergrad courses about the role of student opinion and discussion. (My personal favorite was the discussion as to when, if ever, 1/2 + 1/2 = 2/4 is actually a correct answer. One of my classmates rather vehemently ended his desire to be a math teacher that day.)

The CCSS have become a lightning rod for a ton of simmering arguments that haven’t been settled and aren’t new.

Consensus-building and opinions in mathematics vs. the authority of the instructor and the textbook. Classical literature vs. technical reading. The CCSS have woken up a lot of frustrations that are leading to some high-level decisions such as the Michigan State House of Representatives submitting a budget that blocks the Department of Education’s spending on the CCSS.

It is a little strange thinking that I am making a statement in a fairly-heated national debate every time I give my students some geometry to explore, but it seems like I do.

And I am prepared to make that statement more explicitly as I continue this reflection.

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.

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.

Composite Figures in Context: The Wedding Cake Problem

What you see below is the original post from 2013. Since that time, this problem has taken on some alternate forms. One alternative was suggested by Jeff in Michigan and appeared in a post in March of 2014. The other alteration I made myself in Desmos in May of 2015. Feel free to read on and consider checking out the many different ways there are to approach this interesting (and delicious) mathematical situation.

We’ve started our 3-D unit.

Once we get into the volume and surface area measures for 3-D figures, the textbook leads us to shapes called “composite figures” that look like this.

taken from Geometry, copyright Holt, Rhinehart, Winston 2007, Pg 684 #8

source: Geometry, copyright Holt, Rhinehart, Winston, 2007, Pg 684 #8

This can be a tricky image for student to try to work with, mostly because they’ve never seen anything that looks like that before. But they’ve seen composite figures. They are everywhere. But, removing the context can be enough to take this very applicable, contextual concept and make it abstract enough to be confusing.

In reality, composite figures are wonderfully applicable. (I say again, they are everywhere!) So, here’s my question: Why do we insist on giving them an abstract picture to start with? Why not start them with one of the many composite figures that will draw the students into a real context.

I present exhibit A: The Wedding Cake.

Photo Credit: Flickr user

Photo Credit: Flickr user “kimberlykv” – used under Creative Commons

Your basic wedding cake, like the one shown at the top is three cylinders of differing sizes stacked on top of each other. What I like about the Wedding Cake is that the measures of volume and surface area matter in real time and without too much more background than a bit of story-telling (which I love to do).

Now, let’s toss an additional cylinder into the mix.

This blog does not endorse Betty Crocker, General Mills, or any of their products.

Now, you’ve got yourself a math problem!

Question to the students: How much can the baker of the above cake expect to spend on the lemon frosting that is on the exterior of that cake?

… and see where they go with it.