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.

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.

Common Core: The Blessed Textbook Conflict

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We started working because the textbook stopped.

When we started the process to realigned our curriculum to the Common Core, we noticed that our textbook, which previously aligned to the Michigan Merit Curriculum, stood no chance against the Common Core State Standards. This forced us to make several decisions: First, were we going to replace the textbook with a new one? Second, were we going to keep the textbook and, in a sense, align the CCSS to the book?

After much discussion, we decided to do neither.

And it was the best decision we ever made.

It forced us to meet, research, collaborate, decide, create, experiment, reflect, analyze, adjust, and all sorts of other verbs that show up on the top of Bloom’s Taxonomy.

We are fighting through this year. We have reflected on the lesson’s we’ve learned. It hasn’t been easy. But our geometry team, which includes three teachers, has invested in a product that has resulted in some of the most intense and effective professional development that has forced us to have real conversations about student engagement, assessment, grading procedures, class structures, and all sorts of other goodies.

And none of it would have happened if we went with the textbook.

Common Core Geometry: An update one semester in

End of first semester provides a chance to reflect

Photo Credit: Flickr User “Neil T.” Used under Creative Commons.

This is our first go-’round with the Common Core Geometry. Without a usable textbook, our local geometry team has been responsible for most of the content. So, where are we?

We completed three units: Unit 1 was an introduction to rigid transformations. Unit 2 used rigid transformations to develop the idea of congruence, specifically congruence of triangles. Unit 3 began to formalize the notion of proof by using angles pairs and rigid transformations to discuss parallel lines cut by transversals, isosceles and equilateral triangles and parallelograms. (We should have finished one more unit, but that always seems to be the case…)

So, how did the first semester go? Well, the algebra-writing relationship is an interesting one. In previous years, our first unit was dedicated to writing and solving equations based on geometric situations. To see if the students thought that those two angles are congruent, we would put an algebraic expression in each angle and see what the students did with it. It turned largely into Algebra 1.5 with the mysterious “proof” added in for good measure. It didn’t seem to make much sense.

We have moved away from this for two reasons:

First, proofs are about expressing relationships in writing. It seemed silly that students would learn most of the geometry concepts through an algebraic lens and then we had to change gears to try to develop proof. We thought to start with the writing to smooth out the transition. Then, we could add the algebra back in later. The students have been through three straight algebra-based math courses leading up to geometry, so that will come back much more easily.

Second, we thought that another “same-ol’-math-class” might be what was sapping the enthusiasm and engagement. So, we have gone heavy on writing, creation, and visual transformations. The students have responded well. We’ll see what happens when the algebra makes a comeback in the second semester.

But, improvement is definitely needed. We weren’t prepared for the shift in the needs of our students in a non-algebra class. Our students aren’t learning with a great deal of depth. They are having a tough time writing with technical vocabulary. They are having a hard time making connections across topics. These are problems we are going to have to address moving forward. We were algebra teachers. I know dozens little tricks for solving all sorts of different equations. I don’t know a single one to help a student remember the different properties of a parallelogram.

I think we have done a nice job creating activities that will engage the students, but now we need to make sure the content depth is appropriate as well. It might be as easy as changing the questions that I ask. I can think right now of an activity regarding parallelograms as one that I didn’t draw out nearly enough depth from them. I didn’t facilitate the student thought and discussion. It slipped back into teacher-led note-taking. They struggle with the parallelogram proofs on that test. No surprise.

Please. If you have ideas, resources, processes, thoughts, lessons, handouts, anecdotes, or other helpful offerings, I will be accepting them starting now. Load the comment section up and be prepared for follow-up questions.

 

Oh, and if you are interested in reading a semester’s worth of my previous reflections on our new common core geometry course, here they are:

From Jan 7 – Vocabulary: The Common Core Geometry’s First Real Hiccup

From Dec 12 – Why you let students explore and discuss – an example

From Dec 7 – When measuring is okay…

From Nov 16 – Proof: The logical next step

From Nov 15 – When open-ended goes awesome…

From Nov 2 – Improvement under the common core…

Vocabulary: Common Core Geometry’s first real hiccup

So, my student’s last Geometry unit test force a realization. Computational math classes, which my students have all had up until this point, generally are not focused on vocabulary.

I’ll give you an example:

Suppose a typical Algebra I teacher asks his or her students to solve 3x + 7 = 28. How would they do it?

Well, for the most part, they will probably add seven to both sides of the equal sign. Then, after dividing both sides of the equal sign by three, the answer would be x = 7.

Before this year, I would have been content to accept that as a “full-credit-answer.” My students would have never been expected to know that the reasons that those steps are effective. Namely, the subtraction and division properties of equality.

However, on this most recent unit test for Common Core Geometry, each of the six questions required written explanations. Written explanations require vocabulary. Sometimes a lot of it. And it needs to be used properly.

The first real hiccup in our version of the Common Core Geometry is that this math teacher is not used to having to facilitate the deep understanding of technical vocabulary. I’ve taught skills, procedures, and technical reading, but I’ve never required my students to need to know the vocab as well as they do now. Previous geometry courses that I’ve taught have still been so algebraic that if the students didn’t learn the vocab, they could still get by doing the crazy amount of algebra.

This year, the vocab has taken center stage… and the students aren’t the only ones needing to adjust.

Please add to the comments any tips or pointers you might have in helping develop deep and flexible understandings of math vocabulary.

 

Why you let the students explore and discuss – An example

A triangle with mistakes.

A triangle with mistakes. According to the student who made this triangle, the angles measure 101, 102, and 73 degrees.

You probably can’t read the writing on the triangle above, but the task was to cut out a triangle and measure all of the angles. It sounds fairly simple, right? What happened with it, I couldn’t have planned for.

This particular triangle was produced by a sophomore with reported interior angle measures of 73 degrees, 101 degrees, and 102 degrees. As the students meandered around the room recording triangle angle measures, several students stopped by this triangle to laugh, ridicule or otherwise comment on how silly it seems for a triangle to have interior angles that sum to 276 degrees.

But, the students also noticed that it wasn’t an isolated incident. Even so of the other triangles whose angle measures seemed a lot more reasonable still didn’t always add to 180 degrees. Some added up to 179 degrees, 181, 185, 178. What could be going on?

One student started the group conversation on accident when he asked: “So, the one’s that don’t add up to 180 degrees, does that mean that they aren’t actually triangles?”

As I turned the question back to the class, they weren’t exactly sure how to answer it. It looks like a triangle, but we know that all triangles have angles that add up to 180 degrees. This “triangle” doesn’t. So, is it a triangle-like thing, but not actually a triangle?

Which brought the class back to the red triangle shown above.

Student #1: “Well, this triangle is messed up.”

Student #2: “Messed up? Like how?”

Student #1: “Like, it’s a triangle. I mean, look at it. It’s a triangle. But it says that angle is 101 degrees, but it is an acute angle. So, the triangle could actually add up right, but the person who measured it just messed it up.”

The reason that I like this exchange is because it drives home the idea of math in theory and math in practice, which I made more explicit as a part of the big group conversation.

If I had “blah-blahed” about that, I would have reach 10% of them. Engagement in this activity was closer to 85% and I did way less talking.

That’s why I let the students explore and discuss.