State of the Sphere…

So, I woke up this morning to an energetic discussion going on about an apparent chat on the state of the Math Edublogosphere (as it has come to be called by some). I prefer “math blog community”.

I read Dan Meyer’s response.

Then I read Kate Nowak’s response.

From what I can gather from the tweets and discussion, Chris Robinson was provided the energy for the sake of becoming a more cohesive community and also for the better integration of new folks.

I’ll enter into the record that I have been keeping up this blog for a bit over two years now and I wasn’t told about the discussion. So, you know, there’s that… Anyway…

Two years into this blog experiment (which I still consider an experiment), I feel like I have been welcomed especially by the aforementioned Mr. Meyer but also by Fawn Nguyen and Joseph Nebus, who have been commenting practically since the beginning and by Sam Shah whose contributions to my developing calculus course cannot possibly be overstated. I have also found that keeping a concurrent Twitter identity has helped. Ms. Nowak mentions this in her piece as well.

As I consider what I’ve gotten and contributed to the community, it is a lot easier (especially at the beginning) to take than to give. This was largely because I don’t have a very large readership and also because the community is so vast. I could spend hours chasing links from post-to-post, and blog-to-blog, taking great ideas away from each stop. The primary means of giving back is to comment on the posts that I read. I suspect that for a new person getting involved in commenting on new blogs would be very valuable as it introduces the new blogger to the authors and other commenters. It would also give them an idea of what other bloggers are doing.

But the key is to be authentic and honest. Let your readers know who you really are. Don’t try to be other bloggers. Be confident about what you can offer to the community and be honest about what you would like the community to do for you.

And give lots of shout-outs. Like I am going to do right now. These are all of the people I know personally who also blog: Tara Becker-Utess (focusing on flipped model and instructional technology), Rob Reader (who speaks directly to his students in his blog posts), Jesse Mays and Josh Greve (who are not math teachers and thus blog about other things… as if there’s anything else worth talking about…)

Linking other bloggers let others know that you are reading them, another way to introduce yourself to the community.

In the end, this community is like any other. You give, you take. Each according to his/her strength and according to his/her need. The more you interact, the more the community gets to know you, the more they fire stuff your way.

Developing a Calculus Course – Where I’m at so far…

As I reported back in January, I am working on developing the next generation of calculus at Pennfield High School.

To say this is overwhelming is a bit of an understatement. But the support has been strong from the math edublogosphere. To Sam Shah, Jim Fowler, Shawn Cornally, Justin Lanier, and Amber Caldwell I owe a great deal of thanks. I couldn’t be doing this without you.

Here’s what I’ve gotten done so far. At this point, I feel like I have enough material to keep my student busy for four to five weeks. Thanks most to Sam Shah, I have one unit done. Including handouts, formative assessments and summative assessments.

Also, after examining the incredible amount of resources that I have been freely given, I have decided on a couple of structures including student self-assessment sheets (a structure popular in standards-based-grading) and Friday Free-For-Alls, which give the students the opportunity to look at problems that are likely an extension of their geometry, algebra II, pre-calculus or stats work, but they may want to try to employ some of their newly-acquired calculus tools to find a better (faster, more efficient, more accurate, more realistic) solution.

The handouts and problems for unit 1 are posted under “The Calculus Course” to the right. I look forward to your constructive feedback.

Once again folks, thanks for everything and I look forward to continuing to work with all of you.


Making over a typical geometry textbook problem

So, Dan Meyer (@ddmeyer) recently introduced Makeover Mondays where we, as a math blog community, makeover a series of textbook problems that have some potential as usable contexts, but have low impact delivery for engagement or cognitive demand.

This is my first attempt to offer something to the conversation.

So, here’s the first target:

Book Problem

So, here’s where my mind went in terms of making over this problem: First, the idea of “biggest bedroom” is a fairly appealing idea, except I don’t recall competing for biggest room with my friends. So, insert a new plot twist. Rodney and Emile are brother and sister.

Second, most of the competition for biggest room comes when the rooms are both empty. That is, move-in day. Most of my students are fairly well-acquainted with the idea of moving. So, remove the detached rectangles and insert a floor plan.

Floor Plan

Third, let’s add a bit of complexity. Both of the children move in with their own furniture, but, of course, with one being a girl and one being a boy, the furniture is not the same. Emile has this dresser and this bed. Rodney has a combo piece that includes both bed and dresser.

They are going to also move in with toys, a lamp, a chair for the bedtime book, among several other things.

Finally, the new task: You are the parent in charge of making the decision over who gets which room. Who gets which room?

Teaching and Learning: A Shared Experience

A student left this in place of answering the last question on the final

A student left this in place of answering the last question

I like to think that I have a lot of control of my classroom. I decide the structures, the learning activities, the schedule. We have tests when I say. Shoot, the students need my permission to use the restroom. That’s control, right?

But I don’t see everything.

This week, another group of young people ended their time with me and will get 13 weeks to rest up before they resume their math experiences with someone else. I collected their exams. I gave some high fives, some bro-hugs, and some A-frames. I sat down to grade them completely focused on the amount of grading I had in front of me. I graded. I graded. I graded. The students were gone. I remained.

That was my experience.

But 100 students this year didn’t have my experience. We spent an hour sharing the same space, but they each had their own experience. One student chose to share his experience with me.

This was a nice student, but he struggled. Geometry wasn’t his strength. He and I worked together last year, but he struggled. Once again, geometry wasn’t his strength. He and I had to work together again this year. More geometry. It still wasn’t his strength. He was willing to try, but he wanted to have his own experience. He had lots of strengths. He’s clever and witty and realistic. He has a pleasant personality and an exceptional sense of timing with his off-task comments. He reads people well and he is willing to take responsibility. He knows that he has a hard time staying motivated to do geometry. Plus he’s not a morning person, which was inconvenient because I am (I mean, I really am) and we worked together at 7:35 in the morning.

He missed a lot of school. He dealt with some illnesses in the middle of the year. He was struggling again. I kept reminding him of what he needed to do. I occasionally emailed his mom. She stopped in once. I didn’t feel like I was targeting him. I was just doing my job. That was my experience.

He eventually learned enough geometry, offered enough proof and now will move on to Algebra II. I was happy for him. That was my experience.

When I graded his final exam, I saw the note (the one from the picture at the top). He didn’t answer the final question. He wrote them note instead. Probably wanted to make sure I would read it. (See, clever, isn’t he?) It showed me a window into his experience.

“I had a great 2 years of geometry. Thanks for not giving up on me.”

It surprised me. How many students who repeat a class (with the same instructor) would describe it at the end as “a great two years”? That seems counterintuitive. But it wasn’t my experience. It doesn’t have to make sense to me. It was his experience. He chose to share it with me.

Not sure how I’m going to conclude this. Just thought I’d share. I know I’m not special. I know that teachers all over the country have similar experiences all the time. I hope they share, too. I like to read them. It reminds us that we aren’t simply peddling content. We are managing the experiences for collections of young people every day. And as long as we remember that, I think we’ll be okay.

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.