My Most Recent Thoughts About Student Blogging

I have spent the last few months processing this temptation to integrate student blogging into my instructional practice. I have some medium-rare ideas. And some Iron Chef colleagues who do a nice job of focusing my thoughts and cooking medium-rare ideas. Like this very evening in a conversation with two such colleagues:



Like… bingo. That’s it.


So, here’s are my goals. Here’s what I’d like to accomplish:

A. I want to give the students a meaningful way to explore math topics, or think mathematically when they aren’t in my classroom. I don’t trust traditional homework problems to achieve this goal. I think there is value in understanding that in class we spend an hour exploring thoughts and ideas that have real value during that hour and the other 23 hours of the day. I’d like to create SOME mechanism that enforces that.

B. I want to give the students a chance to develop their own voice when talking, writing, and reasoning mathematically. Too often, I use gimmicky phrases, memorized lingo, and rigid vocabulary to guide student language. There are wonderful reasons for this. But, I want them to develop their own voice, too. I’d like to see them develop their own ability to verbalize a mathematical idea and…

C. I want to open the students’ ideas up to each other and to the greater math and educational community. I feel like this will offer a level of authenticity that simply having the students submit their work to me wouldn’t. Also, I want them to be able to think about the mathematical statements of another student and respond. I want to break away from this idea that the students produce work simply for my review. A mathematical statement isn’t good and valuable simply because I say so.

I think blogging can do that. I am sure other things can do that. Perhaps other things that are easier. Or less risky. Or have undergone better battle-testing. Or…


And as for the second question. The evidence would be a gradual improvement in the math discourse in class. More people talking, and talking better. Explorations becoming richer. Questions becoming an increasingly regular occurrence. Students trusting each other, and themselves, and not looking at me as the lone mathematical authority in the room. We would begin to talk and explore together, and sense-making would become a bigger and bigger part of what we do.

I told you. Medium-rare ideas.

I’m hoping that some more of my Iron Chef colleagues will take my ideas, season them, finish cooking them, and help me turn them into an action plan.


My advice to the newly “en-Twitter-Blogged” (reflection on #edcampmm )

Today I got to meet a lot of folks at EdCamp Mid-Michigan in Charlotte, MI. Some of them are seasoned tweeters and bloggers (Elizabeth Wellfare – @ealfoster or Tara Becker-Utess @t_becker10, for example) and some are just starting out. A couple of people got set up with their very first Twitter handles today. Welcome. I talked to a couple folks who are interested in starting their own blogs (or rethinking the way they use the blog they already have).

Now, that EdCamp is over, we start the “now what?” stage of all the new stuff we learned.

What are we going to do with it?

How intensely do we want to attack it?

How is it going to be useful to us in the practice of constantly improving as educators?

All of these are fantastic questions. We discussed some of these issues already, but I want to offer a bit of encouragement and advice.

First, don’t be afraid to be selfish. (I believe Dan Meyer – @ddmeyer gave this same advice a few weeks back). By that, I mean that you are likely going to take a WHOLE LOT more than you give for a while as you start out in the world of twitter and blogging. That’s okay.

The first major idea is trying to decide what you want the Twitter feed or the blog to do for you and your professional practice. Sometimes the first step in that is seeing what other people are doing. How do they tweet? What do they tweet about? How do they use #hashtags? What do they blog about? What types of blogs/tweets are interesting for you to read?

Tweet and blog about the stuff you find interesting. Your blog and your tweets should AT LEAST be interesting to you.

Second, keep at it. When you first start tweeting/blogging, chances are that you (and a very few other people) are going to be the only ones reading. That’s okay. That changes over time. The more you write/tweet/interact/question/comment/favorite the more you will find people who are trying to do the same things you are doing. And THAT is what you want. You want to begin to form a network of people who are all trying to support each other in common goals.

Now, if you are brand new to this, follow me at @hs_math_phys. When you start your blog, tweet me the link to your blog. I look forward to reading your ideas and thoughts.

Finally, if you want a nice network of people who want to read your thoughts, check out The MathTwitterBlogoSphere homepage for a ton of GREAT bloggers and tweeters. Don’t let the name fool you, it’s not just for math teachers. There are takeaways for educators of all makes and models. They are good people.

Welcome to our world. Please don’t be a stranger. And Please, let me know what I can do to be helpful.

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!



Conversation starter: Is failure an option?

Let’s talk about students failing classes, specifically in high school.

Let’s suppose a teacher spent the last ten years teaching high school math. Let’s suppose further that the same teacher hadn’t had a single student fail his or her class for that entire span. This teacher is going to have that data met with a fair amount of suspicion, whether it is fair or not.

Let’s suppose a different teacher spent the same ten years in a comparable district teaching high school math. Let’s suppose further that for that time span 3 out of every 4 students who started that teacher’s math class left with a failing grade at the end of the year. This teacher is going to have this data met with outrage (and in all likelihood would never have made it 10 years like that.)

So, ten years without a failing student is suspicious, it’s potentially evidence of a rubber stamp course. 10 years at a 75% failure rate is outrageous. It is potentially evidence of a course that is unnecessarily difficult for a high school math course.

So… what’s an acceptable number of failures?

Actually, let me ask this question a different way…

How many students should be failing? It seems a little strange to suspect that anyone should fail a high school course, but is there an amount of failures that demonstrate a class is healthy and functioning properly? Is that number zero? Is it 5%? 10%? 20%?

I’ll tell you what motivated this post: I am aware that some schools impose mandatory maximums of failure for their teachers. It might be 12% or 7% or 2%. In these districts, each teacher in the district needs to make sure that at least 88% or 93% or 98% of students earn passing grades for their class each semester.

The implication is that if more students than the accepted maximum fail to earn passing grades, it is a reflection on the inadequacy of the course, the instructor or the support structures. But, I’m not sure if that’s true. And besides that, how does a district or community decide the acceptable percentage of failures?

There is another side of this argument that says that a school should be prepared to fail 100% of their students if the students don’t meet the schools requirements. This is the only way to motivate students to reach for the standard of proficiency that the community has agreed upon. There would certainly never be an instance where a teacher had to fail 100% of his or her class, but if the students didn’t meet the requirements, the teacher would have the support of the school and the community to every student, even if that meant 100% of them.

We should probably figure this out because failure numbers are starting to work their way into the mainstream, as demonstrated by this Op-Ed from the New York Times which asserts that perhaps Algebra should be reconsidered as mandatory for high school graduation because nationwide, math provides a stumbling block and the subsequent failures are leading to increased dropout rates. (This seems like a highly contentious point in itself, but it doesn’t mean that it isn’t driving decision-making in some communities.)

Here are the issues in play here:

What portion of the responsibility of a single high school student successfully earning a high school credit is the school’s and what portion is the student’s?

What are the costs of high standards? If we want to increase rigor, there is almost certainly a trade off in that there will be an increased number of students who are unable or unwilling to go through the more rigorous process to earn the credit.

What are the implications of community with class after class of students who know that the teachers are pressured to pass a certain percentage of their students? Is this effect overstated?

Has this ever been studied? I’m not sure if there’s ever been a comprehensive, research-based statement made on the topic of student failures and what the optimal percentage are. And if that’s the case, then should we be making decisions based on “what seems too high” or “what seems too low”?

I am looking for some conversation on this topic. Let me know what you think. Links to posts or articles by people that you trust are appreciated, too.

Perplexing the students… by accident.

It seems like in undergrad, the line sounds kind of like this: “Just pick a nice open-ended question and have the students discuss it.” It sounds really good, too.

Except sometimes the students aren’t in the mood to talk. Or they would rather talk about a different part of the problem than you intended. Or their skill set isn’t strong enough in the right areas to engage the discussion. Or the loudest voice in the room shuts the conversation down. Or… something else happens. It’s a fact of teaching. Open-ended questions don’t always lead to discussions. And even if they did, class discussions aren’t always the yellow-brick road lead to the magical land of learning.

But sometimes they are. Today, it was. And today, it certainly wasn’t from the open-ended question that I was expecting. We are in the early stages of our unit on similarity. I had given a handout that included this picture

Similar Quads

… and I had asked them to pair up the corresponding parts.

The first thing that happened is that half-ish of the students determined that in figures that are connected by a scale factor (we hadn’t defined “similar” yet), each angle in one image has a congruent match in the other image. This is a nice observation. They didn’t flat out say that they had made that assumption, but they behaved as though they did and I suspect it is because angles are easier to measure on a larger image. So, being high school students and wanted to save a bit of time, they measured the angles in the bigger quadrilateral and then simply filled in the matching angles in the other.

Here’s were the fun begins. You see, each quadrilateral has two acute angles. Those angles have measures that are NOT that different (depending on the person wielding the protractor, maybe only 10 degrees difference). And it worked perfectly that about half of the class paired up one set of angles and the other half disagreed. And they both cared that they were right. It was the perfect storm!

Not wanting to remeasure, they ran through all sorts of different explanations to how they were right, which led us to eventually try labeling side lengths to try to sides to identify included angles for the sake of matching up corresponding sides. But, that line of thought wasn’t clear to everyone, which offered growth potential there as well.

2014-02-11 13.51.01

By the time we came to an agreement on where the angle measures go, the class pretty much agreed that:

1. Matching corresponding parts in similar polygons is not nearly as easy as it is in congruent polygons.

2. Similar polygons have congruent corresponding angles.

3. The longest side in the big shape will correspond to the longest side in the small shape. The second longest side in the big, will correspond to the second longest side in the small. The third… and so on.

4. Corresponding angles will be “located” in the same spot relative to the side lengths. For example, the angle included by the longest side and the second longest side in the big polygon will correspond to the angle included by the longest side and the second longest side in the small polygon. (This was a tricky idea for a few of them, but they were trying to get it.)

5. Not knowing which polygon is a “pre-image” (so to speak) means that we have to be prepared to discuss two different scale factors, which are reciprocals of each other. (To be fair, this is a point that has come up prior to this class discussion, but it settled in for a few of them today.)

I’d say that’s a pretty good set of statements for a class discussion I never saw coming.

Bankshot 3-Act Revised

In my previous post, I presented Act I of a 3-Act geometry lesson that I called Bankshot. I also called out to the #MTBoS to support me by offering feedback of which I received two excellent comments that were rich in suggestions, particularly in the aspect of improving the student experience.

If you want to go back and look at the first draft and/or read the comments that got left, then feel free to check it out.

Now, all three of us agreed that the action begun and ended too quickly. Danny Whitaker (@nemoyatpeace) suggested that I slow the video down. In addition to agreeing with Danny’s suggestion, Dan Meyer (@ddmeyer) suggested that there was more I could do to set the situation up and make the clear what was going on before the I roll the film.

Danny also suggested that I cut the film before the ball bounces into the wall. Another interesting suggestion that Dan made was to include multiple attempts. I thought that those are both interesting suggestions.

You will see my attempts to respond to the feedback in this second draft of “Bankshot”. I start with a more direct set-up of the situation. I also added a second attempt from when I was filming to give the students something to think about. Now they have at least four guesses they could make. “Both hit target,” “both miss target,” “first hits, second misses,” or “first misses, second hits.” You will notice also that I slowed the playback down which cost us the sound. It’s possible that a bit of background music will be needed in a third draft, but that is something that we can talk about.

All right, #MTBoS, here is my second draft of “Bankshot.” I look forward to more feedback.

Circles from Cedar Street

A sloppy bit of construction work makes for an interesting geometry question.

A sloppy bit of construction work makes for an interesting geometry question.

I was driving to the grocery store. This particular trip took me down Cedar Street. I drove past this manhole cover. It caught my eye in such a way that I decided to pull into a nearby parking lot and, when the traffic cleared, tiptoe out to the middle of the five lane road and snap a photo of it.

So, my mind instantly went straight to rotations. (Which is on my mind because transformations are Unit 1 of the Geometry Course that I start teaching in, like, two weeks.)

What if I started out rotations by showing this picture and simply asking the students how much of a rotation would fix the yellow lines.

My goals would be for the students to explore how to investigate an apparent rotation, learn how to visually represent a rotation, and struggle through the task of explaining it out loud to another person.

It would be okay with me if we made it to the convenience of using degrees as a descriptor of how much something is rotated. That would be up to them. I do suspect that after a short time of “about this far” and “about that much” they’ll like to find something to ease the trouble of explaining the transformation.

If you can think of a way to frame this learning opportunity better, please make me a suggestion. I feel like this is a good opportunity that I don’t want to waste.