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.



There is one thing that never seems to fail…

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This is going to be a short blog post, but it comes with a request.

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I was reminded today that there is nothing quite as powerful the department of meaningful student engagement as allowing students to set things on fire.


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But I’m a science teacher these next two weeks and come fall, I’m a math teacher again. This begs the question: What opportunities are there to allow students to set things on fire meaningfully in a math classroom? (Think Geometry or Algebra II)


I need ideas people! Let me know what you got!

Thoughts from Outside the Education Community

Dan Carlin (@dccommonsense or @hardcorehistory) is not a professional educator. He is a podcaster about politics and history. His podcasts are fantastic. A ton of substance in manageable doses, and he is a fantastic story-teller. He describes himself as a “fan of history” as opposed to “historian” because calling himself a “historian” would create academic structures that would keep him from adding a lot of the sensational pieces to his history podcasts that make them such awesome listening. Historians and academics might consider that irresponsible and reckless. But, he’s got something like 500,000 people currently waiting part III of his current series on World War I. Dan Carlin is clearly not a professional educator.

And yet, Edutopia decided to post a short column by him that they supplemented with a podcast that Dan recorded directly addressed to the Edutopia community. It’s worth recognizing that Dan does a fantastic job of recognizing some problems with history education that are consistently problematic in the math arena, too. From the podcast, about a minute in:

“… we teach it the same way we always did, except we’ve learned over and over, haven’t we, that the vast majority of people don’t like it taught this way. And they don’t remember it. And because they don’t remember it, any rationale you have for why it has to be the way it is because people have to learn these things goes right out the window, right? Because if they don’t retain them, they didn’t really learn them.

Maybe they were good students, studied them for the tests and got a good grade, but they didn’t keep that information a couple years later. It’s like learning a foreign language that you don’t keep up on, right? It doesn’t matter if you took Spanish back in high school if you don’t remember how to say anything, you know, ten years later.”

Educational professional or not, that is a pretty accurate observation of the major symptom plaguing education today. Many teachers I talk discuss how unprepared the students are for their particular class. This problem isn’t a secret. And it isn’t new. (Sam Cooke Sing-along anyone: “Don’t know geography… don’t know much trigonomety…“) In the podcast, Dan urges that the education should be less about what we teach and more about how we are teaching it.

From about the 10:00 mark.

You have to awaken a desire to continue with the subject, and not just in an educational sense, but in their lives – to have an interest in the past. Allow them to choose the subject and you’re halfway there. If a kid’s into motorcycles, let them do a report on the history of motorcycles. They will quickly come to understand how that motorcycle they admired in the showroom window today came to be. They’ll understand the value of knowing the past about any subject, right?

If you have a person in your classroom that’s interested in fashion – same thing. The history of fashion’s a wonderful subject. It’ll teach you how we got to where we are now in terms of fabrics, and colors, and styles. You’ll be able to recognize, “Oh, I see a little bit of ancient Egyptian influence in that dress I saw the other day on the runway.” This is how you begin to teach people that the past is infinitely exciting if you get to pick the subject.

… They can learn all the social studies aspects of these stories down the road, if it matters to them. If it doesn’t matter to them, they’re never going to learn it anyway. Now I don’t know if teachers have any control over this in the classroom, and I realize this doesn’t give them many tools to use, does it? But the truth of the matter is that if we’re going to teach history in a way that less than 10% come out knowing anything 5 years down the road, we’d be better off using that time to teach math.


Now, Dan recognizes his limitations as an adviser of educators, but he brings a lot to the table of value – and not just in the teaching of history. Replace history with math in most of that quote and you’ll find that his sentiments are still pretty applicable.

Why are we teaching math? What are we doing to put students in a position to leave us with anything of value to take with them? We’ve known for years that students often forget the math they study in school. (I am reminded of this every year at parent conferences when the parents remind me how little they remember of their high school math.)

So, why do we continue to do what we’re doing? Why are we spending so much time at the top levels stressing about WHAT we should teach and so much less about HOW we should teach? What should the goals of math class be?

The goals of math class are perplexity, problem-solving, organized logical reasoning, creativity within constraints, patience, persistence, perseverance, the ability to guess well, and then to design a way to check the accuracy of the guess…

THESE are the reasons for math class. THESE are the long-lasting takeaways. THESE are the things that make math class useful to 100% of the students. And THESE are things than can be taught regardless of the content. You can teach those things with linear functions, or visual patterns, or number lines.

And it’s okay that the advice came from a “fan of history” and not an educator.

My experiences with Kahoot!

So, a Spanish teacher across the hall from me encouraged me to try “Kahoot!”. Kahoot! is a online quiz maker that works a lot like pub-style trivia. A teacher makes a quiz. Students log into get a chance to take the quiz. The question goes up on the screen and students try to get it right. Get it right quickly, you get many points. Get it right slowly, you get less points. Get it wrong, you get no points.

So, knowing the typical doldrums that the “last-day-before-a-unit-test” can fall into, I decided to try it as part of my test review. So, here’s how I used it: I posted 9 trig problems around the room. Students paired the students up and sent them around in 90-120 second intervals to solve each one. I encouraged them to show as much work as humanly possible to the point of being excessive. (This is an instruction that often gets ignored.)

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This part took about 20 minutes.
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Then, I fired up the ol’ projector and sent the students to The quiz had a pin# they had to enter when they arrived. Then they could choose a nickname. (I’d advise some fairly clear boundaries on the nicknames. Just sayin’.)

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Then the questions came up on the screen and they could use their laptops, tablets, phones, or wi-fi enabled tech to answer. After each question, the correct answer is revealed and they got a chance to ask clarifying questions. It is possible to set multiple answers correct. The next question doesn’t appear until the teacher clicks “next”. The standings are updated and displayed after each question, too.

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So, what did I think? Well, the students sure enjoyed it. Although, I am curious how much learning got done. I suppose we’ll have the the test to offer some insight into that question. Also, one negative is that if the student device goes to sleep, Kahoot! kicks them out of the quiz. In one larger class (32 students), students were having trouble reconnecting and only about 17 students finished all nine questions. That wasn’t the case in my other class (of 22).

The students get to rate their experience after the quiz is done. Ratings were generally (but not all) positive. Also, the teacher gets an opportunity to download an Excel file that reports out all the data including the answers for each student (whether they finished or not), the breakdown of answers for each question and the student survey results. That is a nice piece.

I would encourage you to chime in if you have experiences with Kahoot! or something like it. I feel like tools like this can be useful, especially in BYOD schools.

Trig Curiosity

There is something about a question not being graded that makes the students aggressive and risky. That can create the conditions for some of the best thinking. There are many days when I think grades and points and the division between problems that I will “collect and grade” versus the ones that I will not.

In the system in which I exist, sometimes bonus questions on formative assessments are the only way to really perplex a student – to push them at the risk of pushing each student beyond their current ability to reason, but still get a solid effort.

On today’s quiz, I added the following question as a bonus:

If you type “Tan 90″ into a calculator, you will get an error message. Knowing what you know about trig, discuss the possible reasons that taking the tangent of a right angle in a triangle would make your calculator show an error message.”

This isn’t something that has come up in any of our discussions. I would like to share with you some of my student’s answers.

From James: “It has an opposite which is the hypotenuse, but it has two adjacents so you wouldn’t know which one to use unless you put it in the calculator.”

From Tyler: “There is no such thing because when you plug in Cos 90 you get 0 and when you plug in Sin 90 you get 1. Maybe it is because since Tangent is TOA, it tries to add up to 90, so like opposite is 30 degrees and adjacent is 60 degrees.”

From Brianna: “Because Tan 90 would be opposite/adjacent, but the opposite side of the 90-degree angle is the hypotenuse and you can’t have the hypotenuse on top.”

From Jeremy: “It shows an error message because the right angle on a triangle doesn’t have a defined opposite or adjacent side length because the angle is touching both legs.”

From Lauren: “With tangent, you are finding opposite/adjacent. Those are the legs, and that 90-degree angle is being made by the legs.”

From Dayna: ” There could be an error because the opposite of the right angle is also the hypotenuse of the triangle.”

Quiz Bonus 3

From Ally: It’s not clear where the negative idea comes from, but it is curious that in a Trig world of decimals and fractions, 90 in the other functions gives 1 and 0.

Quiz Bonus 2

From Victor


Quiz Bonus 1

Perhaps Josh’s picture says it all.


Now, the next question: If the “two-adjacent-sides-so-the-calculator-doesn’t-know-which-you-mean…” explanation wins out…

…then why don’t we get an error message for Cos 90?

Coke vs. Sprite – One Class’ Response to Dan Meyer’s #wcydwt Video

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Almost three years ago, I highlighted the Coke vs. Sprite video that @ddmeyer made. It is a very intriguing question (which glass contains a greater amount of its original pop) without a clear answer.

Today, I let a class give it a go and here’s what they came up with.

First, they chose to model it with integers. Said one student: “I pretended it was a jar with 10,000 marbles.” 2014-04-03 11.07.36

Then they assigned “a dropper-full” to be 100 marbles. So, the first dropper took 100 red marbles and placed them into the jar with the 10,000 green marbles.

Now we assumed the stirring made the mixture homogeneous which meant that there was a consistent 100:1 green-to-red marble ratio in the right jar. So, when we pull another 100 marbles to put back, (with a little bit of rounding) we pull 99 green marbles and a single red marble back into the left jar.

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A little number crunching reveals (at least in this model) that there would be 9901 original-colored marbles and 99 other-colored marbles in each jar.

My original assumption matches their investigation. It seems (at least by this model) that at the end of the video, each glass is containing equal amounts of their original soda.

Another teacher Chris Hunter (@ChrisHunter36) also battled with this video and created an excellent read about his experiences. Check them out.


The Power of Network: The Wedding Cake Problem

I have another wonderful story about the power of the wider math community to support its own. Earlier in March I presented at MACUL 2014 in Grand Rapids, MI. During that presentation, I led the group through an experience with the Wedding Cake Problem, which ended up being a wonderfully energetic interaction.

Sitting in that meeting was a gentleman named Jeff who teaches at a school in Michigan. He wrote me an email some time later that included a message and the following photos:

“I’m planning on using the cake problem this week as review in my Trigonometry class, as well as later in the year with my Geometry students. Well, here are a few improvements, well, really just pictures. See attached.
Pans are 5″, 7″ and 9″. I think I’m just going to give my class the actual pans without the pictures.”








Now, these photos change the dynamic a bit, don’t they? Let’s do pros and cons… What do you like better about giving the problem with these pictures? What do you prefer about the original problem?

I would love some feedback (especially if you have tried either one with your class).