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!

How many baseball are in this bucket?

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Dan Meyer (@ddmeyer) asked me for this picture somewhat relating to this post from a year or so ago. Once I tweeted the picture, it got the attention of a few others who simply wanted to guess how many baseballs were in it. I had forgotten how engaging a “who can guess the closest amount of…” questions can be.

So? How many you think?

Also, how can we use this in a math classroom? it’s tricky to use as a spheres-inside-of-a-cylinder problem simply because of the non-uniform amount of empty space between the baseballs. It makes the answer of actual baseballs less than the theoretical “volume of bucket divided by volume of baseballs” solution.

But does that mean it can’t be used? What do you think? Chime in.

 

Also, if you want to see how many baseball are in the bucket, then see for yourself.

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!

 

 

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.

NPR wants to advise your pizza order…

Quoctrung Bui from NPR says that there are at least 74476 reasons that you should always get the bigger pizza. (The article has an awesome interactive graph, too!)

If we could mix the article with a math exploration, we could provide an awesome opportunity for a math-literacy activity that can combine reasoning, reading, writing, and some number-crunching all in the same experience. That’s a nice combination. Also I suspect the content hits close to home for most students. (The leadership in our district is often looking for opportunities to increase authentic reading and writing in math classes. This seems to fit the bill quite well.)

Here’s an activity:

Although without fail, the menus from a variety of local pizza joints will probably be a bit more engaging. (Look for an update coming soon…)

Shauverino Pizziano

But the big question is why?

According to Bui: “The math of why bigger pizzas are such a good deal is simple: A pizza is a circle, and the area of a circle increases with the square of the radius.” 

Yup… that’s pretty much it.

Okay… I solved it, but how’s that math?

Its on these warm, spring days that some learners tend to start checking out. They recognize our typical reviewing and recirculating attempts to help students recapture some learning before the last tests and exams. But some of them learned the content the first time. Essentially, this time of year can bring with it a lot of down time for our students who learn the fastest.

That’s when I like to pull out my old college textbooks. I spoke before of the power of ungraded bonus problems. If interesting and placed properly, they can provide powerful opportunities for thinking simply for the sake of thinking. I like to give them a window into math that “doesn’t look like math.” After all, most of the content that K-12 mathematics includes has some commonalities that students get used to. They’ve gotten used to “what math looks like.”

Today, four groups got a problem that I adapted from one of my undergrad courses that I took at WMU with Dr. Ping Zhang who, along with Dr. Gary Chartrand co-authored this book which was the textbook for the course I took.

The problem is adapted from Example 1.1 from Chapter 1. It asks the students to create a schedule for 7 committees that share ten people. Now, the purpose of the problem in the book is to give a simple example of how a graph can be used to visualize a complex situation. Often the way a problem is mathematically modeled can change the intensity of the solution process.

 

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Figure 1.1 from Page 1

 

The reason I like to give this problem (and problems detached from the K-12 curriculum in general) is that in May, to curious students, these problems tend to hit the perplexity button just in the right spot. In fact, all the students looked at the handout at first and were unimpressed. Until I asked them to read it… then, they seemed to just want to see what the answer looked like. As one student put it, “It seems really easy at first, then you get into it and it’s actually harder than we thought.”

Graph theory is about creating visual representations. I didn’t want to ruin their experience by pigeon-holing them into trying to represent this they way I knew they could. And given the time, that didn’t stop this group from creating a similar idea. Not with a graph, but they did use crayons.

 

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To hear Kailey explain: “We just gave each person their own color. Then we knew we could have two committees meet at the same time if they didn’t have any colors in common.” That isn’t different thinking, really. Just a different representation.

I enjoy the conversations that come out it. No grade. Just doing math for the sake of thinking about something that’s interesting. It’s especially interesting to students like Katie who said, “Okay… I solved it, but how’s that math?”

 

Reference

Introduction to Graph Theory (2005) Chartrand, G., and Zhang, P., New York: McGraw Hill

My experiences with Kahoot!

Kahoot Student Front

A teacher across the hall (@nolink10) encouraged me to try 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 kahoot.it. 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.