My colleague is obsessed with ninjas in the same way I’m obsessed with superheroes. Whenever she gives her kids a challenging problem, she calls it a Ninja Problem. Students who gain ninja status in her class basically earn bragging rights. My first Ninja Problem went like this: “Is it possible to knock the goalie back into the net with a hockey puck? If no, what would it take?” (Hint: you can do most of the work using conservation of momentum.) Mad props to xkcd what-if for the inspiration.

H’s Hockey Puck Analysis

My student, H. took this Ninja Problem on with a vengeance.

After about 24 hours of thinking time, I shared a video with him that a Twitter pal shared with me. Fun and inspiration ensued.

Here’s his response:

Whoa! That’s crazy. I figured out that in order for a hockey player weighing 151 lbs (126 lbs for average 15 year old and 25 pounds roughly for average hockey gear (68.4924479 kg)) to be pushed .5 meters into a hockey goal in one second, a hockey puck must be launched at the average of the average velocity of a hockey puck (80-90 mph which I chose 85 mph (37.9984 m/s)) and after I calculated the volume of the hockey puck and its required mass, I found that the hockey puck must weigh 4.05729254 grams per cm^3 or .469969705 kg [ed: which is about 5 times heavier than a typical puck]. This means that it closer to Krypton and between Krypton and Yytrium. And in that video I think that guy was moving a little more than .5 meters per second haha. Thanks!

And 5 minutes later:

Whoops I have made a mistake! I multiplied took half of something while multiplying the other side by 2. The real answer is a hockey puck is needed to be made out of samarium or iron.

We talked through the effect of the goalie bracing against the ice (which H ultimately discarded because he didn’t know how to calculate for it), which made me wonder if he’d read the xkcd what-if answer. He hadn’t! When you get rid of bracing, it becomes much simpler to push the goalie back into the net.

N, K, and J’s Solution

This group of students, who elected one to be the star of the video, did a great job of separating the realistic scenario (which they quickly dismissed as implausible) from the hypothetical.

Implications for Physics Teaching

Mythbusters has made asking “what would it take?” fairly normal. A lot of my students understand the general approach of “ok, this thing is impossible as we’ve constrained it, so how could we reframe the situation so it’s plausible?” xkcd’s what-if extends on that. In fact, the hockey puck answer starts off with this gem:

This can’t really happen.

It’s not just a problem of hitting it hard enough. This blog isn’t concerned with that kind of limitation. Humans with sticks can’t make a puck go much faster than about 50 meters per second, so we’ll assume this puck is launched by a hockey robot or an electric sled or a hypersonic light gas gun.

Because high school physics often includes oversimplification to the point of absurdity, the “what would it take?” mechanism helps kids latch on to real problems in meaningful ways.

Points going forward:

1. Teach the kids estimation & rounding skills back-of-the envelope calculations, which don’t require such precision.
2. Find or write more of these questions!
3. Figure out how to engage more kids with Ninja Problems. This problem seriously engaged 5% of my students. I’d be thrilled if the number were closer to 20%. In Doing Whatever a Spider Can, I promised to get kids describing their assumptions more regularly. So far, I haven’t. Ninja Problems may be a nice way to engage kids in this process.

Physics class. The topic is forces and my kids were struggling to solve problems like this:

A student of mass 63.1 kg decides to test Newton’s laws of motion by standing on a bathroom scale placed on the floor of an elevator. Assume that the scale reads in newtons. Determine the scale reading when the elevator is accelerating upward at 0.7 m/s2.

or this:

A basketball with a mass of 0.4 kg is being pushed across a gym floor with a horizontal force of 2.2 Newtons. The coefficient of kinetic friction between the basketball and the floor is 0.2. What is the acceleration of the ball?

Struggling, that is, until I hit upon a way to organize their thinking with a “force table”.

Students fill in the table like it’s a Sudoku puzzle. I think the hardest part now is getting the free body diagram correct. Ooh, just to be sure they know what’s up, I’ve been stressing the importance of completing the last column with justifications.

I like to imagine that all the physics teachers out there trained in physics education went to grad school classes with titles like “How to Teach Kinematics” and “Methods for Helping Kids Who Suck at Math”. In these imaginary courses, y’all received the keys to helping kids past the hurdles of difficult math or “there’s no formula for this, it’s a problem-solving process”. Wait. What? You didn’t have these classes? Then how the heck do you help kids problem-solve? Please share your own organization routines, I’d like to learn from you.

Several folks wanted to see my essay after they helped me brainstorm it yesterday. Here ‘ya go! Help me improve this essay?

Writing prompt: Describe in detail the program of study to be undertaken. Include the personal benefit this study will provide you as a teacher and the value it will return to your students and school.

The Need for Professional Study
Mathematics education is increasingly project-based, exploratory, and based on research into how the brain learns. I began studying these while earning my Masters degree in teaching mathematics. I’ve continued studying with teachers who blog and tweet.

This summer, I have an opportunity to attend a summer conference that will further what I started in graduate school with amazing teachers. The conference is called Twitter Math Camp (http://www.twittermathcamp.com/) because many of us met through the eponymous social/professional media site. We are teachers with a passion for the very best in education.

About the Conference
Twitter Math Camp is a grass-roots conference created by mathematics teachers who first found each other on Twitter and through their blogs. The conference is hosted, staffed, and presented by the attendees. In this spirit, I am both presenting a session and attending as a learner.

Benefits to My School & Me
I see three major benefits to my attendance at Twitter Math Camp: 1) I’ll learn creative-but-rigorous practices, 2) I’ll collaborate on lessons I can bring to my classroom, and 3) I’ll experience productive struggling so I can better model it for my students.

First, I’ll have the chance to learn great new practices from some of the best teachers in the country. Last year, at the same conference, I learned about using GeoGebra with students to create something akin to a mathematics lab. The hands-on session provided “labs” I could use with kids without modification as well as gave me inspiration for creating my own. Also, I learned about the brain-based research behind the idea of building intrinsic motivation – and how to implement it in the classroom. It turns out that students need to understand the purpose of a problem, assignment, or project. When the kids buy-in to my lessons, they are always more motivation. My Math Camp colleagues helped me understand how to structure lessons so students buy in.

Second, Twitter Math Camp offers me the opportunity to collaborate on lessons. The conference organizers are providing time for deliberate planning this year. Last year, the attendees held impromptu planning sessions in hallways during breaks, we were so starved for practical lessons co-created with creative colleagues. I look forward to planning out a project or unit that unifies physics and geometry at Twitter Math Camp.

Finally, the conference will give me the chance to productively struggle on math problems. Math teachers call the process of working on one or several big problems productive struggle. Students shouldn’t be working on auto-pilot, they should be thinking, struggling, and making progress. We will take time to solve problems that are part of the Exeter math curriculum. Over the summer of 2012, I had the chance to work on similar problems and found the experience interesting. For one, how can I structure work time in my class to best take advantage of students’ attention spans? Everyone takes longer to get started, get engaged, then lose focus. How do I honor that in a class of 20 students?

In conclusion, Twitter Math Camp is an awesome opportunity for me to grow as a teacher. The conference is free to attend if I can just get myself there and lodged. If you’d like to read more about Twitter Math Camp 2012, please refer to http://oldmathdognewtricks.blogspot.com/2012/07/best-pd-ever.html.

Do you remember this scene from Spider-Man 2 (2004)? A NYC subway train hurtles toward imminent doom, unless Spidey can stop it. Is it plausible for spider silk to stop a moving subway train?

Suppose a man bitten by a genetically enhanced (or irradiated, depending on the origin you like better) spider can acquire the strengths of a spider proportional to his size. Next, suppose the scene depicted in a popular Hollywood film can give you some clues about the physics scenario afoot. Do that and you have ”Doing whatever a spider can” by M Bryan, J Forster, and A Stone.  The paper was published 31 Oct 2012 in University of Leicester’s Journal of Physics Special Topics Journal. This stuff is golden¹:

Here’s a top view from the movie:

I want to teach my own students to describe their assumptions as well as these students(?) did in building their model². What’s a good way to go about doing that work?

• Demonstrate it in my own work? Build my own examples and walk through my assumptions.
• Learn from pros? By getting kids reading papers like this one, even if we stop after the model parameters section.
• Practice it? Have the kids analyze situations within their own level of physics. This I’ve tried and found to be incredibly painful. I’m willing, here and in public on my blog to commit to having my kids practice assumption-describing daily for 3 weeks. I’ll report back with results.

h/t to Leah Kazantzis, with whom I have the pleasure of teaching!

¹ What’s that you say? You don’t teach physics using superhero examples? Oh, you’re missing out.
² Enough of my friends teach using Modeling Physics that I expect to hear that idea thrown out here. That’s ok, but I’m looking for other stuff, too.

Last week at Global Math Department, we learned from Max Ray (@maxmathforum) about using Noticing & Wondering. As with all the best Global Math presentations, I heard from folks who used the technique the very next day. I always seem to run a little slow compared to my Tweeps, so it took me a few days to find a good entry into my physics classes.

I started here:

Here’s my teaching setup, courtesy of Max:

1. Ask the class to view the clip with this question in mind, “What do you notice?”
2. Give them 1 minute to write individually, 1-2 min to discuss in small groups, then 3 minutes to share the best noticings.Here’s a picture of my 1st period class’s list.
3. Ask the class to think in physics terms, “What do you wonder?” Again with the write-discuss-share thing. Here’s my 1st period class’s list.

I asked them which they wanted to pursue, height of the cliff or acceleration due to gravity. They liked gravity. After we estimated cliff height (which involved the search: “how tall is Wiley E Coyote?”) and the dust settled, we found g was about 3.2 m/s².

When I picked this clip, it was because it reminded me of this, and the gravity question hadn’t even entered my mind:

Holy cow, this N+W is the good stuff. Kids were engaged, the framework kept us on task, we found a great physics problem I’d never considered, and I had an excellent entry into projectile motion.

Khan Style Online Learning

My colleague Frank Noschese said it well,

While Khan argues that his videos now eliminate “one-size-fits-all” education, his videos are exactly that. I tried finding Khan Academy videos for my students to use as references for studying, or to use as a tutorial when there’s a substitute teacher, but I haven’t found a good one. They either tackle problems that are too hard (college level) or they don’t use a lot of the multiple representations that are so fundamental to my teaching (kinematic graphs, interaction diagrams, energy pie graphs, momentum bar charts, color-coded circuit diagrams showing pressure and flow, etc.).

Online learning in the model of Khan Academy (a video library with accompanying assignments) moves classroom focus from the student to the teacher. It becomes about what I’ve taught, not what the kid has learned/mastered. Teachers are not in the business of delivering content. We’re in the business of helping kids learn.

That said, Khan Academy and his competitors, aren’t entirely awful. If you need to reference how to factor a quadratic expression, the video may be helpful. Maybe Khan is most useful when the material is a refresher, not entirely new. In my opinion, Khan Academy-style videos can be excellent tutoring resources but are horrible full-time teachers.

MOOC Style Online Learning

The Massive Online Open Course, MOOC, made a lot of noise this year. You can take a university level class with a university professor (and often for free). Learning from leaders in the field at schools such as Stanford? Wow! Audrey Watters declared 2012 the Year of the MOOC. She gives a great deconstruction of the pedagogy, getting to the crux of the MOOC’s drawbacks with,

much of what’s being lauded as “revolutionary” and as “disrupting” traditional teaching practices here simply involves videotaping lectures and putting them online…xMOOCs might be changing education by scaling this online delivery

When I taught in public schools, my class sizes crept up to 32 students. One colleague taught math to 50 kids in a single classroom. We barely knew or kids’ names, let alone what they understood of our learning objectives. For the same reason, I don’t advocate the MOOC — it fails to address each student’s understandings and misunderstandings of course material.

A teacher with a relatively small (<20) class CAN know every student and track their progress toward learning objectives. For example, I know that not all my students have the same misconceptions, therefore not all benefit from the same instruction. Kids are not widgets in a Ford factory. They require individual attention from a teacher who can address their misconceptions.

Maybe Ok? Flipped Classroom Style Online Learning 

I see promise in some of the flipped classroom pedagogies invented by Jon Bergmann and implemented by Audrey McLaren McGoldrick, Kyle Webb, Graham Johnson, and Ryan Banow. You can see that group share a presentation at Global Math Department in December 2011. One key piece I took from them: flipped classrooms are about YOU the teacher connecting with YOUR students. Not Sal Khan or an MIT professor.

Last semester, I played with video a lot as a tutorial tool. While not a flipped classroom, the videos were effective at letting me respond to student questions asynchronously. Case in point: my videos from December are based on a final exam study guide and ALL were solved based on prompts from students.

It would be fair to characterize my entire argument as one of local control. I form relationships with my students that I don’t believe can be duplicated to a large scale. Those relationships help me understand how to best teach each one of my students instead of talking at them in a traditional lecture.

Why Traditional Lecture Doesn’t Work

My very favorite explanation comes from Derek Muller at https://www.youtube.com/watch?v=eVtCO84MDj8. Check out his graph, below.

On the left are the results of a pre- and post-test when the instruction style was a expository video (aka, lecture). On the right are the results of a misconception-attacking style he’s created. In a typical Derek Muller video, he interviews people with a question (which ball will hit the ground first, for example). Their answers are riddled with misconceptions, just like the students. He then goes on to attack every misconception. Until a kid understands why his conception is wrong, he’ll continue to believe it. Muller blows those misconceptions out of the water. His research proves that a simple lecture is NOT the answer.

Sadly, online learning today (as represented by Khan- and MOOC-style pedagogies) is anchored in the traditional lecture. Until we find a way to individualize the learning and attack misconceptions, I can’t back online learning as the primary mode a student gets their learnin’.

Officially, “Ranking Tasks are an innovative type of conceptual exercise that asks students to make comparative judgments about a set of variations on a particular physical situation.” Let me give you an example from Kelly O’Shea:

Here’s the brilliance I see in the displacement question Kelly asks. Say you’re a freshman in my physics class and you just learned the distinction between displacement and distance. I ask you to rank A-F in the above image. I imagine this internal dialogue (monologue?):

• A and B look the same but I’m guessing that 25 on the y-axis is important.
• C and D are straightforward displacements, the “easy” ones.
• Good gravy! What am I supposed to do with E?
• Whoa Nelly, F is even worse than E. I need to check the definition of displacement.

There’s understanding a definition then there’s applying that definition. Do you love Ranking Tasks yet?

I tried writing my own, wasn’t happy with the results, so I went for a walk on the newish Atlanta Beltline. We saw some amazing art, a skatepark, and spent time with family. Yeah, winter break rocks.

But I digress…

When I got home I realized what I was doing wrong — I tried making the ranking task without a clear idea of exactly what I was testing knowledge of. Wait, what? You mean I hafta think this out before I start drawing graphs? Oh okay…

1. Draw about 2 items that are straightforward applications of the definition/idea being ranked.
2. List the learning goals and common misconceptions.
3. For every item in #1, design a picture or graph to address it.

I’m a rank n00b at these Ranking Tasks, but the Amazon writeup had good-sounding advice I’ll include here, too.

The basic structure of a Ranking Task comprises four elements:

• a description of the physical situation, including any constraints and the basis for ranking different arrangements
• a set of figures showing the different arrangements of the situation to be compared
• a place to record the ranking of each variation
• a place to explain the reason for each ranking choice

I’ve seen a lot written about Ranking Tasks in physics. The book I referenced above is specifically for physics, but why couldn’t these work in math? Off the top of my head: rank these fractions, rank these irrational numbers, or rank these radical expressions without evaluating directly.

———————–

Global Math Department in 2013 is gonna be hot! Join us Jan 8 for an Ignite-style meeting. Teachers will take the stage for 5 minutes each, armed with 20 slides auto-advancing every 15 seconds. The topic? My Favorite classroom ideas.

Jan 8: Global Math Department: My Favorite Ignited

1. Teach the students to manage their stress well.
2. Prepare the students for a comprehensive exam.
3. Use my office hours and after hours time efficiently with the students.

Efficiency

This is always a weak spot of mine. I get into office hours and am constantly distracted by everyone asking me questions from all directions. I knew I needed to be smart about the exam prep window. My mantra: “answer every question once, even if multiple students ask the same question multiple times.”

I took three steps to be efficient and enact my mantra:

1. Embedded help in the Moodle study guide. Wrong answers that match an anticipated algorithm (such as not converting units properly) gives targeted advice (“it looks like you didn’t do unit conversions to base units”).
2. A Google Doc shared with the class where students can ask/answer questions.
3. A YouTube playlist of hint videos.

Embedded help in Moodle: here’s one example that helps lead students to the solution.

The Google Doc:

Every question on the study guide earns a section in the Google Doc. Students ask questions and I answer them or give hints. This is one of the meatier exchanges between students and me. I like that I only have to answer the question once because everyone can read the “thread”.

I’ve been working on getting the kids to help each other through the Google Doc (all semester, actually) but they’re much better at in-person help than online.

The YouTube playlist (also linked from the Google Doc) has been fun to create. See below for a video.

Comprehensive Exams

A semester-long comprehensive exam is always a stressful event. Kids have forgotten important chunks of what they learned back in September. It was interesting to watch them work the study guide and remember stuff. Yesterday I heard kid 1 say to kid 2, “I love Snell’s Law!” Awww, that will long be a top 10 memory of mine.

I believe a good study guide is a key component to helping younger students prepare for a comprehensive exam. The study guide should be pretty similar to the exam so kids don’t feel surprised. The mix of problems should reflect what was most important to the semester. (Am I talking obvious stuff here? Never can be sure…) I explicitly told my students, “if it isn’t on the study guide, you can be sure it isn’t on the exam.”

I do study guides and tests in Moodle, so I get several metrics about my students’ study habits to help me offer individual advice to kids. For example, one young woman was working her study guide with little advance thought, so was having to retry questions 5 or more times. I conferenced with her that she doesn’t know the material if it takes her 5 tries to get a correct answer. Another student, a young man was very concerned that he was rushing things because he finished the study guide very quickly. My question, “Do you make careless mistakes?” led to a great discussion about ways to be sure you’re getting work right.

Stress

My friend John Burk (@occam98) helped me out here with a year-old blog entry, “The no-stress exam package“. The fact I stressed most with the kids was to plan their exam studies several weeks in advance. We’ve spent a lot of time talking this semester already about the value of sleep.

One addition of my own was the exam bonus: if you earn 80% or better on the study guide, you’ll earn +5 on the exam; get 90% or better on the study guide to earn +10 on the exam.

What do you do to be your best and have your students do their best at exam time? 

Catalogued here for my future reference.

Oh, you actually want to know more about these pictures? Pictured is a homework/quiz/test question from Moodle, an open source course management system. Specifically, it’s a Calculated Question, meaning all the numbers in the problem could be regenerated for each kid or each attempt. If you look at the fourth gallery photo, you’ll see what it takes to write solutions in this system.

Wasn’t really the reason for these posts, but you may also find it interesting that these Calculated Questions allow partial credit answers. I write formulae to common mistakes and choose the portion of credit I want awarded. On this problem, for instance, the kids might forget to calculate speed of sound at the given temperature and might instead use the speed of sound at room temperature.

The whole Moodle system is pretty amazing, actually. Many thanks to my new colleague Meghan Bjork for introducing me to it.

One thing that hasn’t changed is that I’m still stealing your ideas. My classroom is a combination of all YOUR classrooms. I’ve taken your best ideas for several years now and shared mine (apparently Waterfall Trivia is still popular in some circles — you’re welcome!). That’s what we do in the best blogotwittosphere on Earth, right?

In the name of sharing my classroom with you guys, here are my top ideas taken from your blogs and your tweets.

Mailing Label Problems

Fawn Nguyen (@fawnpnguyen) shared this photo of her puppy’s craftsmanship and I thought I was going to cry. Why was her loss of a box of Avery Mailing Labels so painful? The idea I stole from her was to put problems (or problem sets) on mailing labels. Fawn’s been using the labels to support her Standards Based Grading implementation:

this year I found the best use for the mailing labels with SBG. School is in full swing now and there are a lot of kids coming in at lunch time for retakes. Currently, and because this is our first year with SBG, we can only manage to assign selected questions from the textbook for reassessments. I either have to tell them what the problems are when they come in or give them a piece of paper that has the problems on it, then they have to copy all this information on notebook paper: section title, page number(s), and which exercises. Without this information, I can’t correct their papers.

I’m using her “old” idea to put problems on the labels. I give my kids a batch of 6 label problems, convenient because there are 30 on a sheet, for them to solve in their interactive notebooks.

Self-Feedbacked Quizzes

Frank Noschese posted a simple photo titled Quiz Day with some arrows drawn on it. Holy cow did that picture ever change my assessing life. Here are Frank’s words:

I set up stations with the answer key and orange pens on the counter around the room. When students were finished with the quiz, they brought their quiz to a station to check their work against the key and use the orange pens to leave themselves feedback directly on the quiz. Then they handed the quiz in to me. What I like about this: students give themselves the feedback they need and I get to see what that feedback looks like.

I still review everything on these quizzes, so it’s not proven a time-saver. Maybe I save a little time because I’m not hunting down the mistake a kid made in a long solution (and yeah, I’m a little in love with a circled term and the words “forgot to square distance”, cause dang! those can be hard to spot).

Whiteboard Groupings

Bowman’s idea to use stickies on whiteboards for class groupings makes the warmup time that much more efficient.  I love the way the kids just know what to do when they walk in the room.

The Mistake Game

Before I ever talked with Bowman about whiteboards, Kelly taught me this whiteboarding game over at Physics! Blog!. Give kids a set of problems and time to work them. Then assign a problem to each group to post on the whiteboard. The catch: they have to hide a mistake that’s crucial to solving the problem. Their classmates later listen to the presentation and question their way to the mistake.

In my classes, we’re still improving our mistake-hiding and finding techniques.

Row Games

This is a great activity for the math teachers in the crowd and I used it a lot in my previous life as a math teacher.

Kate taught me about Row Games, where two people work two different problems (on a row) that have the same answer. I love me some self-checking work where kids cooperate rather than compete and boy howdy! is this ever one of them.

Now, Show Me Yours

Throw ‘em in the comments or (better!) share them at the next #globalmath My Favorite session. Shoot, the idea you share doesn’t even have to be yours so long as you attribute it.

Thanks, peeps, for listening, for stealing, for sharing. About our community, I like to say “We want to be better teachers. We share freely. We are always supportive.”