It’s nearly exam time (hey, no complaining, y’all with a month or more of school left made me jealous last August!). In the past, I’ve been a huge proponent of Waterfall Trivia and math stations as review techniques. Both helped me wrangle large, unruly classes that didn’t really want to review for an exam or test. This year I have a blessing and a curse wrapped into one: my students would actually prefer to sit and listen to me recap the entire semester over 2 or 3 days. “Re-lecturing” is just not valuable in my opinion. The kids are passive, so they’re not likely actually getting anything new from the activity. I’d prefer activities where the kids do most/all of the in-class work — Quadrant I in my chart below. Some teachers aren’t so lucky as to have such academically-minded students, so their review activities need to get the kids who don’t want to, working — Quadrant II.
My criteria for a good review activity with this batch of kids:
- avoids cutsey gimmicks
- hits >= 80% of content covered this semester
- allows serious problem-solving in class
- has me not recapping the whole semester at the board for n days.
With my criteria in mind, here are the best ideas shared by my Twitter peeps.
Recitation Problems from Kelly O’Shea. Kelly writes:
About two weeks before the end of the semester, my students get a big (usually 24 pages), intimidating packet. It has one problem per student*, and the problems are problem+blank-page type of questions (that is, juicy ones that require multiple steps without breaking the question into parts that would structure the work for you). They tend to cover most of the main skills, but especially the ones that my students have found most difficult.
When they get to class the next day, we pick letters A through however-many-students-there-are. Then I give them my pep talk about how they should choose their problem. Whichever problem they choose, they will get to present the solution the class. They will have to become an expert on that problem. So I encourage them to pick the one that looks scariest to them. Pick the one that you would least like to see show up on the exam. Pick the one that will be hardest for you (it will be different for different students, of course).
Recitation Problems hits all my criteria without adding a ton of stress to the kids in their last week of regular classes.
Math Basketball from Dan Meyer. Dan writes:
- You bring in a set of questions related to the previous two week’s instruction.
- You put up a question.
- A kid stands up with an answer, either correct or incorrect:
- If it’s incorrect, the student sits down, reworks the problem, and you wait for another student to stand.
- If it’s correct, the student takes two shots with a miniature basketball into a lined trashcan. You award points according to a) the student’s distance from the trash can, and b) the competitive mode you’ve selected below.
Review Activities Aplenty from Becky Rahm
I wound up doing math stations because they’re pretty easy to set up and help me carve out time to ask individual questions. Here’s the setup:
- Print a set of problems for about 10 minutes of work on a sheet of paper. Repeat for each topic. Spread the problem sets around the room. I taped mine to cabinets, Julie Reulbach uses acrylic frames (way cooler).
- Print answers and hang them in one spot near you.
- Set a 10 minute timer tell students to choose a station with <5 people already there, work problems, and check answers at will. If they can’t get their problems answered by a classmate, they stay with me until station time’s up or question is answered.
Stations are easier to set up if you collaborate with a colleague.
I’ll be sharing, along with Matt Vaudrey, about Exam Review That Doesn’t Suck on Tuesday, May 21 at the Global Math Department. Join us! It’s completely free and online at 9pm Eastern / 6 Pacific.
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:
- Teach the kids estimation & rounding skills back-of-the envelope calculations, which don’t require such precision.
- Find or write more of these questions!
- 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.
[Earlier this week, Tina asked me my blog's name. Truth is, I never named it. Sure, I bought a domain but I never got around to branding the blog with the same name. So, what's up with the domain name? Kalamity Kat was my grandfather's WWII aircraft, a PBY-5A Catalina flying boat. He and his crew were shot down while rescuing downed fighter pilots out of Tokyo Bay.]
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.
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.
I teach in an independent school in Georgia and have the opportunity to have my Twitter Math Camp trip funded through a grant program of the Georgia Independent Schools Association.
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.
a scientific paper on the most unscientific of topics
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.
or, How I used Noticing & Wondering in Physics
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:
- Ask the class to view the clip with this question in mind, “What do you notice?”
- 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.
- 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.
Online learning in the fashion of Khan Academy or the MOOC is an extension of the factory model of education which I believe to be outmoded. One key assumption is that online learning extends a teacher’s reach to more students. My thesis is that students achieve better with individual attention from and dialogue with a teacher.
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’.