The Essentials of Project-Based Learning

On Thursday, I will be facilitating a collaborative session for teachers on Project-Based Learning, which, to be fair, is a topic that I have never considered comprehensively. I’ve never been asked to define it. I’ve never been asked to explain it and, quite frankly, until the organizer of EdCamp Mid-Michigan approached me to facilitate the session, I never considered myself a practitioner of it. I just tried to design lessons that were engaging and built authentic, lasting learning.

But, this EdCamp facilitator, who’s name is Tara, has known me for quite a while. We did our undergrad together. We did our Masters work together. She’s been on an interview committee that almost hired me. She’s aware of my shtick. Maybe she wants me to facilitate this through the lens of how I work. If that’s the case, then this takes on an extra degree of difficulty because I still feel like I have a lot of development left to do before people start emulating my approach.

Besides that, my approach isn’t really that complicated. For any activity I consider offering to the students, I simply try to ask a couple of questions.

1. What can I do to maximize engagement? (I’ve seen plenty of ideas that I have had flop simply because the students aren’t drawn in.)

2. What can I do to facilitate collaboration? (The most effective use of class time that I ever see is when a group of students are effectively working together to solve a problem.)

3. What can I do to create a problem that will provide a variety of ways to solve it? (If there is only one real method to solve it, then as soon as one student gets it, the “collaboration” will become that student communicating “the way to solve it” to everyone else. My favorite evidence of this is when I hear a few “I don’t get how they did it, but this is how we did it and the answer came out pretty close to the same.”)

4. What can I do to make sure that the solution(s) are approaching effective learning outcomes? (While it can be interesting to occasionally have a group find a way to solve (or estimate a solution to) a problem effectively in ways that circumvent my desired learning outcomes, if I am continually putting together problems that don’t push the curriculum the community is trusting me to teach, then my students will be missing something.)

My favorite examples of this process working well are The Lake Superior Problem, The Pencil Sharpener Problem, The Wedding Cake Problem, and the Speedometer Problem. In each case, engagement and collaboration were high. Multiple solutions were present and most of the solution techniques required the students to make sense of mathematical procedures that could be correct or could be incorrect. “Why this formula is better than that other one.” Or “neither of our answers are perfect, this this one is better because this process has less of a margin for error.” Stuff like that. These conversations provide great opportunities to move beyond the memorization of a formula and to push toward sense-making of how that formula is used effectively.

While I’m not sure if this is “by-the-book” project-based learning, I have seen improvements in my students’ learning through the lesson design process I described above. Does anyone have any advice for me? Questions for me to think about? Corrections? Obvious holes in my logic? I appreciate this community because of your willingness to share, so feel free to do so.

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Why the math teacher in me loves the science teacher in me

I spend 9 months of the year being a math teacher and two weeks every year being a science teacher. As time goes, it is hardly a comparison, but I’m beginning to see those two science weeks as an absolutely essential part of supporting the rest of the math year.

For better or worse, my brain has but some boxes around the two disciplines. Science provides the contexts, math helps to generalize them. Science provides the data, math analyzes it. Science gives you a story to support evidence. Math gives you the tools to predict the future or to theorize the past.

I understand those are debatable points. The real borders between math and science are not nearly so cut-and-dry.

But I can’t get away from this generalization: science is story-telling. Some of the stories are exciting. Some of the stories are gruesome. Some of the stories are tragic. But, science has made its business to gather evidence and to create a story that puts all the evidence into a logical explanation. If you look at the evolution of the models of the solar system or the atom you can see the story-telling. Evidence gets a story. More evidence changes the story. The more evidence we have, the more detailed and accurate the story becomes.

People like stories. Story-telling is an ancient practice. A good story is captivating. It draws you in and makes you want to hear what’s coming up next. Sometimes the math I teach gets a little quantitative. Sometimes it gets a little emotion-less and dry. Sometimes I forget that behind every good rule, law, theorem, there is an application, a context… a story.

And it is definitely possible to create a math class that includes story-telling. A simple Bing search for #3Acts math will reveal a variety of math lessons in the 3 act model that most movies use. This type of problem was first designed by Dan Meyer (@ddmeyer) and as he has explained the process further and provided examples, many other talent math teachers have added their own contributions to the online supply of math problems that use the same engagement model as story-telling.

And now, we’ve crossed the half-way point and the summer starts rolling downhill toward the beginning of the next school year. These two weeks remind me of my job as a story-teller. That it is my job to give the students math to explore. That is my job to draw them into an experience. The best science teachers are masters of experience and discovery. They are expert story-tellers and they are experts in giving the students a bit of evidence and allowing them to write and tell their own stories.

Perhaps that’s true of the best math teachers as well.

Learning from Playing Around

These past two weeks have been an awesome time of learning for the students we’ve been working with, but I’ve also done a bit of learning myself.

I’d like to have my students love math and science and naturally be interested in it. But they’re kids. They would prefer to play. People get the most out of that which they put the most in to. If given the chance, students will put a ton into playing around.

These past two weeks I’ve been working with upper elementary-aged students. I normally teach high school students. I’m not sure if the age difference changes anything. The stuff they want to play with might be different, but not the desire to play.

And after 7 years of teaching math, there’s something appealing about a situation where students will be voluntary and enthusiastic participants.

I have just spent two weeks watching students play with two activities. The first was an activity called “Table Timers” where they were challenged to design and construct an apparatus on a table top that reliably moved a marble down an inclined table in ten seconds. Second, The Helium Balloon Problem challenges students to keep a helium balloon rising, but to have it travel as slowly as possible upward. Not every group worked well and not every group achieved these goals, but the engagement level has been high. I suspect this is because they we allowed to play.

Here’s what caught my attention the most: In the midst of their play, the students demonstrated some authentic problem-solving techniques. They had to identify the major challenges to their goal, which they often did. They had to brainstorm possible ways to overcome the challenges, which usually took the form of raking through a tub of blocks or looking through the supply table. They discerned which seemed like the most realistic and then test. Following a test, they discussed what happened, why, and revised. And the students were often quite excited when they got the right answer (knowing themselves that it was right and not relying on me to tell them).

That’s a pretty good learning model. That’s something that I have a hard time getting my students to do with book work.

So, the sharing, the idea-making, the consensus-building, the authentic assessment are all good things. Obviously I am not simply advocating letting the students play around all day. But perhaps by using play, we can improve engagement and the students seem to more naturally fall into a more authentic problem-solving mindset. When I consider helping them draw out the learning, some thoughts come to mind.

First, it seems like during the whole process of exploration, design, construction, testing, revising, and demonstrating, there needs to be an abundance of contents-specific vocabulary. The marble didn’t “bonk into that block.” That block “applied a force” to the marble. Students don’t “figure out how big the shape is.” The “find the area” or “circumference” or “volume.”

Second, students don’t seem naturally inclined to take data or to keep records. In the past two weeks, it seems that students are avid experimenters and do a pretty good job of verbally analyzing the problems if the plan didn’t work. Practically NONE of them documented anything on paper. No sketches, no data, no records of updates. This is an important part of the problem-solving process that would have to be established as a norm.

Third, the activities have to be tiered. Video games are great at this. The entry point tends to be quite low. The first couple of levels are pretty manageable and then the intensity and difficulty pick up. People get locked into video games through that model and people get unlocked quite quickly once the game has been beaten. Both Table Timers and The Helium Balloon Problem worked with this model. Then entry point was low for both activities and it was easy enough to begin to approach the goal, but perfecting the design and executing the plan took much more care. Then, once they hit ten seconds, we’d challenge them to add five seconds to their timer.

Fourth, I think that the groups need to be expected to summarize and present their work to each other and to field questions from the class. Class norms should allow for questioning of each other’s work and students can learn a lot about their own design, but also about the content when they know that they are going to have questions coming from their peers. Also, it would seem like this would encourage more thoughtful designs, too. Besides this, idea sharing gives the students an opportunity to look at other designs, integrate specific vocabulary into more regular use, and get the students comfortable with collaborating.

 

I don’t think that playing around is the answer to everything, but I know that in my own experiences, it seems to be the forgotten learning model and if I’ve learned anything these past two weeks, it’s that an environment that produces enthusiastic student participation shouldn’t be ignored.

Making over another typical geometry problem

It’s time to look at another typical geometry problem to make over. This time Dan Meyer (@ddmeyer) presented this problem for revision.

Dan decided to go in this direction for the revision, which, for the record I really like. I would encourage you to check it out.

I took a try at it, too. I’ll let you decide which you like better.

I like this problem’s basic core idea. Looking at the volume of a sphere (the meatball) and the volume of the cylinder (the cooking pot), in general, this is a pretty tasty set-up (pun intended). Especially considering that I am always a fan of problems that make use of food.

But…

For this problem, food and cooking were actually more of a problem that a support.

First, the cooking pot is sitting on a hot burner and I’ll be the first to tell you, a cooking pot doesn’t have to be full to spill over. So, the question of whether or not sauce will spill over is a bit more complicated that it might seem at first.

Second, meatballs aren’t spheres. They are irregular and rarely are two of them congruent.

So, my first thought was to choose spherical objects that are all congruent: for example, baseballs. Coaches regularly carry baseballs around in 5-gallon buckets, so there is our cylindrical container.

And I figured I’d deliver the task in a video simply because videos tend to improve engagement on their own.

Now, once I made the video (and some meaningful conversation was had among those who are better at this than I am) I found that my task had one glaring drawback. When you put baseballs in a bucket, they don’t pack tightly. There is air between them. A lot of it, in fact.

So, now it seems like if we are to use this video for instruction, we would need to change the question in to multiple parts.

1. How many baseballs can we fit into the bucket? (This would likely end up being a demo or a lab where we collect data. Tricky to calculate this.)

But then we supplement the question above by…

2. How much volume is wasted by packing that many baseballs in the 5-gallon bucket.

This would get back to the original content. Likely the cylindrical volume would need to a unit conversion, and then some analysis of the collective volume of the collection of baseballs.

Now, if we could ind a way to check it. The first thought I had was to fill the bucket with water. Put the baseballs in to displace the water out of the bucket. Take the soggy baseballs back out of the bucket. Find the volume of the water that’s left.

Problems with this idea: 1. Baseballs float which is going to effect the manner in which the water is displaced. 2. Baseballs absorb water. This means that some of the none displaced water would get removed with the baseballs and not counted.

Hmm… I thought of filling the bucket with baseballs and then topping the bucket off with sand. Which would solve both of the above problems, it would also give me an opportunity to make a beach trip.

Any other ideas out there?

Motivating Learners

What could make a bunch of 10-year-olds do this in July?

Today was the opening day of Kids’ College, which is a two-week, half-day science academy for going-to-be 5th and 6th graders at Michigan State University. This is my fifth year getting to lead as an instructor. That makes this my fifth opening day. Today I was struck by some observations that I hadn’t noticed before.

First, I’ll set up the situation. After an auditorium-style presentation with the whole group (there’s 18 instructors each with a group like mine) getting through the get-to-know-you info (lasting about an hour), we split up into individual groups. This year, I am leading 10 young people. I’ve never met any of them. Only two of them have met someone else in the group. After some introductions, we have about 75 minutes to use pipe insulation, tape, a marble, and anything else at arm’s reach to build a roller coaster that met some basic common guidelines.

It is of note (at least to me) that I wasn’t going to collect anything, I wasn’t going to record any grades, truth-be-told I wasn’t going to hold them accountable at all. So, here we go.

It wasn’t quite right, so they fixed it. I didn’t have to tell them.

Observation #1: Off-task behavior was shockingly absent.  These kids had ideas, discussed them, and designed, reality-checked, and made predictions. I told them that I wasn’t handing them a marble until the coaster was built, stable, and ready for testing. My favorite question became “If this coaster has trouble, where do you think the trouble-spots will be?” Both teams had talked about it already. They knew. And they were both right, by the way. Also, no bathroom breaks. No kids asking to stop to eat their snacks. No kids asking what time it is and how much longer we have until we are done. I mean that. None.

There was no grade on the line. He simply didn’t quit trying.

Observation #2: They decided their own “good enough”. I told them the requirements. They weren’t constantly seeking my approval. They didn’t ask questions like, “are we done yet?” On the contrary, in both cases, I had to instruct them to stop after fielding “aww, just one more test run? C’mon, we just need to fix this one hill… hold on.”

This team discussed, sketched, delegated without much direction.

Observation #3: Students developed roles within the 5-person groups quite well. One guy was the tape guy. He held the tape, ripped a piece, applied it where the designer told him to. This person was working on the loop. That person on the curve. This person’s job was to tape the insulation to the wall to create the initial hill. These kids hadn’t ever met. I didn’t see any squabbling. I didn’t see any hurt feelings. I didn’t tell them to divvy up roles. About all I said, “You better get this organized!”

Okay, now I’m already arguing with myself:

“Yeah, but these are learners who are interested in science.” Okay, perhaps, but that doesn’t explain the group dynamics. Besides, putting these kids back on the busses to go back to meet their parents was all it took to reveal to all of use that these were definitely normal 10-year-olds.

“You work with 15- and 16-year-olds. This stuff must be easier with 10-year-olds.” Is that true? I have friends who teach elementary school and they gripe sometimes, too. I’m not sure that simply supplanting my typical group of 15- and 16-year-olds with 10-year-olds magically makes a lesson plan more likely to succeed. Does it? (A bit of help in the comments would be fantastic from those readers in the elementary ranks.)

“You’ve done this activity before and it doesn’t always go this well.” Very true. I have had students in the past that are a bit tougher to motivate. I have had groups with super-dominant leaders who try to monopolize everything. (In fact, this year, I tried to get around that by adding the structured timing… first 10 minutes discussion/sketching… then no marble until the whole design is constructed.) I suppose the student selection forces-that-be may have blessed me with a good mix, but I can’t help but feel like there is something more at work here.

Here is a stand-alone lesson. Didn’t do anything to assess prior knowledge and there wasn’t an assessment following. Nothing was turned in. Nothing was graded. Science isn’t built on that stuff. LEARNING isn’t built on that stuff. Learning is built on the stuff that I saw today. Discussing, sketching, questioning, building, testing, adjusting, asking why. Perhaps we allowed for those things to increase by eliminating questions like:

“Is this going to be on the test?”

“When is this due?”

“Do we all have to turn one in?”

“How many points is this worth?”

I mean, believe me, I understand the role of assessments and obviously I have a situation where I’m not being held accountable much either, which gives me a lot more flexibility. But what if that is the key? What if all the off-task behavior that is getting in the way is being caused by grades, tests, and other stuff? What if I got a window into authentic learning? What if today I saw a formula that worked? How can I integrate the lessons that I learned today into the September-to-June environment?

All I know is that today I saw something work. I want my classroom to work like that.

I don’t know. I guess I have more questions than answers. Perhaps that is why I am asking the questions to all of you. I know that you have more answers than me. I look forward to your perspective.