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Lessons From the Classroom
Deconstructing a Lesson Activity – Part 2
Previously: Deconstructing a Lesson Activity - Part 1
No matter what I write in this Part 2, I hope it's not a wrap-up of this topic. On the contrary, I hope it opens up and extends our conversations on improving the implementation of rich tasks in our classrooms.
Physical arrangements, whiteboards, groupings. The student desks are set up in rows and columns in my classroom. Not terribly exciting, but don't judge a teacher by his/her furniture arrangement. When I'm given 38 desks (I had 37 students in Math 6 last year) and x square units of floor space, my creativity is stifled.
Work with whatever space you have. Push the desks together, pull them apart. Kids don't mind sitting on the floor. (If they do, ask them to stand and see if they like that better.) Can they work in the hallway — or outside if you're in warmer climate — where you can see them from inside the room? Just make sure you are constantly roaming among the groups.
Big-ass whiteboards. Nathan just wrote a letter asking for these. Last summer I sent my principal the link to Frank Noschese's post — and the whiteboards were waiting for me when school started. I got ten 2' × 2.6' boards, each at $10.50 from here. Please get them. By far the single best school purchase, worth their weight in gold. Just how much do I love these? You touch my whiteboards, I'll kill you.
Randomly assign kids to groups. We do group activities often enough that eventually pretty much every kid ends up with somebody new in the group. If you try to group them "heterogeneously" with high-medium-low kids, then you accomplished just that — you just told them who's high, who's medium, and who's low without saying a single word. Kids aren't stupid. I use Instant Classroom to randomly assign. You can always use your discretion to change a few kids around after the computer picks them — but still let the kids think that the computer did all the choosing. I never heard any whining. Kids don't whine at what the computer says.
Group roles. What are these?? (No, I'm asking you!) Like "facilitator," "recorder," "reporter," "budget person," "dietitian," "hairdresser," etc... These roles wouldn't work with problem-solving tasks. I don't want a kid sitting there doing nothing because it's not time for his role to occur yet. Please, no assigned roles. Except the one about trying to solve the problem.
Grading this type of task. I don't see dead people, but I hear student voices all the time. While I enjoy grading as much as I enjoy poking needles in my eyes, I hold certain beliefs about grading problem-solving group tasks (and the student voices that guide mess with me). And my possible reasons/solutions for them?
It is wrong to give a lower grade because they socialized too much instead of focusing on the problem. (We're teenagers and you expect us not to socialize? OMG! Did she just put me and Joey in the same group? He's sooooo cute. How's my hair? This problem is just too hard anyway! We really tried but we got stuck and you were too busy with another group to help us. Laura is such a show-off. I wish Andrew would grow up.) If the whole group is off task, then I'd seriously reconsider the relevance/engagement level of the task and the social dynamics of the group. It's back to that Step 0 of picking the right task that's engaging and has low entries so everyone can get on board. It's my fault that the kids are not on task.
It is wrong to give a lower grade because they did not come up with the correct solution when the bell rang. (Sucks that we didn't win the game today, but we still had a good game, right? Didn't we work well together as a team, especially on defense? Nice block there, Mitch. I almost had a pick right there if my damn leg didn't cram up! Ha, now I know what Coach meant by the hook-and-lateral play!) Our goal of wanting kids to engage in problem solving is to honor the process that they go through — their thinking, their collaborating, their critiquing one another. We want to tap kids' two most abundant natural resources: their curiosity and their need to socialize. I simply cannot justify putting a grade on this.
But bottom line, you grade it if you want to. Don't grade it if you don't want to. I graded fewer than 50% of the tasks that were done in class last year. When I did "grade" them, I gave full credit. To worry about how to grade group tasks is really to sweat the small stuff. That said, if you had a handout for each student that went with the task, then it's fair to give the individual grades.
Establishing a classroom culture of problem solving and finding time to do so. Stephanie Reilly's question in Part 1 helps me shape what I'm trying to convey in this section.
I can't think of a better day to start doing problem solving with kids than Day 1 of school. Kids pick up on what we say we value and what we do to back that up. Set a goal to do one task every two weeks. Too ambitious? Then once a month. Just please don't give up. On Day 1, I might just start with Pyramid of Pennies (Ha! I nailed the spelling there) or the new Bracelet Craze problem. If I were a student and knew that all my teachers would go over "Rules & Procedures" on the first day of school, then I'd be tempted to feign high fever and induce vomit to stay home.
However, you need to come up with guidelines for group work that you will share with kids before they begin. Culture takes time. It takes a lot of reminders too. I'll share what I say [for guidelines] to the kids under "group time" in the last section of this post about implementation.
Post the strategies for problem solving in your classroom. I have these on just regular size paper, but laminated, and we refer to them all the time. You know, strategies like these ones.
Teacher concern: I'm afraid I don't have time to do this because there's still so much to cover in the textbook. You can't do this and feel guilty. (Remember how crazy in love you are supposed to be with the tasks you choose for them?) You have to be okay with not being able to go cover the textbook front to back. The person who tells you that you have to do so is delusional and mean. Common Core does have fewer domains and standards at each grade level. Spend this summer mapping out key concepts and lessons. I believe in having some sort of pacing guide, but I don't believe in having it dictate how we move through the year — the kids and your formative assessments of their learning should govern the flow. I haven't done research or have hard data of my own to give you, but I believe your kids will do better on year-end assessments if they have been exposed to problem solving throughout the year. Trust me? :)
Carve out time by re-examining and possibly eliminating things that you normally do.(For the last two years our students had two periods of math each day. I think this is going away next year, so I have to re-think this through too.) Besides just having better classroom management — meaning it's not taking you 10 minutes to get the kids to settle down and start class — how effective is your use of class time when you do these items?
Warm-ups
Games
Review games before a test
Pre- and post-surveys
Benchmark tests (beginning, mid-year, end-of-year)
Stuff that kids can do at home blindfolded (I think we know what these are.)
Class parties (What the hell are these? I like parties too, but let's have them at lunch time.)
Lastly, please don't forget that these are perfectly good SCHOOL days for doing mathematics: First day of school, last day of school, last day of the quarter, first day of the quarter, whatever day. The day before Christmas or spring break. The first day back from an extended vacation. Sub days. Your sub is perfectly capable of passing out a meaningful handout (it's meaningful because you made/selected it), and it will go well because you have already pre-taught the kids what's on that handout — give them a sneak peek at it! — and shared with them your expectations the day before you leave. If there's one assignment worth grading, then it's the work that they do while your sub is there.
Finally, implementing the task. Thus far I've covered the behind-the-scenes stuff that was missing from my lesson posts. The task itself is actually a lot more straightforward — pretty much what you read on my lesson posts is my best storytelling of what went on in the classroom.If you're doing an actual 3-Act lesson a la Dan Meyer, then you're good to go! These are some of my favorite 3-Acts that I'd written up:
File Cabinet
Taco Cart
Equilateral Triangles
Penny Pyramid
So, this is an outline of how I implement a non 3-Act problem-solving task.
Ask for a volunteer to read the problem aloud (5 minutes). Each kid gets a copy of the problem to follow along. After it's read aloud, everyone reads the problem again quietly to self. Then my questions begin for the whole class:
What are we trying to solve for in this problem?
What information do we know?
Is there information that you wished you knew? Why is it not given then?
What's the first strategy you have in mind that might help you attack this problem? And why did you say 'do a simpler problem'?
Depending on the task, I've also begun to ask — instead of the questions above — these two questions from Annie Fetter (YES! Please watch the 5-minute video if you haven't.) The kids write down their answers, and I randomly call on them to share.
What do you notice?
What do you wonder?
Quiet individual work time (10 minutes). You have to allow for some individual thinking time. I can't work on a problem when others around me are talking. So I set a timer for 10 minutes. Of course it doesn't have to be 10 minutes, it's up to you and depends on the problem, but this is NOT the amount of time in which I expect any kid to solve the problem. If a kid does solve it quickly, then hopefully you have an extension — you should always have an extension — ready for this kid. If a bunch of kids could solve it quickly, then you've chosen the wrong task, too easy. Back to Step 0.
I say something like, "I'm setting the timer for 10 minutes so you can think about and start the problem on your own. There's no talking and no sharing at this time. You'll get in groups to continue to work on the problem after the quiet time. You're welcome to get up without my permission to get any tools (protractor, compass, ruler, graph paper) that you need. Do you have any questions for me before you begin? Remember our rule of NEVER TELL AN ANSWER. Go!"
While they're working, I use Instant Classroom to form the groups and move some kids around if necessary.
Group time (30 minutes). Again, this is a very generic time allowance. You're the teacher, you'll know by how much to shorten or lengthen the time depending on the groups' progress or lack thereof.
I say something like, "You will now continue to work on this with your group mates. You will use the large whiteboards to show your work. Everyone has his or her own marker to use. But now I'll explain more by what I mean by 'never tell an answer.' If you think you have an answer already from working on it just now by yourself, then please don't share it with your group. Choose to be the last person in your group to speak because I actually need to speak with you first.[1]
... Also, every time we do a task and I hope we get to do lots of them, I ask the computer to randomly assign you in groups, so if you have a complaint, take it up with the computer. If your group would like more individual work time, like 5 more minutes, then that's great and fine by me....
I'm interested in your working together to solve this task. I'm not asking you to become best friends. One person speaks, everyone else listens. Argue about it, but be respectful. Ask questions of one another. Don't take so-and-so's word for it, ask him or her to explain it. Don't let others think for you. Help each other out. Maybe this whole structure is new to you, don't worry about it. I'll walk around and listen in and smack you in the back of the head when you don't quite have it right. Just kidding. Not. Yeah, I'm kidding. Go!"
I actually repeat much of this same spiel throughout the year.
[1] So I talk privately to the student who does have the correct solution and suggest a few things:
Can you solve the problem a different way? (It's important that you do not force a student to find another strategy especially when you can see that she has found the most elegant one already — this just seems counterproductive to me.)
I'd like you to try the extension to this problem. What if...?
I need you to go back to your group and practice really good listening skills. I just want you to listen to your teammates talk. Then see if you can help them by asking questions only. Kinda like what I normally do with the whole class. You may give them one hint if they're really stuck. You want to give that a try?
Teacher role during this group time. This is where the book 5 Practices comes in for me. I've been presenting its contents at workshops over the last two years. There's no way I can do it justice here, and I've already written a brief post on it just as a quick review.
The gist of it is that I go around and listen in and check on the groups' progress. I ask questions of specific individuals in the group.
Hey, Julia, can you explain to me what I'm seeing here on the whiteboard? Maybe you didn't write it, but whoever wrote it, did he/she explain it to you?
Jonathan, I'm not sure where this equation/number comes from. Please explain.
I saw this same strategy at Erika's group. Allie, did you come up with this strategy? If not, what is yours? Where is your understanding of the problem so far?
Joey, what has Cindy contributed to the group thus far? (If Joey says, "Nothing," then I'll ask Joey again, "What have you contributed?" I don't remember ever having two people in one group who have not shared anything. Remember they had 10 minutes of quiet time to work on this already. They have something to share!)
Cole, your group is over here. I don't want to tell you that again. (And I never have to.)
Now, when there's one group that has made a lot more progress than the other groups, I ask for the whole class attention and say, "Julia's group has made an important connection, so I'm going to ask someone from her group to share with the class one hint, one strategy, or one something that would help all the groups along. Listen carefully."
If none of the groups has made progress, then the teacher needs to jump in with a hint. But be patient too!! You have to watch the clock. How much time is reasonable? Are the kids mostly working and asking questions of one another? If they're exhibiting productive struggle, then let them be. Nobody is going to die if you extend this lesson another day.
The SHORT version can end here after the groups have figured out the solution. Maybe not all the groups finished, but remember, most of them did. Depending on the task, depending on the students, depending on time, depending on whatever you deem as important, you can end the lesson here and not feel guilty that there was no large-group sharing at the end, no connections made among the different strategies. Instead, focus on all the mathematics that you did allow the kids to be engaged in. I see enough teachers feel discouraged that they "didn't get to do everything that I wanted to do" — it's not about doing everything, it's about doing something to get started, to get better, to suck less each day, to remember why you went into teaching in the first place.
The FULL version includes the "connecting" piece that the 5 Practices refers to. It's about making connections between the different strategies, and you accomplish this by having the groups share their work on the whiteboards. (This step is moot if the task didn't have more than one strategy.) Kelly O'Shea is my whiteboarding goddess. And connecting is also about you the teacher making the connections of all their work back to the original intended learning goal of the task.
Who says you can't add the connecting piece to your short version 2 or 3 days from now (hell, even two weeks later) and make it a complete kick-ass full version? In real life we return to problems all the time. Snap a photo of each whiteboard if the kids need to refer back to their work at a later date but you have to use the whiteboards for another class in the next period. Problem solved.
You can do this. We can do this together.
Deconstructing a Lesson Activity - Part 1
[I've decided to break this post into two parts because I don't want to bore and/or discourage you, and I need to take a breather. These two posts in particular are truly my labor of love because if there's one thing that I find myself proficient at implementing in the classroom it is problem solving. I hope you'll find some parts useful.
I've done a fair share of posting actual lessons and pictures from my classroom in this space and on my 180 blog [that's no longer available, sorry]. But I'm afraid they appear polished and therefore unhelpful to teachers who are trying to implement problem solving, white-boarding, 3-Act lessons, or any task-oriented activity in their classrooms.
So here's my earnest attempt to deconstruct the structure of a lesson, get down to the nitty-gritty, take small bites (and spit out what you don't like), and make it real because if it ain't real to you, then it ain't gonna happen for your kids.
Some important prerequisites. I need you to have this mindset or else we're not going to accomplish anything.
You care that kids learn something meaningful in the 45-minute period that they are with you. You might be thinking, Of course I care or else I wouldn't be teaching. No, I don't mean that. I mean the "something meaningful" part. What did you intend for your kids to learn today?
You might very well fail at implementing a 3-Act in your first attempt. And fail again and again. But you can't give up. You can't give up because the kids need you to persevere, it's the same MP1 that you ask of them. Cry and bitch about it at home. Adopt a puppy if you live alone. Eat ice cream. Drink a beverage with higher alcohol content if you need to. Get a punching bag or go to the gym.
You need to be okay with leaving some children behind on some days. I'm not a miracle worker. Neither are you. One hundred percent student engagement 100% of the time is a myth sold by the snakes-oil salesman. You can't differentiate every lesson. You can't reach and motivate every child. But you will reach and motivate the ones that you can. You'll die trying because you love these kids, but you're going to realistic about it.
Surround yourself with helpful colleagues. They listen and are willing to observe your class and give critical feedback. They remind you to eat. They eat lunch with you. They don't badmouth kids when their lips are moving. They believe Happy Hour is invented for schoolteachers and feel it's sacrilegious if they went without you. The toxic people in your life can just piss off. If no one is around and you really need to vent, please email me at fawnpnguyen at gmail dot com. I am a much better listener than I am a writer.
Piece de resistance. I carry out the lessons through the lens and language of these bodies of work. It's okay if you don't have the 4 books, but I highly recommend them if your school or personal budget allows.
5 Practices For Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein
Thinking Mathematically by John Mason with Leone Burton and Kaye Stacey
Mindset: The New Psychology of Success by Carol S. Dweck, Ph.D.
12-minute video of Dan Meyer's TED Talk: Math class needs a makeover
Improving learning in mathematics: challenges and strategies (PDF file) by Malcolm Swan
The Art of Problem Posing by Stephen I. Brown and Marion I. Walter (I just borrowed this book from UCSB last week. It's wonderful. Nat Banting reviewed it here.)
Picking the right task. Think of this as Step 0 of the 5 Practices. If I picked the wrong task, then no sound pedagogy or fancy technology would be able to save me. I'm done. Lesson sucks. Game over. That's how important this step is. What is a "right" task?
It's age appropriate. I don't mean for you to go searching under tabs that read "6th grade" or "algebra 1" either. What's age appropriate for your 6th graders might be too high for my 6th graders. Know your kids. An inherently good task would cover a wider range of consumers. If it's early in the school year and you don't know your kids well enough yet, then choose a higher level. It's a crime to underestimate children's mathematical abilities. Dan Meyer speaks volumes about "low-entry high-exit" tasks and Ladder of Abstraction.
It has multiple strategies. At least 2 ways of solving. Single-strategy tasks are like culs-de-sac. There's nothing to do except to turn around. Think how fruitless and boring it would be if you asked kids to share their different strategies and there wasn't one to begin with. Also, just because you'd struggled with a task does not necessarily mean all your kids will. Maybe there was a more elegant solution that you did not see. Be humble, ask another colleague or throw it out on Twitter for others to give it a try. (Please tell me you have a Twitter account. Mine is @fawnpnguyen.) And if your gut thinks there's another way to solve a problem, then be honest with the kids and say exactly that. They'd be thrilled to death to learn that they'd helped you see something differently. My favorite moments for sure.
You are crazy about the task. I can't speak for what tasks/problems turn you on, but I know what my favorites are. (And every.single.time we do a new task, I half-jokingly say to my students, "This one is my absolute favorite!" The kids roll their eyes at me, but they know I'm passionate about it.) It's hard to get kids to like things that we ourselves do not care much for. That's kinda fraudulent. I'm be a big fat liar if I say that I like all the tasks Andrew and Nathan have on their sites. Your chosen task is your baby — you've personally nursed and nurtured it. Kids sense this and they'll handle it with care too.
Throw a curve ball. Meaning offer a task that does not line up with your current topic right now. I know this sounds strange. (I've never read or heard anyone else suggest what I'm suggesting). Normally teachers look for a task that lines up with what the kids are learning. Sure, I do these "tasks" too, but I really call them "exercises." Exercises help you practice the skills you're learning. The tasks that this post is referring to are problem-solving tasks, and true problem-solving has no prior diagnosis and certainly no given prescription. Don't do Taco Cart right when you're teaching Pythagorean Theorem. Unless you want to do it as an exercise, then sure, go for it! The beauty of this is you can reach into your folder of best tasks, close your eyes, and pick one! Be a rebel, break the rules. (Don't forget it still has to be an appropriate level task.)
Custom tailor the lesson. This is hard work. I don't care if His Holiness the Dalai Lama himself wrote the lesson, I still need to tweak it so it works for me and my kids.
Great lesson but terrible handout. I see this all the time. Take the time to re-type it. Is there wasted space or not enough? How's the font size, the heading, the outline? Can you improve on the graphics? Are students asked to work on page 2 but keep having to flip to page 1 to see the sketch or data?
Do you have to pass out the handout at all? How about starting from scratch as in having the kids take out their own paper to create data and meaning for themselves? Remember that any question that appears on a handout may potentially rob a kid's opportunity to ask that question for herself. There are certainly good handouts that have just the right amount of information and provide easier access points for kids. Please create them.
What level of technology is involved? Disaster abounds when an activity requires at least 15 computers and you only have 5. Adapt it or scrap it. No more than 2 kids should have to share a computer. Will the server crash if everyone got on the system? Did you review the YouTube video for all the potential peripheral garbage and comments that might be on there? To be safe, how about you projecting the video from your teacher computer instead? And I need to add here that I beg you not to incorporate technology into a lesson for technology's sake. Technology should enhance the student's learning. A shitty lesson on the interactive whiteboard is still a shitty lesson.