Reading this really encapsulates my first year of teaching. More so with my pre-calc classes (as they are 11th and 12th graders), but with most students it’s a similar response of my breaching of their contract.

It was interesting too because I think that deep down most of them felt that what I was doing should have been started when they were younger, and at this point it’s too impractical for them to change.

Hopefully the teacher they have next year will be met with students constantly questioning the theorems and properties being presented to them.

This post exemplifies why I am such a fan of this blog; you look a prevalent attitude right in the face, and not only refute it, but specifically deconstruct the tacit assumptions that underly it, and give concrete steps with which a reflective practitioner can attempt to improve the learning experience for his or her students.

In teaching my Discrete Math class this term, I continually encountered the attitude among my colleagues that ‘the course would be so much fun if you only had the right students’ – a reference to the unfortunately labeled ‘Lower Third’ students I was teaching. I would love to put a copy of this post in everyone’s mailbox. Even with my more motivated students (whose motivation often takes the form of copying down every word on the board rather than active participation), getting them to ask questions (and sometimes even to answer them) is like pulling teeth. I have recognized that my practice currently might not engender the type of participation I would like to see. Thank you for giving concrete rationales, suggestions and steps I can take to create an active classroom environment. It’s great to end the year with such a powerful clarifying strategy.

May I suggest an addition to your “acclimate your students” bullets that takes the “didactic contract” head on.

Next year …. plan a week one that sets the tone for curiosity, inquiry and a routine to come. Make it so grand that it competes with the novelty obsessed brain and show your students that you are not adverse to taking risks in the pursuit of learning. (In other words – Take what they expect from a math teacher and turn it upside down.) Have your students actively participate in the grand lesson based on a human condition and then don’t give them the/an answer (hook) until they beg for it?

Perhaps you could:
– Turn your classroom into a cave with themes to discover throughout the year (time, scarcity)
– Teach a class on top of the school building (fear, perception, novelty)
– Perform a funeral with a real coffin that promotes the death of all they have ever known about Math (mortality, time)
– Speak in a language that does not exist or that they do not totally understand for a period of time (linguistics, culture, humor)

Educators may not like the fact that they have to compete with student life and new “shiny” object engagement but the reality is they do (frankly, I think they always have).

The very question you were asked in Edu school still exists: Is teaching an Art or a Science? In a differentiated classroom it most certainly has to be both and Dan you do a fantastic job articulating and modeling it.

Keep up the great work!

I completely agree and want to piggyback on @richkonar’s mention of class culture and how students will engage when their teacher is engaged and enthusiastic. We can take another teacher’s lesson and imitate/modify the delivery of the lesson, but we can’t imitate someone else’s passion and enthusiasm and humor.

My responses to the 4 groups “secret skepticisms”:

1) “This process assumes every student wants to learn or has the motivation to learn.” — And it’s a great assumption because I shouldn’t be in this business of teaching children and NOT believe that some do not want to learn. A few kids might prove me wrong, but hey, I tried and succeeded with the other 30 kids. I’ll try again tomorrow with the ones I couldn’t reach today.

2) “How do I get students to buy-in when they struggle with any problem solving skills at all?” — Yep, these are SKILLS, and skills can be taught, modeled, nurtured, honed. Find great problems that encourage different types of problem-solving skills. Help them build up their strategies toolbox. Then give them opportunities to re-use some tools, tuning their tools, use a combination of tools. Invent a new tool. Start from Day 1. Oops, didn’t get a chance to start this and it’s April? That’s okay. Start today.

3) “What if my kids don’t know enough math to be engaged?” — Is the task level appropriate first? How much scaffolding can I provide? Low entry – high exit. Dan said so.

4) “This approach is very compelling but this lesson will have additional challenges with students who could care less about getting involved. It is difficult getting any engagement by students who have little interest.” — See Skepticism #1. Teacher’s genuine enthusiasm is huge and contagious.

Thank you, Dan.

If this post had its own “secret skepticisms” section, you might see something like

“This post assumes that every teacher wants to learn or is motivated to improve their practice“

Mike, great thoughts. Patrick, that made me laugh.

From Dan’s qualifying paper:

“Thus, teachers are sympathetic to the distortion because teachers will suffer the immediate consequences of students who are unconfident or disruptive.”

Some teachers, teachers in the aggregate, all teachers?

I think some are sympathetic to the distortion because they see it as a scaffolding tool. We’ll focus first on how the data and procedures interact, then we’ll take away some data, then we’ll take away recommended procedures.

The struggle of not knowing where to begin, although intuitively appealing, can be destabilizing and counterproductive.

Your didactic contract reminds me of the “correct answer compromise” that Howard Gardner writes about so eloquently starting on page 141 in his 1991 book the “Unschooled Mind.” He talks about it in this interview:

http://bit.ly/196g7Q9

I’ll admit right off that I’m not a professional (schoolroom) teacher, although I do a fair amount of coaching of youngsters who are struggling with chemistry at school.
The ones who seem most in need of help are the ones who feel out of their depth because they’ve “lost the plot” – they haven’t been helped to see the bigger picture, the aim, the use, the goal of the nuts-and-bolts stuff. They become frightened of the subject and consequently afraid of confronting their struggles.
My experience is that if you can just get some confidence back, then the light will start to come on and they go forward.
My apprehension with the approach you describe here is that there is a danger if you keep on asking questions, the student will keep on being challenged by their inability to answer – in a nutshell it’s confidence that’s the problem, not lack of curiosity.

Thanks, Dan, for the link to the estimation180 project. My department has been doing a “lesson study” type PD this year & we focused on estimation strategies. This site is the perfect link-up with the work we’ve been doing.

I think Patrick has hit the nail on the head.

We know that there are ways to re-engage students with thinking and learning in the mathematics classroom, and I suspect we will find that the essence of these approaches will help teachers become re-engaged with the act of teaching and learning.

It’s not that teachers (or students) are unengageable, it is that they are not currently engaged, or that they may be fervently engaged in practices which are poor pedagogical practice for their students.

Hi Patty.

I do Barbie Bungee to breathe life into y = mx + b. When we graph drop height vs # of rubber bands, we get to ask why is the graph not at (0,0) and kids will tell you that her height alone is the y-intercept. We get to ask about what things are changing, and they get to tell you that as they add each rubber band, the drop height increases. Slope now means change — a positive change that they were manipulating with.

Then you give them more examples: like club membership dues where there’s an initiation fee plus the monthly fee, like renting something that charges an upfront fee plus an hourly rate, like the plumber who charges $60 just to show up at your door plus $40 per hour of work thereafter. Have them look up bowling and skating fees, iTunes downloads, cell phone plans, etc. Get them to write equations for these situations instead of the other way around (equation is given and they just plug and chug). Get them to do this in a spreadsheet so they get immediate feedback if they’d written a correct equation.

I love that you said, “If I had had to sit through 180 days of my class…” This is how I plan my lessons, Patty. I have to become the student to figure out the level of engagement and get the most bang for the buck. Their attention span is limited, time is limited, resources are limited — but being mindful of these constraints each and every time we design a lesson will help us get better. I suck at one lesson one period, but I nail it the next period. I suck for half a day, but the next day I’m feeling pretty good overall. Teaching should be a constant flux of learning for teachers.

Building upon a short conversation that started on Twitter, http://bit.ly/19zwtU5, what you write about here could very easily be applied to so many other disciplines in school.

The broad take-away that I have comes from the need to foster a student’s sense of curiosity as a natural habit of mind. Curiosity, however, expands beyond just math class, just as math expands beyond the mathematics classroom.

As I read this post, and the links that go with it, I started thinking about connections to student-learning opportunities across their educational course load. Some of them are shared below:

– Consider how you could rewrite the rest of the paragraph beginning with, “After years and years of associating “math class” with a narrow range of skills…”. if you swapped out the course for another subject. What are the narrow skills? What deeper cognitive processes would you use? You could argue that abstraction, argumentation, criticism, formulation, and modeling fit into other disciplines. It isn’t much of a stretch to see this in broader course spectrum.
– The “didactic contract” link focuses on mathematics education and constructivism, but inquiry is not exclusive to math. Inquiry can be used in all disciplines.
– The contract has probably been signed by more than just math students and math teachers. You describe a classroom routine of teachers giving out information and then students regurgitating it, that (sadly) is a pretty familiar way of doing business in other subjects as well.

While you might have been writing specifically about mathematics, you have brought up a pedagogical idea that has a much larger reach than just that subject. Re-reading this post through a lens associated with a different content area, would be an excellent exercise for administrators and non-math teachers that are looking to examine the learning that takes place in their schools.

Thank you again for a great post!

Great post! It’s invigorating when you post about these experiences and provide high caliber content, persuasive arguments, and strong reasoning for 3 Act lessons.
This 2012-13 school year was the first year doing 3 Act lessons all year and I found that starting early on in the year created a curious classroom throughout the year. Modeling curiosity and “what questions do you have” are key ingredients that all teachers (of any subject) need to be reminded about. I feel I should put that in a visible place everyday as I get ready or prepare for my students. The more you can do this, the more mileage these 3 Act lessons will get and I truly enjoy getting questions from students because they give me ideas for additional tasks. The challenge is circling back to all of those questions posed during Act 1. That said, Dan mentions “sincerity” quite often. I agree and need to practice it more. Be sincere with your students or all is lost.
Lastly, I started 3 Act lessons in February of the 2011-2012 school year and it’s exactly what my students, class, and teaching needed. There was no turning back. I cringe when I hear teachers put up barriers.
You were meant to do what you’re doing!

Don’t discount those unmotivated ones. We do final exam essays and there was one student who I knew had potential, but who I also knew had big problems happening in his life. Most days he kept his head down and did nothing. Homework, never saw it. Assessments, he would get a range of 60-70%. His essay, wonderful. He started by saying he was sorry and sharing more than he’s told anyone. Thanked me for proving to be funny and caring enough to give him pause over what he had considered doing numerous times. He gave specific lessons he found engaging, even though he personally didn’t engage. He shared that he was doing better and wanted more henceforth and he promised to start with my final in 2day’s time. He excitedly, not a word anyone would use with him, turned in his papers and they were among the best in all my hours…and once again there was a thank you attached.

Even if they are not buying in, don’t forget they are watching and learning. Took 180 days, but I reached him… I am not sure of exactly when, but I now know I did it…

Scott

This is it, the unspoken barrier preventing forward movement in my school. So much easier to blame the kids than take a hard look at your class and admit that, when it comes down to it, it just isn’t that engaging. I’ve been there.

My goal for next year — take what I’ve been reading here and attempt to implement it in my world history class — and talk with my colleagues to build a shared language of analysis and abstraction we’ll use in several departments: social studies, math, science, ELA. I appreciate what Jim Tiffin said above and believe that we secondary teachers have more in common with each other than is commonly recognized. Why do we spend our limited PD time in department meetings? My students don’t take six history classes, why shouldn’t I be talking with the math and science and English teachers?

My question for the group: who is the Dan Meyer of social studies? I found this blog about a month ago and have slowly been working through the archives. There is a gold mine of ideas here (thank you for your 3 Acts, they saved my 12 year old’s interest in math after a year of worksheets at his school) but not all of it applies outside math instruction. As a social studies teacher, who should I be reading? Who do you read?

Bruce

The teacher needs to own the responsibility for outcomes in the classroom. Period. That doesn’t mean you’ll always be successful, but it does mean that to the extent you fall short, your reflection should be, “I KNOW there is something I could be doing differently that would work. What is it?” and not “See, these kids just can’t do it.”

That said, I think there’s another way to interpret skepticisms #2-3, and I think it gets at a question I have had for a long time about Dan’s teaching philosophy: do students turn off primarily because they’re not interested in what you’re saying, or because they don’t understand what you’re saying and hate feeling dumb? Put more simply, when students aren’t engaged, is the root cause more likely a cognitive factor or a motivational factor? Of course, either problem can lead to the other–if I stop listening because I’m not interested, eventually I may start feeling dumb because I don’t understand (and vice versa).

But which is primary? Does it depend on the kid? Does it really matter which is primary, or the solution the same regardless–either get the kid interested first (if you’re in the motivational camp), or make them feel successful first (if you’re in the cognitive camp).

I’d add to the “steps we can take to acclimate our students gradually to new ways of learning math” this:

Corny as it sounds, don’t give up. The first and second and tenth attempt at -whatever it is that’s a very different approach in your class – a 3Act, a project, a whatever it is — is probably going to either fall flat or fail spectacularly. The kids might get mad and weirdly uncooperative. Things might happen that you didn’t anticipate and don’t have the skills to handle. You aren’t going to get good at planning them until you get some experience planning them. You’re going to suck at this for a while.

The worst thing to do is freak out because you think no one learned anything and go back to your comfort zone. If I hear one more time “Oh I tried something like that once, it was a disaster, so it’s not for me or my kids,” I might pop that person in the mouth. ONCE? Weak. So weak. Stop freaking out. Notice and celebrate little authentic victories over broad, superficial ones. Don’t try to do something radically new every day — pick a thing and do it once a week for a whole semester. You need to keep stretching the rubber band over and over until it loosens up and doesn’t snap back all the way.