Should I use elimination or substitution?

Be forewarn, this is probably not the post you are looking for.

A teacher I was coaching sent our this tweet after a recent observation. The class was looking at solving systems of linear equations using elimination and substitution and we had talked about how he could use data from recent Big Ten basketball games to set up scenarios that might encourage them to use the different techniques. Early in the lesson, several of the students (the class is all boys) made it clear that they were huge basketball fans.

Here are a couple of examples I came up with:

Against Wisconsin, Trey Burke scored 19 points. He made 1 free throw and 2 three pointers. What would his box score look like for scoring?

Trey Burke scored 18 points against Michigan State. He made 1 free throw and 7 shots from the field. What would his box score look like for scoring? 

Christopher Danielson has thought more and deeper about this topic than I, so I defer to his expertise (here). Sorry for the bait-and-switch, but I want to think about how this experience helped me to re-evaluate my homework policy.

About two years ago, I wrote about how overwhelmed our novice teachers are during their first teaching experience. We do this somewhat intentionally so that they can experience firsthand all that is expected of teachers, and so that they can become better at managing their time. Part of that time-management is learning to prioritize what is important and learning how to say, "No!" -- in other words, elimination. (I know that we aren't talking about mathematical elimination anymore, but this is where my mind goes. Pity my wife and my co-workers.) In that post, I went as far as to say, "It is okay to skip this assignment."

Looking back, I think that suggesting this technique, elimination, was a mistake in this situation. Simply skipping work does not match the reality of teaching. In order to prepare them for that reality, what I want them to be good at is substitution. If something else on their plate is more important than one of our assignments, then they ought to make a substitution. However, as they do their other work, I want them to recognize they are doing it on our time and look for ways to synthesize the concepts and skills we have been exploring into their "more important" work. Hopefully, this mindful effort to synthesize across classes will provide practice in attempting to meld ideas in their teaching practice.

Again, my apologies for bringing you here under potentially false pretenses. And for making you wade through the ramblings of my mind. As I tweeted Christopher recently, I need an editor. If you have your own thoughts, please add them to the comments.

What did we learn?

At the end of each semester, I try to make sure that my learners have time to reflect. If their learning is to last, then they must have a chance to consolidate it. This past semester I used three workshops to support their efforts to look back and look forward.

The first workshop asked the learners to focus on the course objectives.

They identified those in which they considered themselves proficient and what contributed to their proficiency. So much occurs during a semester and too often learners do not recognize what was learned. This task represents a metacognitive activity that makes it more likely that the learners will be aware of all they have accomplished. It also provides me with important assessment data that will inform how I teach the course in the future.

In the next workshop, learners write letters to future students as a way to prepare and encourage them to be successful in my course. Here are two from this semester:

I will share the letters with future learners because people often accept advice more easily from their peers than their teachers. This is not the sole reason for the activity, however. It also provides the letter writers with the chance to reflect on their own growth as learners over the semester. I hope that both current and future learners will benefit from this wisdom borne out of experience.

The final workshop asks them to create a 3 minute (or less) TED Talk about what they have learned this semester. This year I found out the power of showing the Student vs Learner clips early on. Many of them commented on how these videos helped to frame the entire semester. I will now try using them the first day in all of my courses.

The presentations are ungraded and usually very informal. Amazingly, this sometimes leads to more preparation on the part of the learners. Regardless of the time they put into them, I find their sharing to be quite profound and at times moving. Here is an example from this semester:

I remember teachers saying to me, "You'll thank me for this later." This typically accompanied some particularly distasteful tasks. I bristle at this notion and hold the belief that I am not in this for people's thanks but because I believe in what I do. Still, I hope I am getting better at accepting people's gratitude as well as their criticisms. After all, both are a part of the learning process.

Is it okay to skip this workshop?

Grand Valley’s teacher preparation program is fairly unique; it has preservice teachers engage in field placements over two semesters. The second semester represents a typical student teaching placement. In their first semester, preservice teachers spend the morning assisting in K12 classrooms and their afternoons and evenings taking seminars in classroom management, content literacy, lesson study, and content methods (in the case of secondary teachers). It is this last seminar, math methods in secondary classrooms, which I currently teach with my colleague John.

The seminar meets once a week for two hours. We use a workshop model (similar to the approach used in literacy instruction) for both class activities and home assignments. Our expectation is that the teacher assistants will put in five hours into the home workshops.

We recognize this is a lot to ask of the teacher assistants (TAs) and begin the semester acknowledging the fact. The idea is that providing too much to do will help them to learn a valuable time management skill – prioritization. I like to think about it using Covey’s model related to urgent-important activities. Unfortunately, while we offered the rationale for giving too much work, support was lacking. I will do this better next time.

Consequently, some TAs shared that they were close to the breaking point. In an effort to address the issue, I sent them all the following email. I wanted to share it because I believe it addresses an issue many teachers struggle with.

It was brought to my attention today that many of you are stressed out. Now this wasn’t a surprise to me as this is a packed semester, and teacher assistants often find it overwhelming. However, the extent of the stress (including physical symptoms) and the cause of the stress (our five assigned workshops) are concerns to me.

We began the semester telling you that we knew we were asking you to do more than you could in the time available. This was an intentional decision in an effort to prepare you to make critical choices as to how you spend your time as a teacher. We wanted to provide a safe place where you could practice making those choices by prioritizing what is important to you and your learners without fear of punishment.

The choices you make also help us to determine which workshops are meaningful to you and which you consider unimportant. It actually helps us in subsequent semesters to select workshops to assign. Essentially, we are trying to put Conditions of Learning (such as responsibility, employment, and approximation) into practice in the seminar.

You all are successful students, however, and some of you are finding it difficult to skip a workshop. The mere thought of it brings on stress and anxiety. You skip it because time does not allow for it but you feel no sense of accomplishment or growth as a decision-maker as a result. These unintended consequences are not acceptable and must be dealt with immediately.

I do not want to reduce the workshop load since this ignores the realities of the time commitments you will face as a teacher. But that means there is still too much to do. So, from here on out, if you need permission to skip a workshop, please do not hesitate to email me. I will do my best to absolve you of any guilt you may feel for not meeting the expectation. Be assured, if I think skipping the workshop is not in your best interest I will be direct about it. Otherwise, I plan on affirming your decision and letting you move on to more important things.

Hopefully, as time goes on, your sense of guilt will lessen and you will find your need for reassurance to diminish. I will try to do my part by adjusting my responses from, “It’s okay to skip that,” to “I trust your judgment,” to “You know what you need to do.” Because I do trust you and believe that you know yourself better than anyone else.

In times of stress, I have a friend who reminds me that everything that NEEDS to get done gets done. The important part is to realize that there is more that I might WANT to get done but time doesn’t allow. And looking back on my life, I see that my friend is right. I have had to make some hard decisions and turn my back on certain opportunities, but in the end everything that needed to get done got done in order for me to get to this place. It is my hope that this is a lesson you’ll learn and remember from this semester.

Peace,

Dave

I am passionate about this issue of making teaching and learning sustainable. Partly, it is because I see how hard my wife works as a first grade teacher. It also stems from memories of my mom (also an elementary teacher) responding to my questions about what she wanted for Christmas with, “Two more hours in everyday, two more days in every week, and two more weeks in every month so I can get everything done.” My dad, a high school math and science teacher, also worked hard but he suffered in silence. Mostly, I am passionate because I see committed and competent preservice teachers facing a system that chews up and spits out new teachers.

So, I offer the preservice teachers I work with absolution for their perceived sins of skipping a home workshops. In other words, I offer them permission to prioritize what they spend time on during their five hours of out-of-class. It can even be something other than the assigned workshops if it makes more sense to them.

Recently, I found that affirming preservice teachers’ critical thinking skills extends beyond homework choices. During a debriefing after a coaching session, a TA asked me about an upcoming lesson. The TA wanted to know if it was alright to skip a particular topic because of a time crunch. Before I could respond, the complete rationale for the choice came out. I smiled and said, “It sounds like you already know what to do. Are you asking my permission?” The TA responded with a nod. I assured the TA that it seemed like a sound decision.

What kind of educational system have we created where intelligent people do not trust themselves to make good decisions?

Not that you need it, but you have my permission to prioritize. You have my assurance that you can make good decisions. And you have my appreciation for the hard work that you do?