pedagogy – Page 3

My hope for group work…and introverts

crowd-of-people

Lately I’ve been thinking about group work.

This past spring, I reached a point in a lesson where I wanted students to work together on a few tasks. Prior knowledge was there. Things were accessible. Heterogeneous groups abound. All the standard stuff. There was no reason why the kids shouldn’t have been good to go.

What did they do? They waited for me. They couldn’t get started without me but, even worse, they couldn’t even use one another to get the ball rolling. Despite being more than capable, they wanted me to feed them…again. I say again because this was a fairly common theme all year. It just took this particular lesson for it to hit me.

Realizing this, I didn’t want to lecture them on how I knew that together they could accomplish the tasks I set forth. So I sat on a desk and stared at them. The result was a bunch of concerned faces asking me why I was so quiet. I responded with silent eye contact to each and every one of them. It took a full three minutes of awkwardness before they pieced things together. Oh, he wants us to figure this stuff out.

In the moment, I was really disappointed with them. I was borderline furious. I overplan my lessons, pour growth mindset into them all year, and live with a low floor and high ceiling. Yet why couldn’t they work together, independent of me?

It didn’t take long for me to realize that I was the culprit. This situation was a direct consequence of me neglecting to develop a culture of interdependency. Now that I think about it, my classes have been like this for years.

Next year I am determined to get out of the way. For everyone’s sake, my students must need me less. I want group work to be the norm. A successful mathematics class is dependent on communication and inquiry – both of these are byproducts of collaboration.

I’m still finalizing a structure, but thanks to a workshop by Phil Dituri, I have some tentative group norms that I’ll use next year.

If you have a question, ask your group before asking me.
If someone asks a question, do your best to help that person.
It is the responsibility of the group to ensure that each and every person in the group understands the task at hand.
If you finish and check your work, you should ask others in your group if they need help.
Discuss different answers and try to agree on one. You should be able to explain your group mates’ solutions as if they were your own.
No talking to other groups.

It will be challenging to develop these norms with students that may not understand how to work together effectively. There are strategies that will be helpful in the process, but I still may have to start with one or two at the beginning of the year and build on those.

I want my students to value collaboration and learning from one another, but there’s another aspect to this talk of group work that’s worth noting. It’s the societal belief that collaboration is the root of all things great and that everyone must collaborate in the same way. Susan Cain argues against this mantra in her book Quiet and I agree with her. She calls this the New Groupthink because it “…elevates teamwork above all else. It insists that creativity and intellectual achievement come from a gregarious place.”

This line of thinking is a huge disservice to our introverted students. I bring this up because of my own introverted tendencies, like preferring one-on-one conversations over group discussions, enjoying listening more than speaking, and leading in non-traditional ways. The need for some students to think and work in solitude is something I get. It’s how I’m most productive. Reading the book was like uncovering so much of myself.

Studies show that one third to one half of us are introverts. The class I mentioned was full of introverts and they needed a structure to work together. I hope that my system encourages collaboration and interdependency while addressing the needs of all my students, but especially my more introverted ones. My norms won’t be a saving grace since research advocates for other strategies to support introverts – such as small groups, individual think time, and supporting individual passions, all of which I could improve upon. But hopefully my group norms help to celebrate introversion and make it easier for students to rely on one another as opposed to me.

When we’re afraid of results

Is it possible that a teacher could be subconsciously afraid of what formative assessment could reveal about student understanding and, as a result, not do it?

I know I’m guilty of this. Especially early in my career.

Looking in the mirror is hard. After hours of planning I’m supposed to accept the fact that my thinking was flawed or incomplete? I’m supposed to realize that my students have not met the objective(s) of the lesson? I’m supposed to openly accept that it’s back the drawing board? For reflective teachers, the answers to these questions are welcomed as a means for growth, but still not always easy to accept.

To this end, it’s easier to get a “feel” for the learning happening in the classroom rather than to strategically measure it. We subconsciously fear that crushing moment when the lack of learning is exposed, so we evade it. We fear a reality that harshly contradicts with our own expectations. We fear what these humbling results echo about our planning and teaching.

I also find that the need to formatively assess is at times disguised by a belief that students should understand the lesson objective(s) based on previous experience or other factors. This, then, somehow equates to implicitly thinking that students are reaching objectives.

This idea came to while speaking to an instructional coach recently and I feel that it happens more often than we think. If we don’t embrace the uncertainty related to students not meeting expectations, if we’re not highly critical of our own practice and willing to accept unfavorable outcomes, then we save face. Things go “well.” We feel comfortable and all of our hard work is justified.

What a tragedy.

Anticipating student responses

A colleague and I recently planned a lesson on developing a need for factoring when solving quadratic equations. It was totally unexpected. He walked into my room after school and we started talking. Two hours later, we had the framework of a lesson.

Two teachers. Two hours. One lesson (sort of).

What struck me was that the bulk of the time was spent anticipating student responses to questions we wanted to ask during the course of the lesson. We went back and forth about the roles of the distributive and zero product properties and how students might interpret these ideas in context. How could we use their responses to bridge an understanding of solving linear equations to solving quadratic equations? We didn’t want to shape how they answered, but simply craft questions that would naturally guide them to worthwhile discussions and new understandings. Whatever question we toyed with throughout the two hours, it always came back to the same criteria.

How might the kids answer? How will their response draw them nearer to the goal? How can their thinking help the lesson tell a story?

Subconsciously, I think I do this. Just not enough. This experience connected well with the principles of my current book as well as providing me a nice reminder to plan the critical points of a lesson so that they pivot on student thinking.

Questions.

Question More

I’ve realized that it has become a goal of mine to improve my questioning. Here’s some of what I’ve been pondering (and doing) as of late.

1. Asking “what if…” questions. This will usually come into play after we finish a problem. I try to change the conceptual nature of the problem, which provokes students to examine relationships and see the problem under a new context. I also really like giving the students a minute or two to generate their own “what if…” questions about a problem after we’ve found a solution.

2. Asking students to find errors within student work samples. I really started focusing on this last year with my exit tickets, but I’m doing it just about every class. I usually pick up someone’s paper and slide it under the document camera for the class the assess. Quick, easy, authentic. Plus, it creates a culture of identifying and accepting mistakes on a regular basis.

3. I’ve also begun asking students to identify potential errors within problems before examining any sample work. The result is always rich classroom discussion over creatively wrong solutions. The goal is for them to identify both subtle and more serious mistakes that could occur.

4. Having students construct their own questions (that are good). I really need to get better at this. I’ve had some success in the past, but usually when I least expect it. I’m thinking of researching more into RQI to find some useful strategies.

5. The other day, out of the blue, I utilized a “convince me” statement to a student during a class discussion. We were factoring and I proposed a (wrong) solution to him. I essentially asked “why is my solution wrong,” but in a way that felt more like a challenge rather than a question. I felt the power when I uttered it. It probably bled through from a workshop from Chris Luzniak a couple years ago on using debate in math class. He has great stuff.

6. Using questions as a foundation of my class. I want my classroom culture to be one that emphasizes the why behind the answer instead of the answer itself. As a math teacher, I’ve always emphasized work and how critical it is. But I’ve never lived out that creed by how I teach my kids. Trying to change that this year. More to come on this.

7. If one student X makes a statement about something we’re studying, I’ll sometimes turn to student Y and ask them to “Interpret what X just said…”

8. During an intervisitation, the teacher I was visiting posed a question to the class and no one responded or seemed to have a clue. He said “Alright, take 30 seconds and brainstorm with a neighbor about the question.” He waited and asked the question again and there were several responses. This was awesome.

9. The questioning doesn’t begin and end while I’m teaching. I’ve started questioning more of what I plan and structure for my students, including things that I’ve done for years. I’ve put my teaching philosophy under a microscope too. It’s changing. This will have repercussions far greater than any question I could ever pose to a student.