Where were we?

or

Why teachers ought to use re-caps instead of warm-ups

With the exception of news and sports, I rarely watch live television. It is just so much more efficient to use our DVR to record a show and then fast-forward through the title footage and the commercials. There was a time when I also skipped the re-caps that started each show - until Lost.

What I came to see was that these re-caps offered more than a simple review of what had happened previously in the story. The information provided at the beginning of each episode was meant to prepare me with what I needed to know to understand what was going on. It highlighted certain points that I might have missed or dismissed as unimportant. At times, it also foreshadowed a plot point that would be uncovered in the episode; this helped me to see the story as connected (and gave me the feeling that I had solved some puzzle). In other words, it got me to engage at a deep level.

This is what I want to happen at the beginning of my lessons. Instead of spending time on a typical warm-up, I want to use a re-cap that highlights what is important and foreshadows what is coming up in the lesson. We know that learning is supported when it builds on prior knowledge and is seen as fitting into some larger structure (How Students Learn). In The Teaching Gap, there is a description of how a Japanese math teacher uses something similar at the beginning of a geometry lesson:

One lesson ... began with pure memorization. The teacher asked students to recite three properties they had learned already about parallelograms ... As it turned out, the three properties they had just memorized were the key pieces they needed in order to work out a proof. Most students were reasonably successful. (pp. 75-6)

As Hattie points out that, "Too often, students are asked to relate and extend with minimal ideas on which to base this task - leading to impoverished deeper learning. It is for this reason, the workshop model puts such attention on the Schema Activation phase of the lesson and why a traditional warm-up does not cut it.

If professional storytellers understand the importance of activating the schema of a viewer (just look at the number of shows that use re-caps in the video below), then why don't educators make better use of this approach?

Here is where I need your help. What would a re-cap look like in a lesson? Is it the First Act in the 3 Act framework (or perhaps Act 0)? Maybe it is student-work or video of students doing work collected previously that the current lesson will build on. Could it entail students developing a video at the end of a lesson synthesizing what had been done that could be shown during later lessons to provide a reminder of important information that relates to new content?

What do you think?

Where does it hurt?

Me: (after a fairly lengthy description of open questions) So what did you hear? What are you thinking?

Teacher: (long pause) I don't know what you want me to say.

Exchanges like this happen more often than I like. People have been trained to believe that when a teacher asks a question, he or she is looking for a particular answer. We want to be good students which means providing the expected answer. It reminds me of a book discussion on Diane Rehm about how patients and doctors fall into a routine that can result in mistaken diagnoses and unnecessary tests.

Proud parents with Dr. Hilary at MSU COM graduation

This book came to mind when the teacher responded as she did. You see, I have tried to get in the habit of asking questions I do not know the answer to; it ensures that I avoid falling into an educational rut, and it makes my job as a teacher much more interesting. I tried to explain to the teacher that my question was an attempt to gather some information about what she had attended to in order to make a decision about our next steps. I said something like, "Think of me as a doctor trying to make an accurate diagnosis of your 'health' in regards to understanding of this topic. It's like I'm asking, 'Where does it hurt?'" She laughed and then went on to describe what she had understood about open questions. As the discussion went on, I would stop every now and then to ask, with a smile, "Where does it hurt?"

This is one of the ways we might use warm-ups more appropriately (see last week's post for my perspective on this problem). We could treat it as a way to diagnosis the readiness of the learners to move on or determine what issue we might need to address. (Here is an example of the latter.)

I saw an example of this earlier in the week. Students worked on some scale drawing questions, and after giving the answers the teacher asked if there were any of the questions students needed help on. A student called out a number. So far, so good. However, instead of doing more of a diagnosis, the teacher fell into the rut of showing the student how to find the answer. After a couple of minutes, the teacher stated, "That means the answer is 1/2 an inch. Okay?"

Fortunately, the student responded, "So 6 centimeters, right?"

Now the teacher could do an accurate diagnosis. The problem was not in finding the answer - it was interpreting the answer. "This is 1/2 an inch (holding his thumb and index finger close together). 6 centimeters would be more than two inches (expanding the distance between his thumb and finger). I wonder - were you thinking that 6 inches is half of a foot, so half of an inch is 6 centimeters? (She nods yes.)"

How often do we jump into treatment before doing an accurate diagnosis? I know that it seems inefficient to spend time listening to the student explain "where it hurts," but is it? Drs. Kosowsky and Wen found that it was important for physicians to take more time listening to their patients in order to get their diagnoses and treatments right. The same could be said for teachers.

Am I getting warmer?

In The Teaching Gap, Stigler and Hiebert examine the details of typical lesson designs found in German, Japanese, and U.S. math classes from the Third International Mathematics and Science Study (TIMSS). A table found on pages 30 and 31 describes three specific lessons and notes whether or not each lesson's features represent the overall teaching in that country. The U.S column looks something like this:

• Teacher asks students short-answer review questions. (Typical to begin with "warm-up" activity.)
• Teacher checks homework by calling on students for answers. (A common way to check homework.)
• Teacher distributes worksheet with similar problems. Students work independently.
• Teacher monitors students' work, notices some confusion on particular problems, and demonstrates how to solve these. (Typical for teacher to intervene at first sign of confusion or struggle.)
• Teacher reviews another worksheet and demonstrates a method for solving the most challenging problem.
• Teacher conducts a quick oral review of problems like those worked earlier.
• Teacher asks students to finish worksheets. (Unusual to not assign homework.)

My work with teachers brings me into a lot of secondary math classrooms, and I can say that not much has changed in the typical math lesson since the printing of The Teaching Gap in 1999. However, I want to focus on just one aspect of the U.S. lesson, the warm-up.

Because of my own interest in engagement, teachers often ask me to focus on when students are engaged (or on-task) during a lesson and what to do when they are not. Probably the most off-task period during many lessons is the first part of the lesson, the warm-up.  This might be for any number of reasons but I have a few ideas.

First, the students find little purpose in this activity. It is rarely collected, usually graded only as a consequence for causing a disruption, and often disconnected from the overall lesson. Without some purpose, it is difficult for students to engage in a task.

Next, there are times when the task is an extension of current work rather than a refresher. It would be like running a race without warming up. Consequently, some learners do not see themselves as having the potential to be successful with this initial task - a tough way to begin a lesson.

Finally, by sixth grade students are familiar with the design of most math lessons. They know that someone will at some point provide the answers to the warm-up. So some students do not work on the warm-up (off-task) but copy down the answers when they are shared (on-task). Others, work on the warm-up (on-task) but pay little attention to the answers because they already have them (off-task). Either way, this seems like an inefficient way to start just about every lesson.

What do you think? Have I accurately portrayed what is going on during the warm-up in many math classes or is this a straw man? If you agree that the warm-up is in need of a makeover, then perhaps in a future post we can discuss the alternatives. Otherwise, I do not want to waste your time any further - going over something that is not really a problem has no purpose and does not make any sense to me.