Thursday, December 27, 2012

Becoming "Unflippable"

This post contains no real lesson or task ideas. That is a rarity for me, but every so often a philosophical battle ignites in my brain. More often than not, the question does not come from an established professional development vessel. Our division provides numerous officially sanctioned "PD" events throughout the year. They serve their purpose, but rarely motivate like those questions that come from within--or, in this case, from a student.

Every teacher is familiar with the following conversation:

Teacher: Can you please pay attention?
Student: I was paying attention.
Teacher: No you weren't. Please put your _____ away.
Student: I was so--I have all the notes.

This infuriates me.

It wasn't until a month ago that it dawned on me:

This is what the public thinks I do for a living...

People think my job is to ensure students get the notes. Why else would parents excuse their children from school to go shopping? or make dentist appointments during school hours? or extend Christmas break by two weeks in the Bahamas? Why else would students gauge their "learning" by the amount of times they visit a pencil sharpener? or the number of pages of scribble they manage? Why do they ask,
"What did I miss yesterday?"
and expect to be immediatley back on the class pace. Students have spent enough time in classrooms to get this notion. Those students become parents... etc.

What do we as (math) teachers do to combat this mentality? Mostly--a whole lot of nothing. Our classes remain predictable in nature. Some students even complain when they should be getting the homework but the activity or lecture goes long. We have literally programmed our students. It is in this light that teachers get so offended when websites like the Khan Academy claim to revolutionize education. Teachers hate to think that they are replaceable by a set of videos when, in actuality, many of our lessons are.

Maybe the videos lack the personal nature and opportunity for diversification. But (school) math is very impersonal, and diversification can be achieved through more videos. They also add convenience to the equation. Anytime, anywhere, and at any pace.

The term "flipped classroom" is slowly percolating into the current educational lexicon. The process involves students accessing video lectures to free up class time for different activities. At first I hated the idea. This wasn't changing teaching; it was switching the medium through which the transmission was performed. I pictured class as a time to test examples and do homework sets. 

My perception changed a month ago when I had the following conversation with a student:

Me: Where were you yesterday? You missed my class.
Student: I was sick; I didn't skip.
Me: The motive was different but the results are the same. You need to catch up.
Student: I'll just get the notes.
Me: It is more than notes. You need to understand why and how we do the math. You need to be in class to learn.
Student: Why? I don't miss anything if I get the notes.

This student is right a lot of the time. I do my best to infuse meaningful mathematical tasks and activities into my room. Many of them are scattered throughout this blog. The burdens of time and curriculum force me into corners, and many classes could be easily captured through a video and a set of notes. I realized that if I wanted students to value the class time, it had to be in a classroom that was "unflippable".

I now gauge my lesson success with a simple question:

Was that lesson unflippable?
Could the students learned the same amount through a video and a set of notes?

These types of questions guide my personal growth as a teacher. They allow me to catch myself when planning gets lazy and when the days get long. Naturally, I have begun to look for ways to free up more time and curricular space for unflippable exploits. Ironically, that has led me toward a flipped classroom model.

Ryan Banow (@rbanow) provides a great starting point here.

Students have responded very well to my Project Based Learning courses over the last couple years. I think the appeal comes in the structure of the class time. Small activities and tasks lead into larger projects; the collegial atmosphere and complexity of the tasks make the process unreplicable through a series of videos and solitary projects. The course is--in essence--unflippable. I am still struggling with the higher-level and increasingly abstract courses. As always, time is at a premium. At least for now it seems like flipping a unit or two may be an effective way to create class time that becomes unflippable.


Saturday, December 8, 2012

My Whiteboarding Framework

This year my department decided to make using whiteboards as formative assessment tools our department focus. This was nice because I had already began to experiment with the process. It just meant that:

  1. I wasn't obligated to try yet another "thing" in my room.
  2. I would be given better materials and funding to work with.
  3. Other math teachers in my building would see the enormous benefits of the technique.
For those of you unfamiliar with the term "whiteboarding" it is very simple. Students are given a miniature whiteboard, a whiteboard marker, and a small eraser. Responses are elicited in various ways from the students--using the board as a medium. There are several ways--and question types--that create different classroom atmospheres. It is my goal, in this much belated post, to detail the three styles of questions that I have used. Each carries with it a specific classroom environment. 

A collection of my boards and erasers
The first style of question I call a Basic Response.
This is a classic "teacher asks, student responds" type of question. Short, sweet, and to the point. The great thing about the whiteboards in this case, is not the fact that they tap deep learning. (we'll see ways for that later). The low floor (everyone can answer), variety of questions (you can ask almost anything), and relative anonymity (takes away from public response) make the response rate close to 100 percent every time.

I have had students place a "?" on their board and hold that up as their response. It provides instant feedback to me about who needs the help--and how badly. I have students turn their boards over and hide their answer. When I see everyone is ready, I ask them to hold up their boards. I collect answers, and we muse on where the mistakes may have creeped in. 

I stress the importance of working individually on these types of questions. Having everyone respond at once cures the "smart kid answers all the questions" syndrome. After an answer is deduced and revealed, I allow the conversation turn to the mathematics. Often times I need to calm down the hum after a question. These types of questions are quick, and easily constructed.

The second style of question I call a Dynamic Response.
This style must include two things:
  1. Student Creation
  2. Student Solution
These questions usually appear in multiple parts. The first step has students create something mathematical according to certain parameters. It could be a set of data with a certain mean, a triangle with a certain property, or a quadratic with certain intercepts. The emphasis is on the creation. The response is dynamic because it involves a passing of the boards. Instead of showing--and getting approval from--the teacher, students swap boards and build, alter, correct, critique, or continue on their classmate's work.

This creation and solution builds deeper thinking models. It also creates a much louder and more active mathematical ecology. Some equate quiet with learning--me? Not so much.

These types of questions are harder to create and should be thought about prior to entering an instructional situation. The tasks need to be small enough to fit on the board, but novel enough to stretch their thinking. Tasks like these might be more typically classified as "new" or "reform" math. (Both phrases appear as pseudo-insults to me). 

It is important to cycle through the groups and see what the conversation is going like. Are there any "rules" we can create? Can we explain our thinking to each other? etc. An example of a dynamic response question is below:

The question was inspired by a previous post, and formatted to fit the whiteboarding structure.

The third style of question I call a Grouping Response.
These questions are designed to have a key divergence or decision. I use this divergence to create groups within the class. Rather than explain the possible schools of thought on the board, I like to discover who thinks in which fashion, and get them to campaign for their thought pattern. 

When the class has been split, it also provides me a chance to spend time with a group of students who could not answer. Essentially the class is split into Type A, Type B, and No solutions. 

Sometimes I ask the students to choose a corner based on their response and explain why their answer is the most efficient. Other times, I ask students to find someone with a different response, and exchange rationale. The questions are designed to get peer interaction kick-started. The whiteboards ensure that everyone labels themselves in a category. 

For example:

Notice that students are still asked to compute or work with some procedural mathematics. The whiteboarding just facilitates an effective mathematical conversation while grouping kids not based on ability, but mathematical preference.

My question categories came from my work on a presentation given in November 2012. The complete presentation slides can be found here. More question examples as well as other classroom benefits are  also included.

Whiteboarding is a great initial change agent. It can be used within a variety of classroom types and adapt to a variety of teaching styles. In the end, teaching mathematics is about creating a vibrant ecology where every student can be reached. Whiteboards have been a huge step toward that direction.