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First, a disclaimer: I am not and never have been a Math teacher.  After teaching Modern World History for 7 years, I went to the "Dark Side" and became an administrator, so I probably don't know anything about teaching Math.

However, I do know a few things about teaching in general.  Furthermore, I have a pretty good grasp of the philosophy of AFL and how applying it in the classroom can increase student learning.  So I'm going to give this a shot.

I've noticed that one of the problems that some Math students have is that they don't practice at home.  I will in no way advocate stopping the assignment of practice to be done at home.  Practice at home is a worthy topic unto itself, but please do not read into what I am about to write that I am recommending not having students practice at home.  In fact, I would recommend assigning practice to be done at home every single night.  But if:

1. Many of our students don't practice at home, and
2. We realize that we cannot control what one does at home, and
3. We believe practice is required to learn the content, and
4. We care MOST about whether or not students learn as opposed to whether or not they make responsible decisions outside of class, then
5. It makes sense to provide as much practice time as possible during class since that is the only time in a student's day we can control.

Of course this idea of giving time to practice in class fits very nicely with the philosophy of AFL.  The AFL teacher would give practice opportunities in class that provide useful feedback for the teacher and the student.  Frankly, I've never known a Math teacher who doesn't give students chances to practice in class.  Usually this comes in the form of a practice problem or getting started on the night's homework.  Typically the teacher will move around the room to see how students are doing and to answer questions the students might have.

There is absolutely nothing wrong with this sort of practice activity, but like everything, it does have limitations.  For example, if a student chooses to just "go through the motions" of doing the practice, then very little feedback will be received.  Also, the student who, for whatever reason, doesn't ask questions will quite possibly not learn as well as the student who does ask questions.  Finally, the teacher is only one person and almost always outnumbered greatly by students.  It can be difficult to give each student the specific feedback they need during such an activity.

One more background observation before I share my idea.  I have noticed that students often take test-like or quiz-like situations more seriously than they do other activities.  In other words, kids who will goof around and disrupt classroom practice tend - in a well-led classroom - to sit quietly and do as they're told during a test or quiz situation.

That's a lot of build up and background to an idea that's not all that earth-shattering.  In fact, I'm sure the Math teachers out there will respond by saying, "Been  there, done that!"  But I still figured I'd share a potential practical application of the philosophy of AFL to the Math classroom.

In a nutshell, the idea is to break up the Math process into steps and then give students a daily quiz on each step as they learn the process.  It would look something like this:

• The Math process being taught is broken down into steps.  For this discussion let's assume we're learning Math Process P which is divided into 3 steps.
• The teacher teaches Step 1 and then gives students a quiz on Step 1.  The quiz will ONLY be on Step 1 and it will be worth X points.
• The teacher teaches Step 2 and then gives the students a quiz on Steps 2 AND 1.  This quiz will be worth 2X points.  The student or the teacher might even  choose to erase the first quiz from the grade book or set it to not factor into the grade.
• The teacher teaches Step 3 and then gives the students a quiz on Steps 3 AND 2 AND 1.  This quiz will be worth 4X points.  The student or the teacher might even choose to erase the first two quizzes from the grade book or set them to not factor into the grade.  
• The teacher reviews the quiz on Steps 3, 2, and 1 and then gives a unit test on all aspects of Process P.  This unit test is worth 10X points.  The student or the teacher might even choose to erase the quizzes from the grade book or set them to not factor into the grade.

Here are some more details:

• A quiz might be given the same day as the respective step was taught.  On the other hand, a step  might take more than one day to teach.  If a step takes a few minutes to teach, then the teacher will quiz on it after giving the students a chance to practice it.  If it takes the entire class period to teach the step, then the quiz will open class the next day.  
• If any step takes more than one day to teach, then the students will take a quiz on that step on consecutive days.
• There will be a quiz given every day.

To me this seems like a way to make sure students are practicing in class.  For example, even if the student did no homework, he would still practice Step 1 three times before the unit test, Step 2 two times, and Step 3 one time.  Beyond just practicing the step, the student would be receiving more feedback and more direct feedback than is typically received when the class goes over practice or homework problems.  Finally, the teacher would get valuable feedback as he or she would know how each student - as opposed to just the question askers - was doing on each step.  Plus the teacher would have the specific feedback necessary to tightly focus remediation efforts, determine what might need to be retaught, and create differentiation efforts.  

So, Math Teachers, what do you think?  Could this work?  What have I overlooked?  Would this type of practice - this use of assessment for the purpose of learning - increase the likelihood of students learning?