math (5)

The Assessment Network has grown to the point where that it now contains many different examples of how the power of assessment can be maximized in the classroom. These ideas are scattered throughout the site. To make this site easier to navigate, this one blog will include links to all of the other classroom AFL examples. It's sort of like an AFL Wal-Mart - everything you need in one blog!


Please note that while these blog posts are grouped by content area, the vast majority of them can be used in any content area. So be sure to explore examples listed in content areas other than your own.
Also, please note that as more examples are added to this site, they will also be added to this blog.

Physical Education
General Examples
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Educators exploring ways to practice AFL in their classrooms will often find some parents and students a little confused as to exactly why teachers are doing what they're doing.  Unfortunately, over the years schools have conditioned people to view grades as summative in nature.  Many parents and students do not understand how to use feedback from a score or grade in part because they have not been given the opportunity to do so.  The feedback they received wasn't formative - it wasn't provided as a way to guide learning but as a way to determine a final grade.  The AFL practitioner, though, understands that students need to use feedback to guide and improve their learning.  Therefore, the AFL practitioner must be very explicit and intentional in how he or she trains students to use feedback and in how he or she communicates with parents about classroom expectations.


Recently, Jenn Shannon, a math teacher at Salem High School, shared with me an email she sent home to parents about one of her AFL practices.  I think it's a great example of intentional communication intended to educate parents about how AFL practices can help their children learn.  With her permission, here is a copy of that email:


Dear Parents/Guardians
I gave each student a rubric on Tuesday to help them self-evaluate how they are progressing in the given unit.  We have worked on filling in the rubric during class, but I encourage you to ask your student to see their rubric.  Students know that they should be striving to have mastery in each area on the rubric by Tuesday, November 1 (test day!) 
 I have attached a copy of what this rubric looks like and how they are assessing themselves. 
I hope that this rubric encourages the students to take responsibility for their learning, as well as provides them a tangible way to know whether or not they are really prepared for their test.
If you have any questions, please feel free to contact me.



I believe that we all have something to learn from a simple email like this.  Let's not underestimate the potential benefits of involving parents by communicating with them very directly.


On top of being a great example of AFL communication, Mrs. Shannon's rubric is also a great example of how to get students to assess themselves.  It's very similar to Anika Armistead's use of a science review sheet as it lets students know up front what they will be required to know and then gives them a means to assess their progress.  Here is a copy of Jenn's rubric in case you would like to use it in your classroom as well:


PDF version of Rubric11148392473?profile=original

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A few days ago I happened to be walking through the library before school. Two female students were sitting at a table doing homework.

One of the students was working on a Math assignment. I heard her ask the other student, "Did you already do your Math homework?"

The other student replied, "No. I wait until after the 'check-up' and then decide if I need to do the homework."

Not knowing the class, the teacher, the exact content, the student, or the student's progress, I can't say definitively that the student was making the wisest decision for herself. However, I LOVE the fact that the student's teacher has obviously been training his or her students to use assessment-elicited feedback to guide their decision-making. It's evident that the "check-up" (what I would assume to be a quiz in traditional educational lingo) is viewed by this student not as an assessment FOR a grade but instead as an assessment FOR learning. Perhaps the student made the wrong decision to not do homework in this instance, but this student is being guided by her teacher down an important path. This student is being taught to assess herself and make decisions based on that assessment.

Are you providing your students with opportunities to assess their learning so that they are aware of what they know and what they do not yet understand?

Kudos to the Salem High School Math teacher who is providing his or her students with regular check-ups!
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An AFL Homework Practice

Sitting this morning in a Student Support Team meeting I heard Beth Moody, a math teacher at SHS, explain her homework practice. It was a wonderful example of AFL in action.

First of all, homework did not count against you. After all, why should practice count against you? Not doing homework or not doing it well does not inherently indicate how well students are mastering content.

Secondly, doing your homework assignments will lead to you receiving an extra grade for the grading period. This is a nice reinforcement of the idea that practice leads to learning. Unlike extra credit, an extra grade does not overly inflate the summative grade, but it does provide an incentive to practice.

Finally, and most AFL-ish, was the fact that Ms. Moody gives students practice problems for homework and then tells them to do as many or as few from each section as they need to do to ensure that they understand the concept. She is putting the students in charge of their own learning by giving them a means to assess themselves and tailor their practice accordingly. Rather than simply assign students 10 practice problems, the students might instead be given 5 examples of one type of problem and 5 of another. Then the students are told to do as many of each type as they need to. So while one student might do 1 of each, another might do 2 of 1 type and 3 of another, and still another students might do all 10.

What a great way to individualize the practice process and give students ownership of their learning!
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Would this work? (A question for Math teachers)

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?

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