I've had some exciting student-self motivation going on in my math class lately.
Here's a little background on how I assess math:
I break up each math quiz I give into "learning targets" or objectives which the students are informed of at the beginning of the chapter. I score each "learning target" on a 1-4 scale (This is an example of what 1-4 means from something my students should have already understood at the beginning of the year). This is part of my standards-based grading approach I adopted for my math classroom last year (The link is a hand-out is one I gave to my students at the beginning of the year to explain it, so hopefully you can get an idea of what I'm doing.) . I hope to blog more about that in a future post.
I started a practice after the second math quiz I gave out this year that has shown to be very beneficial! Approximately two days after each quiz, I give the quizzes back to the students with the problems marked that they missed along with scores for each learning target. I have been pairing or grouping students in 2's or 3's with students who have strengths/weaknesses that complement each other. For example, a student may have gotten a 2 on learning target 1, a 4 on learning target 2, a 3 on learning target 3, and a 3.5 on learning target 4. I try (and usually am pretty successful) to pair/group this student with another, or two others who have a 3 or 4 on learning target 1, a 2 or 3 on learning target 2, and so on. The students then discuss the problems they missed and work them out with a pen on their paper or another sheet. Students are usually able to figure out their errors without my direction, and it requires much more involvement than me fielding questions from the whole class and going through selected problems on the board, or just handing back the quiz with written explanations/answers.
I also allow students to retake any learning targets they'd like (outside of class time) as long as they've turned in all of their "insurance" (homework) on time for the chapter up to that point. The reason I'm so excited about the peer post quiz interaction is that it has skyrocketed the amount of students who have the desire to sign up for retakes (thus proving they have actually learned the material)! I did not do this peer interaction on the first quiz of the year, and I was a little frustrated at the number of students who signed up for a retake. Now, after conferring with their peers, students almost automatically sign up to retake any learning target that they scored a 3 or lower on.
This does take more work and time on my part. I have to have a retake version of each quiz written up, customize them for the learning targets each student wants to retake (because they don't have to retake the whole quiz), copy them off, be present for students outside of class to retake them, check them, as well as change grades in the grade book (only if they scored better-I don't penalize students if they do worse, which they RARELY do.). It really doesn't take as much time as it might sound by that long list, but it truly benefits the students, gives them a chance to prove their learning (because isn't the goal that they learn it and we don't just allow students to do poorly on a quiz/test and move on?), and helps me in the future because the learning of math concepts is often sequential and requires a basis of past concepts to move on to the next thing.