Retesting
When I started teaching, I had some of the weakest math classes in a high school full of weak math classes. I taught the material, tested, taught more material. Of course, depending on the course and the kids, three quarters might have been failing each test. Many attendance issues (you can’t come once or twice a week and really learn), placement issues (put the kid in a course that’s too hard, and what do you expect), classroom issues (combine a novice teacher with unruly classes with bad placements and attendance issues, and just imagine the chaos) and curricular issues (the NYS inspired math courses, then and now, are not logical, coherent courses of study).
Sometimes, when students fail, they should study more and take the test again
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Fast forward 10 years. I can count my attendance issues. I have a role in placement; 95% or more of my students are appropriately placed (I would argue 100%), I can control a class, and our school is allowed to teach algebra, geometry, trig, etc. (I should post about these changes; each has some interesting background).
But I still have students who fail tests. Not so many. In fact, very few. But what to do when they fail? A few years ago I decided, if the topic was crucial to the rest of the course, that all of the students would need to pass. If they failed, they would get tested again. And again. Factoring in my school is a beefy topic. (need a separate post on teaching challenging factoring) And this was the first topic where I gave retests. After the third try, everyone had passed. I still had mixed feelings, but the rest of the year would have been hellish for students who couldn’t factor at all.
Five years on we have two algebra teachers, and we agree that the factoring retest is good and important. We drop the first grade, and replace it with the second (or, very occasionally the third), though we record anything over 90 as a plain 90 (no reward for failing the first time!) It is like the drivers test, you don’t fail it and move on. (Or, it is not like Global, if a student fails “China” they can still study “India,” no handicap). Youstudy it until you learn it.
The kids who passed the first time are glad they don’t have to attend tutoring and double up on homework. The kids who failed the first time think they are getting cut slack. And we end up with students who have learned at least a reasonable portion of a topic that will keep coming back the rest of the year and in future courses.
JD2718 
Yep, I teach college calculus, and I do the same thing with derivatives and integrals. I have a set of quizzes that cover, I think, the most important types of problems, and students can retake versions of the quiz as many times as they want to before the exam (exams come less frequently in college) to get a better score. Then, one page of the exam is just like a derivative/integral quiz. It’s too time consuming to do with every subject, but you just survive the rest of calculus without being able to find a derivative accurately. I sometimes think it’s one of the most effective things I do.
I should definitely do more of this. A couple questions on implementation:
1. Did you write 3 versions of the test? Do you change them from year to year?
2. What do kids who’ve already passed do while other kids are restudying and retesting? How much time elapses between the initial test and the retests?
I think everyone can identify a few “must-have” skills and concepts, but it’s difficult to know what to do with a small percentage of the class that consistently just doesn’t get it. I also suffer hugely from placement issues!
Well, ideally in Global you study the same concept in India and China and the middle east, so if you get three chances to really dig into “cultural diffusion,” rather than one shot to learn the names of the dynasties in China. If you don’t understand “revolution” in France, maybe you’ll get it in Russia or China or India.
My high school math teacher gave a quiz every Friday, and no one could move on until he had an 85 on the quiz. But we were a tiny school in a rural district and he was given carte blanche. (Math was the only subject in which my school had good Regents passing scores.) Somehow he got me all the way through calculus, and I never felt good or confident with math.
Jonathan:
I’m dealing with some personal issues that I will talk about in the future. At present I can’t talk about it
mrc,
each retest covers the same material, with similar but not identical problems, in the same proportions. Generally students have two weeks to prepare for a retest, outside of class. The class continues forward. Notes and calls home are used to encourage attendance at expanded tutoring during that time (the stick) while the right to retest (the carrot) is reserved for those attending multiple tutoring sessions. The actual retest is given after school.
How often does the topic recur through the rest of the curriculum? Clearly factoring is crucial. Systems of linear equations, likewise. Maybe algebraic fractions? Also, a retest too close to a final exam is no good, since students decide that their grade is either hopeless, or already safe, even with the failure.
One of the keys to this working is having high quality tutoring. We use a system of peer tutoring, freeing up teacher one-on-one support for the hardcore cases. I also have upperclassmen in my room a couple of times a week to work as student aides, and part of their work is 1-1 or small group for kids who need a bit extra (usually towards the end of a period, when the balance of the class is engaging in an extra activity)
Sometimes I feel like I teach, reteach and reteach until I am blue in the face and get the same results. Not with my calculus kids, though. They have to score at least an 88 in pre-calculus or they never make it to the class (and they need a 90 in math B to make it to pre-calc.) My problem with teaching factoring is that the kids can do it in a vacuum, but try putting multiple types of factoring on the same test, or problems involving factoring (quadratics, fractions) mixed in with factoring, I lose lots of them.
I know it’s not educationally sound, but I have taught my really limited kids how to get the correct answer on multiple choice section of the regents with their graphing calculators.
Educationally sound? Ha! We didn’t invent high stakes tests. But it’s our job to get as many students as we can to pass them. Of course we use whatever is available.
I think me and a buddy once personally kept my old (big) high school off the SINI list (1-step before SURR) by teaching multiple-failure course I kids exactly those sorts of tricks.
You’ll like this: on the old part 2, for a system of equations, our local rubric usually awarded 6 pts for the first variable, then 2 for the 2nd, 2 for the check. I taught really weak kids to assume the first variable equalled 0, (wrong, -6) solve for the second (dirt easy) and do the checks (one should work, one should fail). Four out of ten.
(Actually used that for buy-in, that we were going to teach them to game the test. In the end most really solved systems)
We had dozens of tricks like that. How about, set up the wrong truth table, but fill it in correctly?
And yup, all sorts of working backwards from the multiple choices, and that kind of thing.
It wasn’t really math, but the testmakers didn’t really care about math either.
I used to have them graph any two lines and find any point. That got them at least a point. Then they checked–two points, even if the check didn’t work–all they had to do was write check doesn’t work.
Now I have them plug numbers into variables and work backwards. They can answer almost every multiple choice that way. Last year in my class 27 out of 28 seniors passed the regents. Up until that point, most had only passed the first term of math A. And you are correct, some did actually learn some math along the way. One of my kids will even be taking pre-calc in college this term.