It’s Sunday night. I need some good ideas. I know you’re reading this. I’d love your two cents before Tuesday…(after then would be useful too).

In our district we take quarterly exams which are the same at all 3 middle schools. 8th graders predominantly take Algebra 1, so there are no district assessments for 8th grade Pre-Algebra or Geometry students. These are the two classes I teach, so for this, I’m on my own (which is fine).

My Pre-Algebra students took their 1st quarter exam on Thursday and I’d like a way for them to re-engage with their mistakes. Of all my students about 5% scored below 50%, 45% scored between 50-70%, 45% scored between 70-90%, and 5% scored above 50%. I am able to scan my students’ answers into the district data-base and create wonderful reports which tell me which questions were most missed, what the most common wrong answers were, etc.

NORMALLY, I have students do a self-reflection which looks something like this:

By circling the questions they got wrong, they’re able to see which topics they need more help in. Then, sometime over the next week, I pull groups to work for 10 minutes on individual white boards. I reteach the most frequently missed concepts. Test corrections are due within a week of when they get the exam back.

BUT…here’s where I need some fresh ideas…my Pre-Algebra class is filled with students who have ALWAYS done poorly in math. They’re used to not doing well and crumpling up an exam the moment it’s returned is like a Pavlovian reaction. I’m slowly breaking them of this habit, but **DISENGAGEMENT** from exams is a long, slow process to undo.

My question is…how best to set up an activity for students so that they genuinely want to re-engage and learn the topics from the exam which are still challenging for them.

My idea, which needs refining (from YOU) is the following…

1) Let students know that they’ll have a change to revise their exam and raise their grade.

2) Spend a class period modeling common mistakes and having groups of students correct those mistakes. I would choose which problems to model after looking at the data analysis of their answers provided by the district. Students wouldn’t have their own exams, but we’d be doing actual problems from the exams, in groups, so they could talk through where each hypothetical student went wrong.

3) Students get their exams returned to them. At the top, I write how many errors they have, but I do not mark which questions are right or wrong. They get a specified amount of time (20 minutes or so), to go through their exam, under silent, testing conditions, to try to find their mistakes.

Please pick this idea apart…make it stronger…help me see what big ideas I’m missing.

I’d really like to **TEACH** these students how re-engagement with an exam is a very powerful skill which leads to deeper understanding. And I know that teaching this will be a process. I’d just like to have a clear idea about how to start…

Thanks.

I wonder whether students who struggled on the test will be able to effectively find and analyze where they made errors. I would be interested in hearing how it goes after you’ve tried it.

I am doing a new test/quiz revision system this year. It’s an idea that I got from the previous math teacher at my school, called a “recycle”. Students correct the work they got wrong on an assessment on one side of their paper and on the other side they analyze what kind of mistake they made. For their first few recycles students get a list of common errors (e.g. careless error, forgetting a negative sign, etc.). So far it has been going well, though the new students are still figuring out the error analysis part.

I was just looking at http://davidwees.com/content/eric-mazur-memorization-or-understanding-are-we-teaching-right-thing and maybe that would help you too. I thought it was very inspiring and taught me a lot about how kids learn.

As a trainee teacher, my college is killing me with information on selfreflection. Therefore I have some thoughts on the self-reflection form you have been using with your students. The focus of this form is “what did I do wrong”. No one likes to have their noses rubbed in their mistakes, which is essentially what this form does. (no offense intended: locating mistakes is a first step towards learning from them, but only once students are ready for that)

Perhaps you could turn this form on its head: could they find the things they do know? And then put them in groups with their lists of things they do know to solve some problems together. Have them tick off things they do know from their list as they use them to solve the problems. In the meanwhile, students who know a little more will explain new stuff to those who lag behind, and hopefully much will have been learned and some selfconfidence will have been regained at the end of it.

Because I have learned one thing: no student is going to do well at an exam if they believe they cannot.

and sorry, I do not like idea 3 at all – doing the same thing again expecting different results is called wishful thinking.

(Looking forward to seeing other’s ideas on this.)

Don’t have time to respond fully right now, but I’ve spent a lot of time thinking about how students should post-process tests.

I strongly disagree with Eva about not focusing on what they got wrong. Students need to learn to identify and discuss their mistakes without shame. If you avoid talking about what they got wrong, that conveys that getting things wrong is so shameful that we can’t even talk about it– I should say reinforces, because it’s something most students have already internalized by the time they’re in middle school. Trying to protect students’ self-esteem this way hurts them in the long run.

I think doing #3 *after* discussing common misconceptions is not “doing the same thing again expecting different results”. But I don’t think I would tell them the number of things they got wrong. Then it becomes an egg hunt, rather than a thoughtful process where each problem is considered carefully. I would probably have them go through and label how confident they are in their original answer, and if they would like to change it, then they could do so.

I have a bonus assignment that I use with my classes (college-level) after every test that I should post about on my own blog. I’ll try to get to that this afternoon, and then come back and drop a new comment.

I blogged about my method of test corrections: http://crstn85.blogspot.com/2011/09/test-corrections.html

I think modeling how to find and correct mistakes is a great idea. I’m also not sure how well students would do at finding the errors in their own work independently (are you seeing more careless errors or conceptual misunderstandings?) but I think that they would do well at doing this in pairs. When I do test corrections kids work independently to try to figure out what they did wrong and if they made an arithmetic error they catch it, but then they need to look in their notes, talk to their neighbor or get a hint from me. I do try to send them to their notes to promote independence, but I’m circulating to explain misunderstandings.

Last week I used Tina’s corrections (blogged above) and found it to be really useful. I am in a school where a lot of cheating and not a lot of thinking happens – and also they remind me of your students see this post for more (http://mathemagicalmolly.wordpress.com/2011/10/15/a-class-full-of-fs-and-f-its/). For quiz corrections in this class I structured an entire class period for correcting their exams. Ideally I wanted them to figure out their solutions independently/in groups of three but it ended up being a mixture of partner assistance and me giving hints. (This type of student does not usually take notes, do their HW or pay attention to have the materials to discover their mistakes/find correct ways). The students who were sort of getting it were able to have discussions, compare things they got right and wrong and help each other. Some groups really worked.

I think my students would panic if I didn’t tell them what they got wrong but I like the idea behind it. Ideally I didn’t want revisions to look like me doing all the work either at their desks or at that board and thankfully that is not what happened. Many students did need a lot more hand holding but because of the classroom set up the students who did not were able to learn and make connections and help each other a little more.

Excited to hear how it turns out!

What motivates your students? I was thinking about your statement about cheating & not thinking. Do you know what your students really enjoy that they would do anything for?

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These are great ideas and important food for thought. I have a plan for tomorrow, but now need to sleep on it. Is telling them how many errors they got going to lead to an egg hunt? That’s a very good question. BUT…my class is a low tracked class of kids who are used to being unsuccessful and I worry that if I tell them nothing, they won’t have a hook to re-engage. I am a bit concerned about trying a whole new idea on more of a high stakes exam (this being the 1st quarter exam, so it counts for a lot, one way or another). I need to think a bit more about what my purpose is…more tomorrow…Whatever I end up doing, it will begin with about 40 minutes of error correction. They will count off into pairs (random groupings), and receive 10 problems of ‘student work’. I analyzed their mistakes and wrote 10 new problems and produced student work of my own which highlights common errors and misconceptions. They will work in pairs to find my mistakes, knowing that out of the 10 problems, 4 are right and 6 have errors. After that, they’ll have time alone with their exam. The question is whether or not I’ll tell them how many problems they got wrong. Still thinking, but off to bed.

Tina – One question, you say that you give them half credit for their corrections, what if the answer they gave originally aloready earned them half or more than half of the points? I teach Science and ussually give my students partial credit for the work they do and I’m currently struggling with deciding how to do this.

I gave back half the points they lost, but I was really stingy with partial credit because I knew they’d have the opportunity to correct. This year I am doing retakes rather than giving points back because I found myself helping them too much with the corrections. They must correct before they’re allowed to retake, but I can help without feeling like they’re getting credit for me walking them through the problems.