It recently came to my attention that there are students who don't FULLY understand how to check their work. During this past semester in algebra 1, we solved equations and inequalities and such. To force them to check their work, periodically I would assign it point value on their homework, so they could get at most 80% if they didn't check their work.

Here are various things I noticed. Sometimes students would start checking their work at the 2nd step or the simplified step of the original problem. We discussed why that was a bad idea (potential mistake at the 1st step, and even though your answer looks correct, it's not for the original problem).

Sometimes students would "check" their work, plugging in their answer, and at the end get some number that had nothing to do with the original equation, and then place a check mark at the end. CHECK. I've checked my work. Done. Not correct, but I don't get it, I think just going through the process and the ever-important check mark at the end is good.

And finally, sometimes students would check their work. It wouldn't pan out. But then they wouldn't take it from there. Oh well, it didn't work. I'm stopping. I don't think to go back and follow my work process to see where my mistake was.

Ideas for next time (or later this year?): write out various problems all worked out, and then have students analyze the situation: is the problem correct? how do you know. If the checking didn't work out, where is the mistake? Find it (and have some mistakes in the problem and some in the checking). Have some problems where everything seems to work out, and the problem has the checking occur from the 2nd step on of the problem and "look" correct but in reality not solve the original problem.

Something a colleague of mine has done in Precalculus that I'm thinking of bringing into my Alg1 and Alg2 classes is pose a worked out solution for the students to find the errors. She would tell them "there are x number of errors in how this problem has been solved. Find and circle them, and work out the correct solution with the errors corrected". It worked well to show their understanding of concepts and helped them check their own work for mistakes in the future.

ReplyDeleteOoh, I like the telling them of the number of errors at the outset. Thank you.

ReplyDeleteMs. Cookie

It's not just in the ninth grade. They come to us in 8th grade with the same resistance or apathy, depending on the student. And, like you, at our school we're really trying to get them to see past the end of the pencil.

ReplyDeleteThe few occasions we've used the incorrect (and sometimes correct solutions--they have to tell us which) have been truly eye-openers. They seem to "get" it better when they are working with real-world problems. For instance, is that a reasonable estimation? How did she get such an answer?

Or perhaps it's just nice for them to see somebody besides themselves moving the decimal place two times instead of one.

The Algebra 1 students, initially resistant to finding the error, (probably because the properties were still new), find it more of a challenge. They are required to be more explicit mathematically in their answers.

Have you heard of Hands-on-Equations? I just used it for the first time this year and can't say enough good things about it. It has kids set up equations as two sides of a balance scale and solve to find out how much each x must weigh to balance. Checks are built in to each problem so students can show how much weight they'll end up with on each side.

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