A simple mistake or something more?

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I’m grading tests this weekend.  My third grade group just finished up an assessment on fractions and multiplication.  It’s been about a 1-2 month journey full of investigations on this particular topic.  Many formative checkpoints were planned along the way and the unit assessment was scheduled for last week.

While reviewing the student work, I’ll sometimes write questions or direct students to a part of the question that would’ve made their answer more complete.  There are moments of pride and moments where simple mistakes drive me a bit crazy.  You see, there are only eight units with my new resource, so the assessments influence grade reporting quite significantly.

After grading the assessments, I have student analyze their results.  They comb through the test and look at how each question aligns with certain skills.  They also determine if a missed question was a fixable mistake.  I want students to be able to recognize when this occurs and fix them when they can.

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In my experience, 9/10 times students believe that the reason they missed a question was because it was a fixable mistake.  That’s not always the case.  There’s a certain amount of self-reflection and humility that’s involved in this process. Being able to be a bit more honest and communicating what a simple mistake is and what it isn’t might be in order before the next assessment.  So, what steps do students take if a missed questions isn’t a fixable mistake?  It’s one step in the right direction to admit that it isn’t fixable, but then what happens next?  Do students and teachers have plan for this, or do we move on to the next unit?

So, was it a simple mistake or something more?  This question comes up more often than not while I’m grading student work or reflecting back on a class conversation.  Some of the answers are more positive than others.  A simple calculation error can vastly impact an answer, but it may be a simple mistake and the student has a solid conceptual understanding of that skill.  But, a number model that doesn’t match the problem tells me that the student might not be certain about the operation that needs to be completed. Was the simple mistake putting the wrong operation sign in the number model?  I guess you could go down many different paths here.

The question type can influence how well and thorough a student responds. Some questions are quite poor in giving educators quality feedback to help inform instruction.  Right off the top of my head, multiple-choice and true/false questions fit that bill.  They sure are easy to grade by human or a machine.  Hooray!  But, they don’t give me quality feedback that I can use immediately.

This also has me wondering about the quality of the assessments that are given.  Measuring how proficient a student is on a particular concept doesn’t always have to come from standardized or unit assessment results. Classroom observations and formative checkpoints are beneficial and give teachers insights to what students are thinking. I want to make students’ math thinking visible.  Whether that’s using technology or not, making that thinking visible puts the teacher in a  better position. From what I observe, some of the best math task questions are open-ended and tend to have a written component where students are asked to explain their thinking.  The quality of the question and openness of the answer helps educators dig deeper into how and what students are thinking.  I think that’s why teachers are always looking out for better math tasks that help students demonstrate their understanding more accurately.

How do you help students determine if a mistake was simple or something more?