Subtraction Observations…the power of working one-on-one with students

math assessment

As you know, formative assessment is a critical part of the teaching/learning cycle. Without knowing what our students know and can do, it is very hard to make sound instructional decisions.  I use exit slips (and entrance slips) ALL the time to try to keep a clear vision of what my students can do–and what more we need to work on.

There are, however, times that I believe a paper and pencil assessment can only give us part of the information we need.  Giving students a few subtraction problems to do can tell us if they CAN get the right answer…but it doesn’t always show us HOW they do it or where they may be getting off track.

For something important like the standard subtraction algorithm, it is critical to see where students who are struggling are going wrong.  This is what I wanted to do on Friday before we move into bigger numbers and lots of 0’s!  Although you can do this with only students you are worried about, I truly wanted to watch each of my students solve two problems so I could look for the following things:

1.  Accuracy 
2.  Fluency
3.  Efficiency
4.  Confidence

I kept a recording sheet right next to me and as they worked, I watched every step they took, asked questions if I couldn’t tell what they were doing, and then jotted down what I noticed.  Did they get it right?  Could they do the algorithm AND use correct subtraction facts to get the right answer? After all, we DO want students to get the right answer, don’t we?

But getting the right answer is only part of the deal–if this was all I was concerned about, I would just give them a paper and pencil assessment (which I will be doing often over the next week or so!).  I really want to get a sense for students’ fluency (speed at which they work) and efficiency (are they using notation and strategies that make sense and contribute to fluency?).  I also wanted to know if they could EXPLAIN what they were doing…not just do it.  All of these things work together to show me their overall CONFIDENCE with the skill.  I have to say–it was time well spent!

Throughout the day, I pulled students one or two at a time (two if I was 100% confident in their skill level) and watched them work the two problems.  I watched them like a hawk to see if they were REALLY having to think through the steps or whether it was smooth and natural.  I jotted down my observations, used the time as a coaching session for any mistakes that were made, and noticed something really important in about 1/3 of my students–how one sentence I had said during a lesson might have gotten them confused!

math assessment
So here’s what I learned about how important MY language is with students!  The other day during my mini lesson, I mentioned to students that it “can be a good idea to look at ALL the numbers you are subtracting from to see if trading will be needed.”  Harmless, right?
Well…something I discovered in my assessment interviews was that I had a number of students who started this problem by doing just THIS–looking at EVERY place and crossing off everything needing a trade right off the bat!  I was confused…in all of the modeling I had done, I carefully and methodically went place by place–if we needed “ones”, we traded for a ten.  If we needed “tens”, we traded for a hundred–one step at a time.
Because seeing this “crazy crossing out” got me curious, I started asking questions…and students all came back to that line–that I had mentioned to look at ALL the numbers to see if they would need to”regroup”–and if they did, they got them ready to trade!  Although some could do this “cross off” and keep their brains organized–most of them went WAY over to the thousands and started working from there–with obviously unsuccessful results!  So, despite my careful (and repeated!) modeling (even with manipulatives), they took hold of that one sentence and went down a dangerous path.
When I saw what these students were doing, I realized how they misinterpreted my suggestion–and I NEVER would have seen it if I wouldn’t have been working with them one-on-one and making those careful observations.  I also would not have seen it on an exit slip–I would have seen the wrong answer but would not have seen the order of steps they took.
So what were MY next steps?  I went back to those other students who had been doing the multiple cross outs and we worked together to correct the misconception.  By the end of the day, I knew which students were extremely fluent and confident and ready to move at a faster speed, which students understood the concept and just needed fluency work, and which students needed a variety of different misconceptions corrected–whether due to MY miscommunication or other errors they  might have been making!  I know now exactly where each student is in their learning–and I know how to group them next week.  As we continue, I will do more observations with students who are struggling so I can continue to guide them with “just right” instruction.  We will also be doing frequent exit slips to check for accuracy and fluency as the problems we do get more and more complicated.  Thanks for stopping by!


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