SBG Guilt

For those of you involved with my twitter conversations, you know my students were really struggling with subtracting polynomials. Out of 36 students I had to pull out about 10 of them to work with individually.

It took me a while to figure out their misconception.

Say the problem looks like this (3x - 8 + 2x) - (4x - 3 + 6x).

I taught them to change the sign in the middle and flip every sign behind it.

Here's what they would do: (3x - 8 + 2x) + (-4x + -3 + 6x).

In middle school they were taught to change every minus sign to plus a negative. When I told them to flip the sign, they would, but they added in the negative which doesn't flip the operation. And even though I stressed every sign about a million times, they would always politely skip over the plus signs. There were other errors too but this was the most common misunderstanding.

With those 10 kids, I pulled them out individually and tried to explain and re-explain what to do and why (I just now realized I should have said to flip the operation instead of flip the sign). Later I realized it was even more confusing because it looks like they are changing the minus sign in the middle to plus a negative. Egad!

Too late I asked the other math teacher what I should have done and he suggested just practicing lots of problems like -(7x - 2 + 4x) so students can really see over and over how the negative sign is distributed.

Anyway, to get to the point of this post...I pulled students out and we went over their mistakes on the quiz. Then I gave them new problems to practice. Then I give them a new quiz. Quite a few students got a 100 on their retest. Some needed to do it three times instead of two but still got the 100. Now I feel guilty. I feel like it's cheating. I feel like I should have pulled out every single students who didn't get a 100 instead of just the ones who did terrible. Shouldn't every student have the opportunity to make a 100? I don't know. It's kind of like forced sbg. I took away their initiative to improve and forced them to 'want' to do better. I practiced with them and we conversed and we identified misconceptions. All the perks of sbg, right?

So why do I feel so guilty?

On my assessments for each method of systems of equations my classes did really well. But maybe we had just practiced enough times that they had the process memorized. How do I know that they truly learned? I guess that just means I need better assessments. How do you assess understanding other than having them show by doing or show by explanation?

I am afraid now that my administration might look at the grades and assume that I am not doing my job or not doing anything for my students to all have high grades. Does that mean I need to make my assessments harder so that more students will fail? Will I feel less guilty if my grade distribution looks more like the 'normal' bell curve?


  1. Don't worry. As long as you retest crucial concepts frequently (not relying just on unit tests right after a unit is taught), the assessments will eventually reflect what the students have retained.

    In fact, you'll probably find that half of the students that you retested up to 100% will have forgotten it all in a month.

    I think that the notion of "unit tests" is itself a pernicious evil. Every test should include a random selection of concepts that have been taught, and many problems should require concepts from more than one unit, so that students get into the habit of retaining concepts for more than a week.

  2. When it comes to "What will my principal think" concerns, it always helps to talk to someone in your department/school who knows how your principal thinks, especially if you're not sure if you'll do more harm or good by having that conversation directly with your principal. But it's not always easy to find such a person who will also keep what you tell them confidential.

    For what it's worth, I read what you did as taking the time to help those struggling students learn the algorithm and then giving them the opportunity to demonstrate proficiency via re-testing in accordance with SBG guidelines. So you not only put an end to their frustration, you boosted their self-confidence when they were successful on their re-test.

    All in all, I think you deserve praise, rather than criticism from your administrator.

    The only thing I could imagine having debated is where you put your cut-off for pull out during class time: should students with less than a 60 be pulled out? less than a 65? less than a 75? etc. But for those students who weren't pulled out, they still have the option of coming in for extra help and to re-test on their own time.

  3. I had to look up SBG (standards based grading). Thanks for the prompt.

    Regarding testing, I had a math teacher email me the other day which prompted this post: http://mathfour.com/cognition/5-phases-of-learning-math

    The gist - test students over and over.

    And I think you're doing fine. I appreciate the guilty feelings, but it looks like you're trying to put too much though into something that you're doing just fine with organically.


  4. The purpose is to bring the low level kids up, so should you feel guilty about the ones that did well the 1st time. Yes and no, as you get close to the end of the semester you can refine their grades by giving them extra chances to improve it, that will help them in the long run.