Posted by: lboudreau | July 21, 2011

Lessons Learned

We’re in the final teaching week of Breakthrough Atlanta.  Eight math interns gave post-tests to students yesterday, and graded them all within an hour.  The results are in: 7th graders saw a fairly significant improvement from the pre-test, while 8th graders saw a much more modest one.  In fact, there was some question for a while as to whether 8th graders had seen any improvement at all.  This, after all the energy and good teaching in and out of classrooms.  All very discouraging.

Now, Breakthrough is in large part a preview of concepts students will see this coming school year, so having a number of students who haven’t yet mastered slope or simplifying radicals (or even adding negative numbers) may not be a surprise.  And these interns/ infant educators haven’t mastered teaching.  They are very good, though, and students showed they knew a great deal in class, so we all had high expectations for post-test results, and found ourselves dismayed.

The next day, though, I think there are lessons to learn in this.

One, although our pre- and post-tests are not as long and rigorous as the CRCT, they are standardized tests, and you just can’t measure everything learned by using a standardized test.  Just as important are the eagerness to answer questions in the classroom, or the statement directed at one intern: “You make math so easy,” or the feedback at conferences that students love math now.  What students share in a class discussion illustrates just as deep an understanding as the paper and pencil snapshot, perhaps taken on an off day.  But these other indicators are harder to quantify than a test, so they often get discarded.

Two, it’s hard to know, really, what a student has learned.  It’s the bottom line in my own classroom, but I never feel like I have an accurate measure of it.  How much more difficult is it for younger teachers?  It’s like I have to look at a portfolio of indicators: tests, questions, tutorial time, projects, engagement in class.  (See lesson #1 above.)  So, how do you know you’ve prepared a student for the next level?  How do you know if that student is truly prepared?  If that’s the case, a poor showing on a test might just have to be a surprise.

Three, on the flip side, you have to take some things on faith.  These interns have middle school students, for whom it’s a miracle that learning takes place on some days.  Interns have planted seeds that they will never see sprout, and it’s important to acknowledge that.  Otherwise, it’s easy to lose all hope of making a difference.

Four, about the test itself.  I made the tests based on input from interns, but even so, it didn’t totally reflect what students had done in class.  Did that matter?  I’ve grappled with this idea that all four interns in each grade level should be in lock step during these weeks.  They haven’t always given the same lesson, or even covered the same topics, on the same day, and that’s worked well.  Each intern had the flexibility to go at the right pace for their students or to interject an activity.  In the end, they got to all of the standards.  (Part of the issue is that the standards are general in places, and not all interns got to, say,  simplifying the square root of 50.)  So, this test of those standards is relatively fair, but not totally accurate.  But isn’t that the nature of the beast?  A test that’s totally fair to every student may be too simple for some.  I think there’s something inherently underhanded– in a good way– about asking kids to combine concepts in new ways on a test.  “Thinking on your feet” isn’t on the list of NCTM Standards, but it could be (maybe they just label it “Critical Thinking”).

Five, this leads to the question of common assessments.  If I were department chair (and soon I will be), I think I’d look harder at purposes for the tests within the context of a class than at how tests match from teacher to teacher.  I would be concerned that, once we all agreed on a test, then we’d all agree on how to teach to it (and only teach to it), and leave a lot off the table.  I acknowledge the importance of having some degree of common experience for students within a course, but there needs to be room for teachers to go to their strengths, as these interns have.  In the end, we all met the goals of the program.

Today, the day after, interns all report that students are engaged in their final math projects for Museum Day.  I witnessed it myself.  Interns feel better.  I feel better.  And we keep at the task of teaching and learning math.


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