All For One

So it's been an up-and-down couple of weeks.

The up: Three days before the last individual exercise set, or IES, (i.e., test) in both algebra 1 and honors pre-calculus, I gave a  practice set under "real" conditions. For algebra 1 I graded the papers, returning them the the next day for the kids to discuss.  The following day was our normal review, which I refer to as me being on the "firing line" because the kids fire questions at me. The next day was the IES, and of 28 kids in the class, 14 got some sort of an A.  This was a solid improvement over the previous IES, so of course we're doing this again with the current unit. With honors pre-calculus, the homework for the evening of the practice IES was to grade someone else's paper (think peer editing from English class), and the next day the kids discussed the papers with their partner.  These were quite possibly the best discussions of the year. There was a gentle but firm honesty and a seriousness of purpose that was really great to see. The following day I was on the firing line, and the day after that was the IES. The grades improved slightly,  but not as dramatically as they did with the algebra 1 kids. Definitely going to do this again, mainly because I do think it helped, but also because something else is going on that I believe is at the root of the lack of improvement in the honors pre-calculus classes, which leads me to...

The down: Normally by this point in the term, the classes are on a slow, steady climb with regard to both the grades and the quality of the daily discussions. There's a certain comfortable hum that takes over the classroom, indicating to me that things are going as they should, that the kids are in it for each other, helping one another learn the material.  This year, however, there seems to be one thing preventing this from happening. The word that comes to mind is "selfishness", but that seems to me to be a bit harsh, even if it's honest.  You see, some of the kids are able to do the homework exercises "on the fly", and they do so during the discussions in class...and by do the exercises, I mean mechanically push the symbols around and get an answer, not explain the material with any kind of clarity or depth.  While this does them some good, it does not benefit the other students, at least not as much as it could. If the students who understand the material would do the homework, they could work through their difficulties at home instead of in front of their group, and be better prepared to help the other students in the class as well as have a more complete understanding of the material themselves.  Their motivation,  however, is to get their participation points, not participate in the discussion for the everyone's benefit.  Sadly, this should come as no surprise.

You see, I've come to the conclusion that we actually teach the kids to be selfish.  We teach them to not share information with one another, to not help one another, at least not when it comes to academics.  The entire thing is an individual competition to see who can get the best grades, who can earn the best score in class, who can "win", for lack of a better term.  For as much as we may want the process to be about everyone succeeding, and by succeeding I mean learning, we are currently in a system that in many ways prevents that from happening.  What we need to promote and cultivate is a culture that values learning over grades. This is what I try to do every day in my classroom.  Many of the students have "bought in", and are doing well in the class, not only in terms of learning the material and in terms of their grades, but also in terms of learning how to learn, which if asked is what I would say is *the* point of education. Those who should be the "top students", those I mentioned above who can do the problems on the fly, are not making any progress because they are content with what they already know, content that they can "win" and get an A (though for several of them this is currently in question), unconcerned that they can mechanically "do the math" without truly understanding it...a fact that is evident from the fact that they struggle to explain the material to the others in the class.

So the question I'm wrestling with is how to incentivise selflessness.  How do I get the top kids to stop the chase for the grade and instead focus on improving their explanation of the material, which would not only benefit the other students, but would also increase their own understanding?  I don't have any answers...yet.  But, just as the students shouldn't stop looking for solutions to their problems, neither will I.

Testing vs. Assessment

I have been told over the last couple years that what I am doing with the honors pre-calc kids can’t possibly be done with college-prep-level students, that it must be nice to have the opportunity to work with the honors kids where discussion-based learning is possible, and that I’ve lost touch with the reality of most classrooms.  I have essentially dismissed all of this, firmly believing that discussion-based learning is the way to go regardless of the “level” of the student.  There was no doubt in my mind that if we don’t prejudge the ability of the students to take responsibility for their own education and give them the opportunity to do so, great things will happen.  

This year, I have five honors pre-calculus classes and one section of algebra 1, which has provided me with the opportunity to run a college-prep-level class by discussions.  With as much work as we have done over the last couple years for the honors pre-calculus class, the preparation in terms of  exercises and so on has been minimal, and instead we have been able to focus almost exclusively on the kids.  However, I have not taught algebra 1 for about six years, long before I converted my classroom to a discussion-based learning environment.   So, the preparation work for that class has been extensive, writing exercises that lend themselves to discovery and discussion (which are sorely lacking in the textbooks).  In addition, of course, there has been the usual struggle of getting the kids to take responsibility for their learning, which is something that the honors pre-calc kids struggle with as well.  That being said, the algebra 1 kids have been, for the most part, far more willing to take chances, make mistakes, and learn from the experience than the honors kids.  As such, I have had the opportunity to watch them in the early stages of solving linear equations, finding an equation of a line, and multiplying polynomials, and then help correct the misconceptions in a much more individualized way.  This informal daily assessment is crucial for any student learning anything, and a discussion-based classroom is the perfect place to allow this to happen.

Two days before the most recent test, I gave the kids a practice test in class, running that day in exactly the same manner as I do the actual test day.  I graded the practice test that evening, which allowed me to see where the misconceptions remained and where the common mistakes were being made.  The next day in class we discussed the practice test exercises, and the kids got to use the practice test as a means of preparing for the real thing. Was the practice test taken for a grade?  Nope.  Did the kids take it seriously?  Yep, most of them did.  They understood the benefits of practicing well for the test, and realized that the only way to correct the mistakes was to make and become aware of them.  

Then came the actual test.  On a test with which students have historically struggled, fourteen of twenty-seven students earned some version of an “A”.  Most of the rest earned a “B”.  The test was the only grade that actually went in the gradebook.  However, the success most of the students had was set up by the informal daily assessment and the formal practice assessment, the more personalized, detailed feedback the students received, and the seriousness with which the students took the feedback they were receiving.  

In other words, testing and assessment are not the same thing.  Assessment is what happens as we prepare the kids to take a test, or at least it should be.  And in my experience, a discussion-based classroom allows the necessary assessment and feedback to happen in a way that a lecture-based classroom never could, regardless of the “level” of the kid.