The Gaps Are Glaring

Coming from the middle school, it was clear where students were struggling.  After all, it was basic, applied mathematics.  Maybe they had a hard time with the conversion of decimals to fractions or vice versa.  Maybe they had a tough time graphing linear functions.  Certainly there were some who had trouble with the exponent rules (let's be honest... who didn't?).  The problem is that we considered them proficient and moved them along for the high school to worry about (or so the high school teachers believed).  

The problem is that this is clearly not true.  Students failed.  Maybe not many, but there were some who failed.  Even worse, there were students who passed because they knew how to do enough extra credit assignments to move to the next grade.  Others knew just enough to slide by the dreadful F.  So, here we are, staring at the grades of my Geometry classes for Semester 1, and they're atrocious.

We just took a quiz based on parallel and perpendicular lines.  This is not a Geometry standard, but its application is.  We have spent 5 days reviewing and working on point-slope, slope-intercept, and the slope formula.  

Without reservation, I would consider this a fair assessment.  The slopes play nice, there are no decimal/fraction answers, and the computations are not jaw-dropping.  This is a measure of where students stand with the basic concepts of parallel and perpendicular lines. Here is a sample:

I can't put any blame on any former teacher that this student had.  He found a way to incorporate a physics formula into a problem relating to the equation of a parallel line.  I'm stumped here.  We can't even get into the geometry because my students struggle with the algebra!

However, this isn't the most confusing.  I can deal with a student using the wrong formula, even if it's WAYYYYY wrong.  What I don't know how to deal with is this:

No attempt whatsoever for number 2 or 4 and no work at all for number 3.  The expectations have been clear since August 7th when we started school that I need to see the path in which the student used to reach a solution.  How do I deal with that?  But wait, there's more... Or less.  I had 3 students who chose not to turn anything in.  Instead of getting 1 point credit for setting up the problem, they chose zero.  I know that I'm not supposed to "give" zeros, but these students have chosen to show me nothing.  Other than a zero, I don't know what to enter into the grade book.  Yes, I'll pull them aside and talk to them tomorrow, but this is insane.

As I sit here after school and contemplate today's lesson, a few things pop out:

• A couple classes rocked.  Class averages of 77 and 74 are good for my students this year, so I'll take it where I can get it
• Quite a few students aced the quiz, confirming that it wasn't unrealistic
• Students still have trouble multiplying fractions
• Students still have trouble multiplying
• Students still have trouble remembering formulas
• The three statements above are frustrating
• There are gaps in these students' learning that I don't know how to fix without serious intervention and complete remediation, yet I'm supposed to pass them........

We are a 2 weeks away from finals and many students still struggle with finding the slope of a line, plotting points, finding intercepts on a graph, dividing fractions, and many other foundational concepts.  As a math teacher, I'm baffled.  As a human being, I feel like we as a society have let students down by allowing them to promote through a system and widen the gaps in knowledge to the point where they begin to overlap and overtake a student's morale.

If we think that this Common Core rollout is a good thing, wait until those students come through the system with the intentional gaps as we transition from traditional to CCSS standards.  Those gaps might just cause the system to overload altogether.

Happy (Gappy) Fishing