An Ah Ha Moment

 Today while teaching my Algebra I class about the slope intercept line I had a breakthrough in my own teaching.  I realized we teach the standard linear equation as Ax + By = C and the slope intercept as y = mx + b. 

In the past I have never shown a connection between the two equations.  Today, I suddenly realized that we assume the students can make the jump from -A/B to m without the connection.

So today I wrote the notes to the left for the students so I showed the connection rather than assuming they would make the jump.  Do you know that many books do not show the jump either?  If you work with students who are a not as good with their math skills, they can easily miss that jump without the additional clarification.  I had my students put this in their notebooks. 

Too often we teach the material in the same way we learned it and with the same gaps.  We assume all our students will make the jump without having that one missing piece.  I remember in one class I took at college, the professor always hit a point in the problem, drew an arrow, stated it was intuitively obvious and then wrote the answer.  I hated that because the arrow was always in the spot I needed to see to connect the dots.  It always made me mad so I understand that missing link.

Perhaps we can look back in our own histories and remember the times that our brains did not make that jump everyone else made when we teach things like this.