A Practicum Experience

I was just ready to start teaching my first Math 10 class on the subject of slopes of a line, when a young lady put up her hand.

Yes, I said motioning to her.

We are the dumbest math class in the school!, she said.

I was caught of guard for a moment, and then I responded, "No one is dumb, it is usually a matter of not knowing something and this tells you what you need to review or study so that you do know the material that you missed or forgot.

I started the class out with a question, "What is the slope in words?"

One student said, "that the slope was calculated from the difference of two points, with the rise being the y difference and the run being the x difference."

Another student said, "putting the two together with the rise divided by the run gives us the slope."

I wrote: slope = m = (y2-y1) / (x2-x1) and put the numbers in for the two points (2,5) and (1,3)

(5-3) / (2-1) = 2/1=2

Feeling that the class was doing fairly well I continued, " The slope for a line segment which you took yesterday is the same method with the two points picked from points on the line."

I demonstrated with an interactive drawing program that if you pick two points and I had students give me the values of them, then this is how the slope would be calculated and this is what the line would look like. I gave them the formula that they took the day before for a line segment and showed them that it worked for a line as well.

"Now, I said, that if you take one of the points along with the slope you just calculated and put it into the same relationship and simplify, you get the equation of a line."

I assumed that they knew about additive inverses or the rule a +(-a) =0 to eliminate the constant from one side of the equation to another and I named and showed them how to eliminate the constant from one side by doing an addition to both sides of the equation. I then simplified the equation into the form y = mx + b.

Another girl in the back raised her hand and asked, "what level university math do you teach at UBC?"

My response was that this was grade 8 or 9 level math.

I had a worksheet with a clearly worked out example in detail with what we covered. I went around the room and ask if anyone needed help? I gave them some HW.


For the next class I rewrote the lesson plan three times to make it simpler, with a better worksheet.

The results from the worksheet were poor, not from the understanding of the method but from being unable to add, subtract, deal with a negative number, deal with fractions and multiply by zero.

I was left in a state of disappointment from the classes poor arithmetic skills.