Giving an algebra final exam today – it’s almost like the first day of class – here’s the problem on the test that is causing the most angst:

*The proceeds from your college talent show totaled $2475. All the tickets were sold so you know that 600 people bought tickets. The cost per ticket for students was $3.25 and for non-students was $4.75. You need to figure out how many students attended the show. Use n to represent the number of students who attended. Write expressions in terms of n to represent the number of non-students who attended, the proceeds from student tickets sold and the proceeds from non-student tickets sold.*

Knowing full well from my experience that this is really difficult for my students, I gave them what I thought was a nice clue as to how to organize the information:

1-Number of students who attended** n**

2-Number of non-students who attended _______

3-Proceeds from student tickets ($) _________

4-Proceeds from non-student tickets ($) _________

It was as though we had not spent a single hour on problems like this, although I know they did work many of them in class, for homework, and (presumably) studying for this exam.

No one knew how to write the expressions for 2-4. Crazy.

It occurs to me that I have no idea how to *make* them learn this – I try again and again and they still can’t seem to get the idea that the letter n stands for a number that we don’t know, and that all of the other numbers depend on n.

If I ask them to tell me how many non-students attended the show if 100 students attended, they can do it.

If I again ask that same question but change the number to 101, they can still do it.

They can do it no matter what *number* I give them for n. But once I ask them to *generalize*, it’s like their brain melts and they have no idea what to do – even though they just did it with *actual* *numbers* 4 or 5 times!

So, they cannot generalize – and this is the final exam! We spent the entire course generalizing – and they still can’t do it –

Makes me wonder if they will ever be able to do it –

They’ve taken algebra courses before – mostly in high school – probably since 7th grade. For 7 years they have had this topic – generalize – and still can’t do it.

If I decided to become a downhill skier, and after 7 years still couldn’t figure out how to put my skis on, I think I would give up.

that analogy isn’t really right – it’s more like, I knew how to put my skis on at Vail, but when we went to Keystone, why that’s a different place so I don’t know how to put skis on there – someone has to help me!

Maybe they need to give up.

Because if they keep showing up, we will keep trying to shove it into their skulls and they will continue to not get it –

I’m sure they’ve had better teachers than me in some past experience with basic algebra – and still they are here, trying again to learn the same things that have not been able to learn since 7th grade –

What is wrong with us?