Algebra and a Mixed Convergence

The title probably makes no sense, but algebra has been in my face lately in a multi-faceted way.

FIRST I'm following a friend's post and comments on facebook about her experience wanting to be an RN or at least get an AA degree, but intermediate algebra is stopping her in her tracks.  She's in her forties; she's a bright, dedicated, mature person and very, very frustrated.  There is even more frustration in the comments of others to her post - about how algebra is from the devil and that no one ever uses it and how awful and how hard it is and that it is the one thing that keeps people from their educational and career goals.  (My first thoughts and feelings on this are that I am desperately sad for her - and that I both love and hate being a math teacher.  I love it that I am in a position to help people who have never liked or been successful with math before - it's quite a high to be part of helping someone succeed where they never thought they could! - but I hate it that I as a person am often disliked or even hated at face value because of the topic I teach.)

SECOND In my Math for Liberal Arts Majors class today my students were giving presentations on mathematicians as part of a math history unit.  One person presented on Rene Descartes whom we have to thank for the Cartesian Coordinate System on which we do most of our graphing.  The student mentioned how by creating this system Descartes put geometry and algebra together, thus making algebra EASIER.  (Yeah, of course, because now you can make a picture of your equation, and you can see how it behaves and where the maximum and minimum points are and so on.)

THIRD In my position as liaison to the tutoring center I was in the center evaluating tutors today.  One thing I observed was multiple tutors trying to help a student who was working on finding graphical information about a quadratic equation.  He needed to find such things as the axis of symmetry and the vertex.  It was an uphill battle to say the least, and it just struck me how this thing (graphing) that was supposed to make things easier (according to my student earlier in the day) had now become its own intense struggle.  The contradiction between seeing and hearing these two things in the same day really struck me!

So I have a lot of thoughts roiling in my mind tonight about all this.  Partly it confirms me in my desire to pursue the history of mathematics.  I think that if we could teach math in a more historical context in order to show students how and why concepts were developed and how each additional topic makes the quest easier rather than harder - that perhaps this would be a good way to go.  I think it would help too for students to understand what the big question that was being answered was back in the day when each new tool was developed, because it would shine light on the meaning and use.

It seems that if the student in the tutoring center had been given a real-life question about a business owner wanting to maximize his profits and an equation that related to that and then the student was allowed to struggle with that for a while - trying to make his way in to the problem - plugging in numbers, trying to find the biggest value, wondering if he had found the largest for sure or not, figuring out how to be certain - and THEN the student was introduced to the idea of graphing, which would give him a picture of the equation - a picture that would allow him to see where the highest point on the graph was, which would also be where profit was greatest - that then a graph,which is a picture of what's happening, would be seen as the help it is rather than as just another topic that was thrown at him.

If I didn't need to earn a living I think I'd like to take a few years off and try my hand at writing a textbook that would allow students to see the benefit of what they are learning and how all of it relates to all the other topics they are learning - where it fits in the scheme of things - what it's good for - and why and when and how it was developed.

Maybe in my next life  .  .  .

For now I'll just do the best I can to help those who come my way and try to change their worlds, one student at a time.