Math

I love eating pancakes, and so do my kids.  I remember that my mother use to make pancakes for special occasions or if we insisted on Saturday mornings too.  I'm different.  I like to make pancakes for no reason at all.  I'm 35 years old, so I've been making pancakes for at least 25 years.  Yet if you put me in a kitchen with all the ingredients for pancakes and said "make pancakes."  I couldn't do it!  Why?  Because if I don't have a recipe I can't make pancakes.  The first step I learned in making pancakes is to get out a recipe and follow it.  I still use a recipe to make pancakes because that's what I've trained myself to do.

Solving math problems (or any other skill) is like making pancakes.  When you work on solving a math problem, if you ask for help (from someone, or something - calculator, text, notes, etc) as soon as you get stuck you will never learn how to solve problems by yourself.  This is because you are training yourself to rely on something outside of yourself.  A lot of students say that they freeze up during tests or have test anxiety.  What is often happening is that the students have learned to work for a few seconds on a problem then give up and ask a parent, teacher, tutor for help, or look up a similar problem and follow it, like a recipe.    So, when they get stuck during a test, their brain says, "Aha!  Get help!"  But no help is available, and so naturally, anxiety arises!  They are asking their brains to do something new, AND it's for a grade!  Of course they have test anxiety!

These students have never practiced working hard at a problem and failing over and over and over again, and trying to really figure out the problem by themselves.  A lot of parents complain when textbooks don't have problems just like the ones their children are doing to look back on.  The parents have also been trained to get help, rather than working on a problem to figure it out and they are teaching their children their same bad habits.

This is one of the reasons why math tutoring doesn't help students become independently math competent.  The students bring their math to do in the presence of the tutor, and then when they get the tinniest bit confused they ask for help.  If they're a good tutor they will help the students see the solution, but even that isn't really helping the students, because the students haven't really tried yet.  Since the students are doing better on their homework, they feel like they are more successful - and if the homework is graded, their scores have improved.  But it isn't truly representative of the student's abilities or understanding.  In many instances, tutoring is a short term improvement, but a long-term disservice because it deprives the student of the needed chance to really start thinking like a mathematician.

Now, there  IS a beneficial way for students to utilize tutoring, or the help available from a textbook, teacher, friend, etc.   It requires a shift in our understanding of the role we want the tutor to play in the learning process.  And that is simply to ask for help only if you are really, REALLY stuck, and then to get as little help as possible.  Think about the pancake making.  The way to internalize (that is, to really LEARN) how to make pancakes is to have the recipe available, but to refer to it as little as possible.  And, over time, over many repetitions, to rely less and less and less on it.

I've been tutoring students in math for 6 years and teaching math in the public schools for three years before that.  No matter how many times I tried to teach my students the importance of doing homework by themselves and only getting help if they got stuck - REALLY stuck, they never really listened.  In all these 9 years of teaching math, only one student was really truly good at this concept.  She was a homeschooled student who was doing Saxon math and her parents had gotten to the point where they couldn't answer her questions any more.  She came to me and I loved teaching her.  She had been trained well.  She did her math work at home and check her answers in the back of the book.  If she found one she got wrong she would do the problem over and over and over.  Finally, after making substantial efforts on her own, she would compile a list of the problems she couldn't seem to get, and then come and see me.  By that time, she was ready to learn, and as soon as I gave her a small nudge, she was able to understand, and then move quickly through similar problems.  While she was intelligent, fundamentally, her strength lay in the fact that she understood the need to put forth a true effort in order to learn.

In my calculus class in college I sat down to a test one day and was faced with this quote written on the front of the test:

A problem worthy of attack shows its worth by fighting back. 

—Paul Erdos

I have remembered that quote ever since.  I learned in college that if I was willing to fight this fight then I would learn, but trying to find the easy way out usually meant that no true learning happened.

As homeschoolers we want our child to be life long learners in math as well as in many other disciplines.  That means life long fighters too.   They need to put forth the effort that will make learning happen.

Now, if I could just put forth a little more effort maybe I'll could learn how to make pancakes without a recipe!