Math tutoring

A tutor is not a teacher in the usual sense: it is not his job to convey information. The student should find for himself the information. The teacher [sic] acts as a constructive critic, helping him to sort it out, to try it out simetimes, in the sense of exploring a possible avenue, rejecting one approach in favour of another. Moore, 1968, pg 18

I've been tutoring math to these kids from Nombuleo for a few weeks, and its been on my mind for the last few days. I read this quote in a paper, and it echo's my thoughts (in part). I have been using the phrase tutoring, rather than teaching, deliberately for some time. I 've put a fair amount of thought into how to approach teaching/tutoring these kids, and these are some of the thoughts/principles I have come up with:

• "First, do no harm" (Innoxa) - At the very least, let me not confuse them, not undermine their confidence, not undermine what they already know, and not undermine their teachers!
• The Baard method - In University Physics tuts, we are encouraged to use the Baard method - named after one of our previous HODs. You get small groups to work togther at different sections of the board, and you walk between them, helping as necessary. I try and use a similar method for tutoring high-school math, where possible. We usually sit around the board and the kids take turns doing problems on the board for us, but the whole group helps and advises, and does calculations on their calculator for the person at the boad when necessary. I was actually quite suprised this method worked - its usually remarkably difficult to get university students up to the board to answer questions for the class, or even in groups! Sometimes it gets a bit difficult when there are quite a few kids - 4 is a comfortable maximum to use this method. Thankfully Brent has been helping me out, so we can sometimes break into two groups.
  
• Tutoring, not teaching - These are kids writing matric math in a few weeks now. Frankly, there is not really time to teach them anything new. And perhaps more importantly, they already go to school, sit in math classes, have a math teacher and learn math. My goal isn't to teach them new things, my goal is to help them apply (unpack!) what they already know, and to help them grow in confidence. The goal is that they can actually *do* math problems. On occasion I have to teach them things (you need to know the special triangles, for example), but that is not the primary goal of my meeting with them. Its much easier to stand at the board and explain the answer to a question to them, much much easier than getting them to figure it out for themselves! But at the end of the day the goal is them being able to do things themselves, not me feeling good about my explanation. Which is part of my motivation for making them do things on the board themselves.
  
• They lack confidence - For the most part, they lack confidence to a detrimental degree. Part of the motivation for tutoring, rather than teaching, is to show them that they actualy know quite alot. And they are more capable than they thought. There is little as empowering as realising you actually *can* do something you initially thought was impossibly difficult. And with a bit of prodding in the right direction, they often can do math questions they really thought they couldn't.
  
• They are generally mentally lazy - So am I. Most of us are. Especially in areas we we lack confidence... there is just no motivation to mentally apply yourself to something you think you have no hope of figuring out! So I have to provoke them to think, allow them to get things wrong and have their class-mates correct them, just wait while they stubbornly refuse to ask questions, try and think of leading questions that will give them just enough of a clue to get started, and then they are engaged and its much easier.
• Helping each other - I try to leave them to correct, encourage and help each other as much as possible. In fact I keep my involvement as minimal as possible. Their first language is Xhosa, so ideally I would like to speak to them in Xhosa, but alas I cannot. So when they all discuss a problem together in Xhosa, thats great. Also, they are all learning the same way, and they have roughly the same information/way of understanding in their heads. I did matric maths yonks ago, so in many respects they are more qualified to help each other than I am to help them. And referring back to the first point - at the very least, I don't want to confuse them. Rather let them explain to each other in a way they are all familiar with, than me giving an explanation that works for me, but that is unfamiliar and intimidating to them. Also, it pulls them all in to engage with the questions. When someone gets things wrong on the board, I often leave it for a while to give someone else in the group a chance to see the error and correct it - which often happens. Sometimes I do step in and correct something, especially if it is a fundamental error/misunderstanding, but I try to keep this to a minimum.

One of the reasons I have thought this through alot is that I heard that you have to be quite careful when to teach kids from non-former-model-C schools (jeepers, what a mouthful). Also just because I'd like to actually be making a difference to these kids, not just wasting 3 hours of their and my lives every Saturday!
If you have any advice or thoughts on the matter, I would love to hear them!