I had my first official tutoring session by way of WyzAnt this Saturday. I will say that it was vastly different from my experience as a teacher. I have been helping students with math for years but in each instance, I had some inkling as to what the task at hand was. Sometimes I would overhear the teacher going over something next door, sometimes I was the one who gave the lesson. Other times I would have access to the textbook that was being used so I could see exactly how something was explained to a student. This was different. I knew that it was pre-algebra material and that there were a lot of word problems involved. However, I was somewhat surprised at how the questions were written. I have seen packets before where students were required to solve a certain type of problem and then create their own but I was not as prepared as I would have liked to have been to tackle these specific problems.
First, I had never seen the packet before, nor have I dealt with a students from that particular school. Every teacher and therefore every school is a little different so sometimes it helps if you have a working relationship with the teacher that created the material.
Second, I have a ton of other resources in my house but I had no idea what to bring with me besides some very basic things. I had an Algebra workbook, some pencils, two graphing calculators and some scratch paper. (I also had my Livescribe Echo smartpen and some digital paper but I tend to have that with me regardless.)
The first question on the first page was simple enough. It had to do with ratios. The second page had to do with least common multiple and greatest common factor. As I was helping the student through this particular problem (and while he was fighting sleep) it occurred to me that some review of lcm and gcf might have been helpful at some point perhaps in the future. Two things about that though. First, I am pretty sure he understood enough to get the answer to the problem on the page. Second, reviewing both of those concepts during a single one hour session might not have been the best way to go about it. This is something that I remember from one of those teacher training session a while back. Let’s say you are teaching the students longitude and latitude. If you teach one and then the other, the students will retain the information better. If however, you teach/intensively review them both at the same time on the same day, they spend the rest of their lives trying to remember which one is which. So I had these things going through my head and I decided not to interrupt my explanation of the problem to go back over the finer points of lcm and gcf. That and the fact that the Algebra workbook that I had did not have anything on lcm or gcf although I could have made something up using the pencil and paper.
Now for the biggest pitfall of the whole thing. I managed to get something wrong when I was explaining the second problem. Here is the problem:
The person is thinking of two numbers. The greatest common factor is 6 and the least common multiple is 36. One of the numbers is 12. What is the other number? The problem gave three hints.
1. Write the factors of 12.
2. Can the other number be three? Why or why not?
3. Can the other number be six? Why or why not?
As I was working with the student, it was obvious to both of us that the answer could not be 3. He thought that it might be six. At first I thought so too until I wrote out the multiples of 6 and 12. It was actually the mom who caught the 24 in both of the lists, after which I saw the 12. So clearly 6 could not be the other number. Then I thought that it could be 12 but that did not meet the two conditions either. Then I began to suspect that perhaps there was a mistake in the instructions. I looked at the information again and that’s when I saw it. It was not a mistake as much as it was an unhelpful hint. Unhelpful for me anyway. Hint number 1 was to list the factors of 12 but that is not what I would have done if given this problem without any hints at all. At this time I knew in my head that the other number was 18. The trick was to explain it to the student in the most efficient way possible. Instead of writing the factors of 12, I wrote the factors of 36. After all, if the lcm is 36 then the answers will both be factors of 36 so the answer will be in there somewhere. We eliminated each possibility until on the 18 was left.
I think that it might be helpful for this tutor to make all efforts to get his hand on that packet so that I can be as prepared as possible for a second session.