I picked up a new class of 40 students today. This class is called “Math Tutoring” or “Math Lab”, depending on who you talk to. The students in this class are concurrently enrolled in another math class and the idea is that they take an additional period of math to help them do better. I’m a bit hazy on what exactly is supposed to be accomplished in this class besides that or how I am supposed to go about doing that, and most other teachers are telling me I can do what I want. There’s no assigned textbook, no curriculum. I probably am not supposed to run the class as a place where students do their homework, however.
The part of me that likes structure and well-defined tasks is very uncomfortable with the vagueness of the whole thing, but I should look at it positively and see it as a chance to do something creative.
One challenge is that some students are taking Algebra 1, some Algebra 2. They are taking math from a variety of different teachers, so even those in Algebra 1 will not likely be learning the same thing at the same time. How to make sure that they are all getting something that motivates, interests and is actually helpful to them? I also don’t want to do things that will steal thunder away from their math teachers. If I divide the class into two groups and plan two activities or lessons, that would be double the work…. Ugh.
Ideas welcome!
Adventures in Teaching 
I am not entirely sure what the goal of this class is supposed to be so the suggestions I give may be way off base… but here goes.
I took a “Math Elective” course in middle school… one of the activities I remember doing was being given a sheet of graph paper with axes labelled and another sheet of paper with instructions in the form of coordinates. The idea was you plotted a point, then connected it to the previous point with a line. If you did the whole thing correctly, you would get a picture of something. I found this pretty entertaining, since generally it was pretty difficult to figure out what the finished picture would look like. I think you mentioned in an earlier post that one of your classes has only just started dealing with naming points and such, but once they have a more solid grasp on it, this could potentially be a fun way to practice those skills. Similarly maybe you could do a “color by numbers” kind of thing which requires solving equations to determine what color goes in a given area.
I am guessing that the school wants you to be tutoring the students in math relevant to algebra or whatever else they are learning in their normal math classes. If not, I would suggest just showing them some cool, fun, not quite-so-formulaic as what they are used to seeing math. I don’t know quite what that would be. Maybe show them some of Prof Benjamin’s tricks (they could probably learn the one where you ask a volunteer to multiply numbers till they have a 6 or 7 digit number then to read off all but one of the digits to you and you guess the last one). Maybe show them pictures of fractals or how Fibonacci numbers and pi and other important numbers show up everywhere. Make polyhedra out of cardboard.
Hopefully at least some of these ideas are helpful… I have been reading “A Mathematician’s Lament” though so maybe they are just crazy. And now I need to go finish my own math homework (oops!).
Missed you at the dinner. From a physics teachers pov, I think it would be great if students learned algebra material that is skipped over because it’s not on the cst. Like, they can probably use the slope formula but don’t have a qualitative sense of what slope represents. Or about rates of change in general. Or you can expose them to symbolic algebra. Developing sense about fractions and decimals… Is 0.010 bigger than 0.1? This seems like it would be a really fun class to teach (if you had time to plan for it).
Hi — Have you thought about pairing up the Algebra I students with Algebra II students and giving them exercises where it might be a bit of a review for the II’s, and a bit of a stretch for the I’s, so the II’s can work with the I’s on them?
If you decide to try this, be /very/ careful about how you implement it…
I was in a science class one year in hs where a handful of us were designated as “honors” students even though that didn’t mean we did anything different. We started out the year with all of the honors students at the same table. At some point she changed the seating chart so that one honors student was at each table. In the process she made some comment about how that meant we could help our classmates… Something about the way she did it gave the impression that she was arranging us that way so that we could teach and she wouldn’t have to. I despised being put in that position (despite the fact that I was happily explaining things to my classmates in Algebra II when we did group work, which happened frequently).
Georgia Tech has a Math Lab 🙂 Though ours is a room that is staffed by TA’s from 11-5 MTWR where students in any of the core-type classes can come by with hw/conceptual questions (so kind of like a scaled up version of AE). Both in the Math Lab here and when I was tutoring summer math (the situations where I have found myself trying to help people that were working on very different things) I’ve found that it works well to encourage people to work in small groups with their peers and to float between the groups answering questions. I’m not sure how that would translate to a situation where they are not supposed to be working on HW though…
Are all of the students taking Algebra I and Algebra II also taking some section of Math Lab? If not, do you know how they decide which students do? How they decide which students take Math Lab might give you some idea of what it would be good to try to cover. Also, are you supposed to end up giving the students in Math Lab a grade?
One of the best ways to learn math is to teach it. My idea would be to have a student led class. They come in with questions from their own homework assignments or concepts from their classes that need clarification. Everyone works together to problem solve. You can split them into groups based on level of math or have them work in groups of mixed levels. A comment from someone a couple of days ago talked about groups that worked together towards a common goal even when there were students comming I would talk to that person and set this class up in a similar way. You can roam and help when necessary but really you would just be a facilitator. That is how I would do it anyway…
I was thinking about the student-led class and that got me thinking about how uncomfortable students can get with doing that kind of thing…so a follow up thought is this: in Aus, the culture is such that by allowing yourself to be almost “made a fool of” (not quite, but you know, let it be known you are not perfect, you can laugh at yourself etc) you can build a certain type of rapport. Maybe this might be a way into lightening the mood and letting everyone feel more at ease? Maybe it’s not quite right for this context or your culture though.