Examples for Geometry:
- Visualization of parts vs. whole (Isolating info from one part of a diagram; combining info across multiple layers / perspectives.)
- Mechanical precision (Measuring and constructing lengths within 1 mm error and angles within 1 degree error; building solid models that won't fall apart.)
- Comprehension of diagrammed instructions (ie. for building anything)
- Attention to details in written instructions
- Judgment of reasonableness (of any physical or visual quantity)
- Effective written and oral communication
- Perseverence and resourcefulness
- Team work
Examples for Precalculus:
- Interpretation of data (Understanding trends / real-world significance / impact.)
- Fluidity with technology (Using graphing calcs fluently and flexibly.)
- Flexibility / creativity of problem-solving approaches
- Risk-taking and reasoning about the unfamiliar
- Precision and clear step-by-step organization of thought process / math work
- Increased self-management of progress, frustration level
- Effective written and oral communication
- Perseverence and resourcefulness
- Team work
Maybe it's just me being cheesy, but I think both the students and I might benefit from my posting these goals on the wall -- especially if I do actually highlight different skills throughout the year, as is appropriate to a given lesson, so that the kids would feel like they're not just learning content for content's sake and we are working towards a bigger picture.
My lists of goals are pretty generic (not really even math-specific, for the most part... Most are just good habits of mind...), but they are reminders of what is most important to me. Naturally, between the freshmen (Geometry) and the juniors (Precalculus), there is quite a bit of a "life experiences" gap. So, my goals for the two groups are pretty different as well. My juniors don't need as much for me to hold their hands on following directions, but they might need a nudge to be more creative and/or persevering. Versus the freshmen, whose first task of this year is to learn to consistently read and follow instructions. :) They each are at a different developmental stage with their meta-learning.
We have an opportunity each day to impact kids, mathemagically or otherwise.
-----------------
By the way, I found some nice graphs for my graph-reading lesson that is coming up. They're neat, even though they are not terribly complex in a mathematical sense. (The textbook's got a couple of nice complex graphs to use for rigorous classwork exercises, so I feel like I could afford to spend the rest of the period looking at interesting -- albeit simpler -- graphs with the kids.) They have to do with the mobile market, digital textbooks, and digital music. I plan to have fairly open-ended discussions about trends in those graphs, who might be interested in reading them, and what their implications might be for those people. And then maybe end with why these kids should finish college.* It could end up being a total flop of a lesson hook, but I am curious to see what these juniors can bring to the table.
If I have time, I am also thinking about adopting a middle-school post-it bar graph activity to composite bar graphs and scatter plots. I would give every boy a yellow post-it and every girl a pink post-it, and we would start a bar graph template on the board -- for example, models or brands of cell phones. They would go put their post-its on the board, in the appropriate column, and we would re-arrange the post-its to stack the pink post-its on top of the yellow post-its, in order to create a composite bar graph showing how many boys, girls, and total # of students have each type of phone. You can also do this exercise with scatterplots (for example, height vs. foot length) and see at a glance 1. what the overall trend is within the class, and 2. what the gender-specific trend is within the class. Using only colored post-its! And requiring maybe only about 10 minutes, discussion included. ...I'll try to squeeze it into my Precalc lessons this week and tell you lurkers how it goes.
*From what I hear, many Salvadorean private-school kids end up dropping out of college in the States, because they either lack the academic skills or -- more commonly -- can't deal with the fact that they no longer have a live-in maid and a designated chauffeur. This waste of an opportunity is terribly sad, considering that their parents can afford them to obtain a U.S. college education, while the majority of people in this country are living in poverty and many are starving. :(
But, can you really blame the kids for this injustice?? They are a product of the system (of huge disparity in wealth). sigh.
