## Tuesday, February 5, 2013

### Good Things and Bad Things

Good things:
• I've been thinking about little changes that have big impacts. For example, recently my colleague asked me for some articles on teaching with technology. When I was reading up on various research done about teaching via graphing calculators, I learned that how the teacher teaches with the calculator actually has a great impact on student learning and flexible problem-solving. If a teacher always emphasizes the connection between algebra and graphical analysis using the calculator, then even when you take away the graphing calculator, more of the students are able to think flexibly of multiple modes of solving problems. So, I have been pushing my Grade 8 students to be more and more reliant on the calculator as a daily tool, rather than just irregularly incorporating it.
• This change has allowed me to take on an even more passive role in my Grade 8 class (which is good, because that means they have to be even more independent). Now when I go over answers to worksheets, we only go over a subset of the answers, during which I call on a student, they provide their answer, and then I turn to the class and say, "Does everyone agree?" If they agree, we go on, and I never have to say true or false. If they disagree, then I pick a person to say step-by-step how they did the problem, and after each step I ask the class, "Do you agree with everything on the board?" Eventually, the class helps them to find their mistake, or we all agree on their answer and other kids try to figure out their own mistakes. After reviewing about half of the worksheet answers, I give the class another 10 or so minutes to verify the rest using a graphing calculator. My 8th-graders have become really good at graphing a function on the TI, adjusting window range, and then using the numerical-entry feature of Trace to quickly verify (x, y) pairs on the graph. They also know that they need to graphically check 2 points on a line in order to verify its equation, and they know how to verify their predictions along the line such as checking the value of k in (1000, k), or checking the value of n in (n, 849). On the test, I built in extra time for them to just check everything on the graphing calculator, and in the end, the kids said that the test really wasn't so bad. (Even though it had at least one quite tricky PSAT problem and other parallel, perpendicular, collinear testing problems that are fairly complex for Grade 8.)
• My 7th-graders are getting very communicative about math. Today, we played a modified Bingo Game to review for our test on Thursday. I had them write in integer values of -5 to 9 in a 4-by-4 grid, with 1 "freebie" space anywhere. Then I started writing questions on the board, one at a time. Nothing special, except we weren't going over the answers like we normally would. Once they determined the solution to a problem, they can cross that solution off of their grid, but they had to put the problem's letter (A, B, C, .... etc) next to the crossed out number, so that if they got Bingo, we could verify that they actually had all the correct answers associated with the correct problems. Sometimes I noticed while walking around that the kids were getting stuck on a problem, so I would ask, "Who can give a hint for how to start this problem?" and kids would eagerly raise their hands to offer hints. Along the way, they offered many hints like, "Cross multiply!" "Reduce before you divide!" "Find the common denominator!" "Check by putting the values into the equation!" and they also helped each other set up the percent increase/decrease problems as proportions, multiplying decimals, and finding "weird percents" like 0.1% of 3000 or 400% of 0.5. These 7th-graders are not just getting really good at algebra, but they're getting all the descriptive terminology down, too! Sometimes, they noticed that they had marked the same number as being called twice during the same game, and they had to go back to figure out which problem was solved incorrectly, and that was another way of having them self-monitor instead of me monitoring them. Eventually, when someone called out, "Bingo!" they would give me the problems and the solutions associated with those problems, and instead of me saying whether each answer was correct, I would ask the class. If the class agreed, we'd let the kid go on to the next number. Else, we stopped to go over the problem on the board. Again, I keep thinking about how I can hand over more and more of the "correctness" control to the kids, and today was a good day in Grade 7 for that.
• I recently started my weekly lunch review session with my 12th-graders. I told them right off the bat that these sessions are totally voluntary, but the kids who come tend to do a lot better on the IB exam. It's not the one-hour studying during lunch that makes the difference. In fact, when they come, they just sit and do independent mixed practice using old exams without my help really. I am helping to model what it should look like to study at home, and my physical presence builds their courage to try unfamiliar problems, I think, knowing that I can be there to help if they do get terribly stuck. The first session went very well last week. I plan to alternate between non-calculator paper and calculator paper each week, in order to build up their ability to switch gears and to think in a different mode during a different setting. So, this week we'll be doing a calculator paper. Whatever they don't finish, they'll just take home as additional homework, since I expect that they're now putting in at least a couple of hours each week to do mixed practice on their own. I have seen them grow a lot during the last year and a half, and I know that they will do well if they put their minds to it.
• In the end, I received some very positive feedback from those of my 9th-graders who had put in a lot of work into their videos project. They said that even though in the beginning, they weren't totally comfortable with the topics that they had chosen and the problems that they needed to explain, by the time that I had made them re-do and re-do it, they thought the concept was very easy in the end. The question that remains is only how I can manage this in the future for all kids, even those who put in minimal effort, and how to extend this level of articulation to all topics, and not just the one that they chose at the semester mark.