Rotation Help

Fellow math nerds: help me out here. I was describing how to rotate a figure 270 degrees clockwise to someone. I told them to reflect the figure over the y-axis, then switch the coordinates to fix the orientation. They told me this was the formula for rotating a figure 90 degrees counterclockwise. Well, yeah. . . . what's the difference? Is there a different formula you're supposed to use for a 270 degree clockwise rotation vs. a 90 degree counterclockwise rotation? I'm at a loss. . .

Project Based Learning

I recently found out that I'll be moving from middle school to high school next year. I'll be piloting a new program with another teacher with Algebra I and Algebra II students in the same classroom.

Our high school is a "New Tech" school, which means it's focused on project and problem-based learning. The tentative plan is to do projects, lead small group workshops, and generally be "less helpful," (to borrow the words of Dan Meyer). We'll have a 1:1 student to computer ratio. No sitting in desks in a row, no lectures, no traditional homework assignments . . . . have we lost our minds? I'm excited, and also a little terrified about how this is all going to work.

We're going to be using a program called ALEKS as the main backbone. I've never used it before, but have heard great things about it. ALEKS is an "artificially intelligent assessment and learning system." To me, it takes standard based grading to a whole new level. Students have to show mastery of a concept before it's added to their "pie." I can also set up assessments on a regular basis - if they get something wrong, it gets taken back out of their pie, so they're constantly reassessed on what they know. And the best part is that the computer grades it all for you! Talk about freeing - I can't wait to have more time to spend developing projects instead of grading papers.

Comic Strip Math

I stole an idea from The Exponential Curve this week. I had my students create comic strips to show how to graph a line. Some of them turned out really good - it didn't scan all that well, but here's a sample:

Illuminations

I often find myself at the NCTM Illuminations website on Sunday nights, trying to come up with an idea for Monday's lesson. They have a lot of good ideas for lessons and activities. I don't usually use the worksheets that come with them, but they're a good starting point and are pretty easy to adapt to fit my classroom.

Last night, I was looking for an activity to review slope-intercept form with my students. I found this. Students place ordered pairs on a graph as battleships. They draw numbers out of a hat to use as the slope and write equations of lines that will "sink" the battleships. NCTM's suggestion was to have students do the activity with a partner and then check each group's paper for accuracy at the end of class. I knew I wouldn't have that kind of time, so I changed it a whole class activity instead. I had each row of students choose a point to place their battleship. I put the numbers for the slope in a bowl and had random students choose one at a time. We worked as a class to figure out which battleship we could sink. They had a little bit of a hard time figuring out where to start on the y-axis, but got the hang of it after a few examples.

Standards-Based Grading

Think Thank Thunk just wrote an interesting post about Standards-Based Grading. Here's a few pieces:

Prob­lem: Kids want to play games to get points in order to get an ‘A’. This is a prob­lem because it puts empha­sis on accu­mu­lat­ing points and not on what the points are sup­posed to rep­re­sent: learn­ing. You must migrate your sys­tem of grad­ing away from grad­ing every sin­gle assign­ment sum­ma­tively (that is assign­ing a sta­tic grade for every­thing a kid does), and towards grades that are indexed by content.

Stu­dents could not care less about their score on “Quiz 5″ from last month; they don’t even know what was on that quiz. Don’t put that in your grade­book. Put the indi­vid­ual ideas that that quiz assessed in your grade­book, so that the stu­dents know what it is you care about.

If you switch to Standards-Based Grading, the "What can I do to raise my grade?" question will become much easier to answer. It's not about accumulating points, or doing extra credit to raise your grade. Instead of telling them to study harder for the next test, or giving them an extra credit worksheet (don't get me started about the kids that ask for extra credit!), you can be specific and look at the areas they need to improve.

I've been pretty blessed at my school since I started Standards-Based Grading. The vast majority of my students love it and would never go back to the traditional quizzes and tests that I used to give. I actually have students asking me: "When do we get to take another concept check?"

I'm just sorry I didn't start this sooner.

Team Challenges

I tried a new group activity in class today (inspired by Riley Lark's post at Point of Inflection ). I took one of my quizzes from last year (I no longer give traditional quizzes and tests now that I've switched to standards based grading - if you haven't heard of it, you really need to be reading dy/dan) The quiz had 8 questions on it, so I put the students in groups of 4. Each student had to solve all 8 problems, but I only graded 2 problems on each paper. Example: problems 1 and 2 from student A, 3 and 4 from student B, etc. I called it a "Team Challenge." Somehow that's incredibly less threatening to middle school students than calling it a Quiz.

Pros: I was really impressed to hear several students explaining their answers to their partners. I even heard two lower achieving students debate which formula to use to find the area of a shape. They were looking in the book for help, getting their notes out, asking each other questions: it was a miracle! For the most part, the students were on task and it forced them to work together to make sure they all agreed on the answers they submitted. (Added bonus: grading 7 group submissions vs. 28 individual ones)

Cons: A few students simply copied the answers their group came up with. How do I avoid this? I know they probably don't know how to solve the questions and don't want to ask for help - how do I change this? I debated making each person explain one problem to me, but that would take forever . . . Any ideas? At least they copied correct, complete answers. Better than doing nothing I suppose.

Overall, I think it was a success. I think I'll try it again next week.

Dot Paper

Dot paper is a great way to create area problems for students to solve. The best part about it is that it forces students to figure out which measurements are important, instead of just giving them a diagram already labeled.

A word of caution: some students will just count the dots instead of counting the spaces between the dots. It's a good idea to do at least one sample problem first.