Wednesday, February 10, 2010

Algebra 1: Systems of Equations

We are finally getting to move beyond basic graphing and finding equations of lines.  It was a long slog, but the skills tests show that the majority of my students are starting to get the hang of it.  I always look forward to the systems of equations unit, because it is a chance for students to synthesize what they have been learning all year - and, in a situated context, no less.  My plan this year is to deepen the emphasis on representational fluency and summarizing, to help build all of those neural bridges we want the students to have.  We started the unit Monday, and I was really blown away by my classes today - all of a sudden, I have students doing algebra!  I had them solving systems in pairs, using mini-whiteboards, where one does the graphical solution and the other does the algebraic solution, and then they compare their answers.  They did a great job, and it wasn't until this activity that many students realized the answers should be the same.  I got a couple of those hilarious, indignant "you should have told us!" comments.  Next week is winter break, which doesn't come a moment too soon; however, I'm worried about how much will be lost over the seven days that nobody is asking them about starting points or rates of change.  No matter, it's worth it to have a rest.  Here are a couple of  examples of what we're doing, and the links to the lesson materials thus far.

Lesson 1 (Intro to Systems of Equations)  doc / GeoGebra files / Keynote / Powerpoint
Lesson 2 (Solving y = mx + b Systems)  doc / Keynote / Powerpoint
Lesson 3 (Practice Solving Systems)  doc

Sunday, February 07, 2010

Language and Retention of Math Concepts

I've been thinking lately that one of the reasons my students have such difficulty with long-term retention of mathematical concepts is due to the small number of times I ask them to thoroughly summarize what they have learned.  They do lots of problems, but the language of the problems often does not enter into their brains.  As we learned in Orwell's 1984, without language, there is no thought.  So I am going to start providing more explicit opportunities for the students to summarize and discuss what we are doing in class.

Comic Strips  (Unit 5, Lesson 9:  doc / keynote / powerpoint)
Quite a few students are still struggling with graphing lines.  They know the general process, but don't pay attention to the details - is the slope positive or negative; if a term is missing, is it the slope or the y-intercept, and how does that change the graph?  So, I had all students draw comic strips to summarize the process in these different cases.  I like how this went, but I definitely did not provide them with enough time to do all I asked.  Here are a few good examples.  The first didn't scan that well, but he did an awesome job.

Think-Pair-Share  (Unit 5, Lesson 11: doc / keynote / powerpoint)
This is a tool that our humanities classes tend to use a lot.  I got some advice from them, and will be trying these periodically during the next couple of units.  We did one so far, and it went reasonably well for a first try.  Students need a lot of practice both writing down their ideas and sharing them out.  Here is the handout I gave (it was used immediately after doing a Do Now problem of the type described).

Tuesday, February 02, 2010

Both Flattering and Disturbing

Students in our Numeracy support class have been working on plotting points to help them with graphing in Algebra 1.  The students just finished a connect-the-dot cartoon graph assignment.  One of my students apparently decided to dedicate her drawing to me.  Like my Speedos?