If anyone is still out there reading this blog after I took a long hiatus, please indulge me with a response. How do you define algebra?
I just came from a great PD led by the lovely Kara Imm. She brought research concerning the lack of “algebraic thinking” in K-6 math, where arithmetic is taught almost exclusively and algebra is the step that follows for “those who are ready.” (I think some high school teachers have this mindset about Calculus. Students need to learn Geo/AlgII/PreCalc really well “to be ready” to start Calculus.)
So if (as research shows) it would be better to teach arithmetic and algebraic thinking from the start, can we first define algebra?
After a lovely dinner with the splendid Sam Shah, I realized how much I love discussion of math and pedagogy and want to get caught back up on this blog! I can’t believe I haven’t written since September. I will get better. I promise…
Anyway, classes have been going well, but one thing I wanted to mention (encouraged forever ago by Sam) is how I handle a lot of theorems and conjectures in my class. I try to make my class as “discovery based” as possible. It is also of interest to me to model how real math discoveries work. So, in my class, students are encouraged to be “the first” to discover a new pattern/idea/conjecture, and as a reward, they get to name the conjecture.
Here’s a great example: I start of PreCalc every year with logic. We explore and/or/if…then statements with concrete examples, abstract symbols (p’s and q’s) and kinesthetically (with this cool note card idea I will blog about someday). When it comes time to discuss the negation laws, students are given a task to find the negation on their own. The students struggle with it the first time, but eventually someone comes up with and names the rule for negating an “and” statement. In the past, it’s been called Kira’s Law or Janelle’s Law, etc…much more fun than DeMorgan’s Law or what my textbook blandly calls Negation Law #1. Blah…After the first one is named the students go crazy (like, CRAZY) to get to name their own law, and they look forward to new laws being discovered (and sometimes come up with their own side laws!) throughout the year.
What was especially fun this year was students started sharing the naming with their partners. So instead of Trevor or Moses claiming they were the true founder of the law, they named it the Mosever Law. Catchy, fun and led to a brief discussion on why some more advanced theorems in math have double names! 🙂