I found this idea on Pinterest, posted by Keri Lewis an elementary teacher on her blog KinderKeri, but I thought I could use it in the high school setting. Basically, you use colorful Wall Pops!, a peel-stick+move dry erase dots on a table. I usually have a cup with lots of different colored dry erase markers (a little low in the photo).
Then when my kiddos come in for extra help, we pull out the colored markers and we work out problems together. The dots make for a non-threatening “third point” for discussion. A third point in a space off to the side of a conversation between a teacher and student provides a psychologically safe place for information, concerns and problems to land that students might bring to a help session. The big dot offers a subtle but critical distancing of the information that may be causing students to feel anxious about not understanding. The dots are colorful, so it initially feels “fun” and the students love to write on them. The act of writing larger than on a piece of paper also helps students slow down a bit while also making their thinking visible to me as I’m trying to help.
What are some strategies you use to help students feel comfortable confronting their misunderstandings and build better grasp of the ideas?
Today in precalculus, I was beat over the head about how important it is for students to truly understand the conceptual underpinnings of learned procedures. I asked students to evaluate a difference quotient expression where the function was the inverse function:
Simplify the expression when : Then evaluate when x = 3 and h = 0.
Did I learn a lot about what students had memorized poorly as well as misconceptions. What a great opportunity to explore via asking the right questions their misunderstandings as well as give them tools for figuring things out when they are not sure how the mechanics work.
This problem also gave us an opportunity to revisit the idea of an undefined value when it is indeterminant in nature; i.e. 0/0 and how that is related to the point discontinuity. Good stuff today!
Today we begin our study of matrices! I so love this chapter! There are so many ways to bring in mathematical topics that aren’t part of the regular prescribed curriculum. There are so many interesting and useful applications of matrices. The beauty and inter-connectedness of mathematical ideas shines through when we use matrices.
My course partner and I decided to try something a little different for this chapter. The mathematical skills involved with matrices are pretty straight forward and we believe our students will pick up the skills relatively quickly…so why “waste” valuable class time demonstrating skills and practicing? We asked ourselves, “should we “flip” this chapter?” I do have my AP Statistics students watch videos pretty regularly to gain skills, but I didn’t think I could find time to create matrix videos for precalculus. What about Khan Academy? These are pre-made videos with support self-quizzes and a way to monitor students completing the required skills. I was hesitant because I find the videos to be very skill-driven and not much pondering or questioning….but how can it be in a non-interactive video. Besides, the purpose of watching the videos is to present skills and have a way to practice the basic process. So why not Khan? There was a good chapter on Matrices and covers all of those “boring” skills in a way that students can control how they receive the information.
Today, we had our students sign up for Khan Academy and then will assign each matrix module in the Khan Precalculus topic as needed while we use class time to dig into the uses of matrices. My students got started: signed up for my Khan Academy class, and assigned the first module-Basic Matrix Operations. Many of my students huddled together to watch a video and then did the prescribed/required 5 correct problems in a row on the video skill. Tomorrow we will begin our adventure into Matrices!