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?
I decided over the week-end that my AP Stats students needed some more time practicing binomial probabilities in context. And I have these great primary school magnetic fishing poles (you know the kind at the kindergarten carnivals?!). Time for Go Fish! but not the card game.
I collected a variety of binomial practice problems, cut them out, put metal clips on them and put them in a big bowl…my fish in a pond. Short “bang for the buck” experience as my statisticians “fished” for their problem, but they liked it anyways! They they had 20 minutes as a group to organized, solve and present their solutions in a poster form. Gave them some guidelines around that should be in their poster (used my acrylic stand-up frames…you can see in the photos)
Once time was up, the groups posted their solutions on my handy-dandy clothespins and did a gallery walk. They were each given 2 post-it notes. They were to put one praise and one suggestion for improvement on their sticky for two different posters. They also checked their peers’ work. I was really happy to see things like: “define the variable” “these are just numbers, what do they mean?” and “careful of your notation…you need P(x>2) not just the work”
Pretty good conversations. Still not sure some of my students are comfortable with the mechanics of the binomial process. Have to use an opener question to test that tomorrow.
Using a sign chart is a visual way to pull together a lot of the concepts and processes related to polynomial and rational function!! I love how my students are like fish to water when we get to this topic. We have discussed, dissected and clarified the ideas so much that when we use them in a more abstract way, they rarely have difficulties.
Opener: For which intervals is the graph of positive? Increasing? How is finding the answer to each of these questions similar and different? How could you answer these questions without using your calculator to look at the graph? Or without looking at a graph?
I used the opener to introduce the idea of a sign chart. First of all, it was a nice review of factoring a cubic function. It was also really interesting to compare the words positive vs. increasing…typically confused when students haven’t been given the time to really think about what each word means.
The one question: “Did anybody do it differently” opens up so much conversation, and regrettably, I don’t ask it every day because of the constraints of the curriculum. But when I do, I end up with great insights into the variety of ways problems can be solved. My classes continue to amaze me with the different ways they think about problems and I leave class with a big goofy grin on my face!!
Today in precalculus, we did a foldable on the key elements of polynomial graphing. I revised one created by Rachel Rosales at Purple Pronto Pups blog. We took about 10 minutes to fill it out, and added some details beyond my kiddo’s last year’s knowledge.
With the foldable in hand, I gave each group a 3rd or 4th degree polynomial to graph in 15 minutes. I had one student ask, ” are we going to be doing this a lot this year?” I asked, “What do you mean?” And the response was, “You know, make posters a lot.” This was an awesome impromptu opportunity to talk about Making Thinking Visible with my students: that when learners speak, write, or draw their ideas, they deepen their cognition. Once again, got a chance to share my learning expectations for my students.
Love to see the “heads together” I was seeing with my students. We’ll find out tomorrow if the activity helped coalesce the ideas for my kiddos.
In precalculus, our first chapter is full of minutia…important minutia but minutia none the less!! So one of the biggest challenges is how to expose my kiddos to these ideas, make them stick while keeping it interesting. So a matching activity seems to work the best. They had 15 minutes to sort, match and produce their poster. Lots of great clarifying discussions while completing the activity!
Last year I used the crop duster problem in my precalculus class as an introduction to the eight math practices. I was very happy with the results, and found that my students were able to identify the practices readily throughout the rest of the year. After reflecting on the activity I decided I wanted to do some changes for this year.
One of the changes was to take away the coordinate axes in the picture , so the students had to think about how to impose a coordinate axes. We had a great discussion about various locations, discussing the pros and cons for each of those locations. Naturally the students decided to use the center of the circular field as the origin, but they were the ones that decided the location rather than being told.
A second change I wanted to do was to take away the questions. I didn’t want the students distracted by trying to solve the problem before the event understood what the situation entailed. Upon reflection, I wonder if I should also remove points P and Q. This would cause the students to realize at some point that they need those points labeled. Anyway, I gave them this information and picture:
After giving them the picture, we took some time to look at the information and determine what was known. After brainstorm eight as much as we could, we then look for possible usable relationships inherent in the problem. They initially balked at the idea saying, “We don’t know what the question is, so how can we possibly come up with relationships?” With a little prodding, they’ve really got into it. Here is a list of those brainstorms:
The third change I wanted to incorporate was to have students generate possible questions rather than being told the questions. By having the students do this, I was asking them to use math practice 2: Contextualize the situation.
Once we brainstormed the questions, we talked a little bit about how we would actually go about answering these questions. The really exciting part of this process is that once the students are given the questions they realize that they came up with most of them on their own AND had figured out how to go about solving the answer them. Awesome stuff!
What are some activities you have streamlined in order to get students to do more thinking and sense-making on their own without scaffolding?
This summer I want to get lost in reading! I’ve been compiling a list over the year based on tweet recommendations, blog referrals and face-to-face endorsements. I’ve whittled down the list to these 5, although I can already tell that I may add a couple others.
- A More Beautiful Question – Warren Berger
- Mindset – Carol S. Dweck
- The Falconer – Grant Lichtman
- 5 Practices for Orchestrating Productive Mathematics Discussions – NCTM
- Embedded Formative Assessment – Dylan Wiliam
What are you reading this summer and why?
Addendum: I’m adding “The Doodle Revolution” to my list. I’ll be posting more about this over the summer. I am so excited about it. It merges my left and right sides of my brain and gives me an outlet for my artistic side.
One of the things I really like to have happen in my classroom is having students take over the discussion. It’s occurrence is more rare than I would like it to be, so when it happens, I celebrate with little “yippees” in my mind. [Note to self: good summer rumination-how to foster more student-led discussions]
We are studying conics in Precalculus and we were looking at this Opener problem dealing with two hyperbolas. Even though I suggested that we only work for 5 minutes, my students just couldn’t let it go.
They worked diligently, and eventually realized that they needed to graph the situation using their Nspires….so they began to put the hyperbolas into function for to enter. Of course, they asked, “Isn’t there an easier way?!” I suggested that they explore that more thoroughly on their own. And one student, excitedly (and somewhat smugly) jumped up and said, “I can show you all!” And he did.
How do you get your students to take over your classroom? I’d love to hear some new ideas to try!
Its the day before a four day Memorial week-end! We were so lucky this year because we didn’t need to use all of the weather-related make-up days in the district calendar. Thus, we have this glorious 4-day, so needed, break!
So what do I do with my Precalculus classes during the last periods of the week?! Derive the hyperbola equation from the geometric definition, of course. And I was so So SO proud of my kiddos because they hung in there during the entire derivation contributing next steps they whole way.
And we were able to see where the Pythagorean relationship “falls out” from the derivation. All in all, I am really lucky to have such engaged students!