Wednesday, March 23, 2016

Open-Ended Algebra 2 Project


Recently a colleague asked Dave Sladkey and I about the benefits we've seen for students by asking more open-ended questions in our classes this year. Here was my list:
-students are more willing to take risks and try questions b/c they know their thinking will be valued 
-students wanting to share a different method for solving a problem with the class and wanting to find different answers than their peers 
-students' willingness to spend more time on a problem b/c the question doesn't have a distinct end/answer 
-creativity in answers b/c they're not trying to mimic my ways of solving closed problems 
-weaker students have more confidence b/c success isn't defined by the right numerical value or having the correct steps all the time.
-more exclamations of "this is fun!" And "let's do more problems/activities like this!"

Here's what Dave added to the conversation:
"Everyone has a voice.  Especially the ones that think differently.  Everyone is willing to try because there isn't much failure in an observation/opinion/guess.  On a teacher note:   I really love doing this and seeing the creativity of my students blossom.  It's more fun now for me too.  I'M MORE ENGAGED."
Last week I assigned an open-ended project in Honors Algebra 2 that is the best project I've ever done in my classroom.  I saw Zach Herrmann present at ICTM in the fall and he shared this Public Health project that he assigned during a probability unit in Algebra 2.  His presentation can be found here.  Here are Zach's slides for the project.  




I assigned the project the same way that Zach presented it, and it worked great.  His suggestion was to assign the project to groups then, for a week, teach regular scheduled lessons for the 1st half of class and let students work on the project for the 2nd half of the class period.  As soon as I assigned the project, students were talking excitedly to their groups.  Students collaborated really well because there are so many layers for them to consider.  I didn't give students any specific requirements for their presentation.  Most groups made a Google Slides presentation and one group made a poster.  I set a 5 min. limit on presentations so that we could fit all groups into one class period.  I didn't focus too closely on the time limit because I wanted students to be able to effectively communicate their plan without worrying about presentation details.
We spent a class period presenting their ideas.  I was impressed about how well students listened to their peers.  They were engaged during other's presentations because every group presented a different plan.  Strategies ranged from testing people 7 times to make sure that the false positives wouldn't be treated with an expensive treatment plan to charging people in the community to be tested.  We opened up the floor for the class to ask the presenting group questions after each presentation.  Their questions were thoughtful and appropriate.  Their questions either led the group to clarify their thoughts and explain them in a better way, or they sparked debate.  I was proud of each group for defending their plan and justifying their thinking.  I loved that students had to "make mathematical and ethical assumptions."  With closed questions, we don't often get to see students's creativity and imagination in math class.  The assumptions they made were very thoughtful and clever.  They came up with ideas I didn't once consider.  I can't wait to do this project again next year!






Sunday, March 6, 2016

How do we make loving math contagious?

The DVC math conference reignited my enthusaism and excitement about teaching math. Eli Luberoff and Andrew Stadel both spoke in such a way that made me want to be a math student again, exploring, discovering and problem solving in an active and engaging environment. As a teacher, creating these opportunities for my students isn't so much of a challenge as it is an invitation. I am invited to create a learning environment where students are honored as thinkers and celebrated as unique individuals with talents and passions. How each teacher accepts this invitation varies based on their unique teaching gifts and personality.
The teacher to-do list is long. When inspired by great speakers and hearing positive success stories, questions about time, difficult students, and limited resources can all pose as boundaries to experiencing that success for ourselves in our own classroom.
I listened to a Ted Radio Hour podcast from NPR, called How Things Spread, that has me thinking about how we can continue to be excited about math education a day, week or month after an energizing conference. The podcast plays clips of related Ted Talks and the host, Guy Raz, interviews the people who gave those Ted talks. This episode was about the "mysteries behind the many things we spread: laughter and sadness, imagination, viruses and viral ideas." I want to spread an excitement for teaching math among teachers as well as a love for learning math among students.
Spreading a passion for teaching
Teachers who are doing innovative, unique things to engage their students have to talk about these lessons and ideas with other teachers, administration and parents. Tweet, blog, email and tell someone else about the great things, big or small, that are happening in your classroom.  When more teachers are sharing their classroom successes, others will want to experience an engaged class for themselves. Sharing our ideas makes our profession collaborative. There's a greater joy in what we're doing when the people around us are as excited as we are about what's going on. Guy Raz interviewed cognitive neuroscientist, Sophie Scott, about why laughter is contagious. In her Ted Talk, Sophie says "When we laugh with people, we are hardly ever laughing at jokes. You are laughing to show people that you understand them, that you agree with them, that you are part of the same group as them. You're laughing to show that you like them, you might even love them." We have to share our classroom successes in order to connect with each other as professionals who respect what is going on in each other's classrooms and as friends who are genuinely happy for each other's delight in our experiences with students. We have to share in order to spread an enthusiasm for teaching that is as contagious as laughter.
Spreading student passion for learning
In order to ignite an epidemic of math love among our students, we have to market our subject.  In the podcast Guy Raz interviewed author Seth Godin about the best ways to market a product. A few quotes from the podcast got me thinking about how we get an idea like "love for mathematics" to spread. "Whatever you're trying to spread, whether it's an idea or brand or whatever it is, those things spread faster when the people you know and like talk about them" -Guy Raz. If a few students enjoy an experience in math class, can their perspective rub off on their classmates?
"Uber isn't big because they ran a lot of adds, they're big because someone took out their iphone and said to their friend 'watch this' and pressed a button and a car pulled up." -Seth Godin 
Desmos has figured out how to do this by making their product something people are talking about. There have been so many times that I've come to the math office after a class and said "look what my students made on Desmos!"  The question is, how do I get students to say to their friends at lunch "look what we did in math class today!"  It sounds cheesy, but I believe it's possible.
As we market our subject, it's important to strategize about which students we will focus on to spread our math passion to a greater student population. Guy Raz interviewed social scientist, Nicholas Christakis, about how ideas spread through social networks. Guy's conclusion from Nicholas' work is that "There are so many things that you could spread by identifying the right people and right entry points." I've had a big focus on differentiation this year.  I believe it's important to see students as individuals and to meet their unique learning needs. However, maybe now is a good time in the school year to pause from looking at each student individually and see my class as a whole.  How do I move the whole class to an understanding of Algebra 1 by May?  Are there a few students in class, that if ignited with a new found enthusiasm could spread the math love to other students? How could I let go of control of trying to orchestrate each students' individual appreciation for my subject and let the joy of problem solving spread through my classroom like wildfire? Having just been at the DVC math conference, the obvious ideas for how to do this would be to assign a new Desmos challenge that would engage students creativity and to use estimation 180 to spark students' curiosity and wonder. I'm not totally sure how to see this goal come to fruition, but my purpose this week is to make loving math contagious.