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!

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