In your mathematics classroom, are you giving students opportunities to think or taking away their need to think?
As a high school math teacher, I encountered many initiatives that helped my classroom be more student-centered. When I first started teaching, cooperative learning was making a comeback, but I did not get much direction on how to implement it, so I put the desks into pods of four and told my students to work together on tasks that did not require collaboration. Not surprisingly, the result was students working on math problems while sitting in groups, not cooperative learning. Then inquiry based education was on the rise again; I tried to talk less and let my students do more, but once again, I did not provide enough structure for myself or the students to allow for inquiry to happen. Instead students struggled, I got uncomfortable with the struggle and eventually told them how to get to the solution, producing few Eureka! Moments. I eventually learned about group worthy-tasks and posed purposeful questions that allowed my students to struggle productively, but it took years until I produced sustainable structures that worked for me and my students.
One reason it took so long for us to develop a student-centered classroom is because inquiry is really hard. It requires trust, risk, and letting go of control a bit. When we embrace inquiry in our math classroom, we are urging our students to think in ways we may not have taught or encountered, and that is scary. It’s scary because students will struggle, they will make mistakes, and they will come up with methods that we, as teachers, may not recognize or understand. Thankfully, many teachers have embraced principles of Growth Mindset and so they encourage struggle and failure (previously written about here: Mathematical Mindsets and here: Mathematical Mindsets continued ). Additionally, teachers need strong content knowledge to understand the different solution methods students come up with and teachers need to be flexible, since they do not know which solution paths students will take. This is scary since lesson planning is a large part of teacher preparation and many of us like structure and fear chaos.
This brings me to today’s topic: the Notice and Wonder routine. In today’s post, I would like to highlight the Notice and Wonder approach and offer two technology-related tools for implementing the approach with your students.
I first learned about this approach to problem solving from Tim McCaffrey blog post on the NCTM website and was immediately drawn to the structure it provided. This approach goes beyond multiple solution paths by allowing students to be the architects of the problem, as well as the solution. Additionally, teachers can offer extensions for students who want to continue working on a problem that is particularly interesting to them. This aligns perfectly with a core principle of my teaching philosophy – position students as sense-makers and knowledge-generators.
We start the Notice and Wonder process by posing a problem and asking students to record what they notice and what they wonder. There is an example from Tim McCaffey above, Dan Meyer’s 3 acts tasks and Robert Kaplinsky’s lessons are great for this, Proofs without words , as well as my personal favorite – Dan Finkel’s Prime Climb.
One way to capture what we notice is with Padlet – an online bulletin board which allows students to post “sticky notes” with their observations. Anonymously, without fear of judgment or ridicule, every student gets to contribute to the class noticing and the collective knowledge base. After that, students start asking questions. Some of these can be answered immediately to give students the information they need – how big is the jar, does color matter, how many locations are there? Other questions are the ones that require further sense-making and mathematical analysis. I suggest adding these to another online bulletin board – Dotstorming, which is similar to Padlet in that everyone adds a note, but students also get 3 votes and teachers can then organize the board by which notes get the most votes. This can help the class decide which questions they want to answer and also adds extensions for students who want to take the problem further. As a class, you may decide that there is one question everyone will answer, you may assign different questions to different groups, or you may let students choose which and how many questions to answer.
Which Notice and Wonder problems have you and your students enjoyed? What other tools do you use to foster inquiry and position students as sense-makers and knowledge-generators? Share in the comments below!
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