I just spent two days earlier this week working with middle school math teachers. Our focus was on the 6 – 8 Common Core Geometry standards, and how they build on elementary geometric concepts and continue to build that understanding that students need when they get into high school geometry. As part of our work, we also focused on the Math Practices, because it’s the intentional alignment of practices and content to create engaging mathematics activities that really help students develop the deeper understandings. By that I mean you shouldn’t be teaching the content standards in isolation – they should be combined with helping students make sense of the problems, choosing appropriate tools to explore and apply the standards, and really explaining and justifying the conclusions they make. Practices and content go hand-in-hand.
In our many collaborative discussions these past two days, as we really dived into both practices and content, what was very apparent was how important it is to create a collaborative, safe, classroom. Mathematics classrooms should constantly focus on vocabulary use (by both teacher and students), modeling, discussing your thought process (in many ways – spoken, written, pictorally), explaining and clarifying your thinking, asking questions, and really focusing on all types of communication. Mistakes or misconceptions that students have should be expressed freely, without fear of embarrassment, and students should be free to try multiple pathways to solutions and multiples ways to express their understanding. Students are not going to talk about mathematics if they feel they will be laughed at or considered ‘stupid’ – and that requires a classroom culture that fosters real communication between students that involves listening, ‘arguing’ against someones responses in a constructive, polite way, and a sense that it’s okay to make mistakes because we are all in this together, learning.
What the teachers expressed as their “ah-ha” from our days together was that in order to create these types of classrooms and math learning, you have to start the process right at the beginning of the year, during those first weeks of school, when students are new and class is unknown, and math concepts are relatively familiar since we are starting, in theory, where we left off at the summer. Those first couple weeks of school are the perfect time to create that collaborative classroom culture.
My suggestion was to start, day one, creating the idea that in this class we will be talking with each other, sharing ideas, and learning together, but we need some guidelines. So day one, don’t go over your rules – students know the rules. Instead, start having conversations – putting kids in small groups, and practice how to work and talk together using something non-math related to help foster the idea that in your class, communicating and listening are encouraged. For example, small groups of 2-3, and each group must decide what the best and worst movie they saw this summer was and give reasons for both. Then have groups share out, using some simple group share out routines like the person in the group with the longest hair tell us about your groups best movie. Be very explicit in how they communicate – ie., one person talks, everyone listens; write down your ideas, so one person records, etc. Day two, do the same thing, but this time maybe use a simple math concept – i.e., in your groups, explain why a square might be a rectangle, or why is a circle different from a square? Something appropriate for your grade level, but something that you know most of the students are familiar with. Again – the idea is to learn how to communicate in the classroom – how to create that culture of collaboration, listening, and justification. Day 3 – maybe introduce a math tool students will be using this year – like a calculator, protractor, compass, ruler, software, etc. Have students explore and write down things they notice (give them simple things to do), things they have questions about. Have other students explain what they found or answer each others questions. Model the use of the tool (s) yourself. Lot’s of options, but the point being to get kids thinking, talking, listening, and understanding that if they have questions or concerns it’s okay to voice them.
Do a little bit each day – change the groups up, do it whole class, do it with partners. The idea is that you are helping students learn to talk to each other constructively so that when you get into the real learning of new math concepts, they are already comfortable with each other, with some of the learning tools they will be using, and understand that in this math class, we work together and listen to each other and support each other.
Learning is not an isolated activity – we, as teachers, are there to facilitate learning and help students become active, productive, problem-solvers. This happens in classrooms where it is okay to communicate, it is okay to make mistakes, it is okay to have your own approaches to problems but that requires justification of those approaches so others can learn from them. The more you create this type of learning environment, the more your students will persevere in tackling those tough learning moments.