- Lucy West says that, "whoever is doing the talking is doing the learning." And so as educators, we need to help move towards a more student-centered discussion where students are arguing and debating and agreeing and disagreeing with their peers. Creating that math talk community and using number sense routines to add to that math talk means that students can clarify and share their own thoughts. They listen and consider the thoughts of others which deepens their own reasoning. And they can listen and consider the reasoning of others. Number sense routines and mental math strategies provide stronger access to the learning for all students. It provides greater access to thinking of their peers which means that all students have access to a wider variety of approaches to the math concepts they're learning. Students who are more reserved can be engaged through listening and multilingual learners need access to multiple representation of mathematical concepts. And they can do that by seeing their stronger receptive language skill, which will help them further develop their expressive language. Number sense routines are short daily routines, 10 to 15 minutes at the most, most which support mental math and visualization strategies. Discussions from these routines provide opportunities for students to defend their thinking, to reason, to prove and their peers can add to it or respectfully disagree with it. So how do we make that magic happen? Well, we give them some structures and we give them something worth talking about. One of the most effective teacher math talk moves is actually not talking. Using wait time to allow students to process, to think, and to formulate their response. Encouraging students to revoice and repeat what their peers have said and to add on and say more. So some opportunities to use those math talk moves might be a math talk image where you ask students to notice, to wonder, to determine how many and how they they know, and then asking them how else they know in order to really push for that deeper conceptual understanding. It might be a number talk, a single question that's designed to elicit a variety of strategies and to support the development of efficiency and flexibility. It might be in a number string, which is a type of number routine where the educator presents a carefully crafted sequence or series of problems one at a time, for students to solve using mental math strategies. And a string would involve a helper question that is accessible to all students and to activate some prior knowledge. Then there would be some additional helper questions that are related to the first one and can be used with the same strategy and then a fourth or fifth question that are a bit of a challenge. And the educator can see whether the students are able to apply the strategy they're working on. Using a daily number sense routine shows that you believe that all students have valuable math thinking to share, that you take student thinking and make it visible. It encourages conceptual understanding versus procedural understanding, that mistakes are valuable and not only okay, but that mistakes are loaded with good math to talk about. And while efficiency might be the long game, flexibility is an important step to building that fluency and efficiency. We also wanna give the message in the number sense routines that learning takes time and that confusion and struggle are part of learning and that we want to encourage and celebrate diversity in thinking.