Do you practice number sense routines in your classroom? Or are you new to number sense routines? Jessica Shumway, author of the popular book Number Sense Routines, Grades K-3 and her newest follow-up Number Sense Routines, Grades 3-5 has offered up her expertise to provide guidance on how to get started or navigate any of those sticky points you might come across in your instruction. Here are a few tips you might find handy!
How do you decide which number sense routine to do?
Knowing which routine to do really depends on your class, where you are, and your purpose. For example, I often start with dot cards at the beginning of the school year. I think that the dot cards are a great platform to get kids talking about math, valuing each other's ideas and understanding that they can learn from each other, that they can really start to expand their own concepts and notions of number by listening to other people's ideas.
What if students have difficulty explaining their mathematical thinking?
Some students have difficulty explaining their mathematical thinking, especially in the beginning of the school year or if students are not used to justifying their solutions. Here are some strategies to consider when students have difficulty explaining their thinking or when you know they have an answer but don’t know how to explain what they know:
- Break it down. Help students step back and be metacognitive about what they’re doing. Ask, What was the first number you saw? What was the first thing you thought about? What did your brain tell you to do next? Just helping them break it down helps makes it easier for them.
- Turn and Talk. Turn and talk is a strategy where students voice their understanding with a partner. This strategy helps students talk out their ideas and then when they come back to whole group, they’re able to voice what they notice and what they are trying to explain.
- Work together. Sometimes students will start an idea that they don't know how to justify, so we have all the students build on that idea together. Through working as a community, you build that knowledge together. When students realize they play a really important role in these discussions, the better they get at it. The more opportunities they have to turn and talk, the more opportunities that they have to justify their thinking.
How do you get students to listen and learn from each other?
Listening and learning from each other is key. That's where students really start to expand their own notions of number and can really learn a lot from other students. Small groups are where I really get that math talk and get those conversations going. It’s a way to help them listen to one another's ideas. I ask them questions like, Stop your own thinking for just a minute and let's really make sense of what this other person is saying, or, Did you understand what Jimmy was saying? Can you explain it in your own words? At the beginning of the year, you often see that kids are still trying to be creative, still trying to get their ideas out there, and there’s a place for that. But by asking these questions and using strategies such as turn and talk, you’ll eventually help them to tune into each other’s ideas and make sense of each other’s thinking. It’s a beautiful moment when that starts happening.
What skills do teachers need to facilitate mathematics discussions around a number-sense routine?
Find ways to deepen your own content knowledge. The more you know about mathematics, number sense, problem solving, and reasoning about numbers, the more you can pinpoint those pieces to highlight and then move everybody's number sense forward. Knowing your content is a major piece in being able to facilitate those discussions.
Teacher questioning strategies is another skill to have when you're using these number-sense routines. One way to start is to ask questions such as, Why? or ask them to explain their thinking. Not just, Oh, yes, you've got the correct answer but how do you know that? Instead ask, Can you justify your thinking? Prove it to us. Convince us that this is what comes next in the sequence. Slowly build your questioning strategies over time and you'll see your students’ discussions grow.
Do you use routines for formative assessments?
Number-sense routines are a really effective formative assessment. You learn so much about where your students are in their thinking when you have these discussions about relationships among numbers. For example, when you highlight a big idea to the class and ask them who understands, but no one responds, that lets me know that I need to set up some experiences where the big idea can be highlighted in a way that's more accessible to everybody. And then we can follow up on that idea let it emerge in other situations.
Want to learn more about Number Sense Routines and how to bring them to your classroom? Download this brochure and start planning how to use these dynamic routines to deepen number sense in your students.