By Leah Silver, Math Specialist (JK-4)
While so much has changed in our teaching in the last few months, the essence of the math classroom has remained the same. Planning, teaching and visiting math classes JK through Grade 5 in recent weeks has helped me sharpen my answers to the following questions: What can our digital tools do really well? And what can our teachers do that our digital tools never can? Our digital tools like DreamBox give our students immediate and targeted feedback on their operational and problem-solving work, and we’re learning how to let these tools help us make the best use of our teaching time.
Our teachers do incredible work every day that our digital tools cannot—and will not—ever be able to do. Our teachers work masterfully to guide our students to better articulate their mathematical thinking, learn to ask excellent questions, make keen observations and get comfortable in solving complex problems, even when the answer isn’t immediately clear. We know that the ability to work collaboratively on complex problems and express ideas clearly will be two of the most valued qualities as this group of students continues to grow up. We also know that our students’ ability to make sense of data presented to them and reach logical conclusions is essential in a world where we receive information from an infinite number of sources. Our teachers prioritize these and many other concepts in their work with students each day — no matter the distance.
While there are so many different strategies teachers use to help students come to new understandings, one is asking the right question at the right time. Whether in a kindergarten Number Corner session or a fourth grade multiplication strategy talk, these three key questions help our students build their computational fluency: solve problems accurately, use efficient strategies and show flexibility.
Question 1: What do you notice?
Teachers methodically ask this throughout their math classes. Asking younger students what they notice helps them to make connections and to sort and categorize — an essential early childhood skill. We ask our youngest students what they notice about a group of objects, about how many days we’ve been in school, about a graph or a chart that collects student answers to the daily question. And we ask our oldest students what they notice about a set of numbers or a particular strategy to help them formulate and articulate math strategies. Asking students what they notice encourages them to put together all the math and logic learning that is in their heads to try to put some order and sense into what’s in front of them.
Question 2: What do you wonder?
Encouraging curiosity is one of the highest priorities in our math classes. Curiosity breeds hunger for more learning and also breeds an eagerness to make sense of what’s around us. Our second grade teachers recently led an activity which gave students the opportunity to come up with questions usually left to curriculum writers. With a given amount of information, what questions could you ask? For example, if you know that there are 124 red legos and half as many blue, what questions could you come up with?
Our students might ask:
- How many blue legos are there?
- How many legos are there in total?
- How many more red legos are there than blue legos?
When we ask students to generate questions, we dismantle the notion that questions only come from those who are ‘in charge’ or older. Giving children the opportunity to come up with their own questions is one way we can show that we value their thinking encourage their developing curiosity.
Question 3: How do you know?
Verbalizing thinking is useful both in and out of the math classroom, and our students spend a lot of time writing and thinking not only about the numbers of math but about the words, too. Teachers are often encouraging students to move beyond a common initial student response, “I just know,” and instead give a reason or strategy. “I know that is ten because I started with five and added two more, which got me to seven. And I know that seven and three more equals ten.” We want to teach students that intuition does have a place in the math classroom, and that there is value to articulating what and how you are thinking.
I am really proud of all of the math learning and teaching at Grace in the last few months, and I can’t wait for the day we get to safely be together, hearing our students excitedly call out everything they notice and wonder.