Notice and Wonder in Kindergarten Math

Are we asking too much of students? How can we help them express what they know? What should productive struggle look like in kindergarten? As a resource teacher, I do not have a classroom of my own but have spent the last year working with kindergarten teachers across my district. I wanted to work with them to maximize productive struggle in their classrooms, but the tasks designed by our curriculum to launch our lessons were not providing meaningful insight into student understanding.

As the book Principles to Actions: Ensuring Mathematical Success For All states, “Tasks with high cognitive demand are the most difficult to implement well and are often transformed into less demanding tasks during instruction.” I started to wonder: How could the tasks be adapted to maintain high cognitive demand and provide the opportunity for students to engage and reason daily?

Heavy Text Loads for Young Learners

The tasks written by our curriculum required heavy text loads, and our young learners were getting overwhelmed in the directions. In one example, students would be asked to select a specific color crayon, count jumps on a number line, circle the numbers on a number line, write the number, repeat the process with another number in another color, compare the numbers, and explain their thinking. The teachers were finding that in order for the task to be completed, the specific directions needed to be modeled. This modeling was turning the students into professional mimickers of their teacher’s strategy. 

The result of these heavy text loads was a less demanding task with little opportunity for students to reason independently. I was in search of a shift that would eliminate some of the auditory directions, allowing students to engage in the math without worrying about completing the task correctly or in the correct order. 

4 Steps to Maximize Productive Struggle

I decided to apply the Notice and Wonder routine to the visual images linked to the tasks in our curriculum. Notice and Wonder is connected to several of Margaret Schwan Smith and Mary Kay Stein’s five practices. Combining the two strategies can be a simple way to help you maximize productive struggle in your kindergarten class in four steps.

1. First, identify the goal of the task and anticipate what students may notice and wonder about the illustration. What mathematical ideas do we want to emerge when we present the illustration? In some cases, we searched for a different image, while in others, we added to the image via Google Slides to make it work for us. This is also a quick solution if your curriculum does not offer an illustration correlated to the task.
2. As students start discussing and writing their ideas down, monitor their thinking and identify ideas you want to advance during the Notice and Wonder conversation. This could include representations, strategies, or new ideas. I annotate student ideas on the board throughout our conversation, allowing me a reference for step 3.
3. As you facilitate the discussion, select student ideas, representations, or strategies you want to engage in more deeply or highlight to the class.
4. Connect the student strategies. As you are facilitating discussion, be sure to highlight the connections between the strategies that students are sharing.

Putting the Model into Practice

My co-teacher and I decided to try Notice and Wonder with a task that required students to combine two groups to find a total. Rather than reading the directions, I presented only the illustration correlated to the task and invited students to share what they noticed about the image by writing it down on their paper or raising their hand to share. In this case, the image consisted of two pink flowers and three purple flowers all being held in someone’s hand.

Notice: As students shared and worked, I annotated their thoughts using pictures, numbers, and small words to help everyone keep track of the discussion.

Jacob was eager to share, so I called on him first. “Jacob, tell me what you notice.” Jacob said, “I see different colors, and then it’s easy to see the five of the flowers.” I responded, “How do you see the five flowers?” He replied, “Like if I had them all be in one hand, that is what they would look like.” I said, “Tell me more.” He said, “Like there is two pink and three purple, and that there’s five in one hand.”

I saw that Alexia had written 2 x 3 = 5 on the paper in front of her. When I asked her about it, she said, “Well, I see the two flowers here and the three flowers here, and then 2 and 3 is my 5.” I responded, “Tell me more about that symbol [the x]—how did you decide to draw that?” She replied, “Well, it’s my first time trying out that thing, but I’ve seen it before, and I think it has to do with my groups of flowers.”

Rylee was also eager to share her thoughts: “I matched up the flowers, and one pink did not have one to go with.” I replied, “Tell me more about that idea. How did matching the flowers help you?” She said, “It’s easy for me to see that there’s five because that means that there is two and two and then also one more who is alone.” (She pointed to the groups of flowers who each had a partner as she was talking, and then pointed to the lone flower.)

Wonder: After spending some time on what students noticed, I asked them to share what they wondered about the picture. Their wonderings brought in new ideas, such as inquiry about the flower’s environment, as well as numerical wonderings, like how many more flowers were there that weren’t in the illustration.

The ideas that emerged from the Notice and Wonder discussion included: counting strategies, one-to-one number correspondence, connections to the real world, flexible representations, addition by counting up, addition by counting on, addition by combining two groups, and cross-curricular connections.

We found that additional ideas emerged as well that might not have come up if we had presented the task with the prescriptive and long directions attached to the task. From this discussion and the annotations my co-teacher and I made as we observed our students thinking, we gained insight into their thinking. Their use of manipulatives, drawings, and ideas allowed us to identify how students used concrete, pictorial, more abstract thinking processes. This insight helped us to strategize for small group instruction as well as discuss what misconceptions or concepts should be explored further or in the whole group setting.

After a year of exploring how to maximize productive struggle in the kindergarten classroom, it became clear that presenting the visual illustration of the task as a Notice and Wonder consistently increased opportunity for students to access, engage, and reason with the task. By providing an access point, we were able to implement a task that promoted reasoning and problem-solving, in accordance with the Mathematics Teaching Practices. This easy shift can provide consistent access to high-level student thinking and reasoning and make progress toward student growth in the long run.