As an educator, it was frustrating when my grade level standards stated that all my students need to be at point X by the end of the year, but in my classroom, I had a room full of students ranging from point A to point Z. The research we have been studying points to a clear developmental trajectory that students go through to develop an understanding of the concept of number. By attending to students’ thinking in mathematics, we can understand where they are in this trajectory and provide the most beneficial experiences to help them progress to a deep understanding of the concept of number. We need to meet students where they are in this development no matter what grade level they are enrolled. The video highlight this week reminds us of this.
The video is composed of three segments (students in kindergarten, first and second grade) adding eight and four. The first clip is of two kindergarten students engaged in playing a game where they have to find out many pennies are in the piggy bank. They have two cards in front of them with the numerals four and eight on them. The little girl uses her fingers sequentially to count from one to eight and then can extend her count four more to end at 12. The second clip is of a 1st-grade student in a small group explaining how he solved joining four and eight. The students have cards with numerals on one side and the same number of “worms” on the other side so they can count and check. The boy had the numeral eight and four in front of him. The teacher asks him to share how he solved the problem. He showed her a finger pattern for eight and then counting four more sequentially on his fingers and ends at 12. The last video clip is of second-grade students engaged in a task where they are given a card with pictures of an amount of candy. They have to count the amount and put that many “candies” (blocks) in a bag, then they roll a die to that has numerals on it to determine the amount in the second bag. They do not count out any blocks and have to solve for how many “candies” there are in both bags. In this example, both students count from one on their fingers to solve the problem.
Even though these students are in three different grade levels, based upon what we see in the video, they are essentially in the same place in their development of understanding number. Regardless of the student’s grade, the teachers presented the student with tasks that are within their reach and knows what questions to pose to push them a little further. The video validates the need for teachers to differentiate instruction for students based on knowledge of where they are at based on classroom observations. How do you differentiate instruction for your students based on their needs? We would love to hear from you.