As we look back on another fun- and sunshine-filled Walkathon, our annual trek through our 14-acre campus in support of professional development for teachers, Learning Specialist Autumn Vavoso shares how teacher learning is evolving and enhancing student engagement and hands-on academic experiences in lower school math.
By Autumn Vavoso, Learning Coach In-Residence at Hillbrook School
Counting Collections in Kindergarten:
We have been working hard as collaborative math teams to test some new ideas. The kindergarten team began by researching this article on Counting Collections. One team member was also able to attend the National Council of Teachers of Mathematics (NCTM) conference in San Francisco earlier this spring where a session on counting collections was offered by a team of researchers from UCLA. As a collaborative teaching team, the resources and experiences garnered at the conference were then brought back to the group at Hillbrook. Together, we collaborated and used the ideas from the article as well as the conference conference to plan a series of math workshops around investigating how to count collections.
We wanted the children to explore different types of materials as well as varied quantities, and so we created an experience where kindergarten students engaged in counting collections of eyeballs, pink and purple shiny lips, fruit, spheres, and fuzzy pom poms. With these colorful and engaging articles in hand, the the children were off to count!
As they worked their way through their task, our young learners soon quickly discovered that making piles by equal numbers (2’s or 10’s) can help make the counting more efficient. Meanwhile, making groups by color really did not help us get to the total number in the collection efficiently. After a few days of exploration the children were then asked to represent their thinking around how they counted their collection.
Ryan made groups of letters. His first and second piles had 10, his third pile had 15 and his fourth pile had nine. We interviewed Ryan to see how he was planning on finding out how many in his collection. He counted:
“Ten and ten is twenty and 15 more would make – pause – thirty and five oh, 35! And then nine more would be like ten more but one less. It is 45 but one less and that would make 44.”
The students and teachers were amazed with the way Ryan could think with flexibility about numbers. We believe that the continued practice of counting collections with meaningful grouping will build the ability to think flexibly about numbers in all students.
Number Talks in Fourth Grade:
The fourth grade team and learning coach collaborated on introducing Number Talks, a mental math problem solving strategy, and designing inquiry lessons around area and perimeter. Mrs. Butler and Mrs. Vavoso also attended the NCTM conference where they learned a great deal from Sherry Parrish, the author of Number Talks, about the importance of using this collaborative strategy to help students build flexibility in mentally solving computation problems – together. We jumped right in with the students and had them mentally solve a string of related problems while we recorded their mathematical process for other students to see. The children were then encouraged to solve the string of problems in a different way. As students listened to each other they learned efficient strategies other students are using that may also be able to help them.
As a team, we then all worked together to design a series of inquiry math workshops around area and perimeter. The students were given graph paper and three sentences to consider: What do you know about area and perimeter? What are you wondering?
And after the exploration: What do you now understand about area and perimeter?
Students were then challenged to draw shapes and find the area and perimeter of each. They were then asked to come up with a few theories to test in their “I Wonder” section.
Chris amazed us when he found out that any rectangle that has one side with a perimeter of two will always have a perimeter of the area plus four. Wow! As we move to exploring the area and perimeter of composite shapes our fourth graders will continue to investigate and test their mathematical theories.
Once we feel these theories can hold true after being tested, we added them to our classroom chart of “Understandings.”
Taking the time to investigate and logically think through the ideas around area and perimeter help solidify children’s understanding of these core concepts. Before teaching them formulas, we wanted the students to be anchored in their understanding of area and perimeter for a deeper, sustainable learning experience. Sometimes, formulas without conceptual understanding promote a “going through the motions” approach to math, where the “why” is never clearly investigated by the learners themselves. We want more for our students!
The synergy of a collaborative faculty team that believes in sharing work along with the opportunity to partake in professional development opportunities that promote leading-edge educational practices are helping to transform classrooms everyday. These moments, that combine faculty collaboration with resources made possible through a leading-edge commitment to professional development, continue to offer our students new resources that promote subject mastery through deep-dive understanding as well as the joy and profound enrichment of collaborative learning.