In the media, we are bombarded with stories about teachers who are struggling and frustrated with implementing the Common Core standards in their classrooms. In Westside Union School District in Southern California, I am continuously impressed by teachers who are effectively teaching their students through rigorous and well-executed lessons. One such first grade teacher is Caitlin Negrete.
Ms. Negrete is a second year teacher who holds high expectations for herself and her students. I have had the pleasure of coaching her throughout the 2014-15 school year and witnessed great strides in the development of her instructional methods to help her first grade students understand complex concepts. The last lesson that we planned together was a Math lesson addressing the following Common Core Geometry Standard:
Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
Ms. Negrete taught the lesson with eloquence.
Since this was the students’ first introduction on partitioning shapes, Caitlin decided to focus on the concept of halves for this lesson. In analyzing the Independent Practice demands that the students would encounter, Caitlin recognized that while the skill of partitioning the shapes in half would be easy for her students, the language and the variety of demands in the problem sets might be challenging.
Deciding on the most effective Concept Map, Caitlin saw an opportunity to organize the concept of Equal Parts in a “tree map”. After teaching the key ideas that whole shapes can be divided into equal parts, Caitlin focused her modeling around how she would analyze and think about the demands to demonstrate and articulate dividing whole shapes into 2 equal parts.
She began her model by expressing that there are different ways to show how whole shapes are divided into 2 equal parts. In referring to the “tree map”, Caitlin used the concept map to show the students how her mind organized her thinking, how she used the map to help her make decisions, to help her determine if her answers were reasonable and how she could articulate her results using the newly acquired academic language.
Ms. Negrete understood that the skill was easy, but the rigor would be found in the following:
the conceptual understanding,
the variety of models a student might encounter and
the articulation of why the results were sound.
As Caitlin gradually released the students to tackle problems, she used simple and effective techniques to check their understanding like, “After you have read and analyzed the problem, point to the option on the “tree map” that matches the type of problem you will need to solve. Once students had solved a problem, Caitlin engaged the students in partner discussions to articulate their results using language frames with embedded academic language. “I know that the whole _____________ is divided in ____________ because it has ______ equal parts.” Or “I colored 1 ________ of _________ parts“. In the Closure of the lesson, Caitlin engaged the students in an error analysis. “Miss Negrete did a problem. Is it right or wrong? Tell your partner, Why is it wrong?”
After a lively discussion and many accurate corrections to Miss Negrete’s problem solving, my favorite part of the lesson happened when one remaining student raised her hand. Miss Negrete called on her and in her quiet little voice she stated, “(Miss Negrete), if you had said your sentence frame at the end of your steps, you would have seen that you didn’t divide the whole shape into two equal parts!”
You’ve got to love first graders! They’re pretty dang smart, and having a smart teacher like, Caitlin Negrete makes for a sonic boom of excellent mathematical thinking too!