Four different standards-based instructional programs to meet the needs of Hillcrest’s very diverse student population (Spanish bilingual, Cantonese bilingual, English Language Development, and Speech and Language Resource Specialist Programs). In a school environment rich in linguistic, cultural and ethnic diversity, every classroom features learning activities that are rigorous, relevant, and relational.  A small group of educators at Hillcrest became interested in Lesson Study in 2014 and by 2016 the interest had grown school-wide.   Together, educators at the school developed a school-wide Research Theme and Theory of Action to focus their work:

School Wide Research Theme:

How can teachers facilitate and promote accountable talk and academic language to engage students in high-level problem-solving and productive discussion? 

Theory of Action:

IF WE AS TEACHERS move from focusing on process-based questions to conceptual questions, THEN students will collaborate on a deeper level, RESULTING IN a stronger understanding of the content.

Hillcrest’s Research Conception Map below shows how they linked their long-term goals and theory of action to their study of a particular mathematics research lesson.

In one of their first research lessons, a question from a visiting mathematics educator sparked Hillcrest teachers to add in-depth content study to their lesson study cycles. The research lesson was the first lesson in a fifth grade unit on how to divide a fraction by a whole number. Teachers drew on an area model that students had successfully used in a prior unit on multiplication of fractions, and posed a real-world problem that entailed division of ½ by 3.  They anticipated the following (correct and incorrect) student responses.

The lesson powerfully revealed student thinking, including the fact that many students got stuck and could not explain or justify the answer. In his final commentary, the visiting educator asked: Why did you choose those numbers? Are they too difficult? He compared the trajectory underlying the team’s work with a trajectory that might enable students to build the reasoning underlying how to divide a fraction by a whole number. A graphic of his board notes, with the teachers’ content trajectory on the left and the proposed trajectory (from Japanese curriculum materials) on the right, is shown below.

Sparked by this experience, Hillcrest lesson study teams studied the mathematical content of each future topic in depth, and added a unit plan and content trajectory to their future research lesson plans.  An example is found in the Teaching section.