This manuscript focuses on practical questions in a study that describes the perceptions of four teachers at the beginning stages of Common Core Mathematics implementation in a historically underperforming school district. The overarching goal was to understand the collaborative inquiry experience in a lesson study that focused on teaching the mathematics practice of critiquing reasoning. Focusing the lesson plan on the mathematics practice of critiquing reasoning required teachers to first develop their own understanding and definition of this practice. This article describes the planning, debriefing, and revision of the lesson, while examining teachers' perspectives and rationales for instructional decisions during the lesson study. Different teaching mindsets affected teachers' understanding of the learning goal as more product oriented (students will define critiquing in mathematics; students will make a mathematical critique) or more process oriented (students will develop their understanding of critique; students will work toward making a mathematical critique). Teachers engaged in a continued process of disequilibrium and reflection as they clarified learning objectives and determined effective instructional strategies.