TRU

considering the perspective of the students

It is useful to think of what the classroom experience looks and feels like from the perspective of a student – students, after all, are the ones experiencing the instruction! The questions below provide an orientation that helps in seeing lessons from the student perspective.

The Mathematics

The extent to which the mathematics discussed is focused and coherent, and to which connections between procedures, concepts and contexts (where appropriate) are addressed and explained. Students should have opportunities to learn important mathematical content and practices, and to develop productive mathematical habits of mind.

From a student’s view:

  • What’s the big idea in this lesson?
  • How does it connect to what I already know?

Cognitive Demand

The extent to which classroom interactions create and maintain an environment of productive intellectual challenge conducive to students’ mathematical development. Students should be able to engage in sense-making and productive struggle.

From a student’s view:

  • How long am I given to think, and to make sense of things?
  • What happens when I get stuck? Do I get to struggle or does someone “rescue” me?
  • Am I invited to explain things, or just give answers?

Equitable Access to Content

The extent to which classroom activity structures invite and support the active engagement of all of the students in the classroom with the core mathematics being addressed by the class. No matter how rich the mathematics being discussed, a classroom in which a small number of students get most of the “air time” is not equitable.

From a student’s view:

  • When and how do I get to participate in meaningful math learning?
  • Can I hide or be ignored? In what ways am I kept engaged in math thinking?

Agency, Ownership, and Identity

The extent to which students have opportunities to conjecture, explain, make mathematical arguments, and build on one another’s ideas, in ways that contribute to their development of agency (the capacity and willingness to engage mathematically) and ownership (recognition for being mathematically solid), resulting in positive identities as doers of mathematics.

From a student’s view:

  • What opportunities do I have to explain my ideas? In what ways are they built on?
  • How am I recognized as being capable and able to contribute?

Formative Assessment

The extent to which the classroom activities elicit student thinking and subsequent instruction responds to those ideas, by building on productive beginnings or addressing emerging misunderstandings. Powerful instruction “meets students where they are” and gives them opportunities to deepen understanding.

From a student’s view:

  • How is my thinking included in classroom discussions?
  • How does instruction respond to my ideas and help me think more deeply?