Teaching practice, teaching practices, teaching moves

In this course, we view teaching practice as encompassing anything that teaching entails. Teaching practice contains teaching practices: recurring work in teaching that happen across different topics being taught. Teaching moves are actions that happen as a part of a practice. The same move could be used in multiple practices. Here's a schematic depicting this relationship.


Instructional goals, norms, and routines

Instructional goals

In this course, we view instructional goals as what you want students to accomplish as a result of your instruction. There are many aspects of learning that goals could address. Here, we focus on some goals for mathematics and how to work:

procedural fluency
conceptual understanding
mathematical practices

(goals for mathematics)
small group

(goals for how to work)

"Collective" refers to building on each others' knowledge as a whole class.

Examples of mathematical "practices" include those from the Common Core Standards of Mathematical Practice.

Norms and routines

Norms are informal and formal rules of interaction that reflect rights, responsibilities, and values. (The interaction could be between students and math, students and other students, students and calculators/compasses/protractors/technology, etc., etc. etc.)

Routines are structures in place to help ensure the norms happen.

Examples of norms

Example of a routine

Mathematical point

In this course, a mathematical point includes the mathematical learning goals for an activity, as well as the connection between the activity and its goals -- in other words, what an activity is intended to accomplish mathematically and how it is intended to do so. For example, the mathematical point of an example could be to provoke a common student error in order to develop students’ understanding of a particular concept.

We use the phrase teaching to the mathematical point to talk about these three overlapping aspects of teaching:

(The idea of a "mathematical point", formulated as above, as a way to think about what's happening in teaching is due to Laurie Sleep's dissertation.)

Analyzing a mathematical task for its mathematical demands/learning opportunities

(These are a summary of the class discussion in Fall 2012 about what was useful when analyzing a task for its mathematical demands/learning opportunities. We noted that "mathematical demands" and "learning opportunities" capture two perspectives on what a task offers: the first emphasizes the mathematical, and the second emphasizes students.)

Notes on task setup

(These are a summary of lessons learned in Fall 2012 about task setup after rehearsals of setting up a problem addressing concavity. I've selected some notecard comments to represent the lessons.)