Mathematically Accountable Talk
Accountable Talk: Teaching Students to be Mathematically Smart
adapted from Phil Daro and Lauren Resnick
Further background on Accountable Talk:
excerpt from article by Lauren Resnick
excerpt from Institute for Learning website
Students can be taught how to be smart in mathematics. We have
seen it done on a large scale in literacy and on a small scale in
mathematics. The key strategy is to create social norms for `talk'
that model cognitive norms of smart people; that is, to translate
mental habits of smart people into social habits for all students.
These habits of talk get internalized and all the students start
talking and thinking like smart students. Lauren Resnick and others
have named these habits of talk "Accountable Talk". Accountable
talk is based on the idea that people can "learn to be smart": that
social, concrete experiences help us internalize methods "smart
people" use automatically.
Accountable talk sharpens students' thinking by reinforcing their
ability to use and create knowledge. Teachers create the norms and
skills of accountable talk in their classrooms by modeling appropriate
forms of discussion and by questioning, probing, and leading
conversations. For example, teachers may press for clarification and
explanation, require justifications of proposals and challenges,
recognize and challenge misconceptions, demand evidence for claims and
arguments, or interpret and "revoice" students' statements. Over time,
students can be expected to carry out each of these conversational
"moves" themselves in peer discussions.
Accountable to the conversation.
Just because it's your turn to talk, you don't get to change the
topic. The speaker is accountable to the group to cite the ideas of
others, explain how her ideas relate to what has previously been
said. Is the relationsip logical? An analogy? An example or
application of what someone else said? A request to explain? A
disagreement? An alternative?
This habit of connecting my talk to the talk of others models the
mental habit of connecting the idea on my mind right now to ideas
previously thought. In other words, this habit of talk teaches me
how to link my own ideas into longer chains linked by logic and
analogy. I can make complicated ideas in mathematics just like the
ones smart people make.
Mathematically Accountable talk.
- Generalization of mathematical statements
- Is it ever true?
- Is it always true?
- When is it true? Under what conditions?
- Good strategies for seeing and showing when a mathematical statement is
- Seeing through multiple approaches to problems
- Every student understands every approach
- Approaches that didn't work: Why didn't they work?
- Approaches that worked:
- How are different approaches alike?
- How are they different?
- How do the mathematical ideas in each approach make the
problem easier or harder?
- Multiple representations: What do different representations
- Ask when you are confused (assume you are the canary in the
mineshaft). Sometimes it is valuable for everyone to understand
what can be confusing about the concept, procedure,
representations or problem. Many times it is the language.
- "What does [term] mean?"
- "What does [representation] mean?"
- "Is there a useful analogy? A better analogy?"
- "Is the book confused?"
- "Is the teacher confused?"