Developing Adaptive Reasoning in the Math Classroom: Part I
Adaptive Reasoning is one of the key components of Mathematical Proficiency. Students with adaptive reasoning can think logically about the math and they can explain and justify what they are doing. The key to getting students to engage in mathematical discussions is to create a talk friendly environment. It is important that students feel that what they have to say will be considered worthy and important. They need to know that they will not be mocked, ridiculed or belittled.
We have to set talk as the norm in the classroom. The idea of using accountable talk in math class gives us a sturdy framework. Accountable talk in math class means that students talk about the math in a variety of ways. They learn to express their ideas as well as entertain the ideas of others; they learn to question themselves publicly as well as respectfully question the ideas of their classmates and teacher.
Here are some great resources to get you started. Cunnigham notes that “not all talk sustains learning. For classroom talk to promote learning it must be accountable to the learning community, to accurate and appropriate knowledge, and to rigorous thinking.” This is a key idea here. We want talk that promotes learning, that expands thinking, that contributes to the intellectual community.
Cunnigham has created a great graphic poster displaying various types of accountable talk- click the link at the bottom of the post – http://toolsfordifferentiation.pbworks.com/Accountable-Talk
Ramirez wrote a great teacher friendly article about getting students to be effective speakers in class when discussing the curriculum. See the article here and be sure to look at the chart she created with the specific skill sets http://www.teachersnetwork.org/tnli/research/achieve/Ramirez.pdf
Holyoke Public Schools created a very interesting curriculum map where they map out the accountable talk in a unit on fractions and decimals – see page 7 for a great list of teacher/student questions and see page 10 for an example of mapping the talk directly into lessons- http://www.hps.holyoke.ma.us/pdf/curriculum_math/grade4_fractioncardsanddecimalsquares.pdf
You absolutely must Google: Accountable Talk Toolkit and then open the toolkit (it comes up as an attached word document). It is phenomenal with very specific examples and ways to get started.
You also should Google: Lucy West – Robust conversations at every level. In this powerful powerpoint Lucy notes that students should be held accountable to the learning community, the content knowledge and mathematical reasoning. They should be encouraged and required to explain their thinking, based on the math topic at hand. They should talk like mathematicians and use math language in their explanations. Lucy quotes Tom Alec (The Tao of Democracy) – “Dialogue is the central aspect of co-intelligence. We can only generate higher levels of intelligence among us if we are doing some high quality talking with one another.”
To be continued….