The Teacher Tip
Establish Repeated Reasoning
January 9, 2018
Adapted from Routines for Reasoning by Grace Kelemanik, Amy Lucenta and Susan Janssen Creighton
If you were able to watch students’ thinking in slow motion as they used repeated reasoning, you would notice several different steps to that reasoning. These steps might happen more quickly or more slowly for different students, but all of them would occur in some form. They would:
- pay attention to the process: turn their attention to a process of counting, calculating, or constructing in their work
- sense the regularity: use their different senses to identify a pattern in the process
- “shortcut” the process: they can start to see some regularity in some of the steps and no longer need to work through each individual step
- connect the process to an “input” value: connect their repeated process to some value that they know in the problem that can serve as an “input value”
- generalize the process to a rule: a rule in words, or a rule written symbolically
To help students learn to identify and focus on repeated reasoning use the four Rs: repeat, rephrase, reword, record. You can look for opportunities to repeat any cycle of steps a student describes to help all students hear (and sometimes see) the rhythm in the repetition. Rephrasing helps students clarify what the repeated steps are, so in some places, you may want to ask a student to rephrase what was repeated. Rewording allows you to introduce more formal mathematical language. Recording then helps students organize and track the process, so they can identify the repetition, and particularly supports students who are strong visual-spatial thinkers. Recording language can also support language development through more precise rewording.
To learn more about Routines for Reasoning: Fostering the Mathematical Practices in All Students and to download a sample chapter, visit Heinemann.com.
The Heinemann Teacher Tip app is a free download.