OK, the Latin in the title is my own. The second half is supposed to mean "tenacity to learn" in my version of Latin. But the title was inspired by a very thoughtful article today by Linda M. Gojak, President of the National Council of Mathematics Teachers, called "What is all this talk about Rigor?".
Evidently people have been writing that the Common Core requirements for mathematics include the word "rigor," although she says it is not there. She and a group of math coaches investigated the meaning of the word (as in rigor mortis, but more appropriately “thoroughness”and “tenacity”) to see how it can be applied to the teaching of mathematics. They came up with the following table, which I have borrowed intact from her article.
This is what teaching should be about, although I wish they'd come up with a better word, since rigor also means "rigidity" and "suffering," according to their research! That sounds more like the drill & kill methods I experienced as a student teacher, and which they define as not having rigor!
The left column should apply to all learning experiences, not just in mathematics. Children are born with curiosity, a need to be challenged and a lot of tenacity. This I experienced this past summer as my year old granddaughter tried again and again to crawl across a very difficult door opening (threshold!) until she figured it out. She was enormously proud of herself as well. I was amazed when my teacher sister-in-law got impatient with my granddaughter's efforts and just lifted her over the threshold. But the child went right back to working it out after that.
We must provide thresholds for students to cross, where they can see intriguing unknowns that awaken their curiosity. Children who are helped to everything must lose their love of a challenge and their curiosity early on. As a high school teacher I find that I have to help students regain their curiosity and encourage them through a challenge until they proudly can see they have overcome it. That is how we all learn!
Evidently people have been writing that the Common Core requirements for mathematics include the word "rigor," although she says it is not there. She and a group of math coaches investigated the meaning of the word (as in rigor mortis, but more appropriately “thoroughness”and “tenacity”) to see how it can be applied to the teaching of mathematics. They came up with the following table, which I have borrowed intact from her article.
Learning experiences that involve rigor … | Experiences that do not involve rigor … |
challenge students | are more “difficult,” with no purpose (for example, adding 7ths and 15ths without a real context) |
require effort and tenacity by students | require minimal effort |
focus on quality (rich tasks) | focus on quantity (more pages to do) |
include entry points and extensions for all students | are offered only to gifted students |
are not always tidy, and can have multiple paths to possible solutions | are scripted, with a neat path to a solution |
provide connections among mathematical ideas | do not connect to other mathematical ideas |
contain rich mathematics that is relevant to students | contain routine procedures with little relevance |
develop strategic and flexible thinking | follow a rote procedure |
encourage reasoning and sense making | require memorization of rules and procedures without understanding |
expect students to be actively involved in their own learning | often involve teachers doing the work while students watch |
The left column should apply to all learning experiences, not just in mathematics. Children are born with curiosity, a need to be challenged and a lot of tenacity. This I experienced this past summer as my year old granddaughter tried again and again to crawl across a very difficult door opening (threshold!) until she figured it out. She was enormously proud of herself as well. I was amazed when my teacher sister-in-law got impatient with my granddaughter's efforts and just lifted her over the threshold. But the child went right back to working it out after that.
We must provide thresholds for students to cross, where they can see intriguing unknowns that awaken their curiosity. Children who are helped to everything must lose their love of a challenge and their curiosity early on. As a high school teacher I find that I have to help students regain their curiosity and encourage them through a challenge until they proudly can see they have overcome it. That is how we all learn!
This makes me think of my new favorite video "Rigor in the Classroom"... I think you will enjoy it:
ReplyDeletehttp://www.youtube.com/watch?v=iOcYfrZJWi8&feature=share
Wonderful! Thanks for sharing!
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