Thursday, May 23, 2019

About transformation in math education

Note to CLIME Community
As I mentioned in my previous blog, CLIME is retiring from service to NCTM as of June 1, 2019. But that doesn’t mean I’m retiring from working towards my vision of math education. This final entry of CLIME Connections informs that vision. Our new blog will be


In a recent blog Larry Cuban writes about the hype of “transforming” teaching and learning.
Three years ago, I published a post. I didn't expect anything much to happen with the over-use of the word "transform" and nothing did. The word continues to be used both seriously and casually without much scrutiny.
I agree with Larry that defining transformation in relation to education is difficult. But though I can’t define it with precision, I know transformation when I see it in the classroom.

In his article “Integrating Technology in the Classroom using the SAMR Model: Substitution, Augmentation, Modification, and Redefinition” Parker Duwelius describes the latter two as transformational.

He writes:
“The first and easiest piece is substitution. This is the most basic form of technology integration in the SAMR model, and consists of merely replacing a traditional lesson item with a technological equivalent.” 
The substitution method was a very popular intervention during the early days of the  CIESEmath project (2000-2007) that I managed. A lesson example would be to pose a problem using a projection device controlled by a computer instead of writing out the problem on a black or white board. Then the teacher would distribute handouts of the problem that was projected on the board. (See, for example, the Road Sign problem and Bus problem.)

On the surface the Bus and Road Sign problem appear to be only examples of standard substitution. But both problems take one step closer to be transformational in that they inform students to reflect metacognitively on what they did wrong and come to a new understanding of the problem. (Read the teacher notes for clarity.)
Duwelius continues: “This next form of technology integration is augmentation, which is very similar to substitution except that it provides a clear enhancement to the student in the activity through the use of technology.”
The Exterior Angle of a Triangle activity demonstrates how dynamic geometry software (like Geometer’s Sketchpad) augments a lesson that would otherwise be a static experience (e.g. using a compass to measure angles).
Duwelius: “Both of these (substitution & augmentation) are considered to be ‘enhancements’ because they still convey the material in the same way, but can often bring benefits with them that expand the learning taking place for the students.”
Now we’re going to find out a little bit more about the “transformation” pieces.
Duwelius:Modification is taking a traditional learning task and significantly changing it with technology.”
See the Factor Game as an example of modification. The activity begins as a whole group game using 3 x 5 cards pasted to the white board. Once the rules are mastered through playing the group game the students play the factor game on the computer. Thy can play individually against the computer or with a partner using the 2 player option. The game is challenging and encourages productive struggle on the part of the students.
Duwelius: “Then, finally, there is redefinition which takes a traditional learning task and completely transforms it in a way that would be impossible without technology. By using technology to transform the learning task, the teacher is integrating technology in his or her classroom at the highest possible level.
In the Noon Day project the students use a geometry theorem that is usually taught separate from any particular context to help them understand how Eratosthenes in 250 BC came up with a method to measure the circumference of the earth. (Geometer’s Sketchpad is used here.)
Duwelius: “These two pieces of the framework (Modification and Redefinition) are rightfully called “transformative” because they change the way the lesson runs, and the way the students interact with the content.”
Over the years of the CIESEmath project (which ended in 2007 with my retirement) our team developed many transformative activities and projects which I am currently revising and making them available here. This is an ongoing project so check in often to watch the progress.

Closing thought:
Math education does not need reform as it equates to rearranging chairs on a sinking Titanic. We need to build a new ship.