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Are all 75% averages created equal?

Designing Along the Jagged Edges
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Consider the following two data sets. The first table is a listing of the final marks for Marta, a Grade 10 student at a public secondary school in Ontario. The second shows final marks for Shekar, a classmate of Marta's at the same school. 

Marta J:
Math: 52%
English 69%
Science 65%
History 72%
Phys-Ed 74%
Visual Arts 88%
Music 92%
Comm Tech 85%

Shekar R
Math 88%
English 75%
Science 88%
History 72%
Phys-Ed 72%
Visual Arts 65%
Music 67%
Comm Tech 70%

 A couple of questions to begin. First, how would you likely react to these two reports if you were:
  • a parent
  • a school administrator
  • a secondary school guidance counsellor
  • a University/College admissions board
Second, who would you predict would have the best chances of success in moving forward towards graduation? Finally, who would you predict would be most engaged in their high school coursework?
Now, I realize that there are plenty of moving parts at work in the typical Canadian secondary school. There's a real sense in which simply laying out a set of final report marks doesn't really speak to the complexity of situation but that, perhaps, is the whole point!

The fact is that, on paper, both of these students have an overall Grade 10 average of 75%. So, they're both very similar in terms of success, right? Yet, I'm wondering how many of us would naturally assign more value to Shekar's results. After all, his scores in Math and English will resonate with those who subscribe to the belief that success in these two areas are a strong predictor of success in school, work and even life. In fact, many systems would automatically flag Marta as a candidate for some sort of remediation as she prepares for assessments in both of these areas. In many cases, Shekar would be considered the smarter of the two students.

But in his book, The End of Average, Todd Rose introduces a different way of looking at the idea of success in complex systems and organizations. He uses the Jaggedness Principle as a way of challenging us to look at the limits that are imposed on our vision when we insist on judging and valuing people using narrow definitions of success. Human ability, according to Rose, is a complex, jagged thing—there is no smooth "line of best fit" that can be used to measure talent, ingenuity, intelligence, creativity, imagination—those complex dimensions of our humanity. Yet our instutitutions of opportunity, like schools, continue to pretend that all of this can be adequately captured by a system of one dimensional "tests" and the mathematics of aggregation.

To be sure, aggregating data can appear to smooth out the jaggedness, but this is an illusion that, on the one hand, prevents us from seeing the rich deposit of talent and potential inherent in the individuals that walk into our schools every day and, on the other, takes our focus away from some deeper conversations about school and program design. 

In Rose's words,
A quality is jagged if it meets two criteria. First, it must consist of multiple dimensions. Second, these dimensions must be weakly related to one another.

So, let's go back to the two reports that I presented at the beginning. It's clear that, while our attention may have initially been drawn to the fact that one student was clearly "stronger" in measures of math and literacy, we may have missed the multi-dimensional nature of each student. The underlying assumption that there is a strong relationship between success in math and language and future success as a student (and an employee) puts us at risk of missing the fact that Marta shows obvious strength in the Arts and Communications Technology.
 
It's an assumption that would cast Marta in a deficit position when, in reality, it is very likely that she has developed as the result of her work in these areas. In fact, we would likely find some strong alignments to the competencies that many are calling for as part of the 21st Century learning conversation.

Now, I'm not arguing for one minute that math and language are not important aspects of a students' development. They are. And I'm not arguing that Shekar's competence should not be recognized. They should, and likely are! I am suggesting, however, that our current narrative of the successful student might lead many to place more value on one set of results over another. And this, I believe, is problematic.
So two questions have emerged for me in viewing our school systems from the perspective of Todd Rose's Jaggedness Principle. 

First, how can we begin to think about schools in such a way that more of multi-dimensional dynamic of students is recognized and allowed to shine through? And second, how might the Jaggedness Principle offer new insights and perspective on how we plan programs, design curriculum and value the competencies that are developed throughout the schooling process?

 
As always, I'm hoping that this is something that we can continue to discuss in a variety of contexts. I'm still allowing this to rattle around in my mind. I would be interested to know where your conversations lead!

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In our reductionist search

In our reductionist search for simple rather than complex outcomes, we end up with the averages of nothing. And we've been satisfied with that. Don't question, just do it. To see the multidimensions is to see the multiple intelligences, which in high schools, should have us examining the whole notion of what an "honours" or "A" student is. Learning is social and collaborative and yet we assess with a belief that an individual is solely responsible for their own understandings, unconnected. Complex systems are connected systems. I'd like to see us recognize multiplicities and accept many different ways of making meaning and building new knowledge and demonstrating new understandings. If we become unable to compare, then we've achieved seeing the unique jaggedness of each individual.

I'm seeing that "tension" in

I'm seeing that "tension" in the way that my two young boys are reacting to formal schooling. So, how do we break these conversations open in a way that is going to matter. I think that the communities outside of the schoolhouse are an important place to engage people in thinking differently—for the very reasons that you identify. Schools exist within a wider culture of "average" thinking. It's evident in our day-to-day conversations, in the metaphors that we use and in the way we deal with the jaggedness with which we're presented every day!

And I think that one of the side effects of all this is that we have been "conditioned" (I've been reading Krishnamurti this week) to not fully appreciate our own uniqueness and jaggedness!