learning assessment

Discursive or recursive? The fractal nature of education

Posted on by David Grebow


We’d like to share the article below by Steve Wheeler, Assoc. Professor of Learning Technology in the Plymouth Institute of Education at Plymouth University in England.  We admire Steve not only for his thinking about the future of learning and education–but also for the clarity and beauty of his writing. His blog can be found at:  Steve Wheeler

I presented a keynote at the Curriculum Enhancement Day for Portsmouth Business School recently, and chose this bright coloured image as one of my opening slides. It is as beautiful as it is intriguing, and it’s known as the Mandelbrot Set. I didn’t choose it solely for its visual impact, although as you can see, it certainly is quite a stunning image, and there are many variations. I chose it because I wanted to use it to make a point about what education is, and what education can become. You see, the image represents a mathematical formula that is recursive. In other words, as you zoom in to the image, which represents data points of a mathematical calculation, it continually reproduces itself towards infinity. Mathematicians will understand the explanation below from Wikipedia, but the rest of us might struggle:

The Mandelbrot set is the set of complex numbers ‘c’ for which the sequence (c, c² + c, (c²+c)² + c, ((c²+c)²+c)² + c, (((c²+c)²+c)²+c)² + c, …) does not approach infinity. The set is closely related to Julia sets (which include similarly complex shapes) and is named after the mathematician Benoit Mandelbrot, who studied and popularized it. Mandelbrot set images are made by sampling complex numbers and determining for each whether the result tends towards infinity when a particular mathematical operation is iterated on it. Treating the real and imaginary parts of each number as image coordinates, pixels are coloured according to how rapidly the sequence diverges, if at all.

Follow that? Me neither. The rest of us simply admire its visual appeal or marvel at its fractal properties and how it is never ending. The point I wanted to make at the conference was that much of our education systems are fractal in nature. Education is delivered recursively, where students are required to reproduce knowledge that is already known.

It’s a safe approach to education, and learning can be easily measured. Those that become teachers continue this tradition, teaching their own students the same knowledge, in more or less the same style they were themselves taught. Assessment of learning also has fractal features. Standardised testing is based on reproducing knowledge. Final examination success is premised on the student’s ability to reiterate what has already been taught in lessons. There is no room for exploration or creativity in summative assessment.

My point was that when education is conducted in fractal mode, it does not obtain its full potential and students are disadvantaged. I asked my audience to consider the difference between recursive and discursive education approaches. In recursive education, we see reproduction of knowledge, and we see students learning content towards a product – memorising facts and then reproducing them for the examiner. In discursive education, students are allowed to digress from the pathway, investigate new and untravelled pathways, and discover for themselves. Instruction is minimised, learning takes centre stage in the process. This kind of learning can be found in project work, problem based learning and personal research and many other progressive approaches.

My question for my audience was this: How can we as educators provide discursive opportunities for our students?

What would it take for us to leave the safe and mundane world of product based, recursive education behind and adopt new pedagogies that promote self discovery, digression from prescribed pathways and learning by a process of serendipity?

It would be a major risk for many institutions, and there would be some personal cost. But if we don’t try, how will we make any progress? This is an initial foray into this area for me and I would interested in your views on these ideas. As ever, I am open to discussion and revision, because I’m wholly committed to discursive enquiry.

Steve can be reached at S.Wheeler [@] plymouth[.ac.uk]

Online assessment: Find out if you’re already a learning culture

Posted on by David Grebow


This post written by Susan Fry

The question I’m asked most frequently these days (besides, “ATM or credit card?”) is “How do I start to create a learning culture in my organization?”

I’d actually prefer to start with a different question, which is “How close is the current culture in my organization to a learning culture?”

Many organizational cultures–and maybe yours–already have some of the key characteristics of a learning culture in place.  Finding out where you stand is the logical first step.

We employ a variety of tools to help organizations understand their culture because it helps makes for a smoother, faster transition from an obsolete “push/training” mode into the “pull/learning” culture.

Below, you can view a sample from one of the assessment tools we use. In the left column , you’ll see brief descriptions of key characteristics that  encourage learning; on the right, you’ll see descriptions of those that block it. Beneath the sample you’ll find instructions for taking and evaluating the assessment. new assessment captureTake a moment to answer the questions yourself.  Some of your answers are likely to be surprising.

You can view the full, printable Learning Culture Assessment here.

How to use this assessment

The assessment asks respondents to rank you organization on each characteristic by writing a number in the square at the bottom of each section.

The number “1” indicates strong disagreement with the statement, while “5” indicates the strong agreement. Adding all the  numbers in each column will show whether your organization is currently perceived to be a learning culture.  Questions that received the lowest scores indicate areas that need the most attention.

After you’ve taken it yourself, I suggest that you distribute this assessment to a group of people within your organization. Choosing as many audit participants as possible from diverse areas and levels of responsibility will provide you with more accurate information.

The survey has an additional benefit: it will communicate that you are starting to take a hard look at how good your organization is at providing learning opportunities that enable employees to do the best job possible.

This assessment was first published in Creating a Learning Culture: Strategy, Technology and Practice (Cambridge, UK; Cambridge University Press, 2004). I’m grateful to Marcia Conner, my colleague from my Peoplesoft days and friend of many years, for recently bringing it to my attention. (Check out her blog at http://marciaconner.com/

In case you didn’t note the publication info above, let me point out that this assessment was published more than ten years ago. In Silicon Valley terms, that makes it almost ancient — and yet I constantly meet people who think the “learning culture” is a radical new concept!