Wednesday, 7 January 2015

The paradox

Many years ago, myself and a friend, who worked for the TEC, attended a numeracy training course. The course was on 'how to teach numeracy' and we were drilled in constructivist approaches. However, during one part we were informed that tutors were no longer teachers, tutors, educationalists or trainers, but rather - facilitators.

Now my TEC colleague took exception to this, and proceeded to exclaim loudly that this was rubbish ("You mean we can't teach them anything!"), and thus started a class debate through which the 'facilitator' lost all control.    

I remained quiet, because I actually agreed with both of them.  I had been immersed in constructivist thinking and was a believer, and still am (a Jo Boaler convert). BUT, I did not like the Orwellian attempt to reduce my chosen vocation to that of facilitator (it simply does not impress at functions)!

This has come up many times since that workshop, and the conversation always misses the deeper issues at hand.  At best, the discussion situates on how much we can 'tell' students versus how much we should expect them to 'construct' understanding.  And all the opinions in between, like the much quoted, "it would take too much time to let them figure it out by themselves" to "if you just tell them they just forget it all anyway".  Part of the real issue regarding numeracy, and why the answer is anything but easy, is discussed below.

The paradox

The conflict is actually situated in the middle of an educational paradox.  Here is the issue - to develop an adult's numeracy skill several things must happen.  One, they must learn content, and two, they must develop agency.  Agency is the learners ability to take action independently for their own purposes.  Third, they must be able to apply their knowledge with agency to unique and novel situations.  Numeracy skill is the ability to take what you know and apply it to situations you have never seen before, and in ways never done before (rather than the reproduction of memorised methods).

Now here is the paradox.  To enable learners to use numeracy in unique, novel, and self-directed ways, the tutor can only ever create conditions in which this MAY happen.  If the tutor shows, tells, explains, scaffolds or models to the learner what to do, then they prevent the learner of autonomously using their skills in unique ways.  And the learner never becomes autonomous or self-directed!  

Do you see it?  You cannot make someone autonomous!  Everything the tutor does to produce the behaviour in the learner they want, deprives the learner of the necessary conditions to do so!  In fact, according to Brousseau and Sarrazy, (2002) the only learner who develops these skills, is the one who actively rejects the teacher (in favour of their own methods).

This is one of several educational paradoxes that settles down around the role of the tutor.  It requires some real thinking about how we balance the numeracy instruction so as to meet both content and agency needs.

So, back to the argument.  Both my friend and the facilitator were right, but they both failed to appreciate the depth of the issue.

However, one thing I do know, the term 'facilitator' is demeaning of someone attempting to create the conditions in which a learner may develop agency and autonomy.  That role is more closely aligned with 'master designer' or 'situational engineer' or... 'grandmaster'.

Love your thoughts.


  1. This has me thinking that a teacher/tutor must teach the learner how to find answers rather than providing answers. The teach a man to fish concept, if a tutor can facilitate conditions in which an enquiring mind can learn how to explore and question with purpose it would seem to me they have unleashed unlimited potential!

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  3. Yes. One big problem for maths or numeracy teachers is that they very rarely act like mathematicians. For example, mathematicians generally work on problems that no one knows the answer to, or the method to solve them. When you are teaching a class, it is very risky to demonstrate to students how to solve a problem you have no idea about (because you might fail), yet this is EXACTLY what students need to see teacher doing. Unfortunately, all students see is teachers answering questions they already know the method to solve - so they never see the struggle, the experiments, the dead ends and mistakes or the thinking process, and end up thinking someone good at maths is someone who knows a way to solve problems. Actually, someone good at maths is someone who can self-learn, innovate and experiment until they figure stuff out.

    Not many teachers are prepared to solve a novel, non-routine problem with no clear solution strategy in front of the students.