14th September from ‘The Consultation Community’
Tonight I have one clear point to make, which runs through all my thinking and analysis of management and leadership in maths education, so in true lecturing style, I will tell you it, I will explain it and contextualise it and than I will tell you it again.
Say it:
In planning mathematics education it is extremely useful to make a deliberate and determined split between two forms of mathematics education.The first form is the teaching of key mathematics vocabulary to aid the communication of ideas and of core techniques for the purpose of fluency.The second form is the nurturing and development of students as mathematical thinkers and of their connected mathematical understanding.If you analyse the new programs of study, it could be said that section 3 lies within the first form of mathematics education while sections 1, 2 and 4 lie within the second form.
Explain it: part 1 of 3 – the background to the technique of splitting concepts
It is essential in the definition of concepts that we challenge the vocabulary we are using.When we use words are we clear what we mean?Do we all mean the same thing when we use the same term?These processes of discipline in using languageare sensible and obvious.What is less obvious is that sometimes we use one word thinking it refers to one concept when in fact it refers to more than one concept.By splitting our concept and our vocabulary we gain much greater insight into our subject and make greater progress with it.And so it is with maths education.But before I go further into this I want to explore a different part of management theory where this has been done with great effect.
Explain it: part 2 of 3 – a rich and powerful example of the technique of splitting concepts.
One of the key components of management studies is the study of motivating employees.Now this theory made little holistic progress until Herzberg pointed out that we have a natural human propensity to see motivation and de-motivation as being equal and opposites within the same concepts.So if someone is de-motivated, giving them a good incentive will somehow more than balance that out and they will end up being motivated.What Herzberg did in a disciplined way was to separate motivation and de-motivation as concepts.So the opposite of being motivated is not being motivated.The opposite of being de-motivated is not being de-motivated.This led to much more powerful insights into how to deal with de-motivation and how to increase motivation than had previously existed (obviously you can find more on the internet about Herzberg should you wish to do so).For me this is a lovely example of concept splitting because I have often found maths teaching to be both incredibly motivating and de-motivating at the same time.And while motiviation and de-motivation are clearly linked, the segregation of concepts is valid because these things do not just balance each other out to leave me ‘neither motivated nor demotivated’.
Explain it: part 3 of 3 – the validity of this split
Now I leave motivation and de-motivation aside and return to maths education.The split I propose is one which I have used in many forms and contexts over the years both in practice and in academic articles and in the form I now present it in and I have found it to be robust.Much of my work has been about the synthesis of the two forms of maths education and I have found that in order to exploit the benefits of their synthesis it has always been wise first to consider them to be separate entities.
Conculsion: Say it again and name it:
The purpose of this post is to clearly define and explain a split which I make in my definition of maths education.To understand what I say about excellence in the leadership and management of maths education you have to understand this split because I will often refer to it.So once again the split is:The first form of mathematics education is the teaching of key mathematics vocabulary to aid communication of ideas and of core techniques for the purpose of fluency.The second form of mathematics education is the nurturing and development of students as mathematical thinkers and of their connected mathematical understanding.I’m going to call this split ‘The Hanson Split’ in order to keep this definition tight and to prevent it being used fluidly.
Postscript:
This split is never intended to lead to schism between parts of mathematics education, it is just a tool to aid thinking.