This weekend, I found myself doing something I've not done before - disagreeing with Professer Derek Haylock. Giving his second lecture to Edge Hill MaST cohort 1, the man who's seminal work "Mathematics Explained for Primary Teachers" has pride of place on my shelf, said some things that didn't quite hang together for me.
His lecture was on the subject of mathematics anxiety - something that most adults have either experienced or can empathise with. His main point was this: if you teach mathematics well, you don't get students who are anxious about maths. As someone tweeted on the day "My God I never thought of that. I hope the person giving this advice is paid a fortune." Given that the audience was a room full of primary maths specialists, or 'maths champions', the advice is more purposeful if given a more negative slant: don't allow bad maths teaching in primary - you'll just get adults who are anxious about maths.
Briefly I will sum up what I thought were his main points and then I'll say where and how I disagreed with him.
- Many adults experience anxiety in maths when they are afraid to make mistakes in public, or given a mathematical challenge they cannot think clearly to carry it out.
- These adults can trace their feelings of anxiety back to a single experience usually between the ages of 9-11 at primary school.
- This experience is always a negative interaction with a teacher - Prof. Haylock quoted adults saying that their teacher had shouted things like "why can't you just get it right?" There was a real emphasis on the negative experience being when maths is thought of as either right or wrong.
- Many of these adults reported they could only learn maths by learning a rule by rote and couldn't master any conceptual learning.
- Some of these adults become primary teachers.
- Teaching styles are to blame for mathematical anxiety - 'traditional methods' create more anxiety; a 'problem-solving / relational approach' creates less anxiety. Quoting from Newsted, he described a traditional approach as one of direct instruction, followed by practice and application, whereas in the 'problem-solving approach' the teacher acted as a facilitator, with the children suggesting their own methods and strategies for solving problems.
Aside from the dangers of telling rooms full of teachers that 'rote learning is always bad' and 'this is the only way to do it', my main disagreement was the way he linked the single negative experience with a given teacher to the traditional teaching method. It doesn't take the room being in rows or table groups for you to have a bad experience with a teacher. Neither does it mean that you if are using a 'problem-solving approach' then teachers can't lose their tempers and make everyone frightened of maths.
In my own experience I've tried both traditional and 'problem solving approaches'.
I would call them using a rigid scaffold and using a negotiated scaffold. In the former, the teacher plots the course through the learning (the scaffold) and takes the students through that course through direct instruction, practice and intervention; in the latter the student and teacher negotiate the path through the learning.
Both approaches work.
In fact this time last year I did an experiment where I did 6 weeks of negotiated scaffolding in maths, then 6 weeks of rigid scaffolding in maths. The children made progress in both periods.
Delving a bit deeper into the Newstead report I see that the traditional approach includes: "The teacher decides what is right or wrong and intervenes in the case of mistakes. Later word
sums may be used as application of methods. Social norms are more static and involve more discipline, rewards and teacher authority." Now to me that's not traditional teaching. Traditional teaching is where direct instruction is followed by practice, yes, but then appropriate intervention from the teacher. And so now it leaves me thinking that Haylock, quoting Newstead isn't comparing 'Problem Solving' with 'Traditional', but is comparing 'Problem Solving' with 'Bad Teaching'.
I'll go on to say that Haylock is right by saying that for a student to have one-to-one negative interactions with an authority figure such as a teacher will cause anxiety, in any subject. The teacher that chooses 'traditional teaching methods' but can avoid the negative interactions can still teach a class without causing anxiety amongst the students. And a teacher that attempts to be a 'facilitator' but then loses their temper when the students don't choose a method they were anticipating will also cause anxiety. It's not about the style, or dare I even say it the teaching, it's about the teacher themselves.
Good teachers reduce anxiety.