Theme 10: Teacher knowledge

Effective teachers develop and use sound knowledge as a basis for initiating learning and responding to mathematical needs of all their students.

What teachers know and believe about mathematics and what they understand about mathematics teaching and learning impacts directly on the way they organize their mathematics instruction in the classroom and upon the learning experiences for their students.

Teachers at all levels need to know their learners too, they need to be able to anticipate the difficulties that their students may encounter in their mathematics learning, to challenge and extend their students, and they should be able to describe learning trajectories and next learning steps.  This demands a skillful response to teaching situations rather than simply an adherence to scripts or texts.

In some of the stories below, the writers highlight particularly well their understanding of the need to have sound pedagogical content knowledge in order to recognise and act on moment by moment teaching opportunities, to understand students’ thinking, to recognise misconceptions and to work with these, and to represent mathematical ideas appropriately in multiple ways.  

     

Exemplars:

I have done two postgraduate university papers in maths which provided me with in-depth pedagogical content knowledge. 2010 paper: Mathematical Literacy for Lower-Achieving Students.

 

Being involved in this project has been an exciting journey for me. I have really enjoyed seeing the joy on these children’s faces as they achieved success.
Much of what I have learnt and tried has flowed over into my classroom programme and I believe is helping to boost the achievement of all the children in my class.
Throughout the process, I also developed a deeper understanding of mathematical pedagogy and realised that I could trust my own skills and knowledge to meet the needs of the students to make a significant difference in their learning. I was comfortable adapting a more creative rather than linear approach to instruction and using a variety of resources rather than just the ‘Pink Books’.
Teacher knowledge. Teachers need deep knowledge of mathematical ideas and how to implement them successfully. Professional development needs to be ongoing and linked to effective practice. Many teachers recognise gaps in students' learning but are unsure of how to meet the need.
Another ‘result’ was a marked change in my attitude to, and confidence in, teaching maths. I felt more inclined to relinquish the ‘Pink Books’ more confidently and trusted that my knowledge, resources and skills were enough to make a big difference to the children’s experiences and ultimately to their learning. Learning did not have to follow a neat linear path according to the book. Rather it took a path according to needs and growing knowledge and strategies. Also, I felt more confident in knowing where or who to go to ask for help or ideas, as well as being more creative with what I could bring to the children.
My curriculum knowledge and teaching of maths has improved greatly. I feel I have become more explicit in making links between knowledge and strategy. My maths programme is running more smoothly and tighter as a result of this.
There are huge pedagogical demands that this intensive work puts on the teacher. When the student encounters a difficulty with a concept there are so many decisions facing the teacher in that moment:
So what other concept is linked to that one and should that be highlighted now?
Which piece of equipment is the most appropriate to address this misconception and where will I go next with this student?
How much scaffolding should I give this student?
If I give too much they will start to sit back and not do the cognitive work that is needed for them to make the links in their own mind?
If I push too hard and they start to experience failure they will tend to withdraw or give up?
Have a specialist run your programmes for underachieving students. The people running these programmes need to be acutely aware of the need to be explicit with children. They also have to have the content knowledge and pedagogical knowledge to be able to support students' progress, especially if you wish to accelerate their learning.