Two Things I Learned in My Teacher Training that I Still Use Today

Fourteen years ago I was starting my teacher training course. I had already been teaching a little (two undergraduate courses at university) and been to a mathematics education conference and numerous seminars. But I felt as though I knew nothing about teaching as a discipline and a career. After leaving my teacher training there were still so many things I did not know!

It’s impossible for teacher training courses to completely prepare teachers for what lies ahead. Mostly I hear other teachers say that they learned nothing of use in their training. But there are two things I still remember and draw from daily or weekly, fourteen years later.

1. Students need to experience an idea in order to learn it.

I was greatly impacted by reading Experience and Education by John Dewey. (It was a set text in my Philosophy of Education class.) In it, I learned that students need to play around with ideas in their pursuit of understanding. They need to create, investigate, take apart, put together, describe, and explain. Students shouldn’t be told what to think but come to think it for themselves. Additionally, students need to come at a concept from many angles before they gain a deep understanding of it. (Some of the other ideas in Experience and Education don’t sit so well with me anymore. That’s another blog post.)

For several years after first becoming a teacher I was struggling to keep pace with my workload and found it really hard to help students experience ideas. But I decided to make sure I thought about this in detail during my planning time once a week, or twice a week, or more often as I became able. Now it is the founding statement of my education platform: students must experience mathematics in order to learn it. I ask myself, how could a student come across this idea? How could them come to investigate it?

Recently I’ve added a new mantra to this one: the first time students see an idea they don’t have to produce exam-ready solutions. Getting to grips with an idea is important first, then coming to a deeper understanding, then being able to apply that learning. Exam-ready answers to exam-style questions on that topic can be introduced along the way, but aren’t needed at first.

2. The context for a mathematics problem can be “real world” or just plain “intriguing”.

My mentor and biggest influence during teacher training was a professor who studied and celebrated problem solving in the classroom. He didn’t care if a problem was based on some real life context or just really interesting.

In fact, working with him led me to prefer a puzzling situation over an over-simplified, meaningless “context”.

Thanks, John Grant McLoughlin, for embedding puzzling problems into my teaching. (He is still at the University of New Brunswick. See him in action in this video.) John is a huge fan of problem solving and non-routine questions and caused me to not really worry about real world connections; my students are intrigued by the problems and they are engaged in solving them, so I’m happy they are thinking about the concepts that I want them to learn.

Recently, I’ve been revisiting this idea thanks to reading about Peter Liljedahl‘s work on Building Thinking Classrooms. One of his recommended practices is to start each lesson with a quality problem.

I reinvigorated my love for problems this year; for the last term I set myself a goal of using a problem in every year 8 lesson that I taught. Here’s one of the problems I used. (It’s from a collection of problems devised for AQA GCSE [the link is a pdf].)

My students loved this problem and we spent most of a lesson talking about it. I used my visualiser to show several of the students’ solutions on the interactive whiteboard. They had lots of ideas about how to show the required idea – and this was one of the first times they used algebra to prove something. It was thrilling!

Do you still use ideas that you first encountered in your teacher training?

Better Group Work

I just finished reading an article called “When Smart Groups Fail” (Barron, 2003). It’s a study of groups of three sixth graders solving maths problems. Barron divides the groups into less successful and more successful at solving the problems and then analyses what features of their group work were significant.

Surprisingly to me, the success of a group of students was not influenced by:

  • the amount of talk
  • the average achievement level of the students
  • whether anyone in the group had a correct idea

Instead, Barron found that group success was marked by:

  • accepting or discussing correct ideas rather than dismissing them
  • correct ideas were brought up when they related to ideas that were being discussed at the moment
  • group members paid attention to each other and if the others were paying attention to them
  • group members physically showed their togetherness by eye contact and standing around or pointing to a common workbook

This article’s findings indicate to me that my classroom culture can lead to better group work. I can help students learn to discuss a mathematical idea by building on each other’s thoughts. A well-managed whole group discussion can lead to more cooperative group work sessions. I want my students to learn to listen carefully to what is said and then agree or disagree or ask questions. I can request these responses in whole class time. Then students will see they are the norms that also should guide their group work.

Furthermore, the groups in Barron’s study were of mixed ability and their previous achievement levels did not correlate with their success as a group. This adds to my feelings about the benefits of mixed ability teaching. If students of differing abilities can be helped to communicate well, they can all achieve well.

The study also found that students in successful group went on to be more successful in individual tasks. Interestingly, students in less successful groups did as well as if they had worked on their own. Thus poor group work neither helped nor hindered their achievement. However, good group work improved the success of individual students in to a significant degree.

The school year is just about to start and I am looking forward to inculcating a culture of social, mathematically focused talk.

Barron, Brigid. “When Smart Groups Fail.” The Journal of Learning Sciences 12.3 (2003): 307-359.

Thinking Systematically

One of my goals at the moment is to encourage systematic thinking. My students should learn to think mathematically, and systemisation is an important part of that. Tomorrow’s year 10 starter will be there two little questions. They are from the ATM book Eight Days a Week.

My students are very algebra-focused, so these questions are good because they cannot resort to a formula!