My experience as a teacher with ‘developmental learning’

Background:

As a veteran teacher, I have taught beginner’s mathematics to many first-year classes. Each time I have found that the pupils are able to make significantly faster progress through the syllabus. Even though I increased the pace, I still found myself looking for more challenging exercises to stimulate class activity. Traditional lessons comprise a teaching session, reviewing new material, and then the pupils engaging in similar activities. This is just how it was in my classes as well – a little boring and monotonous.

I worked in teacher training for many years, which is how I met Natasha Blank, a lecturer in mathematics at the University of Stavanger. She introduced me to some Russian textbooks that immediately caught my attention. The exercises were varied, and seemed more exciting than anything I’d seen in Norwegian textbooks. In the autumn of 2009 I had the chance to try out a Russian curriculum designed for first-year pupils. Natasha Blank was willing to help me with translation of both textbooks and guidelines, for which I am extremely grateful. In the media this was described as “Russian mathematics”, but it is really “developmental learning”. The project lasted for 4 years, and was used with two classes in this period. I was very excited about both the exercises and the way they were supposed to be implemented.

What is so good about “developmental learning”?

The Russian textbooks were exactly what I had been missing. There was rapid progression, with challenges and variation in the exercises presented to the pupils. Moreover, there were different ways of approaching the various tasks, meaning that the children had to remain alert and attentive – they were kept continually active. This spurred and engaged their curiosity, encouraging an open attitude towards new and unfamiliar exercises. Since the books contained exercises on such varied topics as geometry, measurement, and numbers, they avoided dwelling on any one topic for too long. I believe that this variation had a very positive impact on the pupils’ engagement with the subject. If someone is struggling to grasp a particular topic they are working on exclusively for a long time, it can sap their motivation. At times I was concerned that exposure to so many different topics at once could prove confusing to the pupils, and that they would not be able to take in anything thoroughly enough. It soon became clear that the different topics were constantly being repeated and revisited, which meant that we could actually move forward even faster!

What was different about implementing teaching based on Zankov’s principles?

A lot of weight is placed on conversation and discussion among the pupils, summarizing regularly along the way. Most teachers are familiar with Vygotsky’s theory on proximal developmental zones and their consequences for classroom teaching, but this was the first time I’d been able to put these ideas into practice. It was a challenge at first to allow the pupils to speak and explain so much. As a teacher I had to learn to hold back with my own explanations, and let the pupils speak for themselves. The questions were often open: What are you discovering here? What do you see? In other words: more learning and less teaching!

What sort of preparation is required?

I spent a lot of time planning each lesson. Which exercises would be worked on as a full class, and which would be carried out in pairs? Which tasks were best suited to individual work? How long would each exercise take? Which questions and issues were appropriate to the tasks at hand? What sort of answers could be expected? What might prove challenging for the pupils? I looked through and solved several tasks myself before each lesson, to be as prepared as possible. It was important to acquaint myself with the different tasks the pupils would be facing by thinking them through myself beforehand.

 What about implementation/follow-up and marking?

In this approach, the teacher takes on a supervisory role. You should help the pupils arrive at the answers by themselves, taking care to provide appropriate hints and assistance at the right time. The teacher must keep a close eye on both the whole class

and the individual pupil, work within the available timeframe, and be sure to leave time to sum up the lessons learnt and move forward. This also keeps the teacher constantly active throughout the session. The advantage of using this form of education is that the pupils are able to discuss things and help each other. There were few raised hands, and it was not difficult for me as the teacher to hurry around the room helping anyone who needed it. Many tasks were worked on jointly, and these weren’t marked. I marked the tasks the pupils worked on individually in the last 15-20 minutes, to keep track of what individual pupils had mastered. When I write “marked”, I don’t mean that I always went through every calculation, but rather that I looked through most of it to keep track of each individual pupil.

What the pupils have learned

If nothing else, they’ve learned to think! The pupils have learnt a lot of maths, and I’ve never had such academically strong pupils in my time as a teacher. The exercises have sparked creativity – it’s not unusual for the pupils to find other solutions or answers to those that I as the teacher had found or expected. The pupils often faced challenges when trying to solve the tasks. They have learnt to persevere and work through these challenges. I think this approach would be highly transferable to other subjects, and could prove useful in later education and beyond. Through conversations and discussions they have learnt to use precise terminology, and how to explain things to each other in a fairly sophisticated way. As a teacher, it has been extremely satisfying to be able to stand to one side and listen to what they’re saying. I’ve often been impressed by the standard and substance of the academic conversations I’ve heard while walking around the classroom. The pupils have also learned to pay attention to one another, and to display their tolerance and social skills when working with others.

Evaluation

These have, without a doubt, been my most interesting years as a teacher. Teaching based on Zankov’s principles has been exciting. When I look at the active pupils receiving their tasks, talking, asking questions, and using the correct terminology, it feels good to be a teacher. Seeing the joy and excitement of pupils as they proudly came forward to the board to show off their solutions was deeply inspiring. In the individual assessment notes written by pupils from both classes at the end of the project, all of them expressed similarly positive attitudes towards maths as a subject. This pleases me enormously.

Gerd Inger Moe