1. Where can I read more about “development learning” and Zankov’s system?

You can read about “Development learning” and Zankov’s system in, for example, the folowing:

  • Davydov, V. V. (2008). Problems of Developmental Instruction: A Theoretical and Experimental Psychological Study. New York: Nova Science Publishers.
  • Vygotsky, L. (1986). Thought and Language (Revised Edition, A. Kozulin (Ed.)). Cambridge: MIT Press.
  • Zankov, L. (1977). Teaching and development: A Soviet investigation. New York: M. E. Sharpe.

2. Who is the Mathematics 1-4 textbook intended for?

It is suitable for all pupils. The work pays particular attention to pupils who need extra time, while ensuring that pupils who tackle things more quickly are also suitably challenged. The textbook is well suited to teachers who want to engage in inquiry-based learning.

3. Does the textbook follow the Norwegian syllabus?

Yes.

4. Is the textbook difficult for teachers to use?

As with all teaching, it requires good preparation in advance of each lesson. Teachers who want to start with this must take time to familiarise themselves with the underlying principles, believe in them, and implement them as best they can. Vygotsky is well known within Norwegian pedagogy – this system illustrates how his theories can be implemented in the classroom. Teachers who have worked with this system in Norway have found it exciting and interesting, and didn’t want to go back to using other textbooks. In the long term it will be useful for teachers to work together as part of a teaching network, so they aren’t working alone but can support and receive help from one another.

5. Is it difficult for the pupils?

Yes, it is demanding, because one learns mathematics through understanding rather than simply mechanically repeating what the teacher says or points to. This makes for emotionally intense independent work, which we are convinced opens up a child’s potential. Working with this system is interesting, exciting, and challenging, for pupils and teachers alike.

6. How does customized training work with this textbook?

Customized training is allowed for through the use of exercises with questions at different levels. Getting underway with the exercises is easy, but they also contain additional questions that lead to further development. Pupils are also encouraged to look at problems from different angles and learn different strategies, which is vitally important to succeed in mathematics.

7. What characterises the Mathematics 1-4 textbook, and how does it differ from other Norwegian textbooks?

First of all, the textbook is structured and constructed in a different way. It doesn’t address one topic at a time – rather, one works with several topics at once. There is great variation in the types of exercise, and repetition is taking place all the time. Overall, this way of organising material leads to far faster progression.

The book contains significantly more text than Norwegian textbooks at the same level. At the start the text is mainly aimed at the teacher – these are the questions one should ask to spark the pupils’ thought processes. This foundational approach is central to the book. Many of the exercises have multiple alternative answers, and the choice of answer always requires justification. Proper academic concepts and terminology are introduced early, which in our experience helps the children to put words to what they are doing and thinking.

The books feature a systematic step-by-step build-up of mathematical knowledge, through which the pupils receive systematic strategy training. This means it is important to follow the book’s progression. There are many rewarding exercises which serve to introduce new concepts and stimulate the children’s creative skills, and which develop new modes of thinking that can once again lead to new discoveries for the children. There is a lot of work with inverse problems.

8. Why is there so much text in the book? Is this not a problem for pupils who have only just learnt to read?

At the earliest stages, the text is primarily intended for the teacher – the pupils can follow along as the teacher reads. This serves as motivation, and the pupils will eventually begin to read for themselves.

9. Why does it use such difficult words and expressions instead of more everyday language?

First and foremost, our experience has taught us that this isn’t a problem for the pupils – they learn new words and expressions all the time. The problem is rather with adults who think that the words are too difficult. The use of academic terminology is quite deliberate, and builds on Vygotsky’s theory that language shapes thought. Everyday language is also used alongside the academic terms.

10. What characterises a lesson built on Zankov’s system? What must I look out for when I plan this sort of lesson? How should one use the exercises in a classroom environment?

A typical lesson is characterised by lively discussion in which all the pupils participate. This creates a safe classroom environment where pupils aren’t afraid to make mistakes, come up to the blackboard, or ask questions, where they have faith in their own ability to solve the problems. There is a mutual respect and trust in the classroom, where the pupils experience the pleasure of intense mental work. They understand that it isn’t always expected that one should understand things at the first try. They learn how to learn.

When planning a lesson, it is important to make sure that it is suited to the abilities of each individual pupil. There are no standard lessons. The teacher needs to be creative, while at the same time making sure that Zankov’s five teaching principles are being applied in the lesson (see this article about Zankov’s teaching system).

While working on the exercises, the teacher must be sure to listen to and take seriously the pupils’ input and suggestions. One creates mathematics together – the teacher is a learning partner, rather than just the person with all the answers. The teacher must purposefully lead classroom discussion so that as many pupils as possible are involved.

11. Isn’t the sort of teaching described here very teacher-led? What about pupils-driven learning?

It’s true that the teaching is very teacher-driven. At the same time, a great deal of pupil activity is featured. According to Vygotsky’s theory of development and learning, teacher-led education isn’t a negative thing but rather something necessary to push development forward. The teacher’s main task is, according to Vygotsky, to broaden the proximal developmental zone of each individual pupil.

12. Can we use other textbooks alongside it – for homework, for example?

This is not recommended. Other textbooks use different principles. Homework should be a systematic continuation of what has been done in the classroom.

13. Can one change to a different textbook after using Mathematics for one or more years?

Yes, this is unproblematic from an academic standpoint. The reverse, however, is not recommended. If one wishes to use this textbook, one should start from the first year.

14. Can the books be used as additional resources for pupils following a different textbook?

One can find a great many good exercises and ideas for types of exercise, but using the textbook in this way will not achieve the same things as using it as a foundational text.

15. Is Zankov’s system developed only for mathematics?

No, Zankov’s system can be used for any subject. It is, however, closely tied to the course materials, and at present these materials are only available in Norwegian for mathematics.

16. Is your goal for everyone to teach using this model?

No, absolutely not. This is an alternative. Teachers are different, with different teaching styles and philosophies. Those of us who have worked with this model have found the work extremely rewarding, and we are convinced that there are other teachers who have been looking for something like this. In our opinion it is vital that the desire to teach using this model come from the teachers themselves rather than, for example, school management.

17. Are there maths Olympiads/competitions for primary school pupils?

Kenguru is a fantastic competition that children at a primary school level can take part in. It’s just for fun! Matematikksenteret (Mathematics Centre) has information about the competition on its website:
http://www.matematikksenteret.no

18. Do you have any tips on how to manage a classroom?

Decorate the classroom with maths posters, whose content can be changed periodically. They could be colourful posters which stimulate and strike curiosity, or they could be homemade posters showing definitions or summaries of what the class has learned. If the pupils make the posters themselves, they should be checked by the teacher to make sure the content is correct. For the youngest classes, the sequence of the natural numbers should be as obvious a thing to have on the wall as the alphabet.

When it comes to specific materials we would recommend prioritising items with a broad range of functions (such as dice, counting sticks, etc).

These questions have been answered by Kjersti Melhus and Natasha Blank, of the University of Stavanger.