I am the mother of a child in the 6th grade who is homeschooled. I am looking for an exercise book in mathematics adapted to the competence objectives. I found your book and read a bit about the educational background and think it is suitable for us. Now I wonder if we can use the book without other children and to reach the competence goals for the stage? We have already worked with decimal numbers and now need geometry.
The books can be used alone (although having other children to discuss with can be an advantage). They are also suitable for self-study, but this assumes that the student is quite self-driven. Most people probably need some guidance from an adult.
This curriculum has a rapid progression - when a subject comes up again at the next grade level, you move on without repeating as much as many other textbooks do. (The idea is that the teacher must repeat if necessary.) The order of the topics is also carefully considered - f.eks. it is planned that you have finished all the essentials within the subject of fractions before dealing with decimal numbers. This means that going straight to the books can be a disadvantage 6. trinn, without having visited them on 5. step first. Then you may be missing a basis that is intended to make working with decimal numbers easier. (Fractions are dealt with in 5B and 6A, decimal numbers in 6B.) So it might be a good idea to take a look 5. step first (without necessarily going through everything)
The books for the steps 5-7 went to press before the final revision of the curriculum was completely ready (The subject renewal). But they still cover the plan well (it is rare that a textbook alone covers the entire curriculum, you usually have to supplement with something). The books cover e.g. work with the core elements very well! (Better than any other textbook on the market, I want to say). Some topics will be covered at another stage (the relationship between circumference and radius in a circle is e.g. a goal of 6. trinn, but is treated with us in Grunnbok 7A).
You say that discussion is central to UOM (Evolving training in mathematics) and that the material is clarified and elaborated through discussion in common. How can the training then be carried out if the schools have to close and the pupils have to have home tuition?
In accordance with Zankov's model, the assignments are made so that the student constructs knowledge himself. Therefore, it is important that each student has a basic book and exercise book. In basic books, the mathematical content is developed systematically, and emphasis is placed on presenting the material in an inductive way so that both weak and strong students find something that suits them and that promotes their development. Special attention is given to the choice of tasks (most are problem-solving tasks). Each assignment contains something new that the student learns by solving the assignment. Through a series of guiding questions in each assignment, the students get the opportunity to solve the assignment, and through an exploration process, students can come up with several solution strategies (then one can choose the most effective solution methods). In this way, the thesis forms a basis for new knowledge. This will enable students to work independently.
There are no traditional explanations or examples that show how a task can be solved, and there are few drill assignments in the textbooks. Knowledge is not disseminated, with the exception of terminology, symbols and other information that should be conveyed. The exercise books contain both assignments that will strengthen skills and assignments that are challenging and creative.
We believe that by using the basic books and exercise books, it should be easy for the teacher to give the students good follow-up so that they enjoy home school and get a high learning benefit..
I do not find mathematical subjects such as. geometry in the table of contents of the books. This means that the textbook does not contain geometry?
In, that does not mean. The headlines show only one main line. This textbook is organized in a different way than what is usual in other Norwegian textbooks. Each chapter consists of assignments. These are grouped into blocks, where each block consists of 2 to 4 tasks. It is assumed that the students work with such a block in a teaching session. The one task in each block is a main task and corresponds to a topic to which the task is linked. The others are "support tasks" that are a little smaller in content. The point of these tasks is that they:
- develops and expands reviewed material
- strengthens knowledge and skills acquired previously
- prepares for learning a new subject
Among these assignments, you will find important content elements that are not under separate headings in the books (as text assignments, geometry, symmetry, combinatorics, probability, statistics, elements of algebra).
At the end of each chapter there are varied tasks from the whole chapter. It is a collection of somewhat challenging tasks (5.-7. trinn) to those students who need it ("Puzzle"). It is also a sample suggestion ("Test yourself").
Suitable textbook for developing mathematics to the requirements set for mathematics in the new curriculum 2020?
The principles behind this textbook is based on Vygotsky's views on training and fits very well to the core elements of mathematics in the new curriculum. In textbook dialogue (communication) central. Students are encouraged to talk and cooperation. Most tasks have an element of exploration and Troubleshooting, with appropriate difficulty pupils. The tasks provide excellent opportunities for the teacher to adapt the teaching. They are varied and developed in order to create curiosity and motivation.
The students learn to observe and distinguish what is important from what is insignificant. They learn to reason, reflect, abstract, generalize, justify and argue for results. They must represent their thoughts in different ways (oral, writing, visually, …). Learning Administration helps students develop different strategies and models through algorithmic thinking. They are able to apply their knowledge in a safe and independent way. Depth Learning and development is in focus - students learn to learn!
The mathematical knowledge areas are well covered - progress and distribution of the threads is very thoroughly thought. This textbook offers a lot more than the minimum requirements described under the individual steps. We want to keep since our main goal is a maximum development of every child.
There are also plans to develop additional digital teaching aids.
Where can I learn more about "evolving training" and Zankovs system?
"Evolving training" and Zankovs system can f. example. read about in:
- Davydov, IN. IN. (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.
- Ankov, L. (1977). Teaching and development: A Soviet investigation. New York: M. E. Sharpe.
Who fits the textbook Mathematics 1-4 for?
Det passer for alle elever. Administration shows special attention to students who need extra time, while students who take things more quickly receive appropriate challenges. Learning Administration suitable for teachers who want to conduct a dialogue based teaching.
Following textbook Norwegian curriculum (Knowledge Promotion)?
And.
Is it difficult for the teacher to use this textbook?
As with all teaching requires good preparation for each hour. Teachers should start with this, must familiarize themselves with the principles that underlie, believe in it and undertake its best efforts. Vygotsky is well known in the educational community in Norway - this system shows how Vygotsky's theories can be implemented in the classroom. Teachers who have worked for this system in Norway think it's exciting and interesting and do not want to go back to other textbooks. In the long term it will be an advantage for teachers to go together in learning networks, equal that one is not left alone, but can rely on and help each other.
Is it difficult for students?
And, It is demanding, since learning mathematics with understanding and not only repeats mechanically what the teacher says or shows. It takes an emotionally intensive independent work. We are convinced that this opens the child's potential. Working for this system is stakeholder, exciting and challenging for both pupils and teachers.
How does customized training in this textbook?
Customized training is safeguarded through tasks that contain questions on different levels. It is a low threshold for getting started with tasks while containing additional questions that lead to development. In addition, if one looks at problems from different angles and learn different strategies, which is very important for success in mathematics.
What characterizes textbook Mathematics 1-4 and in what ways does it differ from other Norwegian textbooks?
Firstly textbook another structure and structure. It does not address the subject of the topic - however one works with multiple threads simultaneously. There is considerable variation in the types of assignments, and repetition going on all the time. Overall leads this way of organizing substance at a far faster progression.
Learning Administration has considerably more text than Norwegian books for the same step. In the beginning the text is as much aimed at the teacher - here are the questions you should ask to get started thinking among students. The grounds are central. Many of the tasks have multiple choice and the choice of answers always requires justification. Academic concepts and expressions are introduced early, which in our experience helps children to put into words what they do and think.
The books have a systematic buildup of mathematical knowledge - brick by brick, in small steps. Students receive a systematic strategy training. It is therefore necessary to follow the books' progression. There are many rich tasks that lead to the introduction of new concepts and stimulation of children's creative skills and developing new thought models that may lead to new discoveries for children. Efforts lot with inverse (reverse) tasks.
Why is there so much text in books? Is not there a problem when students barely learned to read?
At the first stage the text is intended for teacher. Students can follow when the teacher reads. This can be a motivating factor, and students will eventually begin to read themselves.
Why is it so difficult words and phrases instead of more mundane words?
First and foremost, it is our experience that this is not difficult for students - they learn new words and expressions all the time. The problem lies preferably in adults who believe that words are too difficult. The use of terminology is deliberately, and is based on Vygotsky's theory that language develops tank. In parallel with the technical terms are also used colloquial.
What characterizes an hour that builds on Zankovs system? What should I watch out for when scheduling such hours? How should one work with tasks in the classroom?
A typical time is characterized by lively discussion in which all students participate. It created a safe classroom environment where students are not afraid of making mistakes, get up on the blackboard or ask questions, where they believe that they should be able to solve the problems. There is a mutual respect and trust in the classroom where students are experiencing great joy of intensive mental work. They understand that it is not always meant to be getting things on the first try. They learn to learn.
When one hour is planned it is important to ensure that it complies with the individual students' abilities. There is no typical hours (standardtimer). The teacher must be creative and at the same time ensure that Zankovs five teaching principles implemented hour (see article on Zankovs education system).
During work on the tasks the teacher must take care to listen and to take students' opinions and suggestions seriously. Man creates mathematics together - the teacher is a learning partner rather than the one who sits with the key. The teacher must purposefully lead the discussion in the classroom so that most students involved.
Is not teaching described here very teacher-directed? What about student active teaching?
It is riktig that teaching is a teacher crash. At the same time aims for a high degree of student activity. Based on Vygotsky's theory of development and learning are not teacher-led instruction negative, but on the contrary absolutely necessary to draw future developments. Teacher's main task is to follow Vygotsky to expand the zone of proximal development of each pupil.
Can we use another textbook next, f.eks. to hjemmearbeid?
We will not recommend. Other textbooks use other principles. Homework should be a systematic continuation of what has been done in the classroom.
Can I switch to another textbook after spending Mathematics in one or more years?
And, it is unproblematic from a professional point. The reverse, however, we do not recommend. Should we use this textbook should start either on 1. eller 5. trinn.
Can books be used as additive / extra books for students who follow another textbook?
One can find many good exercises and ideas to task types, but using the textbook in this way achieved anything but if you use it as grunnbok.
Can we start with the textbook Mathematics for 5. step if students have used another textbook from 1st-4.trinn?
And. Important concepts and material from 1 to 4. Steps to be reviewed thoroughly in 5. trinn.
Is Zankovs system developed only for mathematics?
In, Zankovs system can be used in all subjects. However, it is strongly linked to learning materials and so far, there is only material for mathematics in Norwegian.
Is it a goal for you, that all shall teach after this model?
In, absolutely not. This is an option. Teachers are different, they have different teaching style and different teaching philosophy. We who have worked with this model seems the work has been very rewarding, and we are convinced that there are other teachers who have been looking for something like this. It is in our opinion essential that the desire to teach for this model comes from the teacher himself and not from eg. school policy management.
Is there Olympiads / competitions in mathematics for pupils in primary schools?
Kangaroo is a wonderful competition that kids among others. at the primary level can participate in. This is just fun! Mathematics Centre has information about the contest on its pages: //www.matematikksenteret.no,en
Do you have any tips for how one should equip a classroom?
Garnish up classroom with math posters where content customized for each. It can be colorful posters that stimulates and creates curiosity or it can be self-made posters like. the definitions or summarizes any class have found. If pupils themselves making posters should these "quality assured" by the teacher so that the content is accurate. For younger grades should sequence of the natural numbers be as obvious to have on the wall like alphabet.
Regarding specification materials we would recommend to prioritize materials that have wide range of applications (f.eks. dice, counting pieces, pinner, etc.).
The questions are answered by Kjersti Melhus and Natasha Blank, University of Stavanger.
Will textbooks based on Zankovs model be released 5-7.trinn?
We have only positive experiences with teaching based on the Russian textbook that only goes up even 4.trinn. We are very happy that we started with it. Several schools have steadily adopted these books.
We have sat down to write textbooks for middle school after receiving several inquiries from both teachers and parents.
Working with textbooks and exercise books are in the initial phase. We will continue to give out one step in the year. We obviously hope to get external resources to complete the textbook for all the intermediate stage, but we do not know at present whether we get it. Lower secondary education is also applicable.
Questions regarding teaching model can be directed to the working group at the University of Stavanger, Department of Education, Sports Science.
Contact:
- Associate Natalia Blank: natalia.blank@uis.no
- Assistant Professor Kjersti Melhus: kjersti.melhus@uis.no