- Challenges for teacher
av GERD INGER MOE OG SVERRE MOE
Evolving training in mathematics, known Russian maths, is a method that gets increased support. The scheme may, however, pose challenges in relation to the teacher's practice.
Here we will explain the theory and the key principles that underlie the approach Evolving training in mathematics (also known as "Russian mathematics"), and show how such an approach to begin training can challenge some widespread educational beliefs and habits. It begins to be quite a few Norwegian schools that have adopted this method and the Norwegian edition of the textbook, and some teachers might get problem when they will practice such a project without the simultaneous change their praksis.¹ We do not go into detail on teaching and progression, and to the extent that we draw this into, is the first class we show til.²
Evolving training in mathematics
Opplegget ble utviklet i forbindelse med omfattende reformer av det russiske skolesystemet på 1980-tallet, where excellent pedagoger, psychologists and mathematicians took part (Ankov 1977).³ Theoretical rests at heavily on Lev Vygotsky (2001) thinking and modern cognitive psykologi.⁴ The key feature is that child development should take place by means of teaching. This applies to absolutely all children. Everyone must feel that they succeed in school. The target applies to all subjects, but limited to mathematics, it is about "learning to think", ie learn to think logically, focused and without contradictions, develop the ability to draw inferences, reason and convince, and learn to think through the fabric before starting to work with det.⁵ program is strongly focused on children's cognitive development, and the whole is characterized by working with tasks that require little more than what they already know.
The plan steeped, shortly said, of?) focus on thinking ahead teaching, b) focus on the theoretical, abstract knowledge with emphasis on universal, precise concepts and symbols, c) focus on the relationship between observation, thinking, speech and writing, d) focus on observation, analyse, systematics and grounds and e) focus on amounts, former, sizes, relationships and categories (more / less, most / least, first / last etc.). This means that the teacher must put less emphasis on teaching, explanation and drill, that focus on specific object being toned down in favor of abstract concepts and symbols, that the emphasis on activating perception and thinking, and that verbal communication is highlighted (waiting around with paper and pencil). The figures connected to the quantities and sizes in a meaningful way, and they operate accordingly not with digits one by one detached from context. The theory behind it all is synthesized in five basic principles: 1. teaching at a high level, 2. theoretical knowledge has leading role, 3. quick review of the syllabus, 4. awareness of children about their own learning process and 5. systematic and targeted development of each child (Melhus 2015). We will elaborate on all this in the following.
Teaching at a high level
Hva betyr det at undervisningen skal ligge på et høyt nivå? The reasoning is found in the concept of children's Zone of Proximal Development (Vygotsky 2001). The basis of this concept is the assumption that to learn something new, must build on what the learner already knows. The proximal development zone indicates the child's learning potential and what the teacher may expect from the child already knows. These are individual assumptions that can vary widely in a school class. Where one six year old has the potential to learn fabric right up to 2. og 3. klasse, there may be others who have a significantly narrower development horizon. This means more challenges. How does one determine pupil proximal zone, and how should the teaching ensure that each student can develop according to their individual abilities? How ensures learning of the weakest students? Generally requires the solution that the teacher knows the students' abilities and has good contact with the guardians. When it comes to knowledge of assumptions, all this in the first place about the knowledge children have when they start school. Which has the tallbegrep? How do they relate to the sizes and quantities? One of the first teacher must do, is therefore to chart their knowledge in mathematics. It need not be extensive, but enough that the teacher knows what can be expected. After such a round teacher has a rough, but adequate picture of each student's abilities and opportunities. Often we see that children have knowledge that exceed the requirements and expectations that central planning sets. When class gets underway, this regularly monitored and controlled.
Regarding cooperation with guardians, Emphasis is placed on early contact, and it is expected that parents follow up with support and assistance. Some tasks require guardians read the text for your child (we're still talking about six year olds). It also provides advice on how best to help. How does the actual teaching on the principle that education should be about something that is just over the individual can? How make this when students' abilities are different? We can not go into detail, but a typical hour is that students encounter a problem on the board when they enter the classroom, and act immediately to resolve one or more problem (not exercises with known drug, as is often done). The first tasks trades such as the arrangement of the quantities and sizes (most / least, equal / different, over/under mv.), which further follow up of numbers and mathematical expressions, and later with the addition, subtraction, etc.. In working with tasks gives teacher only hint where necessary. The point is that the children will be encouraged to observe, analyze and think. The teacher should first and foremost be an adult who sets thinking Started, and this may be something of a challenge for teachers which is often used to describe and be in the center of the process. Such a practice is wrong in this method,. Instead it is intended that the teacher and peers helps the individual. For this reason, emphasis is much emphasis on discussion (cooperation in pairs), meaning that there is less emphasis on writing (adding pencil aside) and that it will be "produced" answers. Equally important is it to get forward thinking. How has one? How came you to the answer? In this context it is important that the teacher emphasizes getting all students to participate (with questions that activates all, explaining etc.). Summarising we can say that teaching at a high level about the children face challenges they can master with a little work.
Teoretisk kunnskap har ledende rolle
Hva forstår man så med teoretisk kunnskap? Also this is a term taken from Vygotskij (2001), and the point is, loosely, that children's knowledge (and language) goes from being what we might call object knowledge in preschool age to be theoretical knowledge of school age, and the school's main task is to help children to develop such knowledge. Object Knowledge trades primarily to name the "thing" (learn words). Theoretical knowledge about general, universalist rendering concept, precise expression and symbols that enable us to observe, compare and synthesize (deduktivt) an overall of the whole elements.
One may notice that this is a mindset that emphasizes learning concept and abstract expression (which is important in a subject like mathematics). The aim is to replace the object of knowledge with knowledge of universal characteristics, necessary connections and logical thinking. One sees that this is a mindset that is contrary to perceptions that emphasizes the use of "concretes" and "practical mathematics". Such approaches involve happy that you get problems with the transition from the object knowledge to theoretical knowledge. It is important to emphasize that neither weak students should meet with such practices. Their development may actually be hampered by such a method. Otherwise there is simply no prohibition against drawing into concrete and practical subject matter, but the point remains that theoretical knowledge shall be the. Theoretical knowledge is knowledge that has a scientific character (Vygotsky 2001). Barna observes, For characteristics, analyzes, synthesizes and conducting logic operations. They come with proposals that are met with acceptance or objections, and the discussion may even with first graders get a highly factual and focused feel. Through collaboration and discussion they get good training in planning exercises, reflect on own and others' suggestions, and that they are trained in justifying their own thinking.
Not least they get in the way training to generalize from the conclusions they hit, thus derive the mathematical rules that result of work tasks. It's not about first learning rules which shall be applied, but that pupils come to the knowledge of the rules and their validity, theoretical knowledge. The emphasis on theoretical knowledge means that children should study mathematics as a subject with its own terminology and distinctive symbol. From the first day they meet precise term (joint, sum, gave, rectangle, circle, square etc.). This learning fast, and it is a great help when they should analyze and explain how they solve tasks. We remind you that we are talking about first class where the danger lies in the teacher intentioned uses everyday language and approximate educational structures («Animal venner", «Consultation» osv.).
Quick review of the syllabus
Læreren skal gå relativt raskt gjennom nytt stoff for så å la barna begynne å arbeide med oppgaver (Ankov 1977). Work is varied, challenging tasks, also with several themed same week. Many tasks introduces topics that you will come back to. This stands in contrast to the ways of thinking that emphasizes cramming of one and the same subject over an extended period, often with many
relatively identical tasks to be solved by the same rule. The point is again that developing education in mathematics has as main objective to develop pupils' thinking and their ability to problem-solving, and that it is constantly speaking about development in children proximal zone. It should be learning Hourly, and it assumes challenge on the basis of the student at all times. The requirement for quick review of the new drug might be evident when considering that teaching and learning are not identical concepts. The teacher uses a lot of time teaching, does not necessarily mean that it thereby follows much learning, Learning is a mental process in another system. The teacher should not spend more time than necessary to present substance, but at the same time be sure that the work is summarized (and repeated when new tasks). The principle of varied tasks comparable to teaching strongly influenced by drill and repetition. Evolving training in mathematics does not exclude drill and training where necessary, but the general rule is that the varied tasks leads to improved motivation and higher "learning pressure" than what is achieved through practicing almost identical tasks. Varied exercises can also provide varied opportunities for different children with different interests and backgrounds.
Bevisstgjøring om egen læreprosess
Utviklende opplæring i matematikk betyr at barna blir aktive deltakere i sin egen læreprosess med alt hva det innebærer av ansvar, Rights and learning. Specifically, it means that they are covered by a teaching method and a learning process that they themselves are active participants in. The method is therefore no teacher to keep concealed for students, as well is usual to do (Moe 2000,12off), but the whole class (and the guardians) working, a type of work which involves various forms of responsibility. We will not go further into this, only infer that it can include pretty much and that it can easily become a reference point when it occurs different forms of confusion and frustration. It follows from this that the children will become familiar with working procedures, at least sufficient that they can answer why they work the way they do. It is especially important that such involvement helps them to become more aware of what knowledge they need in order to accomplish the tasks at any time is relevant (cf.. "Learning to learn"). What they need to practice? Because they observe each other, they can also help each other out from such knowledge.
Utvikling av hvert enkelt barn
Her kommer vi tilbake til noe av det vi alt har sagt om det enkelte barnets proksimale utviklingssone, namely the task of ensuring that every single child in the classroom have the best possible development through education. How to ensure that all, Also the weak and the best, get a good cognitive development? Instead of differentiating class from level (level groups) and / or to withdraw students who are academically weak, one accepts that each child has its own development zone, thus one can not assume that everyone in a class experience and think alike. Differences are always present, something you quickly notice when kids are working on tasks, and the principle is that the class works together on tasks. The exercises are designed so that they contain problems of varying difficulty, so that everyone feels that they are getting something. Furthermore, it is so that the teacher organizes students in a conscious way, and that discussion in class seems inclusive. In addition, it is obvious that the teacher is active when it comes to energize weak students, ask questions that they can answer, give praise etc.. The scheme operates naturally with minimum what knowledge a must achieve. Beyond that is the principle that one should strive for maximum development. Weak students who are struggling to achieve the minimum will be followed up, for example when they have to practice more at home. The minimum requirement («Target») first grade is relatively high compared to what is often the case, which for example means that even the weakest pupils to math because concepts, terminology and symbols, Addition and Subtraction, basic algebra, simple equations and geometry. It lowers thus not the basic objective of the weakest.
TO NOTE
¹ The scheme adopted by some fifty Norwegian schools.
² For more details on tasks, learning materials and other information, see the www.matematikklandet.no which is home to the Norwegian adaptation of the scheme.
³ Since 1995 is introduced as an official state system. It is now used by about. 25 percent of all elementary schools in Russia.
⁴ In Norway program academically anchored by Mathematics Section, faculty of Humanities, University of Stavanger. Se også Blank m.fl. (2014.)
⁵ Research clearly shows that good start instruction is of great importance, especially in a subject like mathematics.
Litteratur
Blank, N., Melhus, K., Moe, G.I. and Tveit, C. (2014). Evolving training in mathematics, Education, 13/22, s. 50-53.
Melhus, K. (2015). To stimulate children's ability to think, key, 2.
Moe, G.I. (2015). Children can more -!, key, 3.
Moe, S. (2000). learning Poems. Systemic-constructivist pedagogy, Oslo: Universitetsforlaget.
Vygotskij L. S. (2001). Thinking and speech, Oslo: Gyldendal
Ankov, L.V. (1977). Teaching and Development: A Soviet Investigation, White Plains NY. M.E. Sharpe.
Gerd Inger Moe er pensjonert lærer. She holds adjunct and is used as instructor in Evolving training in mathematics. She is employed by the municipality of Sandnes in implementing Evolving training in mathematics in the municipality, and University of Stavanger as Lecturer for teachers who practice this approach. E-post: gerd.inger.moe@lyse.net.
Sverre Moe er dr. philos og professor emeritus i sosiologi. He has published numerous books and articles, including Sociology hundred years (1994), one widely used textbook in his subjects. Moe has written a lot about education sociological and educational theme, including Learning Poems. Systemic-constructivist pedagogy (2000). E-post: Sverre.Moe@Lyse.net.
The article has been in the "Better Education» 4/2016 and is reprinted with permission from "Better Education».