How does a child progress from concrete to abstract in the use of the Mathematics Material?
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How does a child progress from concrete to abstract in the use of the Mathematics Material? Introduction Some ten years ago, while struggling with the trigonometry sums my Math tutor had given me, I asked her why we needed to study mathematics. Her answer was sadly, forgettable, and so were the sines, cosines and tangents that came along with algebra and geometry. Throughout my school days, mathematics had been a nightmare. It was not until now, ten years later and after understanding all about how mathematics is taught the Montessori way that I truly realized how wonderful and interesting mathematics could be! In this essay, you will read about the importance of mathematics in our daily life. I will also discuss why a good foundation in Practical Life and Sensorial activities is necessary before starting on Mathematics. I will explain the concept of the Montessori Math Materials and lastly, talk about how the materials itself provide concrete experiences that lead to abstract understanding of Mathematics. Mathematics Everywhere The primitive people used sticks, notches and stones to count. The earliest records of counting came from physical evidence, in the form of scratches on sticks and stones, as early as 30,000 B.C.
In order to do this, the Mathematical activities are organized into six groups: Group 1 Introduction to numbers Group 2 Introduction to the Decimal System Group 3 Introduction to teens tens and counting to 1000 Group 4 Operation of the Decimal System Group 5 Introduction recording and arithmetic tables Group 6 Abstraction Group 1: Introduction to numbers The math materials at Montessori classroom begin with an introduction to numbers. These materials include: Number rods, Sandpaper numerals, Number rods & cards, Spindle box, Cards & counters and Number games. These materials give the child a sensorial "feel" for numerical properties. By manipulation of these materials, the children grasp the natural order of one to ten. They understand the value of each number and are also able to recognize the relationship of the names with the quantities. Group 2: Introduction to the decimal system When the child has mastered the concept of one to ten, the decimal system is then introduced concretely. The child is taught the names of the powers of ten and given a visual sense of units, tens, hundreds and thousands in the form of beautiful hand made glass beads or golden plastic beads.
Conclusion In traditional instruction, children are expected to learn by internalising knowledge straightaway; teachers simply correct the errors and present the right answer. We know this method only turns the subject into something boring, tedious and cold, even creating math phobia. The main point is that an enjoyable and interesting introduction to all areas of mathematics is present in the environment. In the Montessori environment, the child is introduced to each activity when she is ready, and given a choice of whether or not to work with it. Repetition in the math exercises refines the child's senses, perfects his skills and builds up his competency and knowledge. Students who learn math by traditional method often have no real understanding or ability to put their skills to use in everyday life. Montessori students, however, use hands-on learning materials that make abstract concepts clear and concrete. Therefore, " a child who is allowed to explore with real mathematical objects at an early, motor-sensorial age stands a good chance of becoming a real math lover later in life. If his passions lie elsewhere, at least he will be exempt from the math phobia which many of us experience because of our own less-than joyful introductions to this area of learning."- Michael Olaf, http://www.michaelolaf.net/1CW36math.
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Here's what a teacher thought of this essay
This is a very interesting essay. It is rather specific to one area of teaching and learning but is well researched and explained.
It could be enhanced by including some theory- either relating to the actual process or contrasting ideas to widen the discussion.
Interesting and a little intriguing all the same.
Marked by teacher Sam Morran 01/05/2013
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