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在montessori杂志上曾经专门介绍了关于数学学习的问题，觉得是个好的介绍。
每个人的思维都是从形象到抽象的，用形象来认识，不是为了一直形象下去，而是为抽象打下坚实的基础，让那些数字的抽象概念在脑子里成为坚定的木桩（经历），从而随着年龄的增长，可以自如地抽象思考。同创造性是一个道理。
看英文吧。
Concrete To the Abstract（从形象到抽象）
Students who learn math by rote often have no real understanding or ability to put their skills to use in everyday life. Learning comes much more easily when they work with concrete educational materials that graphically show what is taking place in a given mathematical process.
Montessori students use hands-on learning materials that make abstract concepts clear and concrete. They can literally see and explore what is going on. This approach to teaching mathmatics, based on the research of Dr. Maria Montessori, offers a clear and logical strategy for helping students understand and develop a sound foundation in mathematics and geometry.
The Montessori Math curriculum is based on the European tradition of unified math, which has only recently begun to be incorporated into the American math curriculum.
Unified Math introduces elementary students to the study of the fundamentals of algebra, geometry, logic, and statistics along with the principles of arithmetic. This study continues over the years, weaving together subjects that traditional schools normally ignore until the secondary grades.
The concrete Montessori Math materials are perhaps the best known and most imitated elements of Dr. Montessori's work. These elegant and simply lovely materials hold a fasination for children and adults alike.
They proceed through several levels of abstraction,beginning with concepts and skills that are the most basic foundations of mathematics, presented in the most concrete representation, up through the advanced concepts of secondary mathematics, which are represented inincreasing levels of abstraction, until the students grasps them conceptually.
The Passage to Abstraction
By this stage, the children are recording their work on paper, although many won't be able to solve the same problems if asked to work with paper and pencil alone without the visual aid of the Montessori materials.You have to remember that most young children under the age of seven or eight find it difficult, if not impossible , to grasp something as abstract as quantities above three and what's really happening when we add, subtract,multiply, or divide. The concrete Montessori materials make it possible for the child to see and understand,slowly internalizing each concept until it becomes fixed and clear in her mind.
Naturally, children can't depend on the materials forever. Can you see your child at age sixteen walking in to take the SATs carrying the Golden Beads?
The entire purpose ofthe Montessori Math curriculum is to make the abstract concrete, until a childcan close her eyes and visualize mathematical processes at work. Step by step, the materials become less concrete and more symbolic. Step by step, she is challenged to demonstrate her understanding by teaching what she has learned to younger children, which also tends to reinforce and clarify the tutor's grasp on the subject as much as teach something to the one being tutored.
这里介绍一种教具，关于学习立方的。
Cubing Materials
Montessori introduces children to pre-algebraic concepts at the early childhood level through concrete materials such as the squares and cubes of the numbers 1 to 10 illustrated by the materials of the Bead Cabinetand the Binomial and Trinomial Cube.
At the upper elementary level, students use the Cubing Materials (sometimes called the Polynomials Box) to continue a more advanced exploration of the nature of polynomials and the relationships between their component parts. Where, with the Trinomial Cube, which represents thepolynomials (A+B+C)3, and in which the three component elements were fixed bythe material's design as 2cm, 3cm, and 4cm [(a+b+C)3=a3+b3+c#+3a2b+3a2c+3ab2+3b2c+3bc2=3ac2+6abc],the cubing materials consist of one cube and twenty seven wooden squares (1 cmhigh) for each of the quantities from 1 to 9 (shown as squares)from the one cmcube to a square of 2cm, 3cm, up through 9cm, contained in a special box to keep everything organized.
Using the cubing materials, students can build binomials,trinomials, quatrinomials, and larger polynomials, varying the values for the component parts. This is all designed to help students grasp pre-algebraic concepts at an abstract level.
数学乘法的学习。
除法的学习
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发表于 2014-12-3 18:56:16
组图打开中，请稍候......
发表于 2014-12-3 19:41:06
楼主
发表于 2014-12-3 21:38:16
也想这样啊。 这。。能通过训练达成么？
，脾胃，中间轴心有问题 
