#trinomial cube

[themontessoriacademyofarlington]

Early Childhood - Trinomial Cube

Look at that focus! The binomial cube, when first introduced to the child, is presented as a challenging, three-dimensional puzzle. The cube is made up of a number of colored blocks, which fit together in a specific way. Assembling it uses a child's fine-motor skills and requires the ability to discriminate between the blocks based on multiple characteristics. Some blocks have one color, others have two, and some blocks are cubes, while others are rectangular prisms. This makes the binomial cube a more complex sensorial material, and it requires organized thinking to master. The binomial cube's big brother, the trinomial cube, is a child's more complex next step.

Like other sensorial materials, the binomial and trinomial cubes are self-correcting: when properly assembled, the blocks form a cube that fits perfectly inside of its wooden box. Even if the cube is built outside of its box, visual cues alert the child to any errors they might have made.

[kidadvancemontessori]

Buy Montessori Trinomial Cube

27 painted wooden cubes in a wooden box with a lid. The box is hinged and opens out to display the cubes. The lid is printed with the trinomial square pattern.

• Dimensions: 5.5 x 5.5 x 4 inches • Recommended Ages: 3.5 years and up

Buy now: https://kidadvance.com/trinomial-cube-preorder.html

[samueldays]

Apropos of nothing, I'm reminded of a toy I had as a child: the Montessori Trinomial Cube.

It's about six inches a side, split into segments of 1, 2 and 3, forming 3 sub-cubes and 24 prisms. The square sides of all blocks are colored, the others are black. (A smaller Binomial Cube also exists.)

I liked it and learned to speed-assemble it blindfolded. A teacher who knew me commented that practicing with it was part of why I was so good at maths later in life. In retrospect, I think that's an example of statistical confounding: The cube was not causative, I was good with the cube and good at maths for a shared reason.

[baandek]

Work in the Baan Dek classroom

[mathbff]

Find a Limit Algebraically.. How?

There isn’t any one algebraic method that will works for finding every limit. Here are the different methods:

1) Direct Substitution (0:22) When trying to evaluate a limit algebraically your “go to" method should be direct substitution. If direct substitution works, simply plug in the value that x is approaching, and evaluate the function.

2) What about if I get 0/0? (1:25) If you try direct substitution and get 0/0 (the indeterminate form), you should try to simplify the function and then try direct substitution again.

3) Factor to Simplify (2:17) If you see higher powered polynomials in the function, you should try a form of factoring to simplify the function. Whether it is a difference of squares or cubes, a perfect square trinomial, a trinomial with or, or even a grouping situation, factoring will usually get you to the result. Once you’ve simplified by factoring, try direct substitution again.

4) Use a Conjugate to Simplify (4:28) If you see a root in the function, you should try multiplying by the conjugate of the root to simplify the function. Once the function is simplified, try direct substitution again.

5) Use Expansion of Polynomials to Simplify (7:09) If you tried factoring and weren’t able to simplify, you can try expanding any polynomials which are raised to a power, then check for anything that cancels out. Once you’ve simplified by canceling out terms, try direct substitution again.

6) Simplify With a Common Denominator (8:38) If you have a complex fraction, you can try using a common denominator to simplify the fractions. Once you’ve simplified the fractions, try direct substitution again.

[midwestmontessori]

I’m so thankful for this moment of Montessori joy. We got the opportunity to visit our children’s classrooms one evening where they could show us anything they’d like. Simon was so proud to show us the trinomial cube. In a few years he will be working out the mathematics behind this material. How awesome is that?! https://www.instagram.com/p/B37ovael4Ju/?igshid=18i0e4lels5zh

[zwoelffarben]

So, what factoring does, and the reason it is useful is it takes your polynomial full of addition and subtraction, and it turns it into smaller chunks of addition and subtraction that are then all multipied together.

This makes the factored form of any expression easier to find the zeros of. Because anything times zero is zero, if any part of a factored expression equals zero the whole thing equals zero.

I'll grant you that the examples they always give in these sorts of excercises are really contrived and don't tend to help anybody understand the point of the process.

And that's especially true when teaching the sum of cubes since the trinomial factoring them spits out always associates with a complex root and most of the time you don't care about the complex roots polynomials. I'm of the opinion that it shouldn't even be taught beyond maybe a 'you can factor this further but dont bother' unless you care about complex numbers sort of passing mention, because it just confuses people to the point of factoring (but what do I know I'm not a math teacher).

Anyway, yes factored polynomials are the messier form, but if you care about finding the zeros of the function, its messier in a way that makes that particular task easier.

What in the name of fuck is the point of factoring?

How do you even do this? Is this like cube roots and shit where you just have to memorize what numbers are factors of other numbers or is there some chart you're all referencing that I didn't get a link to?

How is the bottom row an improvement of the top row? How does that clarify anything?

This feels like my math class is shaking me down for my lunch money until I can get more than thirty characters factored out of a single integer.

[themontessoriacademyofarlington]

Early Childhood - What are the Binomial and Trinomial Cubes?

The binomial cube, when first introduced to the child, is presented as a challenging, three-dimensional puzzle. The cube is made up of a number of colored blocks, which fit together in a specific way. Assembling it uses a child's fine-motor skills and requires the ability to discriminate between the blocks based on multiple characteristics. Unlike Montessori's iconic pink tower, for example, the binomial cube does not isolate only one quality. Some blocks have one color, others have two. Some blocks are cubes, while others are rectangular prisms. While the pink tower blocks vary only in size, the binomial cube’s blocks vary in color, size, and shape! This makes the binomial cube a more complex sensorial material, and it requires organized thinking to master. The binomial cube's big brother, the trinomial cube, is a child's more complex next step.  Like other sensorial materials, the binomial and trinomial cubes are self correcting: when properly assembled, the blocks form a cube that fits perfectly inside of its wooden box! Even if the cube is built outside of its box, visual cues alert the child to any errors they might have made.

Children return to the cubes time after time, manipulating them with a focused sense of purpose. After a child has mastered building the binomial or trinomial cube inside of the box, he may then try building it outside of the box, or building each layer separately in order to observe similarities in patterns. Over time, the child’s familiarity with the cube’s physical aspects will lead to an internalized understanding of the abstract concepts the cube represents.

[kidadvancemontessori]

Exploring the Trinomial Cube with Kid Advance Inc.

Kid Advance Inc., a family-owned business, has been a beacon of quality in the world of Montessori learning materials since 2006. Our commitment is to provide high-quality, affordable resources to schools and parents, fostering an environment where children can thrive academically and creatively. In this blog post, we'll delve into the realm of one of our standout products—the Trinomial Cube.

[baandek]

Work in the Baan Dek Classroom

[ss1986us]

ncert solutions for class 7 maths

class 7 maths

 Foundation of any subject is important specifically when you are taking about maths . maths is important subject for your academic journey and class 7 maths build your interest as well we as solid foundations in the subject in this class you start learning the algebra and its applications . so always take class 7 maths studies seriously . you must be wondering what is the best approach to study class 7 maths ? how to score good marks in class 7 maths ? so to answering to your questions lets discuss the right approach of studying class 7 maths .

 Right approach to study class 7 maths

 About class 7 Books: Selection of right books will help you to have better understanding of the concepts so always make NCERT maths book for class 7 your primary book , follow the sequence of chapters given in NCERT book don’t skip any chapters . after doing NCRET take a reference book or follow entrancei notes which are prepared such a way that it will build your solid foundation in class 7 maths 

About class 7 maths class: Always attend the class in school or in tuitions never skip any class , if you have any work or family function or you are sick plan the missing topic during the holidays and be reedy your topics before the next class. In class listen what teacher wants to explain and make all important points notes in your note book . ask your questions don’t hesitate while asking silly questions in class 7 maths .   

Brief descriptions about Important Chapters covered in class 7 maths

 1. Class 7 maths chapter- NUMBERS

 Natural Numbers: The counting numbers are called Natural Numbers.

          Thus, N = {1, 2, 3, 4, 5,....} is the set of all natural numbers.

Whole Numbers: Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, …

           Thus,   W = {0, 1, 2, 3, 4, 5.....} is the set of all Whole Numbers.

Integers: Integers are like whole numbers, but they also include negative numbers ... but still no fractions allowed!

 So, integers can be negative {-1, -2,-3, -4, -5, … }or positive {1, 2, 3, 4, 5, … }, or zer{0}

We can put that all together like this:

              I or Z = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }

Rational Numbers: A rational number is a number that can be written as a ratio (p/q form). That means it can be written as a fraction, in which both the numerator (p) and the denominator (q) are integers and q not zero.

The number 8 is a rational number because it     can be written as the fraction 8/1.

Likewise, 3/4 is a rational number because it     can be written as a fraction.

Even a big, clunky fraction like     7,324,908/56,003,492 is rational, simply because it can be written as a     fraction.

 Equivalent rational numbers: Numbers that have the same value but are represented differently.

 2.  Class 7 maths chapter- DIVISIBILITY TESTS, SQUARES, CUBES,SQUARE AND CUBE ROOTS

OVISIBILITY

DIVISIBILITY TEST:

Test of Divisibility by 2 : A number is divisible by 2, if its units digit is any of the digits 0, 2, 4, 6 and 8.

 Example:  Each of the numbers 24, 36, 78, 192, 310, 214166 is divisible by 2.

Prime Factors: A factor of a given number is called a prime factor if this factor is a prime number.

Example: The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. Out of these 2, 3 and 7 are prime numbers. Therefore, 2, 3 and 7 are the prime factors of 42.

 Common Factors: A number which divides each one of the given numbers exactly, is called a common factor of each of the given numbers.

 Example: 4 divide each one of 212 and 356 exactly. Therefore, 4 is a common factor of 212 and 356.

H.C.F. (HIGHEST COMMON FACTOR) OR G.C.D. (GREATEST COMMON DIVISOR) :

 H.C.F. or G.C.D. of two or more numbers is the greatest number that divides each one of them exactly.

 3. Class 7 maths chapter- ALGEBRAIC EXPRESSIONS AND IDENTITIES

 In the previous class, we have learnt about algebraic expressions and their addition and subtraction. In this chapter we shall study multiplication and division of algebraic expressions in the form of monomials and binomials etc.

Constants: A symbol having a fixed numerical value is called a constant.

Variables or Literals: A symbol which takes on various numerical values is known as a variable or a literal.

We know that the perimeter of a square of side a is given by the formula, P = 4a.

Here 4 is a constant, while a and P are variables.

We may give any value to a and get the corresponding value of P.

Algebraic Expressions : A combination of constants and variables, connected by +, - , and is known as an algebraic expression.

Types of algebraic expressions:

 1.           Monomial : An algebraic expression containing only one term, is called a monomial.

2.            Binomial : An algebraic expression containing 2 terms is called a binomial.

3.           Trinomial: An algebraic expression containing 3 terms is called a trinomial.

4.           Multinomial: An algebraic expression containing more than 3 terms, is called a

              multinomial.

Factors of A Term: When numbers and literals are multiple to form a product, then each quantity multiplied is called a factor of the product. A constant factor is called a numerical factor while a variable factor is called a literal factor.

Constant Term: A term of the expression having no literal factor is called the constant term.

Coefficients: Any factor of a term is called the coefficient of the product of other factors.

4. Class 7 maths chapter- EXPONENTS

 INTRODUCTION:

we know that can be written as that is read as two raised to the power three. Similarly, 10 times = , read as three raised to the power ten. In general, if x is any number and m is a positive integer, then we have

m times.

 The number x is called the base and m is called the exponent or the index of the exponential expression.

 5. Class 7 maths chapter- FACTORISATION

Factorisation:

When an algebraic expression can be written as the product of two or more expressions, then each of these expressions is called a factor of the given expression.

 G.C.F. or H.C.F of Monomials: The greatest common factor of given monomials is the common factor having greatest coefficient and highest power of the variables.

G.C.F. or H.C.F of Monomials = (G.C.F. or H.C.F of numerical coefficients)

(G.C.F. or H.C.F of literal coefficients)

 6. Class 7 maths chapter- SETS

 Objects: Everything in this universe, whether living or non living, is called an object. Well-defined collection of objects : A collection of objects is said to be well-defined if itis possible to tell beyond doubt about every object of the universe, whether it is there inour collection or not.

Set :       A well-defined collection of objects is called a set.

              The objects in a set are called its members or elements.

              We usually denote sets by capital letters A, B, C etc.

              If x is an element of a set A, we say that x belongs to A and we write, .

              If x does not belong to A, we write.

              There are two methods of describing a set :

              (i)     Roster Method or Tabulation Method.          

              (ii)    Description Method or Set-builder Form.

 7. Class 7 maths chapter- QUADRATIC EQUATIONS

 Quadratic Equations: A polynomial of degree 2 when equated to zero, gives an equations, called a quadratic equations.

Solving Quadratic Equation:

By solving a quadratic equation, we mean finding its roots.

Zero Product Rule:

If a and b are any two numbers or expressions, then ab = 0 a = 0 or b =0.

    8. Class 7 maths chapter- LINEAR EQUATION IN TWO VARIABLES

 In this chapter we shall we shall learn how to solve linear equations in two variables. For this we shall learn graphical representation of a point in a plane. We shall represent a point with the help of two numbers known as coordinates of that point. The concept of coordinates was given by the French Mathematician Rene Desartes, which integrates Algebra and geometry.

 9.  Class 7 maths chapter-  SPEED, DISTANCE AND TIME

Speed: The rate of change of distance is known as speed.

When an athlete runs a race, the change in the time taken is directly proportional to the change in the distance covered. A change in speed is directly proportional to the change in distance covered. More the speed more is the distance covered in the same time.

Units of Speed: Speed is measured in i) meters/ second or m/s

                                                ii) Kilometers/ hour or km/hr

 10. Class 7 maths chapter- Simple Interest:

                               When money is borrowed, interest is charged for the use of that money for a certain period of time. When the money is paid back, the principal (amount of money that was borrowed) and the interest is paid back. The amount of interest depends on the interest rate, the amount of money borrowed (principal) and the length of time that the money is borrowed.

                             Simple interest is generally charged for borrowing money for short periods of time. Compound interest is similar but the total amount due at the end of each period is calculated and further interest is charged against both the original principal but also the interest that was earned during that period.

                               Interest = Principle x rate of interest x time

   CO

ORDINATE SYSTEM

[edivupage]

Mathematics Terms That Middle School and High School Students Should Know

Of all of the K-12 subjects that I studied, math was my least favorite. Not because I wasn’t a decent math student; the issue was that many of the math teachers that I had throughout my life have been less than stellar. They made their lectures hard to follow and analogous to pulling teeth. Thankfully, I mastered mathematics in spite of this. One of the things that helped me was learning all of the terminology associated with algebra, statistics, trigonometry, etc. and then determining the basic rules that governed each math discipline.

In this article, I will list and define the mathematics terms that middle school and high school students need to know. This is by no means an exhaustive list, but it is close to it. By learning the foundations of math, I hope that your students will parlay this into math fluency.

Acute angle – Is an angle that measures below 90°.

Acute triangle – A triangle is containing only acute angles.

Additive inverse – Opposite of a number or its contrary. A number plus its additive inverse equals 0.

Adjacent angles – Are angles with a common side and vertex.

Angle – Are created by two rays and containing an endpoint in common.

Arc – Set of points that lie on a circle and that are positioned within a central angle.

Area – Apace contained within a shape.

Average – Numerical result of dividing the sum of two or more quantities by the number of quantities.

Binomial – Expression in algebra that consists of two terms.

Bisect – Dividing into two equal sections.

Canceling – In the multiplication of fractions, when one number is divided into both a numerator and a denominator.

Cartesian coordinates – Are ordered number pairs that are assigned to points on a plane.

Chord – Line segment that connects two points on a circle.

Circle –  Set of points that are all the same distance from a given location.

Circumference – is the distance measured around a circle.

Coefficient – Number that is placed in front of a variable. For example, in 6x, 6 is the coefficient.

Common denominator – Number that can be divided evenly by all denominators in the problem.

Complementary angles – Are two angles in which the sum of their measurements equals 90°.

Complex fraction – Fraction that contains a fraction or fractions in the numerator and/or denominator.

Congruent – Exactly the same. Identical regarding size and shape.

Coordinate graph – Are two perpendicular number lines, the x-axis and the y-axis, which make a plane upon which each point is assigned to a number pair.

Cube – Solid with six sides, with the sides being equal squares and the edges being equal.

Cube root – Number that when multiplied by itself twice, results in the original number. 

Degree – Measurement unit of an angle.

Denominator – Bottom symbol or number of a fraction.

Diameter – Line segment that contains the center and has its endpoints on the circle. Also, the length of this segment.

Difference – That which results from subtraction.

Equation – A relationship between symbols and/or numbers that is balanced.

Equilateral triangle – A triangle that has three equal angles and three sides the same length.

Even number – An integer which can be divided by 2, with no remainder.

Expanded notation – To point out the place value of a digit by writing the number as the digit times its place value.

Exponent – A positive or negative number that expresses the power to which the quantity is to be raised or lowered. It is placed above and to the right of the name.

Exterior angle – In a triangle, an exterior angle is equal to the measures of the two interior angles added together.

Factor – As a noun, it is a number or symbol which divides evenly into a larger number. As a verb, it means to find two or more values whose product equals the original value.

F.O.I.L. Method – A method used for multiplying binomials in which the first terms, the outside terms, the inside terms, and then the last terms are multiplied.

Fraction – A symbol that expresses part of a whole. It contains a numerator and a denominator.

Greatest common factor – The largest factor that is common to two or more numbers.

Hypotenuse – In a right triangle, it is the side opposite from the 90° angle.

Imaginary number – The square root of a negative number.

Improper fraction – A fraction in which the numerator is larger than the denominator.

Integer – A whole number. It may be positive, negative, or zero.

Interior angles – Angles formed inside the shape or inside two parallel lines.

Intersecting lines – Lines that come together at a point.

Interval – The numbers that are contained within two specific boundaries.

Irrational number – Number that is not rational.

Isosceles triangle – A triangle with two equal sides and two equal angles across from them.

Least common multiple – The smallest multiple that is common to two or more numbers.

Linear equation – An equation where the solution set forms a straight line when it is plotted on a coordinate graph.

The lowest common denominator – The smallest number that can be divided evenly by all denominators in the problem.

Mean – The average of a number of items in a group (total the items and divide by the number of items).

Median – Middle item in an ordered group. If the group contains an even number of items, the median is the average of the middle items.

Mixed number – A number containing both a whole number and a fraction.

Monomial – An expression in algebra that consists of only one term.

Natural number – A counting number.

Negative number – A number less than zero.

Nonlinear equation – An equation where the solution set does not form a straight line when it is plotted on a coordinate graph.

Number line – A visual representation of the positive and negative numbers and zero.

Numerator – The top symbol or number of a fraction.

Obtuse angle – An angle that is larger than 90° but less than 180°.

Obtuse triangle – A triangle that contains an obtuse angle.

Odd number – An integer (whole number) that is not divisible evenly by 2.

Ordered pair – Any pair of elements (x,y) where the first element is x, and the second element is y. These are used to identify or plot points on coordinate graphs.

Origin – The intersection point of the two number lines of a coordinate graph. The intersection point is represented by the coordinates (0,0).

Parallel lines – Two or more lines that are always the same distance apart. They never meet.

Percentage – A common fraction with 100 as its denominator.

Perpendicular lines – Two lines that intersect at right angles.

Pi (π) – A constant that is used for determining the circumference or area of a circle. It is equal to approximately 3.14.

Polynomial – An expression in algebra that consists of two or more terms.

Positive number – A number greater than zero.

Power – A product of equal factors. 3 x 3 x 3 = 33, read as “three to the third power” or “the third power of three.” Power and exponent can be used interchangeably.

Prime number – A number that can be divided by only itself and one.

Proper fraction – A fraction in which the numerator is less than the denominator.

Proportion – Written as two equal ratios.

Pythagorean theorem – A theorem concerning right triangles. The sum of the squares of a right triangle’s two legs is equal to the square of the hypotenuse (a2 + b2 = c2).

Quadrants – The four divisions on a coordinate graph.

Quadratic equation – An equation that may be expressed as Ax2 + Bx + C = 0.

Radical sign – A symbol that designates a square root.

Radius – A line segment where the endpoints lie one at the center of a circle and one on the circle. The term also refers to the length of this segment.

Ratio – Comparison between two numbers or symbols. May be written x:y, x/y, or x is to y.

Rational number – An integer or fraction such as 7/7 or 9/4 or 5/1.Number that can be written as a fraction x/y with x a natural number and y an integer.

Reciprocal – The multiplicative inverse of a number. For example, 2/3 is the reciprocal of 3/2.

Reducing – Changing a fraction into its lowest terms. For example, 3/6 is reduced to ½.

Right angle – An angle that measures 90°.

Right triangle – A triangle that contains a 90° angle.

Scalene triangle – A triangle in which none of the sides or angles are equal.

Scientific notation – A number between 1 and 10 and multiplied by a power of 10. Used for writing very large or very small numbers.

Set – A group of objects, numbers, etc.

Simplify – To combine terms into fewer terms.

Solution, or Solution set – The entirety of answers that may satisfy the equation.

Square – The resulting number when a number is multiplied by itself. Also, a four-sided figure with equal sides and four right angles. The opposite sides are parallel.

Square root – The number which, when multiplied by itself, gives you the original number. For example, 6 is the square root of 36.

Straight angle – An angle which is equal to 180°.

Straight-line – The shortest distance between two points. It continues indefinitely in both directions.

Supplementary angles – Two angles that when combined, the sum equals 180°.

Term – A literal or numerical expression that has its own sign.

Transversal – A line that crosses two or more parallel or nonparallel lines in a plane.

Triangle – A three-sided closed figure. It contains three angles that when combined, the sum equals 180°.

Trinomial – An expression in algebra which consists of three terms.

Unknown – A symbol or letter whose value is unknown.

Variable – A symbol that stands for a number.

Vertical angles – The opposite angles that are formed by the intersection of two lines. Vertical angles are equal.

Volume – The amount which can be held, as measured in cubic units. The volume of a rectangular prism = length times width times height.

Whole number – 0, 1, 2, 3, 4, 5, 6, 7, 8, etc.

X-axis – The horizontal axis on a coordinate graph.

X-coordinate – The first number in an ordered pair. It refers to the distance on the x-axis.

Y-axis – The vertical axis on a coordinate graph.

Y-coordinate – The second number in an ordered pair. It refers to the distance on the y-axis.

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[essayprof]

WEEK 2: SPECIAL FACTORING STRATEGIES137137

WEEK 2: SPECIAL FACTORING STRATEGIES137137 unread replies.208208 replies.This week we continue our study of factoring. As you become more familiar with factoring, you will notice there are some factoring problems that follow specific patterns. These patterns are known asa difference of squares;a perfect square trinomial;a difference of cubes; anda sum of cubes.Choose two of the forms above.…

[hoihoi-glocal]

モンテッソーリ教育（モンテッソーリきょういく、英：Montessori education または the Montessori method）は、20世紀初頭にマリア・モンテッソーリによって考案された教育法。

イタリアのローマで医師として精神病院で働いていたモンテッソーリは知的障害児へ感覚教育法を施し知的水準を上げるという効果を見せ、1907年に設立した貧困層の健常児を対象とした保育施設「子どもの家」において、その独特な教育法を完成させた。以後、モンテッソーリ教育を実施する施設は「子どもの家」と呼ばれるようになる。

シュタイナー教育と共に、既存の教育に不信感を持つニューエイジャーの支持を集めた[1]。

目次

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1モンテッソーリ教育法

2日本におけるモンテッソーリ教育

3モンテッソーリ教育を受けた著名人

4脚注

5関連項目

6外部リンク

1.1子供の家

1.2感覚教育

1.3自発性と「敏感期」

1.4｢整えられた環境」と教員養成

1.2.1教具

2.1教員資格

2.2モンテッソーリ・スクール

モンテッソーリ教育法[編集]

モンテッソーリの木製教具

オランダの教室 1915年

アメリカの教室 2007年子供の家[

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1907年、ローマに最初に誕生した｢子供の家（Casa dei bambini）」は、瞬く間に欧米を中心に世界各国に広がった。特にアメリカ合衆国では2度にわたってモンテッソーリ・ブームが起こり、アメリカ全土にその教育法が普及した。現在、アメリカの私立をはじめ数百の公立学校でもプログラムが導入され、3000ヶ所のモンテッソーリ・子供の家があるといわれる。日本には1960年代に紹介され、モンテッソーリ・プログラムを導入する幼稚園やモンテッソーリ教育を専門に行う｢子供の家」が創設された。

感覚教育[

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モンテッソーリ「子��の家」の教室に入ると、整然と並ぶ色とりどりの「教具｣と呼ばれる木製玩具が目に飛び込んでくる。これらはモンテッソーリの感覚教育法に基づく教材で、モンテッソーリとその助手たちが開発した。モンテッソーリ教育法では教具の形、大きさは無論、手触り、重さ、材質にまでこだわり、子供たちの繊細な五感をやわらかく刺激するよう配慮がなされている。また、教具を通し、暗記でなく経験に基づいて質量や数量の感覚を養うことと、同時に教具を通して感じ取れる形容詞などの言語教育も組み込まれている。

教具[

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ピンク・タワー（pink tower）：1cm3 - 100cm3 までの立方体

円柱（cylinder blocks）

茶色の階段（broad stair, Brown Stair）

長さの棒（red rods）

色付き円柱

色板（Color tablets）

幾何たんす（Geometric cabinet）

幾何学立体（Geometric solids）

二項式（binomial cube）

三項式（trinomial cube）

構成三角形（constructive triangles）

実体認識袋（The mystery bag）

触覚板（Rough and smooth boards）

温覚筒（Thermic bottles）

重量板（Baric tablets）

圧覚板

雑音筒（Sound cylinders）

音感ベル（Bells）

味覚びん

嗅覚筒

数の棒 (Spindle box)

自発性と「敏感期」[

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常に子供を観察し、そこから学ぶ姿勢を貫いたモンテッソーリは、感覚教育と同様に重要と説いたのは、子供の中の自発性を重んじることである。どの子供にもある知的好奇心は、何よりその自発性が尊重されるべきで、周囲の大人はこの知的好奇心が自発的に現われるよう、子供に｢自由な環境」を提供することを重要視した。また、子供を観察するうち月齢、年齢ごとに子供たちの興味の対象がつぎつぎ移り変わる点に着目し、脳生理学に基づき、さまざまな能力の獲得には、それぞれ最適な時期があると結論付け、これを｢敏感期」と名づけた。モンテッソーリ教育の特徴の一面とされる一斉教育を行わない教育形態は、この子供たちの「自由｣の保証と｢敏感期｣を育むモンテッソーリ理論の視点に立つものである。 モンテッソーリは、集中して遊んでいた子どもが玩具に夢中になり、目を輝かせていた幼児を見て、挫折しかけた研究の道を再度探求することとなった。敏感期の子どもに触発され、モンテッソーリ教育が構築されていったのである。

｢整えられた環境」と教員養成[

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モンテッソーリ教育では、子供たちが安心して自由に遊び、作業のできる環境整備が重視される。教室が清潔に保たれ、子供の目線で教室を見渡せることにも配慮が求められる。また、モンテッソーリ教育法における教師の存在は、教室や教具と同様、整えられた環境の担い手の一つと考えられている。彼らには、教具などを扱う技術や管理する能力も要求されるが、何より子供を注意深く観察する態度が要求され、各々の子供たちの欲求に沿ってその教育を提供する注意深さが求められる。また、子供たちの集中時、それを妨げない心遣いや、子供の自発性を待つ姿勢も養成コースにおける重要な要素となる。晩年のモンテッソーリが力を注いだ教員養成方法は現在も世界各国で実践され、この厳しい教員養成もモンテッソーリ教育の特徴のひとつにあげられる。