Montessori teaching methods and educational philosophy

Montessori

Key philosophies that the Montessori mathematics teacher must keep in mind preparing the 3- to 6-year-old student's classroom

The child is an active learner, learning everything without knowing he is learning it, first through the senses.

It is during this age the child develops his senses through sensory curiosity

Teaching mathematics through the senses must be done so in a way that it provides a basis for learning in an orderly manner that is needed for future neurological and psychological development but reaches the child in a meaningful way that does not render mathematics into a merely abstract discipline.

Children learn things in a concrete fashion before learning it abstractly.

Section II

How do you think the below listed activities assist the child to develop an understanding of the relationship between concrete experience and mathematical concepts?

A a) the prepared environment:

The child at this age does not separate between 'school' and 'play' in his or her mind. Both play and school activities must teach the child concepts but also engage the senses. An engaging environment help develop the child's powers of observation such as attention and concentration.

A b) Mats and trays:

Mats are tactility engaging, and easily manipulated by the child's fingers. They can be touched by the child, and different textured mats can be sorted according to groupings. This can show the child similarities and differences, critical concepts in mathematics. The teacher can engage the child with questions such as 'how many smooth red mats do you have,' or even teach the child simple multiplication, as they count how many groups of smooth and rough fabrics they possess. Different colored and shaped trays can also teach the child order, sequencing and placing -- all vital concepts in mathematics.

A c) Establishing classroom routines:

Children at this age crave structure and routines. Having a routine and a timetable teaches the children to tell time, and gives the child a sense of comfort and predictability -- they know that their favorite activities will happen at specific junctures of the day, for example -- this also shows that numbers have an impact on their lives.

A d) Calendar activities:

Children are engaged with the passing of time in an emotional fashion, such as when they are anticipating an exciting event, like a party or a birthday. Again, this makes math part of daily life. Teaching mathematics, like addition with the passing of time, or concepts like past and present, makes math real and emotionally engaging for the child.

A e) Sensorial extension activities:

Extending the child's ability to extend his or her senses, like using cylindrical blocks to teach concepts of thick and thin or tall and short, through manipulating the objects, seeing if the objects do or do not fit through various 'chutes' (or using, to take another example the 'pink tower' of ascending sizes which the child may assemble or descending) refines the child's sense of discrimination and ability to experiment with objects in a hands-on fashion. As well as spatial concepts, ideas such as when something is missing, like a variable in an algebra problem, are introduced when, for example, one object in the 'pink tower' is taken away, and the ascending or descending order is broken.

A f) Geometry materials:

1) Cabinet:

The geometric cabinet consists of a cabinet with six drawers containing circles, rectangles, and different types of triangles, polygons, curvilinear figures and irregular figures.

Through feeling, touching, matching, and playing games with these figures, the concepts of geometric space becomes sensorial and meaningful to the child, and the child can relate the shapes to physical sensations and things he or she sees in his or her life by manipulating the shapes into frames that must fit the shapes.

These types of geometric games also teach concentration and attention, as the child must experiment with what frames work and do not work.

2) Solids:

Working with geometric solids in a tactile fashion is an excellent way to teach children how to understand parallelograms and other mathematical concepts very early on in a memorable fashion.

While it may not be meaningful to encourage a young child to memorize what is a hexagon, by manipulating a polygon, the child is able to remember the shape through associating the feeling of the shape with real-life tactile experiences.

By seeing how other shapes do not fit into frames designed for other objects and feeling the more difficult shapes the child learns coordinated manipulation and independence of thought,.

3) Tesselations: Floor tiles or tessellations teach coordination and independence and 'patterning' sequences

4) Constructive triangles:

The geometric cabinet consists of various different triangles of different types. By manipulating the differently colored triangles to create new triangles of different types, the child gains tactile preparation for later geometry.

5) Fraction boards.:

Understanding fractions not as numbers but as spatially and sensorially meaningful 'partial' objects is reinforced through this activity.

6) Binomial and trinomial cubes:

Doubling and tripling as physical entities through manipulation of cubes first used to teach simple numbers helps build upon previous sequential learning of tactile concepts.

A g) Montessori materials for concept and symbols 1 to 10:

1) Number rods:

Red rods' which vary only in length, from one to ten centimeters in high, indicate variation in length and how numbers ascend in value from one to ten in a visually meaningful and observable fashion.

2) Sandpaper numerals:

Matching smooth and rough surfaces teaches discrimination and 'pairing' while tracing sandpaper numbers teaches how to write the numerals and reinforces student physical coordination.

3) Spindle box with introduction to "zero": The concept of zero, an abstract concept, is rendered visually and physically understandable in this activity.

4) Cards and counters:

Using cards and counters allows the teacher to ask what or who is missing. It empowers the child to find the necessary card, even if it is out of sequence. Counters reinforce notions of sequencing, which cards allow the child to visualize and then see when something is out of sequence in the line of cards.

5) Secret numbers and memory and number games:

Number games makes memorizing numbers fun and gives a child a sense of excitement of the unknown of a particular solution, and reinforces the need to remember numbers sequentially and nonsequentially in a way that gives numbers meaning.

6) Writing numerals:

Writing numerals, beyond their importance in math, helps students understand how concepts and written symbols relate to concepts like ascending or descending amounts, and again teaches coordination through manipulation of writing instruments.

Section III

List ways in which a mathematically prepared environment meets the child's developmental needs. Give reasons based on Montessori philosophy and developmentally-appropriate practice for your choices.

'prepared' environment:

Reinforces sensory concepts

Teaches concepts of identity and difference through sensory exercises

Develops concepts like order, concentration, coordination and independence which are all are important for mathematics mind.

Order is the basic foundation of math because of the importance of sequencing in the above-cited activities.

Concentration on a task is important to develop logical thinking and problem-solving skills. Tasks must be fun and engaging to generate such concentration, and be relevant to children's lives.