Montessori Education is a doorway to lifelong love of learning. It isn't the only entry but it is one that is structured to be very accessible to young children.

Practical Life is the invitation to this structure. It is like stairs to the doorway, an inviting floor to walk on. It supports the rest of the curriculum by allowing the child to gain precision movements and strength of hand as well as the ability to focus on the work at hand. It provides that opportunity to develop the social skills to work well with others.

Sensorial is the keystone that holds up the arch of the entry door. The development of the senses allows the child to better investigate the world around her. It leads and supports the math curriculum through investigation of dimensions with the red rod, pink tower and like materials. It also sets the ground work for geometry and algebra with the geometric cabinet and triangle boxes and binomial and trinomial cubes.

Math and Language are the door posts and walls that enclose the structure. They flow from the floor of practical life and are supported by Sensorial education. Like a fine grained wood they are composed of many strands that run together and support each other. In my Math album there are 14 structured lessons to lead the child to understanding numeration. These encompass using 8 different materials and take advantage of the young child's need for movement.

Sensorial exercises assist the child in building up their Mathematical mind. The Mathematical mind is a concept proposed by Pascal who said Man’s mind was mathematical by nature and that knowledge and progress came from accurate observation. Montessori looked at the Mathematical Mind as that of a mind that works with precision taking precise observations and working the new information into their existing framework of knowledge. Work with the Sensorial materials builds up this precise mind by sharpening the observational skills of all the senses.

The Pre Numeration lessons are a bridge between the Sensorial exercises and

the Math Curriculum. They also allow for assessment of the child’s understanding of the conservation of numbers, volume and length. Matching, grading and sorting are all pre-numeration exercises. These exercises are also occasionally taken off the shelf by 4 and 5 year olds looking for relaxing work following work that was long and exacting.

The Math curriculum can be broken down to mathematical concept area. Numeration, Decimal system, Linear Counting and Operations. Operations can be further broken down to addition, multiplication, subtraction and division. Each of these is further divided into process, counting and memorization. Like the structure of the wood of a doorpost each of these sections is comprised of several lessons that reinforce the concept being presented and the sections are not presented in a linear fashion but rather are offered concurrently by running in parallel they create a strong and deep understanding of mathematics.

Each concept in the Math curriculum is first presented as concretely as possible and then moves towards the abstract. The Golden beads material is a good example of the concrete presentation that run through the curriculum. This materal is used in Numeration, Decimal System , Linear Counting and all the Operations. It provides the child with both the visual and tactile/kinesthetic feedback that larger numbers are visually and by volume larger than smaller numbers. The Hundred Board, any of the symbol alone presentations and bead frame or fingerboards are examples of more abstract materials.

Numeration imparts an understanding of the numerals and the quantity with which they are associated. First the Red and Blue Rods are counted orally and they are placed into the stairs. The stairs are familiar to the child through the sensorial exercises with the Red Rods. The numerals are presented visually, auditorially and kinesthetically through the sandpaper numerals. As with many materials the 3 period lesson is used to assess and insure that the child is able to both associate from the oral name to the visual numeral and that the visual numeral is able to elicit the name.

Ordering the wooden numerals is yet another exercise that helps the child

become familiar with the visual representation of the number and placing it in order. Once the child is familiar with the numeral and with counting quantity the 2 activities can be merged in the Red and blue Rods Symbol and Quantity presentation, Spindle Box, Cards and Counters and Stones, Chestnuts and Shells. These activities focus on quantity and symbols from 0 to 10. The concept of zero is introduced with the Spindle Box. The Hundred Board is a more time consuming activity that introduces numerals to 100. This does not mean that the child is counting to 100. The first presentation is sensorial in nature with the child matching the numeral tiles to the control chart. The

Memory game is the last presentation in the numeration section but it could be presented before or concurrently with the Hundred Board. The Memory game challenges the child to recognize the numeral and remember it while not looking at it.

The Decimal System presentation again starts with a sensorial presentation with the Demonstration Tray. It provides the nomenclature of unit, 10 bar, hundred square and thousand cube. The child can visually see the difference is volume and feel the difference in weight. Again, like with numeration the quantities are presented before the symbols or numerals and then the quantity and symbol are associated. The Comparison Tray leads the child into comparing and relating the quantities of 1, 10, 100 and 1000 through the use of the golden bead material. The Nine Tray and 45 Layout continue to reinforce the concepts of the decimal system. Composition of Numbers allows the child to compose large numbers using the wooden cards and golden bead bank. This skill is added onto when we get to operations. We can add, multiply and divide with the number cards and golden bead bank.

Linear counting is counting object in a line. It as the other areas starts with a sensorial presentation of placing the colored bead bars into stairs. This is followed by matching bead bars and then counting the beads in the bead bars and later associating them with numerals. The bead bars are then combined with the teen board and then the ten board to count concretely to twenty and then to 100. This work interacts with the work of the Hundred Board of numeration and the 45 Layout of the Decimal

systems. The Bead Bars are seen again with the Bead Chain work which includes skip counting leading to multiplication and the relationship of numbers to their squares and cubes.

The four mathematical operations, addition, multiplication, subtraction and division are all taught in the same general format. First process is taught. This allows the child to focus on the how. The materials used for process are golden beads, Stamp game, Dot board (for addition and multiplication) and bead frame (for addition, multiplication and subtraction). After the process has become familiar the child can

move on to counting, these materials allow the child to understand the answers they get from their problems by using materials they can count, these materials include red and blue rods, tabletop rods, colored bead stair and snake game. In addition to these the Multiplication board and subtraction strip board are also used.

The final piece to the operations is memorization. Memorization is important an important skill, it allows the child to go into further into math and to answer problems quickly. Memorization materials include the addition and subtraction strip boards, control charts and finger boards, Multiplication and division boards.

Fractions, time and measurement all cross reference with practical life. Fractions and measurement can be used in cooking, color mixing and other activities.

Again I have this visualization of all of these threads reinforcing the learning that is happening in each individual lesson as materials are used to present related concepts in each area of the curriculum. Like creating yarn, where each individual fiber is short but overlaps with all the other fibers and twists together to form a strong unified piece of yarn each lesson overlaps and integrates with the other lessons both in the same sequence and the others to provide the child with the necessary experiences to have a strong understanding of math concepts.