I Love MontessoriUnderstading the Math Environment Series: Part 3 Important Math conceptsJuly 24, 2008 by Miss Norma | No comments
The concept of temporal relations means having some understanding of beginning and ending, of order of events, and having some grasp of time (minute, hour, day, etc.). An understanding of this concept is needed for math because it gives the child knowledge that will help him/her to be successful with the Red Rod (or gradation) and any of the operations (addition, multiplication, subtraction, and division). The child acquires these concepts through circle time lessons, stories and movement activities. It is also acquired by keeping track of the days, weeks and months with calendar activities, and sequence puzzles.
Spatial relations concepts are important for the child to know. Spatial relations are defined as concepts that involve positioning, such as over, under, on, beside, etc, and as concepts that involve directions and distance, such as towards, away from, near, far etc. The child gains knowledge of these concepts with activities involving the Three Period Lesson, movement, and verbal locating games. It is important for Math because it gives the child a better understanding of Linear Counting, place value, and the four operations.
“The Child’s mind is not prepared for numbers, by certain preliminary ideas; given in haste by the teacher, but it has been prepared for it by a process of formation, by a slow building up of itself” (Montessori, 1914, 165). In giving a child the experience of interacting with materials that further develop his understanding of our numerical system as soon as he shows readiness we allow him the opportunity to really grasp the full meaning of how his environment evolves around mathematical concepts. Math will always be an important part of his daily life.
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Understading the Math Environment Series: Part 2July 9, 2008 by Miss Norma | No comments
Working with the Practical Life activities is one of the first ways the child will begin to gain concentration, order, coordination and independence which are necessary to work successfully with the Math materials. The Practical Life exercises involve working through a process; one thing being built upon another. Working through these activities, the mind begins to control the body as a sense of logic and order is developing. Most of the Practical Life materials prepare the child for Math because it is here that the child learns to succeed and develop his concentration, coordination, order and independence.
Practical Life is the base for all of the curriculum areas because the child learns all the basic things he needs to know and as a result the child becomes more confident and independent. This allows the child to be able to succeed in more difficult activities such as the ones for Math. Table scrubbing is something basic and simple to do, but it is one of the activities that is most helpful for preparing the child to work with the Math materials. One can say that scrubbing a table is similar to working with the 45 Layout because both activities require a lot of steps, concentration and coordination. Practical Life also helps teach the child the importance of paying attention to details, which is something that is extremely important when it comes to Math. This sense of order and physical control are the foundation that is needed for the child to be successful with the Sensorial and Math materials.
The Sensorial materials are a system of mathematical abstractions in concrete form. Dimension, size, length, width and form are all represented within the Sensorial apparatus. The base of ten, which begins our Decimal System, is found here in the Knobbed and Knobless Cylinders, Brown Stair, Red Rods, and Pink Tower. Through these materials the child’s perceptions of same and different are becoming fixed as he explores and manipulates these didactic materials. This also becomes the basis on which he begins to understand the concept of “sets” as it applies to concrete quantities, a very important aspect of the abstract mathematical thinking that will begin to take place with the actual Math materials. These materials also give the child experience with 1-1 correspondence and gradation. The Triangle, Rectangle and Hexagon Boxes, and the Geometry Cabinet are materials that help the child develop a mathematical mind and his knowledge of geometry.
Like the materials above with this equipment the child gains knowledge of 1-1 correspondence, gradation, combination, and differences. The Color Tablets, Fabrics, Sorting, Baric Tablets, Thermic Bottles, Sound Cylinders and the Bells give the child a foundation of similarities in preparation for Math.
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Understading the Math Environment Series: Part 1June 15, 2008 by Miss Norma | No comments
Math is a crucial part of a Montessori classroom because children have a natural interest in numbers and counting. Children will innately go to the math area without even being invited for a lesson. Children usually have some previous knowledge of numbers before going to school because numbers are a part of their daily life. Addresses, clocks, streets, and their ages help them experience numbers daily. This is why they need to learn about Math. Most likely they will know how to count up to three but rarely will they know what the quantity three is. As we go through our daily routines in the classroom, I help the children to keep their growing knowledge of numerals alive; counting how many cookies they are having for snack, counting how many friends are in the classroom, when coming in from recess counting to make sure all our friends are in line, etc. The Math area is what gives them the knowledge of the symbols and their names and helps develop their mathematical minds. “In our work, therefore, we have given a name to this part of the mind which is built up with exactitude and we call it the mathematical mind” (Montessori, 1967, 185). At this age children have an absorbent mind and this allows them to learn about things by internalizing them. They also are experiencing Sensitive Periods and this might help the child learn things easier if one goes by their particular interest, which can be any of the following: order, small things or details, movement, beauty and language. This depends on how old the child is. The Sensitive Periods will play a huge role in what the child will show interest in the Math area. “That the mathematical mind is active from the first, becomes apparent not only from the attraction that exactitude exerts on every action the child performs, but we see it also in the fact that the little child’s need for order is one of the most powerful incentives to dominate his early life” (Montessori, 1967, 189,190).
The sequence for the math curriculum begins with 0-10 Activities (2 ½ - 4 yrs old) and then one may begin with Linear Counting (4 – 7 yrs old), the Decimal System (4 - 5 yrs old) or Addition (4-5 yrs old). It does not matter which way you as long as you follow the child’s interest. Once the child has a base, the 0-10 Activities, the child can move on to any of these areas. All three areas reinforce counting and help the child develop their knowledge of higher numbers. The 0-10 Activities start with the Red and Blue Rods, because you must first start with the concrete (or quantity) before you move on to the abstract (symbols). After that, you move on to Sandpaper Numerals. Eventually the child will be working in more than one of theses areas at a time because they interrelate. After Linear Counting, the Decimal System and Addition the child moves on to Multiplication (5 yrs old and up), Subtraction (4 – 6 yrs old), Division (5 yrs old and up) and lastly Abstraction (5 yrs old and up).
As mentioned above, what I try to follow when I am guiding a child through the math curriculum is the concrete to abstract rule of thumb and their interest in the math materials. It is very important to go with what the child knows and with what he will be successful. When I guide a child in choosing an activity I make sure they are ready for it by observing what he has been working with and how he is using it. This will let me know where the child is and what he might be able to work with next. When working with the child I always use language that is familiar to him/her. For concrete, numbers and quantities I say “this is” and for the abstract, numerals and symbols I say “this says.” I also try to do a lot of repetition so that the child can grasp the concept. For example, when giving a lesson on the sandpaper numerals I try to have the child trace the number two or three times and then if they are ready I have them write in the sand tray. When counting the spindles I make sure they count into their hands and then count again into the box. “The Teacher, …., must have a kind of faith that the child will reveal himself through work” (Montessori, 1967, 276).
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