The Teaching of Numeration, Introduction to Arithmetic, Auto Education - Essay Example

Question/Answers
1. Skip-counting and base ten operations are learned through constructing objects and observing them in relation to each other.
Sensitive Periods are durations of time during which the intensity of interest in specific objects in the environment is at its peak. The sensitivity and responsiveness to particular stimuli decline with time. These periods indicate the opening of increased developmental opportunities.

The absorbent mind refers to the ability of children to absorb information or impressions from surroundings through the senses without involving effort.

2. Explain Arithmetic (Chapter 4 P 164-182)
Arithmetic is the knowledge of numbers and associated processes such as addition and subtraction, which is intuitively learned at the early stages of childhood and developed gradually, through repetitive exercises, observation, and experience. It helps the mind to distinguish and relate objects by means of symbols and ideas such as shape, space, identity, difference, and quantity. For example, a child learns gradation in numbers, such as 1,2,3,4, and recognizes them as distinctive entities by adding or subtracting identical units.

3. Introduce the main point about Chapter 10 P 149-152
In contrast to the older teaching systems, The Teacher describes a new method or system of teaching, which values the teacher as a guide or connecting link between objects and the student. This system does not rely on objects as help to the teacher but as a help to the student himself with the assistance of the teacher. The role of the teacher has been modified from an active corrector of mistakes to a more rigorous but patient guide, who acquaints herself with knowledge of objects and then guides students in using those objects on their own while perfecting learning and maintaining order in the environment. The teacher should be prudent enough to facilitate the needs of both the more and less developed minds at the same time.

4. Explain Spontaneous repetition, development of the mind, normalization, observation, and prepared environment
Spontaneous Repetition refers to the tendency of a child to master an activity by repetition. It helps them to identify and comprehend small differences in the environment.
Development of Mind describes the psychological self-construction in children while interacting with their environment. It is a continuous process that begins when new sensitivities appear and gradually fade until new ones emerge, and helps in orderly intellectual development through time. For example, the ability of the mind to choose without conscious intent indicates development.

Normalization refers to the state when a balance between urge and inhibition has been achieved and development proceeds normally. Four characteristics such as love of work, concentration, self-discipline, and sociability are central to this process.

Observation refers to the role of the teacher in the learning environment, in which she observes for purpose of guiding, perfecting, and maintaining order. Prepared Environment describes a setting that contains selected materials for learning and encourages free activity. However, it ensures cleanliness, maintenance of order, limitations in access to materials, and free movement.

5. Introduce the main point about Chapter 19 P 276-279
In chapter 19, it has been argued that younger children are surprisingly capable of solving advanced arithmetic questions such as simple algebra, square root extractions of up to four figures, and memorizing algebraic formulae for cubes of binomial and trinomial. This capability was observed when children were provided with objects such as beads of colored glass, and a larger cube cut into unequal parts which were colored differently but in a specific order. By the practice of arranging beads in different orders, children were soon able to perform four operations on numbers as large as thousands. Through rearranging and ascribing symbols to smaller unequal parts of the cube, children even memorized algebraic formulas for the cube of a trinomial. Thus, it was revealed that children can remember quantity and order through visual memory of objects.

6. How sensorial and practical life activities relate to Montessori Math curriculum, control of error, direct and indirect Aim of Montessori Math Materials
Sensorial activities include geometric materials such as cubes, prisms, and rods, which aim at refinement of chi