**UNITY TEACHING "OPERATIONS MATHEMATICS"** **(novelty!)**

**Teaching activity for the unwinding of four "Operations mathematics" **

In the Unity **"Operations mathematics"** (Table 2) is possible to proceed the unwinding of four generic operations, not in column, carried out operations in self-possessed formal procedure from vocal messages interactive that signal the eventual mistakes. This work was structured for the unwinding of simple operations and table based on the mnemonic calculation, without procedures in column (for the four operations in column see the unity that follow).

It reads vocal all the operations, from the multiplication table until the most complex operations, emphasizing time for time the scopes of writing and of reading and

putting in projection the colored numerical histograms means values. Easy way of learning Mathematics operations, addition, subtraction, multiplication and division, with interactive software.

Mathematical software to be used by Teachers, Students and Parents. To consolidated learning, to help with accelerated learning.

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*(Table 2 - Operations mathematics)*

*Demonstrative VideoScreen "Operations mathematics" *

(All the present functions in this form, and of continue listed, are available also in the operations mathematics in column "Additions", "Subtractions", "Multiplications" and "Divisions").

The operations mathematics to develop can be loaded from file, or, written directly from the pupil and resolved under the control of the vocal messages interactive that read the varied procedures and signal the eventual situations of mistake. The lessons of mathematics can be aranged from the insegnante like task, in the form of file. txt, containing a series of operations and loaded means the key **"Load lesson"**.

The key **"Listen to"** allows to proceed the automatic execution and to the listening of the given task, and of the relative results, means the reading of the vocal synthesis.

This work formal procedure reads vocal and resolves any task assigned, written in a file. txt, containing a mathematical series of questions, using without distinction the four operations, from the multiplication table, until the most complex operations with composed numbers until ten figures.

The key **"AnswerYou"** agrees to pass the impromptu execution, aside of the pupil, of the whole task assigned, writing the result in the appropriate editor.

All the work's procedures with the varied formal procedure of **"ScriviFacile Math Algebra"** result simple and immediate: to the pupil is request the alone capacity of to press the replies from the keyboard, without to use the mouse.

All the operations come read from the vocal synthesis and the situations of mistake come immediately signalled.

In the situations of difficulty, pressing the key **"Help/Mistake"** the question comes resolved and it is gone automatic to the successive one, but the help asked comes signalled and increased in the automatic counter of mistakes. With the key **"Evaluation"** it's possible to monitor every action to the phases of writing, in the scope of the unwinding of the task. It allows the calculation with numerical values and values percentages of the mistakes carried out in connection to the useful replies. With the key **"Assign test"** is possible to plan the program for the unwinding of tasks and checks, to assign a work from file. txt and, means password, to deactivate the functions of the program that do not serve leaving profitable alone those indispensable to the pupil to carry out the work assigned. With the key **"Evaluation"**, you can enter in the window that collects the relative data to the task and to the carried out check. The evaluation comes carried out with numerical values and percentages with respect to the whole of the given replies and to the mistakes committed, besides, translates the results achieved according to the parameters of **"Synthetic evaluation"**, according to the level of conventional evaluation in use in the School. Finally it develops functions for the filing and the comparison of all of the thoughtful data.

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**UNITY TEACHING "ADDITIONS"**

**Teaching activity of mathematics with "Additions" in column** **(novelty!)**

With the teaching unity **"Additions"** (Table 3) it's possible to proceed the vocal reading and to the guided unwinding of additions arranged in columns (two addends), using

operations with composed numbers until ten figures.

*(Table 3- Additions in column) *

Demonstrative VideoScreen "Additions in column"

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In this formal procedure the work procedures come conducted from the coloring of the individual vertical columns and from the vocal reading that intervenes during the individual operations of calculation. The numbers of the individual operations in column and the eventual amount to be carrieds, colorings come, emphasized and read vocal (Ex: eight more four, oner of amount to be carried, equal). To the digitazione of every individual answered it comes signalled the eventual situation of mistake. Concluded the whole operation the program reads vocal the result of the final product and goes automatic to propose the successive operation.

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**UNITY TEACHING "SUBTRACTIONS" **

**Teaching activity of mathematics with "Subtractions" in column** **(novelty!)**

With the teaching unity **"Subtractions"** (Table 4) it's possible to proceed the vocal reading and to the guided unwinding of subtractions arranged in columns (minuend and subtrahend), using operations with composed numbers until ten figures.

*(Table 4 - Subtractions in column)*

*Demonstrative VideoScreen "Subtractions in column" *

In this formal procedure the work's procedures come conducted from the coloring of the individual vertical columns and from the vocal reading that intervenes during the individual operations of calculation.

The numbers emphasized come read vocal, come carried out the eventual loans, subsequently comes asked for to press the consequent reply, comes signalled, finally, the eventual situation of mistake.

Concluded the whole operation the program reads vocal the result of the final product and goes automatic to propose the successive operation.

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**UNITED TEACHING "MULTIPLICATIONS"**

**Teaching Activity of mathematics with "Multiplications" in column** **(novelty!)**

With the teaching unity **"Multiplications"** (Table 5) it's possible to proceed the vocal reading and to the guided unwinding of multiplications arranged in column.

*(Table 5 - Multiplications in column)*

*Demonstrative VideoScreen "Multiplications in column" *

The work's procedures come conducted from the coloring of the numbers in two factors and from the vocal reading that intervenes reading the numbers and the varied passages during the individual operations of calculation. (Ex:" four multiplication by six, more three of amount to be carried, equal").

The product of the individual operations and the eventual amount to be carrieds, come emphasized and read vocal.

To the type in of the reply it comes signalled the eventual situation of mistake.

*(Table 6 - Multiplications in column)*

Concluded the multiplications to the individual numbers of two factors, the program goes automatic to the additions in column (Table 6), emphasizing and reading vocal the varied numbers and the operations to develop, signalling the eventual mistakes.

Concluded the whole operation the program reads vocal the result of the final product and goes automatic to the successive operation.

**UNITY TEACHING "DIVISIONS"**

**Teaching activity of mathematics with "Divisions" in column** **(novelty!)**

With the teaching unity **"Divisions"** (Table 7) it's possible to develop all of the mathematical procedures relative to the division (dividend until nine figures and factor until five figures) driven from the vocal reading that advises and leader in the unwinding of the work.

*(Table 7 - Divisions in column)*

*Demonstrative VideoScreen "Divisions in column" *

The varied numbers and the work's procedures come read vocal, emphasized means color and illustrated in entire manner, from the beginning until the last phase of the unwinding of the operation, included the relative passages to the subtractions to establish the remainder of every line and the figures of reference to carry out the calculations, the differences and the eventual loans. (Ex:" three multiplication by six, add one of loan, difference with twenty-eight, equal").

**Teaching usefulness of the functions for the learning of the mathematics and of the algebra**

The formal procedure of unwinding of the activity of mathematics above listed, like too the work formal procedure in the scope of the algebra that follow, can constitute moments of large innovation in the teaching one because offer positive a lot of appearance and of large usefulness for the pupil that it is found to operate in interactive environment, with the orderly scanning of the actions to develop and with the immediacy and the timeliness in the report of the situations of mistake.

The possibility of to work in an environment stimulating, dynamic and interactive, it develops important functions in the organization of the ability and in the development of the skills in mathematical scope because it favors, besides proceeded of learning more rapid and consequent, also the organization of procedures and behaviors more precise and coherent.

**UNITY TEACHING "ALGEBRAIC EXPRESSIONS WITH POSITIVE NUMBERS" (novelty!)**

**Teaching activity with "algebraic Expressions with whole numbers positive" **

This function is in a position of to collect and to monitor it together of the variegated survey of the rules and of the formal procedure of unwinding of the algebraic expressions, with the use of three parenthesis and of the whole numbers positive, and represents an absolute novelty in the scope of the teaching one. With the teaching unity "algebraic Expressions" (Table 8) it's possible to develop any algebraic expression, until fourteen operating, with the use of the positive numbers, with the use of three parenthesis, with the vocal reading that develops interactive functions, ready to intervene every step, to correct, to advise and to guide in the unwinding of the work.

Easy way of learning Algebra, positive numbers and rational numbers, with interactive software. Mathematical software to be used by Teachers, Students and Parents. To consolidate learning, to help with accelerated learning.

*(Table 8 - basic Form extensive for "algebraic Expressions with whole numbers positive")*

*Demonstrative VideoScreen "Espr. Alg. n. positive (extended)" *

The Table 8 presents the functions for the unwinding of the expressions with positive numbers, with the varied elements introduced in every pigeonhole with the varied colors and arranged for extended in every line. These data, during the unwinding, come transcribed automatic in the editor upwards, available place to be saved on computer support or to proceed directly to the printing.

**Writing facilitated to the algebraic keyboard of expressions.**

The activity of writing is able to be carried out easy, with three fingers of the left hand, using to write the parenthesis the visible keys in the image (Table 8, 9, 10, 11, 12), while the hand right hand can develop the work of writing from the numerical keyboard or from the other keys.

*(Table 9 - Version rationalized for "algebraic Expressions with whole numbers positive")*

*Demonstrative VideoScreen "Espr. algebraic n. positive" *

These statements of default of the formal procedure of writing can be changed

according to the actual requirements, using any other series of keys, changing simply the letters of association to the individual marks in the form arranged to the right of the image.

**UNITY TEACHING "ALGEBRAIC EXPRESSIONS WITH RATIONAL NUMBERS"**

**Teaching activity with "Algebraic expressions with **

rational numbers"

The Table 10 presents the functions for the unwinding of the algebraic expressions with rational numbers (positive numbers and negative numbers).

*(Table 10 - Form for "algebraic Expressions with *

rational numbers")

*Demonstrative VideoScreen "Algebraic expressions rational numbers 1"*

*Demostrative VideoScreen "Algebraic expressions rational numbers 2"*

**UNITY TEACHING "ALGEBRAIC EXPRESSIONS WITH RATIONAL NUMBERS AND POWERS "**

**Teaching activity with "Algebraic expressions with**

rational numbers and powers "

The Table 11 presents the functions for the unwinding of the algebraic expressions with rational numbers and powers.

*(Table 11 - Form for "algebraic Expressions with *

rational numbers and powers")

*Demostrative VideoScreen "Algebraic express. rat. numbers and powers"*

**UNITY TEACHING "ALGEBRAIC EXPRESSIONS WITH FRACTIONS, RATIONAL NUMBERS AND POWERS "**

**Teaching activity with "Algebraic expressions with fractions, relative rational numbers and powers"**

The Table 12 presents the functions for the unwinding of the algebraic expressions with fractions, rational numbers and powers.

*(Table 12 - Form for "Algebraic Expressions with fractions, rational numbers and powers")*

Demonstrative VideoScreen "Espr. alg. fractions, rational number, powers"

This form allows to develop, in easy way and with simplicity to the keyboard of the PC, any expression algebraic assigned by the teacher.

All the rules of the algebra and all the procedures in use with the fractions, the relative rational numbers and the powers, are checked and assisted during all the development.

Every error is immediately signalled by vocal messages of correction, memorized and brought at the end of the job for the evaluation of the teacher.

Likewise to the preceding unities, this form (Tav. 19) allows to the pupil to proceed with the same procedures and with the same method of job in use on the notebook.

The operations developed with priority are signalled with the followings colors:

**teal: for the parts to be copied;**

fuchsia: for the powers;

red: for the moltiplcations and the divisions;

blue: for the additions and the subtractions;

navy: for the sums and the subtractions with fractions;

brown: for multiplications and divisions with fractions; yellow: for the simplification of the fractions.

The unity for the development of Algebraic Expressions with fractions picks up and checks all the rules and the formalities of the algebraic expressions with the use of the three parentheses, of the relative rational numbers, of the powers and of the fractions. In this environment job, interactive and dynamic, are effected controls on every single action and any situation of error is signalled with timeliness and immediateness.

To every action of the pupil, correspondes controls of the software, to verify the correctness of the procedures, of the calculations, of the rules and of the priorities that belong to the algebra.

In this environment of job, are proposed to the pupil the best situations of learning, favoring in the pupil the assumption of virtuous behaviors, of coherent attitudes, of vigilant attention and of self-control.

All the procedures of job are effected with simplicity and quickness to the keyboard of the PC. The pupil must only to proceed footstep for footstep in the work, assisted and facilitated in the realization of the procedures by the interactive functions that guide to the develpment of the whole expression and the whole job.

**Formal procedure of unwinding of the algebraic expressions with the three forms **

(Table 8, 9, 10, 11, 12)

The beginning of the activity can be carried out writing directly in the first line the text of the expression, or, using the key **"Load lesson"**, can be loaded from a file of text pre-existing a series of expressions to develop. The activity of unwinding of the algebraic expression in the successive lines comes tightly inspected and monitored to every individual action, signalling timely, means communication vocal, any mistake of unwinding, of method, of calculation, of wrong utilization of the parenthesis and the eventual mistakes in the transcription of the data, until the conclusion of the whole expression. These modality of unwinding agree with the pupil of to have a precise sight of the operations of calculation to develop, with the varied passages emphasized from the colors:

red for multiplications and divisions;

dark blue for additions and subtractions.

Every individual mistake comes restored in the square **"Data-Evaluation"**, for the successive evaluation of the Teacher, according to the following data:

**- parenthesis of mistakes number; **

- mistakes of copying of the numbers;

- mistakes of operating mathematician;

- number miscalculations;

- carried out number expressions;

- total number mistakes.

During the phases of writing come carried out automatic controls to facilitate the correct disposition of the numbers, of the marks and of the parenthesis, and, besides, to emphasize means coloring the eventual open parenthesis, to verify the correctness of order in the disposition of the parenthesis, to emphasize in red or in dark blue the operations to

develop with priority, to monitor the formal correctness of the expression during the whole unwinding.

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**METHODS OF TEACHING SETTING THE UNIT FOR THE TEACHER**

With **"ScriviFacile Math Algebra"**, the teacher can arange and structure the actual teaching unity, the tasks and the checks in every their part, writing them directly to the computer, or loading either predisposing file. txt from other computer supports or from scanner.

It's possible, besides, to transfer whole teaching unity from the paper support and to introduce them, complete of images and text, in **"ScriviFacile Math Algebra"** and to give back the usable to the pupils in a new multimedia garment, stimulating, dynamics and interactive. The works to assign can be written in the form of text, with requests adapted to the level of learning of the pupil.

The teaching unity of mathematics and of algebra can be arranged in the form of text containing a mathematics operations of series or of algebraic expressions to assign the pupil, for the unwinding in entire autonomy, directed to the development of the varied ability: to leave from the multiplication table, to the impromptu calculation mnemonic or reasoned, to the calculation with a mathematics operations of series to develop according to the formal procedure in column, or ability of calculation in algebraic scope with positive and rational number.

The possibility of structures the actual lessons and of to build the actual work file allows to the insegnante of to increase the teaching availability of material to use for traveled aimed and personalized, for the accomplishment of specific lessons and tests, assigned immediately or in defered in the time, according to the actual planning and according to the requirements of the pupils. The same lessons are able to be proposals to the foreign pupils using the functions of support for the linguistic integration, connecting them to the images and to the dictionaries in foreign tongue.

The files of the images and of the dictionaries are open to the possibility of integration and updating aside of the insegnante and allow the entire accomplishment of lessons based on a multimedia dispensation with interactive functions.

The validity and the capacity of an open and flexible system do not consist alone in the summation of the varied functions, but above all in the possibility, offer to the Teacher, of to update and to adapt the technological system to the requirements of the teaching one and in the opportunity, for the student, of to enter a richer repertory of functions and of available actions on the plan of the formation.

This system produces a together of potential interactions and of stimuli to the learning a lot richer of the summation of its individual functions.

All the unity modulate profits, above listed, not propose the matter in manner "static", how happens in the books of text, but in profitable manner with the scanning and with the execution on time of functions and procedures, with the display of models and work procedures, with multimedia communications impromptu that intervene in dynamic and interactive manner in the unwinding of the task assigned.

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**The functions to favor the accessibility to the persons without manual ability limiting the manual writing on the notebook **

**"ScriviFacile Math Algebra"** performs important functions such as assistive technology useful to promote accessibility and learning.

Important mathematics opportunity comes offer in the to allow the unwinding and the acquisition of the ability of calculation with the four operations mathematics in situations whitout manual ability limiting the manual writing.

**"ScriviFacile Math Algebra"** allows the persons whitout manual ability limiting the manual writing on the notebook, of to proceed the learning of the ability of calculation with the four operations mathematics in column, with the same formal procedure and with the same procedures of unwinding in use on the notebook.

All of the procedures of unwinding of four operations in column, included the varied intermediate passages of calculation, are able to be carried out with a manual ability limit to use only of the numerical keyboard, or, means the access with a special keyboard (special keyboard enlarged or other).

During the whole unwinding of a developed task from a mathematics operations of series or algebraic, to the pupil is asked for to answer to the individual passages of calculation and to the individual questions mathematical proposals from the vocal synthesis, means simple selection to the numerical keyboard, all of the passages of progress of the procedures and of the work method proposals in automatic scanning from the program come until the conclusion of the whole task assigned.

All the carried out activity with **"ScriviFacile Math Algebra"**, relative to the acquisition of the ability of calculation, to the algebraic unwinding of expressions, to the learning of the writing and of the reading, come always monitored from vocal messages interactive, with a tight feed back between the varied phases of production, of control and of check of the work procedures and of learning.

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