MATHEMATICS GUIDELINES

CODING

In the past year, Computing in general and coding more particularly, have received increasing

attention at a politicial level. An increasing number of countries have already started or at least are

thinking about integrating Computing as a subject or coding and programming as elements within the

subject into their national curricula.

Even if there is an increasing awareness of the economic and social importance of having

citizens who understand how to manipulate computers, Romanian curricula doesn`t provides content

for IT in secondary school.

COMPUTING TERMINOLOGY

Clarification of educational terms:

Computing means the broad subject area

Digital literacy is the general ability to use computers.

Information (and Communication) Technology (IT, ICT):

The use of computers in industry, commerce, the arts and elsewhere:

Computer Science means the rigorous academic discipline.

Coding: The writing of programs

Programming could mean:

- in the most narorow sense just coding:

- in the widest sense the whole process of software development;

What concepts or skills should we be focusing on when we teach computing?

• Analytical thinking

• Working independently

• Perseverence

• Be a teamplayer

• Communication

• Language – English is very important as language for ICT because most of the information

about computing is always in English also in multinational teams.

• Lifelong learner

• Collaboration

• Perseverance and develop independent work while being a team player and knowing how

to work collaboratively;

• Know how to be a lifelong learner and know how to learn by yourself;

• Understand and use the communication skills while being fluent in various languages,

especially English.

Concepts, Methods , Ways of Thinking

CONCEPTS

Computational thinking is a basic skill that all students should develop. Among other things it

helps them solve real life problems. Students must understand that we use algorithms in our everyday

life.

Computational thinking principles can be present in any subject matter, because the history of

computing is the endeavour of automating human thought and activity. It is, therefore, a reflection of

what humans do naturally and trying to optimize it.

This will involve problem identification, defining the objective, codification of steps to reach

the objective, representations of inputs/outputs, variable abstraction for codifying the problem,

prototyping solutions and incorporation of feedback.

This is evident in any repeatable process: cooking, writing, choosing which line to stand in at

grocery, even playing an instrument. At the heart of computational thinking is the study of artificial

intelligence. Teachers can begin to incorporate it by becoming aware of and purposefully pointing out

the meta-cognitive processes that we activate when solving everyday problems.

Computational thinking needs to be taught from the early years and is not a course you can take.

It's a skill that you keep perfecting your whole life. Many students and adults lack these skills because

we always want a black and white answer in an ambiguous world. Unfortunately the educational

system that many of us grew up in was based on rote memorisation and a set of specific answers. The

entire educational system needs to be revamped from the early years in order to cultivate youth with

computational abilities.

Computational Thinking Characteristics:

• Formulating problems in a way that enables us to use computer and other tools to help solve

them:

• Logicaly organizing and analyzing data:

• Representing data trough abstractions such as models and simulations:

• Automatic solutions trough algorithmic thinking (a series of ordered steps):

• Identifying, analyzing and implementing possible solutions with the goal of achieving the

most efficient and effective combination of steps and resources:

• Generalizing and transferring this problem solving process to a wide variety of problems.

One of the key problems of coding and programming is that it is often perceived as very

technical, nerdy and abstract. But this is simply not the case and our role of teachers should include

making it clear how relevant these skills are in so many other fields of work. One of the ways we can

do this is to establish links with other subjects at school, joint projects that highlight the cross-

curricular relevance of what we do in computing.

Almost in any subject we can use computing to create websites. There it could be shown all

good practices that have been used.

For instance, students can create animations in Scratch as an add on to story writing and

geometrical objects as an add on in math. Teacher can develop together with the students as a part of

Math curriculum programs to stimulate situations taken from real life in which maths topics considered

during lessons are needed: loans credit tables, the position of sun at same time in cities at different

latitudes, reflections of a ball with the walls of a table when is hit and so on.

They can make a project combining English language, Ecology and Digital literacy. The topic

can be exploration of the types of pollution and how recycling can help us. They can work in teams of

three and an end product can be a PowerPoint Presentation and a digital poster on recycling.

METHOD

Pair Programming

In pair Programming, two students are working together as a team on the same computer,

because two heads think better then one. They are working together in an interesting kind of way. In

Pair Programming, one person is the driver and the other is the navigator, just like driving a car. The

driver is sitting on the computer and use the keyboard, the mouse and the touch-screen and controling

the main actions on the computer. The navigator helps the driver asking questions or observing

potential problems or mistakes. Communication is the key of successful pair programming. The driver

have to explain what he/she is doing and the navigator can suggest what to do next, thinking about the

big picture and the driver focuses on the details, because both rolls are important.

Visual programming tools

SCRATCH

Scratch is a free tool and exists in 40 different languages. It is constantly being further

developed with many different iterations of it and the best thing about it, is it's huge community behind

it ( http://scratch.mit.edu.)

It is a useful tool to develop critical and creative thinking and the most important thing is that

this tool can be used as transversal tool through all subjects and finally, all the projects can be share

through web pages, blogs, virtual bulletin board etc.

It can be used for creating presentations, games, stories, animations, cards, projects, geometrical

games.

Geometrical game: https://scratch.mit.edu/projects/106231069/?fromexplore=true

GAME DESIGN TOOLS

In order to choose the right game design tools, we should consider what are the aims of using

them:

• Ease of use

• Target Age Group

• Target grade level

• Programming Paradigm

• Availability on various platforms and Opening Systems

• Limitations on the kind of games you can make

KODU http://www.kodugamelab.com/

Kodu lets kids create games on the PC and Xbox via a simple visual programming language.

Kodu can be used to teach creativity, problem solving, storytelling, as well as programming. Anyone

can use Kodu to make a game, young children as well as adults with no design or programming skills.

The important thing to know about Kodu is the visual programming language to use, is a

language specificly invented for this product and it operates a very high level of abstraction. Students

love Kodu for the fantastic rich games that it can be produced in short time. It is easy to create visually

impressive 3D game environments.

ALICE: http://www.alice.org/index.php?page=what_is_alice/what_is_alice

Alice is an innovative 3D programming environment that makes it easy to create an animation

for telling a story, playing an interactive game, or a video to share on the web. Is a freely available

teaching tool designed to be a student`s first exposure to object-oriented programming, that`s why it is

used for creating geometry shapes and bodies. It allows students to learn fundamental programming

concepts in the context of creating animated movies and simple video games. In alice, 3D objects (e.g.,

people, animals, shapes and vehicles) populate a virtual world and stundents create a program to

animate the objects. In Alice`s interactive interface, student drag and drop graphic tiles to create a

program, where the instructions correspond to standard statements in a production oriented

programming language, such as Java.

Alice allows students to immediately see how their animation programs run, enabling them to

easily understand the relationship between the programming statements and the behavior of objects in

their animation. By manipulating the objects in their virtual world, students gain experience with all the

programming constructs typically taught in an introductory programming course.

HOUR OF CODE

For creating a lesson plan for the hour of Code, we can use a very nice tool, the Learning

Designer which was developed by the London Institute of Education.

The reason of using this tool is not only because it is excellent in it's conceptual design but also

because it allows you to easily share your creation. There are examples of lesson plans created in the

Learning Designer.

The learning Designer suite of tools enables teachers to share their good teaching ideas. It is

intended to help a subject teacher see how a particular pedagogic approach can be migrated

successfully across different topics. There are sample patterns to browsw and edit, or you can design

your own from scratch.

http://learningdesigner.org/

http://learningdesigner.org/viewer.php?uri=/personal/giorgiagroza/designs/fid/94145e999e11a3

8ea8b8519ac4ea429d53452cd237976b075568411e47c29439

http://learningdesigner.org/viewer.php?uri=/personal/giorgiagroza/designs/fid/590597cb7ffd1ca

eda8f979140297f6abc4943eade2cc4f47d8b8e0d9cb03ece

http://learningdesigner.org/viewer.php?uri=/personal/giorgiagroza/designs/fid/174e0b288b043d

a092373851107c527466408d92127898f1bd93ce19d065677c

ARITHMETICS

Arithmetical signs are written figures and geometric figures are drawn formulas.. David Hilber

The fast pace of solving competition in all areas of activity requires us to think quickly and well. The

mathematics contribute, in very large measure, to the development of logical thinking, spirit of

openness, of reasoning, etc.

In Primary school the students shall adhere to the basics "Tools" with whom the student will "operate"

throughout life and that the whole system is built of mathematical education. If students encounter

difficulties not to adhere to the time these terms. A student who has not learned to calculate correctly, if

it spends extra energy and can follow the thread of reasoning, an exercise or a problem. The difficulty

that greets them does it mobilizes for new trials and lead to loss of trust in his powers.

If the student feels that the penetration of basic concepts in mathematical core, if he lives the

joy each success, big or small, all these feelings grow interest and love of mathematics.

Students today must already understand and involved in day-to-day activities involving the use of

arithmetic concepts and concepts (counting, measurement, estimation) change to help them acquire

independence in various shares of everyday life.

The activity of solving math school constitutes an optimal framework for nurturing creativity in

particular for the development of logical thinking, especially since logic does not appear as a discipline

of study than in high school. The process of thinking it triggers whenever we cannot cope with a new

situation, a situation-the problem merely means learned.

Life constitutes a permanent provider issues as practical and theoretical activity of man occur

frequently in trouble. That's why thinking is continuously solicited and increasingly confronted with

the most varied issues what is resolved.

In the complex of goals that they involve mathematics teaching-learning in primary education,

problem solving is an activity of depth of analysis and synthesis of superior. It involved mental effort

of understanding and application of algorithms learned with creative, inventive structures conduct, all

amid a Dominion repertoire of mathematical knowledge, concepts, definitions, calculation rules,

techniques, and skills for their application.

Put to the test problem solving in the highest degree of intellectual abilities of their pupils, they

require all the mental availability, especially intelligence, which is why in classes I-IV syllabus math

grant greater attention problems. Mobilising pupils in problem solving is superior to other

mathematical representations because students are put in the situation to discover ways of remedying

them himself and the solution, to formulate hypotheses and then to verify, to make associations of ideas

and unusual correlations.

Creativity thinking cannot produce than on the basis of properly formulated skills, techniques,

skills to establish logical rationalizations, a rich volume of knowledge in order to develop a realistic

content enunt. Potential development of thinking and creativity is accomplished through activities that

require independence, intelligence, originality. That's why the teacher should be responsive to what you

are interested and like children at what they want and can achieve full-force because of their activities

and satisfacandu them all interests.

To develop creative thinking of the students must be encouraged in activities, to be appreciated

the effort and be stimulated even when they will give full answers. And will address questions such as:

"Think about it, how we can calculate? How can judge? It is not possible and otherwise? How more

can we say? ".

Class to "natural numbers and lower assembly may guide students ' thinking toward problem

situations whose solution does the inductive character, starting from the idea of the possibility of

finding optimal more possible, which have a value as a means of cognitive creativity.

Starting from the type of exercises? + ? = 10, ? + ? = 4 in which students were put in the

situation of thinking more variants of writing a number.

Math problems represents the transposition of a situation or a complex situation in quantitative

numerical relationships, some other girl and face value is known, asking based on numerical rules, the

value unknown. The student should be taught to think good reasoning, which is the most important

thing in solving problems.

In the assimilation of this discipline, we avoided learning efforts of mathematical rules, starting

even from primary school: endless hours and learning exercises to numeratiei in concentrele 1-10; 1-

100; 1-1000; exercises of oral and written calculation; exercises to increase and decrease of a number

with a few units or a couple of times; exercise of comparing numbers, sums, differences, products or

caturilor, by finding out the distances, until arriving at the beautiful issues subject to solving. n this

perspective, it is necessary to knowing the steps that underlie the art of problem solving: Understanding

of communicative sentence structure) is a prerequisite to solving the problem and correct

communicative sentence structure of reasoning correctly.

b) repetition of communicative sentence structure with and without the help of supplementary

questions, is needed to determine if students have learned the meaning and each stated sizes. In this

phase, the main parts of the problem: unknown data, condition and requirement.

c) Solving itself requires good general methods of teacher manuite. After careful examination,

shall identify the method of synthetic or analytic problem-solving.

For the cultivation of mathematical skills, it is important that students be encouraged to find different

possibilities to find the correct result.

Another aspect which should be taken into account is learning centered on the pupil.

Assignments should be made in the light of those with sema and backlogs in learning and those who

can perform.

Within hours of mathematics requires the sequence in which students interact with each other in order

to find the correct solution or to follow correctly a calculation algorithm.

It is important to approach the teaching of mathematics in terms of interactivity. In this sense,

the lessons taught by means of sports devices have a special contribution in this respect.

innovative tools proposed, very necessary for diversification of hours of mathematics and to prepare

items for children able performance.

GEOMETRY

The surrounding world is replete with examples of bodies which highlights the elements of

geometry. Architecture, decorative arts, painting, sculpture are a few domains using technology with

elements of geometry.

Scramble in the Upper Paleolithic and early Neolithic, in his paintings on pears specifications

on the Charging Upper Paleolithic and early Neolithic, in his paintings on Perry's Cave specifications,

etc, on the bones of mammoth, horse figurines or carved out of bone on et c., man used the parallel

lines perpendicular lines-, zigzags, spirals, position angles in various specifications , diamonds.

Territory in the country, were found vessels of Cucuteni culture (5500 î.Hr-2750 BC) painted with

geometric signs and figures with incised geometric motifs, these representing the highest level of the

civilize take pre-and rehabilitating human appear to accumulate take writing. Geometry continues

today to follow man in scientific and technical revolution of the era.

Everyone must understand the importance of knowledge, concepts of geometry, whereas the

practical applications of geometry we accompany in daily life. The concepts of geometry helps us

observe and apply in our work, simple properties of planar and spatial forms and to recognize simple

symmetry properties of drawings; to discover, to recognize and use in various contexts and correlation

sequence of objects or data associated by the rules; to solve real-life problems involving knowledge of

notions of geometry. For example, figures/geometric bodies made of wood can be assembled in such a

way that they can take the form of objects existing in real life, but those who build them must know the

concepts of geometry and beyond.

Addressing definitions in geometry classes contribute to primary students of some spatial

representations, the development of logical thinking, of reasoning (deductive ipotetico-,

inductivanalitic). Knowing and using the elements of geometry ensures the connection with other areas

of mathematics, but also in other disciplines, such as: education, fine practical skills/education of

technology, computer science (ICTs).

Referring to the TIMSS (Trends in International Mathematics and Science Study), the

international assessment of the level of learning in mathematics and natural sciences, applied to

samples of students of class IV, concepts relating to the geometric shapes and Geometric Shapes and

measures/represents 35% of the Measures areas of content (50% is the area called Numbers, and 15%

field Displaying the data). Each area of the content has several topics; each one is presented as a list of

objectives contained in the mathematics curriculum in most of the countries participating in this type of

evaluation (among those countries being and Romania).

These specific objectives are written in terms of understanding or skills that are designed to

performance specification aștepate on behalf of the student. The field of geometric forms and measures

include: points, lines, angles and shapes that they-geometric figures (circle, triangles, quadrilaterals,

polygons), the properties of geometric figures, the line of symmetry, three-dimensional geometric

forms-bodies, areas and volumes (for example, to estimate the area of a geometric figures by covering

with a specific shape or geometric body volume estimation by Manoj fill with cubes).

In the literature, there are several methodological requirements whose fulfilment depends on the

success of the teaching-learning the elements of geometry, namely

a). teaching notions of geometry through processes intuitive and their formation about intuitive;

b). scientific notions of absolute geometry;

c). knowledge of geometry functionality.

The concepts of geometry should follow the path of the image to the specified materialized

through drawing and image attached by language. Students will be able to represent the geometric

element without having the object or figure drawing and use the new and varied contexts, to use the

term geometry mathematical language. In teaching-learning concepts of geometry to be used effective

teaching strategies (teaching methods and processes, and learning and teaching materials, forms of

organisation).

Teaching methods and procedures used mainly within lessons containing geometric are learning

through discovery (method of exploration of reality) and problem-solving (oral communication

method), which besides the acquisition of knowledge by pupils and the formation of habits and skills,

specific leading to logical thinking, the active participation of the pupils. The teacher must provide a

balance between methods based on intuition, the supposed organic, in order not to arrive at the abuse of

intuition, but no formal education without support many Modeler and mathematical notions are left

without a sufficient coverage intuitive.

Depending on the style of teaching and teacher creativity, you can use the methodological

structure in which you can enter and interactive methods, which are the modern ways of stimulating

learning and personal development since the early ages. These teaching methods are modern tools

facilitating cooperation through their children, direct and active involvement, the plane of ideas,

experiences, knowledge. In different moments of the lesson, you can organize and carry out methods

and techniques such as brainstorming, cube, method method R.A.I., Venn diagram, its clusters are

double-entry journal, role playing and more. Students can create situations where they can probe the

importance of knowledge and use of the notions of geometry: for example can make over învățări own

reflections in a situation of a builder of wooden toys for children.

To better understand the importance of mathematics in daily life, it is necessary to detreminate

the student to observe carefully all around us and so will find that the geometry has a major role in our

lives. Even if intuitive underlies the teaching of learning the elements of geometry, geometric notions

correctly served in whatever the student explore/investigate environmental information, as well as in

solving problems of adaptation.

"If the student does not endorses organic once with his culture and by the very general concept

of straight line accuracy, and everything that will occur at a later stage: crafts, industry, factory,

homemaker, household life, everything will come out crooked." Mircea Malița, romanian

mathematician.

LOGIC

In Romania, the logic is a subfield of mathematics. Does not appear as a distinct discipline, than

at secondary school. Logical thinking training derived from the study and grasp the basic concepts.

Children like usual to solve logic problems, for it combines challenge and are regarded as a

play. And when the logical problems are given in a group of children (for example, at school), the

challenge is even greater:). Logical thinking helps the child in situations where the difficulty, you have

to analyze a situation, to extract information from it and deduca the most suitable solution.

Abstract thinking, logic, is the one that begins to outline when the child lies around the age of 6

years. In the vision of Piaget, children with an aged between 7 and 12 years stood between concrete

operations.

The logic is, still, until the age of 12 years, but one particular General induction, as opposed to

the later, when will be the type of deductive. He can understand now that the basics as well as abstract

death, homeland or like people, but also the concrete, as well as the length or area, remains constant,

regardless of how the rest of the factors would vary. This happens thanks to a feature of the logic,

acquired recently, and called the preservation of invariants. A consequence of this is thinking right

now, the child can accomplish more complex mental operations, such as those with classes and

relationships, such as rankings and also begins to perceive and reversibility (A-A = 0 or B = B = > =

A). In terms of fewer offices, it means that the little one can now understand equality between people,

the effects of his actions upon others or some correlations between actions.

In the primary school logical thinking development is done by problem solving. Because the

activity of problem solving to materialize the virtues of formative towards the development of logical

thinking it needs a content of the issues and a problem-solving activity appropriate to their purpose.