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General guidelines for the testing course TECHNICAL DRAWING II 2012-2013

cover-copia.bmpThe last few years have been responsible for preparing the exams tests Drafting selectivity or university entrance, (Pope), corresponding to those attached to the Universities of Madrid and Guadalajara centers.

Its design has been modified, for a couple of courses, consisting from the traditional four years to meet the current needs, varying the shape measurement of the courses contents and the objectives attained by our students. The criteria that have been designed thinking of improving the evidence does not cease to raise controversy in the educational environment, any change introduced in this system.

Here are some of the most important aspects in this regard are detailed.



course 2012-2013

Contents, objectives, program and evaluation criteria of the subjects of Technical Drawing I and II taught in high school that are evaluated in the corresponding PAU's, detailed in Decree 67/2008, of 19 June, Governing Council, by establishing for the Madrid School curriculum, Ministry of Education (B.O.C.M. No.. 152, Friday 27 June 2008, pp.. 6-84) In particular in APPENDIX I – MATERIALS FOR THE BACHELOR and point II. MODE SUBJECT – to) Arts and mode b) Modality of Science and Technology (curriculum of this course is the same for both modes) Technical Drawing I and II (B.O.C.M. No.. 152, pp.. 38-41)

On first course a general and instrumental view is provided of matter by filing, with varying degrees of depth, of content that are considered basic, consolidation and deepening which will be addressed in the second year, while the curriculum is completed with new.


The acquisition of knowledge and graphic skills this subject that are of theoretical and practical nature, could materialize in three phases:

  • The first is intended to encourage ability to understand and represent spatial reality by graphical methods.
  • The second skill development and application to the formal resolution and spatial problems.
  • In the third capacity solve real problems derived from the world of technology, of building and engineering.

It is able to develop the capacity for idealization of physical systems via a script that allows both the representation of objects and their application through logical troubleshooting of obtaining size and shape of geometric elements inference. The widespread use of this discipline to higher cognitive processes goes through a pre-realization in elementary problems that can be immediately applied in own examples of engineering.

The contents of the subject can be grouped into three interrelated sections together, although entity itself:

  • Geometría plana
  • Descriptive geometry
  • Normalization

Geometría Plana

The metric geometry applied, used to solve geometric problems of definition or configuration forms in the plane, is the central subject of this formative stage. Provides the scientific content area but assimilation is subject to the maturity of our students.

power from an interior point

Provides basic metric relations and presents the abstract aspects of logic graphically. Allows the development of the capacity of idealization and modeling problems using graphical techniques of thought and analysis.

The classical problems of this area cover a broad agenda in which the theorems of Thales and Pythagoras are the basis of his study. The geometric constructions are the result of relations of its use.

Descriptive geometry

The descriptive geometry can represent on a two-dimensional geometric shapes support the different space.

straightThe study of the techniques of representation is complemented by that of bodies or surfaces and volumes in space.

Provides instrumental projection models / section along with other basic topological nature (intersections).

This matter has been associated with the so-called “spatial ability” or possible “imagine” and understand the three-dimensional space.


The standardization provides rules and conventions used to simplify the representation of technical objects.

Tecnico_2_solucionRepresentation systems have given us the geometrical models for a theoretical representation. Normalization serves to simplify, standardize and objectify graphing technical.

It is the most informative part of the three and therefore more easily assimilated, but uses its own models of descriptive geometry and therefore difficulties associated.

Along with the above thematic areas must accompany the necessary information technologies and communication, especially programs using computer-aided design (CAD), to be included in the curriculum not as a self-contained, but as tools to help develop the content of the subject avoiding replace the graphic essence of the approach procedure for systematizing the application itself.


Evaluation Criteria baccalaureate

The evaluation criteria of the school should serve as a basic guide for subsequent application in PAU's. These criteria should measure skills and content that are due to reach minimally in this formative period.

  1. Solve geometric problems evaluating the method and reasoning constructions, finishing and presentation. The reasoning of the buildings should not be limited to the statement of the construction phases; rather must justify the concepts used in the reasoning process settlement model every year. The written transcript of this process is an exercise in itself that provides adequate maturation of abstract concepts.
  2. Run Drawn different scale, using the scale previously established and standardized scales. The concept of how the measurement is added, and in particular those relating to relations between the parties (forms resemblances).
  3. Solve tangencies isolated or inserted in a form defining, whether this industrial character, Architectural simply the geometric. These problems are the basis of more complex, and allow a minimum conceptual foundation in the subject.
  4. Solve geometric problems relating to conic curves involving major elements of the same, intersections with straight or tangent lines. Trace curves techniques from su definition. Conics are a clear example of cross-application of the concepts of tangents.
  5. Using the dihedral systems and axonometric to solve problems of positioning points, straight, plane figures and polyhedral bodies or revolution, finding distances, true magnitudes, obtaining sections and developments and transformed. In general the treatment of cylindrical projection systems since they are widely applied in science and engineering.
  6. Perform the perspective of an object defined by their views or sections and vice versa, executed freehand and / or delineated. Restitution of spatial forms from its views, or generating them from a single object corporeal form the basis of the standard representations.
  7. Represent key elements in conical perspective, flat shapes and simple geometric volumes. Tapered perspectival systems will generalize concepts at the basic level.
  8. Define graphically industrial parts and components or construction, properly applying the rules referred to landmark, views, cuts, sections, breaks, simplification and dimensioning. Knowing the rules of simplification representations of elementary bodies.
  9. Finish the work of technical drawing, using different graphic resources, both traditional and computer systems Computer aided drawing, so that they are clear, cleaner and meet the objective for which they have been made.

Guidance on the assessment of the PAU's

The general criteria for evaluating the school should form the basis for the relevant evidence to enable access to university courses.

The current structure of the Technical Drawing II tests can be divided into two distinct blocks which measure key aspects of the teachings of Graphic Expression:

  • Metric geometry: Is evaluated by a single exercise representing 40% note of the evidence. In this part of the subject can be requested by the graphical representation of the solution, written arguments on the theoretical model used (Reasoned explanations).
  • Solid geometry: Encompasses the different systems of representation (Diédrico, Axonometric ...) standardization with necessary technical drawing. Is evaluated through two periods represent 60% note (30% + 30%)

pizitoThis examination structure are the most abstract concepts differentiating logical-geometrical nature mainly applied in the plane, those relating to the interpretation of three-dimensional space and operations and techniques used for the representation of objects.

It is therefore configured each of the two options presented by the student three years to resolve graphic constructions. Each of the options will offer exercises appropriate level to the teachings of the subject, adequately compensating for the difficulty and time required for implementation in the time available. Logically, to be a test set, should opt for general types of problems that address the program in its fundamental aspects, both conceptually and in its implementation. Thus, over the course of the academic year, should choose to study models that allow generalizing the corresponding concepts appropriately, reversing the class time to reinforce those concepts most used in the course.

In each of the exposed parts must seek ways of learning to simplify the settlement of more theoretical knowledge:

  • So, training criteria such as the study of metric geometry, theorems of Thales and Pythagoras are useful to the study of the power of a point on a circle, basis of the different problems of tangents and their application to the study of conics as loci (centers circumferences tangent to the focal and passing through a focus). This chain of concepts, from the most generic to implementation techniques curves as in this case, allow its assimilation and use by facilitating cross-learning, ultimate goal of knowledge.
  • The notions of similarity for understanding the concepts of scale, particularly as the dilation transformation, will differentiate the geometric shape of size, allowing to make transformations that preserve the appearance of the object. Investment, however, while retaining the angular relationships, will be presented as a transformation that will address, as tool, Different problems incidence.

From the spatial point of view, parallel study of the different systems of representation can allow generalized treatment, simplifying their assimilation,

  • So, incidence problems (intersection) can be generalized regardless of the system used in its representation.
  • Measurement concepts (euclídea) cylindrical systems differentiate (orthogonal and oblique) of the conical.
  • Projective transactions (turns and glooms) may be related to geometric transformations (Affinities) to be so purely spatial.

Analysis of these diversities help geometric construct a mental model in our students, avoiding the memorization of isolated buildings and facilitating the exercise of geometric reasoning supported by the graphic constructions.

José Juan Aliaga Maraver, professor at the Polytechnic University of Madrid, main coordinator for Technical Drawing II tests.