...achieving meaningful learning. This paper reflects the outcome of research project undertaken at Universidad Nacional Experimental del Tachira (UNET), Venezuela, investigating different ways teacher and students may use concept mapping in physics. This paper hopes to engage educators on a discussion of this important issue and will focus on answering the following questions: What are Concept Maps? How are they constructed? What is the theory that supports Concept Maps? What are they used for? How can they be used with large groups of university students to facilitate the teaching-learning process? According to our experience, there are some possibilities to use Concept Maps in physics courses. Although we have faced difficulties in building individual concept maps with large groups of students, we are convinced that Concept Maps help to improve understanding of a given subject and facilitate building student's own knowledge, as long as the student has the opportunity to use, criticize, analyze, question or improve expert's maps or Concept Maps generated by his own peers.

Introduction

Many students at the Universidad Nacional del Tachira face difficulties in science learning. They find it hard to understand a whole body of information and to build their own knowledge about complex conceptual structures. They also find it difficult to link concepts and handle adequate representational techniques either to show or sum up information.

To help solve these problems we have found in Concept Maps a powerful help that facilitates students comprehension of physics at university level. Convinced of its advantages, we want to report our experiences hoping math teachers who have never worked before with Concept Maps may get involved and begin to use them with their students.

This paper is organized to answer, from our perspective, the following questions: What is a Concept Map? How is it constructed? What is its theoretical background? What are they used for? And finally, what strategies involving Concept Maps can be used with university students?

What is a Concept Map?

The first difficulty someone who attempts to comprehend a text faces is to understand what it is all about. That is, to grasp the global sense of the communication, understand its elements and the relationships among them. Imagine a student seeking information about frame of references finds the following text:

A Cartesian frame of reference is a set of two elements: a Cartesian, linear coordinate system and a clock used to measure time. Cartesian coordinates are rectilinear two-dimensional or three-dimensional coordinates which are also called rectangular coordinates. The three spatial axes of three-dimensional Cartesian coordinates conventionally denoted the x, y, and z-axes, are chosen to be linear and mutually perpendicular. Frames of references are used to describe and analyze motion in one, two or three dimensions (using one two or three oriented axes).

The student may understand some of the concepts involved in this definition. These concepts are linked by words forming whole sentences that seem to make sense. However, trying to understand the overall conceptual structure is more difficult. In our introductory physics courses at university level, it is a commonplace that there is no difference between a Cartesian frame of reference system and a Cartesian, linear coordinate system. Students that read carefully may notice that the two concepts are different. Moreover, one of them is included in the other.

Let the same information be presented in a different way (Figure 1).

It is probably easier for many students to grasp a whole sense of the concept frame of reference when faced with a graph like the one shown above. This is due to the powerful visual effect that a graph has in order to facilitate understanding of a concept or a conceptual structure.

[FIGURE 1 OMITTED]

This graphic is essentially a concept map. It is a map-like illustration that shows meaningful relationships between concepts (events, objects). Observe that this is a knowledge representation about a particular main idea (in this case: frame of reference), in the form of a graph comprised of boxes connected with labeled lines. Words or phrases that denote concepts (events, objects) are placed inside the boxes, and relationships between different concepts are specified on each line. Propositions (node-link-node triads) are a unique feature of concept maps, compared to other graphs. Propositions consist of two or more concept labels connected by a linking relationship that forms a semantic unit (Novak & Gowin, 1988).

And you may feel reading the above paragraph, if not familiar with concept maps, exactly as may have felt the student who saw for the first time the text about frame of reference: lost in the dark. That is, you may know some of the concepts mentioned before as separate entities but have no clear relationships among some of them. Obviously this makes difficult to understand the whole conceptual structure concept map. Let us then discuss some of the concepts involved in this definition: object, event, concept, proposition and meaningful relationships, to be able to understand what a concept map is.

Novak says the construction of new knowledge begins with the understanding of the terms event and object (Novak & Gowin, 1988). We represent event in Figure 2.

[FIGURE 2 OMITTED]

And also we may explain, following Novak's definition, what an object is in Figure 3.

[FIGURE 3 OMITTED]

Now that we understand what objects and events are, we can define concepts as perceived regularities in events and objects, or records of events or objects, designated by a label (Novak & Gowin, 1988). Also, concepts are mental representation of objects or events with the following characteristics: a) correspondence among the concept and what it represents, b) absence of ambiguity and c) optimal use of the language involved. In concept mapping, concepts are usually written inside cells or boxes. Today you may design cells as you like. The important thing is that the graph highlights concepts visually in a clear and distinctive way.

But concepts are not isolated in a Concept Map. They are connected by labeled lines or arrows called links which consist of words, phrases or verbs that explain meaningful relationships between concepts by words or signs/symbols. Arrows, if used, designate the directionality of the relationship. Otherwise, the concepts must be arranged in a hierarchical way, from the most abstract and inclusive concepts on the top of the graph to the most concrete and specific, and it is assumed that the direction of the relationship is downward. This facilitates the reading of concepts and the links among them as whole sentences.

Relationships among concepts are diverse as seen in Figure 4.

[FIGURE 4 OMITTED]

Canas, Safayeni and Derbentseva (2004) classify them as static or dynamic relationships. Static relationships between concepts help to define, describe and organize knowledge for a given domain. Classifications and hierarchies are usually captured in relationships...

NOTE: All illustrations and photos have been removed from this article.



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