La Generación de Conocimiento en Castilla y León

The significance of “active learning” is being promoted by researchers in education for many decades. As Laurillard (2006) put it,

“Whatever their original disciplines, the most eminent writers on learning have emphasized the importance of active learning. The choice of language may vary:

• Dewey’s inquiry-based education

• Piaget’s constructivism

• Vygotsky’s social constructivism

• Bruner’s discovery learning

• Pask’s conversation theory

• Schank’s problem-based learning

• Marton’s deep learning

• Lave’s socio-cultural learning

but the shared essence is the recognition that learning concerns what the learner is

doing, rather than what the teacher is doing, and the promotion of active learning in a social context should be the focus of our design of the teaching-learning process”

(Laurillard 2006, p. 73).

As mentioned in Chapter 2, Piaget’s constructivism emphasizes that the learner needs to construct their own knowledge based on their previous knowledge. Ackermann expresses a more radical approach,

“To a constructivist, knowledge is not a mere commodity to be transmitted – emitted at one end, encoded, stored, and reapplied at the other– nor is it information, sitting ‘out there’ and waiting to be uncovered. Instead, knowledge is (derived from) experience, and actively constructed and re-constructed by subjects in interaction with their worlds” (Ackermann 2007, p. 149).

In addition to constructivism, Vygotsky (1978) emphasises the impact of society and language in knowledge acquisition. He stresses that learning is possible only if the new knowledge is apprehensible with relevant social support. In Shank’s problem-based learning, students were given relevant problems in the subject domain that they need to

try to solve with the aid of mentors and peers. Constructionism, an instructional theory invented by Papert, suggests that in order to construct knowledge learners should engage in some sort of meaningful creational activity. While comparing Piaget’s constructivism and Papert’s constructionism, Ackemann put it,

“Because of his focus on learning through making (on could say learning as design) Papert’s “Constructionism” sheds light on how people’s ideas get formed

and transformed when expressed through different media, when actualized in particular contexts, when worked out by individual minds. The emphasis has shifted from general laws of development to individuals’ conversation with their own representations, artifacts, or objects-to-think with” (Ackermann 2004).

She further adds “Unlike Piaget, Papert thinks that “diving into” situations rather than looking at them from a distance, that connectedness rather than separation, are powerful means of gaining understanding. Becoming one with the phenomenon under study, in other words, is a key to learning.” (ibid, p. 20).

An instructional strategy called Problem Transformation is a special kind of constructionist approach which encourages students to actively involve in creating relevant new artefacts by systematically transforming some existing artefacts. The next section describes this approach in detail.

4.2.1 Problem Transformation

Traditionally, instructors use analogies and metaphors for teaching complex concepts. Problem transformation is a particular kind of constructional approach wherein the learners are encouraged to create some material based on existing materials, or to systematically transform some artefacts from one representation (source) to another one (destination), or to transfer a given problem into an alternative form (Kemp et al. 2001).

The source and the destination may have the same, or different, levels of complexity. In any case, the transformation process should involve a significant constructive task; it should be challenging and motivational and within the learner’s cognitive ability. If the transformation process involves complex cognitive skills, the scaffolding technique may be used. The topic to be learned may be the source discipline, or destination discipline, or the transformation-process itself. Similar to the other constructionist learning approaches,

learners actively in the relevant knowledge building process. Moreover, as the transformation involves some pre-existing model, learners are brought into the relevant context fairly quickly. This is an additional advantage based on constructivist learning theory.

There is very little theoretical knowledge in this specific stance, and also there are only a few empirical studies have been reported in the literature. Some examples for different types of problem transformation approaches (particularly used in learning systems for programming and formal methods) will be given next.

Some Example Systems

In ZAD/ZEL (Morrey et al. 1993), transformation of specifications from a formal

notation to computer program is utilized. ZAD/ZAL aims at teaching the source discipline- formal methods. Though scaffolding is not used explicitly, the transformation process is partially automated and the animation process is hidden from the learner. Also, in MEMO-II (Forcheri et al. 1994) transformation from a formal notation to a computer

program is used for instruction. Similar to ZAD/ZAL, the transformation process is partially automated. However, MEMO-II aims at teaching the destination discipline- computer programming.

Sun et al. (2001) describe a system that converts Object-Z specification to UML models,

which they claim could be used for teaching semantics of both Z and Object-Z. This system aims at teaching both source and destination disciplines. The system transforms a model from a complex domain to a less complex domain. A software development process may follow the following order: informal specification (text) Æ semi-formal specification (UML) Æ formal- specification (Object-Z) Æ code (Java). Usually, more information will be added to the model during the transition. However, during backward transformation some potential information may be lost.

Kemp et al. (2001) describe various examples of this approach. A concrete recent

example is Leopard Tutor (Kemp et al. 2003). It is a visual supportive environment that

programming concepts. Basically, learners are encouraged to create class diagrams from computer programs to learn the fundamentals of object-oriented computer programming. Similar to ZAD/ZAL, Leopard Tutor is also designed to learn the source discipline. Leopard Tutor, like Sun et al.’s system (2001), uses backward transformation. However,

unlike ZAD/ZAL – where the system does much of the transformation process Leopard enforces active learning by encouraging the learners to perform the whole transformation process (although some support is given). Both, understanding a solution of a problem and designing a solution to a problem involves different but related cognitive skills. Leopard Tutor, the authors claim, is designed to bridge such gaps in object oriented programming. In the 2003 version, learners are asked to create relevant class diagrams from the given Java code (and comments). Comments are used to build the semantic meaning of the program (the authors call this a task level class diagram).

In this study, students will be engaged in transforming UML models to Object-Z specifications. UML is a graphical semi-formal notation, and Object-Z specification includes complex mathematical notation. Transforming UML to Object-Z is a significantly challenging process. The next section outlines the current state of the research related to this transformation process.