In light of Vygotsky’s developmental theory, discuss Gal\'perin\'s program (syst

Question

In light of Vygotsky’s developmental theory, discuss Gal'perin's program (systemic-theoretical instruction) for elementary math. Specifically, explain: (1) How children learned the concept of number as a tool for measurement. (2) In what way was that experimental instructional design successful in helping children advance their logico-mathematical thinking? Explain how a genuine concept of number mediates children's thinking and helps them overcome ‘preoperational’ ways of thinking (e.g., about the properties and magnitudes of objects). (3) What does that type of instruction say about Piaget's assumptions that logico-mathematical thinking develops spontaneously and does not benefit from social transmission? (4) How is the relationship between teaching-learning and development conceptualized and operationalized in Gal'perin's approach? In what way does systemic-theoretical instruction (teaching-learning) lead to developmental changes (i.e., development of mental processes and functions)? (5) Explain how systemic-theoretical instruction avoids stark opposition between transmission of knowledge versus spontaneous discovery and invention of knowledge? How can knowledge be an effective, empowering tool?

Explanation / Answer

Within this program children are taught such fundamental concepts as that of number. Traditional instruction often fails to enable children to form genuine mathematical concepts. For example, numbers are often empirically introduced as single discrete objects (i.e., one stands for 'one pen', two for 'two apples' etc.) without any further explanation. Children are taught that 'one' (object) is one, not two or more, and this is something to memorize, accept ,and follow. The logic and function of the concept of number -- that is, how and why numbers have evolved in human practices -- is not revealed. As a result, children tend to confuse mathematical numbers with discrete objects.

In general, as in the teaching of elementary mathematics, this program has resulted in a spectacular cognitive-developmental change, in that children advance from a naïve-empirical way of thinking to one that is theoretical. Importantly, the systemic-theoretical teaching in these and many similar programs leads to substantial progress not just in children's knowledge but also in their wider cognitive functioning. In particular, significant improvements occur in children's abilities to analyze, plan, and reflect upon their actions, to set goals and systematically control how they are attained, as well as in their memory and even in their imagination. No less significant is that trial-and-error learning, so typical of traditional instruction, becomes rare and incidental, and also that the time it takes children to learn new knowledge or skills significantly decreases.

This element concerns the 'cultural tools' provided by teachers and learned by children in the course of instruction, thereby inducing activities that can be transformed and internalized into powerful instruments of mind. These new instruments provoke development, in the full sense, as they empower learners to become active explorers and thinkers. Thus, the development of the human mind is seen not as a process separate from teaching and learning, but as part of a system that encompasses all three activities. In this sense, Gal'perin's approach fills the gaps so typical of previous frameworks in both psychology and education. It also allows us to understand what lies behind developmental change and thus adds greater specificity to Vygotsky's insight that development is driven by teaching-and-learning. Ultimately, it is in this sense that Gal'perin's theory is a contribution simultaneously to developmental psychology and to education.

Students learn to distinguish essential features and to base their further actions and thinking on them. Specifically, form of analysis includes a) discriminating between different properties of an object or phenomenon, b) establishing the basic units to analyze a particular property, and c) revealing the general rules (common to all objects in the studied area) whereby those units are combined into concrete phenomena. The method makes extensive use of symbolic and graphic models to represent basic relations between different properties of the object.

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