Setting an object of knowledge in motion through Davydov’s learning activity
Paper in a Symposium (Symp)
4:50 PM, Tuesday 29 Aug 2017 (30 minutes)
Convention Center - 205 B
In this study, we discuss learning activity as an educational tool to enhance the goal of setting an object of knowledge in motion and thus developing students’ theoretical thinking. Radford has argued that In order for an object of knowledge to become an object of thought and consciousness, it has to be set in motion. It has to acquire cultural determinations; that is, it has to acquire content and connections in process of contrast with other things, thereby becoming more and more concrete. And the only manner by which concepts can acquire cultural determinations is through specific activities (Radford, 2015 p. 10-11). We are particularly interested in presenting some results about the motion of objects from a study based on the so-called Elkonin-Davydov mathematical program and learning activity. The aim of the study was to make students experience rational numbers as numbers through measuring lengths. In the study, two groups of teachers tried to find ways to explore rational numbers in five groups of Grade 4 students, aged 8 to 10 years old, in a Swedish compulsory school. As the initial step, a problematic situation was introduced to the students. The situation was designed to be transformed by the students into a learning activity (Davydov, 2008; Zuckerman, 2007). They were given a length (e.g., a black Cuisenaire rod) and a smaller length to use as units of measure (e.g., a red Cuisenaire rod), but making the black rod have an equal length with red rods was not possible. This problematic situation can be described as a double stimulation in which known methods and tools are experienced by the students as insufficient (i.e., they could not choose other rods). To overcome the problem built into the situation, the students need to find a new method or model (Sannino, 2014; Vygotsky, 1987). This type of need is central to Davydov’s model and is seen as a source of students’ engagement in a problem-solving work. In a situation like this the students may ask themselves questions such as: What problem do we need to solve? What tools do we have access to? What problem is related to the tools and models we know? What type of model can we design that will help us solve the problem? How can we explore and test different models? How efficient is the new model? If the students engage in a type of work like this, according to Davydov, a learning activity is established. In what ways can this also be understood as “a specific activity,” in which an object of knowledge is set in motion? In this specific activity, the students and the teacher discussed the object of knowledge by developing a model for rational numbers, inspired by the work of Davydov and TSvetkovich (1991). This model evolved from a discussion of the fraction part in a mixed number as “a little bit more” (represented as B = W + “a little bit more”) to a general model represented as B = W + p/w (B for a black Cuisenaire rod, W for the whole part, p for part, and w for the white Cuisenaire rod in the fraction part). From this general model the students wanted the model to be changed the specific measurement: B = W red + p/w red. The model started in the general and became more and more concrete. In this study, we argue that when the students realize that “a little bit more” of the red rods is needed, the development of a possible model emerged (H. Eriksson, 2015). The model of rational numbers was developed through the collaboration between students and the teacher. The results show that the students, together with their teacher, discussed 1) the whole in relation to the parts, 2) the units in relation to the object to be measured, 3) whole numbers in relation to fractions, 4) the numerator in relation to the denominator, 5) the smaller unit in relation to the units, 6) entities in relation to units, 7) rational numbers in relation to x and x+1, and 8) the indefinite integers in relation to the indefinite rational numbers.