Lev Vygotsky

Lev Vygotsky focused on a social constructivist theory of learning.  He emphasized the social contexts of learning and also showed that social interaction aids in the construction of knowledge (Gauvain, 2011).  Vygotsky's approach stresses the importance of students working with the teacher and peers to discover knowledge and explore their possibilities.  Vygotsky's theory includes the idea of students possessing a zone of proximal development (ZPD).  This zone contains all of the tasks that a student cannot accomplish yet, but will be able to achieve on their own after the assistance of a peer or teacher.  Vygotsky also believes in the idea of scaffolding knowledge.  This basically means that teachers build the scaffolds for knowledge to be constructed and aid the students in the construction, but then we slowly take away the scaffolding until the new knowledge is able to stand alone.  Teachers remove scaffolding by allowing the students to work with progressively less aid from the teacher after having been taught about the subject.  One method to remove scaffolding on students is through group work. By carefully constructing groups such that students of varying ZPDs are working together on a task, the teacher allows students to work to remove the scaffold by working in a social environment with their peers. (Daniels, 2011).

A possible task in geometry for this would be to ask the students to develop the formula of a trapezoid.  Students will also be broken into carefully crafted groups.  Each group will consist of students at varying places in their ZPD so that the students who understand more about geometric relationships can help the students who cannot see a method with which to work.  I will craft these groups by assessing their previous understanding of area formulas and place students of high understanding with those of lower understanding.  Most students will already know that the area of a trapezoid can be found by multiplying the height by the sum of the lengths of the bases and then dividing the entire thing by two; however, students may struggle to identify why this formula works.  There are over a hundred different ways to derive this formula; however, most students will realize that they can split the trapezoid into two triangles and add the areas of these together (2.5).  If I asked the students to find the formula after doing a section on the area of different shapes or after showing how to find the area of a parallelogram, then I would have successfully put up the scaffolding for the students.  I would have given them the general idea, but then, by enabling them to work in groups to find the area formula for a trapezoid, the other group members will be removing the support from each other and allow them to show that their knowledge stands alone.  Some students will be able to figure the area out on their own quickly, but other students will be in a lower ZPD and need the support from them to figure out what operations to perform once they have figured out how to divide the trapezoid into triangles.