Conjectures Through Graphing: Video Analysis

The use of socio-cultural theory in education was introduced by Lev Vygotsky, a Russian psychologist who was also the founder of the theory. In socio-cultural theory, he explored broad interdependence between social and individual learning processes (Ormrod, 2011). Lev Vygotsky postulated that the observed step-by-step changes which occur in children’s behavior and thinking during development are derived from social interaction. Besides, extent of the changes varies across different cultures (Ormrod, 2011). Ormrod (2011) expounds that Vygotsky’s theory can be interpreted as combination of cognition and social environment owing to the fact that he explored development of children in terms of thinking and behavior. He argued that the latter are acquired from interacting with a more knowledgeable people whom learners can desire to emulate. Hence, children who belong in this stage of development perceive a skilled and competent person as role model from which they can acquire thinking and behavioral patterns that are culturally specific (Ormrod, 2011).

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The socio-cultural theory is rooted in three basic assumptions. The most basic of these assumptions is that children acquire learning through social interaction with people as well as tools present in a specific culture. Cultural specific tools contribute positively to a child’s perceptual view of the world as they provide the much needed foundation for cognitive development. Ormrod (2011) postulates that the cultural tools highlighted in the theory are transferable from one person to another via three different paths. The first mode of transfer is through imitation whereby learners tend to copy their peers who are perceived to be more knowledgeable in certain tasks (Ormrod, 2011). The second mode is whereby instructional learning is used to acquire knowledge. According to this mode, learners are given chance to listen and later recall instructions as given by the teacher. They are then supposed to apply the given instructions as part of developing into self-regulated learners. Finally, these tools can also be passed to other via collaborative learning. Ormrod (2011) exemplifies that collaborative learning is achieved when peers come together in a group. They embrace mutual understanding by working together towards acquiring specific skills.

The second assumption is based on what Vygotsky referred to as Zone of proximal development (ZPD). According to Ormrod (2011), ZPD is the assumption that a child’s potential of cognitive development depends on development of this zone. ZPD mainly refers to the highest level of learning that a child attains as a result of participating in social interaction. When such a child is well exposed to social interaction, full ZPD development is attained and vice versa. The assumption is that children achieve a lot through interacting with peers as well as being guided by adults. The aforementioned practices have been found to accelerate development of skills of such a learner contrary to a child who has been brought up in isolation. For ZPD to be successful, two key features have to be present. The first is what Ormrod (2011) calls subjectivity. It is a situation whereby at beginning of learning session, each learner has a different understanding of the task, however, sharing of information eventually leads to a shared understanding. The second feature is scaffolding, where a leaner attains higher levels of cognitive development through interaction with adults, peers and teachers, who helps them fill gaps in problem solving and thinking (Ormrod, 2011). However, high levels of ZPD can only be developed if a learner actively participates in learning process.

Videos analysis: Application of socio-cultural theory

In Mr. Cabana’s class, several elements of socio-cultural theory can be observed. In Conjectures through Graphing (n.d) video, Mr. Cabana conducts the session in the form of group discussion. The arrangement can be aligned with the theory which asserts that learning occurs in a well enhanced social environment (Ormrod, 2011). The social setting observed usually lay foundation for cultural tools to be transferred. From the video, the cultural tool in question is the previously acquired knowledge in Algebra that the students use in calculus class to complete the task at hand. The cultural path being used by Mr. Cabana to transfer the cited tool is referred to as collaborative learning (Ormrod, 2011). His students in their respective groups work together to come to come with the derivative function. Each of the students contribute to the discussion based on their understanding of Algebra which eventually leads to mutual understanding whereby students acquire the much needed skills in Calculus (Conjectures Through Graphing, n.d; Ormrod, 2011).

Mr. Cabana also exploits the element of ZPD to advance awareness among his students. From Conjectures Through Graphing (n.d) video, both subjectivity and scaffolding elements of ZPD as postulated by Ormrod (2011) are present. To begin with, at the beginning of the group discussion, it is evident that each group has different understanding of the task. However, the teacher creates a mutual understanding when he pin-points one student to explain the concept to the rest. On the other hand, scaffolding is evident when the teacher goes round answering questions and assisting the group members where they are stuck (Conjectures Through Graphing, n.d). Likewise, students themselves support each other when one does not understand what the task entails. Mr. Cabana goal is to engage higher level of ZPD among his students as exemplified in the theory. Vygotsky recommends that a teacher should give his/her students tasks that stimulate high level of thinking to make them achieve their highest level of potential (Omrod, 2011).

Lesson redesign

Mr. Cabana can apply the cultural tool of instructed learning by evaluating whether learners have attained self-regulation. As noted above, he has successfully used imitation and collaborative learning to transfer cultural tool (Calculus skills). He can give his students another task whereby they are required to derive the same formula using a different perspective. Since he has already directed them on how to derive equation, he should only offer limited assistance until he is satisfied with their responses.

In addition, the theory asserts that students ZPD level varies from one individual to another (Ormrod, 2011). Therefore, he can find a way to establish whether each student has fully comprehended the concept. After identification, he can assign such a student to the peer who is more knowledgeable to lead in problem solving.

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Finally, in order to evaluate mutual understating among his students, he can possibly call another student forward to demonstrate how the group arrived at the solution. The technique will help Mr. Cabana to identify any disagreement that might hinder understanding.


To recap it all, Mr. Cabana in Conjectures Through Graphing (n.d) video utilizes several elements of socio-cultural theory in teaching his students how to go about mathematical problems in calculus. His techniques are well aligned with the theory since he utilizes collaborative learning alongside exploiting the elements of ZPD to make his students reach their full potential.


Conjectures Through Graphing (n.d). Web.

Ormrod, J. E. (2011). Educational Psychology: Developing Learners (7th edition). Upper Saddle River, NJ: Pearson.

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