Otten – SME 954

Norton, A., & D’Ambrosio, B. S. (2008). ZPC and ZPD: Zones of teaching and learning. Journal for Research in Mathematics Education, 39, 220-246.

Research Questions:

  • What are the pragmatic differences between the zone of proximal development (ZPD) and the zone of potential construction (ZPC)?
  • What aspects of ZPD and teacher assistance promote the development of mathematical concepts?
  • Secondarily, when does a teacher’s assistance generate meaningless habits and when does it promote development? (p. 221)

The overall approach of this study is qualitative. It is essentially a semester-long “teaching experiment” based on interactions with student pairs. The student interactions were observed a video-recorded, and analyses of these interactions were used to plan subsequent activities.

The questions originated in the prevalence of the constructivism philosophy in mathematics education and the need to bring two related schools—social constructivism and radical constructivism—into dialogue with one another, especially with regard to the practical implications of their respective ZPD and ZPC constructs.

In terms of theoretical frameworks, Norton and D’Ambrosio (2008) is an interesting article because it attempted to transcend two particular theoretical frameworks for the purpose of comparing and contrasting their instructional implications. In other words, this article tried to detach itself from both frames and look on them objectively. However, I would still say that the piece has a broad constructivist perspective overall and a worldview that values qualitative methods.

The two theoretical frameworks that are alluded to above are social constructivism and its zone of proximal development (ZPD), and radical constructivism and its zone of potential construction (ZPC). The former is marked by an assumption that knowledge exists in society and is constructed within the mind of a student as that student is guided (not over-guided, but slightly guided) through problems that they could not have solved on their own. The latter posits the beginning of all knowledge in the minds of individuals, and the ZPC refers to the “potential reorganizations” (p. 222) of this knowledge in the mind of the student.

Based on the student protocols and analyses with regard to ZPD and ZPC, Norton and D’Ambrosio concluded that interactions alone do not sufficiently explain the student knowledge constructions; the existing constructions of the students must be taken into account. The development of one student in particular, who lacked the operational schemes of another student, did not progress substantially until the teacher worked within his ZPD and ZPC. A primary result of this study was the evidence indicating that assumptions behind the past work of others (i.e., the neo-Vygotskians who posit that teachers should provide the goals for learning and make “mathematics less problematic for their students,” p. 244) were flawed. Instead, they must pay greater attention to the “objects and operations that might exist on the internal planes” of students (p. 245).