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
Otten – SME 954
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).