M1 – Week 5


In class today (11/10/16)…


Later in the week…

Here is the text I prepared, as required, on a single A4 page for Week 5 of the Learning Theories module on 11th October 2016:

Learning Theories Module – Paper 1 (Work-in-Progress Presentation)

Van Hiele Model – A theory that describes how students learn geometry

by Gerard Kilkenny

00 – Introduction (300 Words)

The purpose of this paper is to examine how the van Hiele model can be used as a framework in the teaching and learning of geometry to Junior Cycle Maths students.  It goes on to explore how elements of the classical learning theories of cognitivism and constructivism are embedded in the van Hiele theory.  In particular, it provides a comparative analysis of the Van Hiele model wih the theoretical learning frameworks of Gagne, Piaget, Bruner and Vygotsky.  The concluding section discusses possible implications of the Van Hiele model for eLearning design.

10 – Van Hiele Model (The 5 Levels) (480 Words)

Level 1 (Visualisation), Level 2 (Analysis) Level 3 (Abstraction), Level 4 (Deduction), Level 5 (Rigour).

20 – Van Hiele Model (The 4 Properties) (110 Words)

Property 1 (Fixed Sequence), Property 2 (Adjacency), Property 3 (Distinction), Property 4 (Separation).

30 – Van Hiele Model (The 5 Phases) (180 Words)

Phase 1 (Inquiry), Phase 2 (Directed Orientation), Phase 3 (Explanation), Phase 4 (Free Orientation), Phase 5 (Integration)

40 – The Gagne Van Hiele Connection

Gagné et al (1992, p.44) list “verbal information” as one of the “five kinds of learned capabilities” (R-40, p.44) and this can perhaps be mapped to van Hiele’s Level 0 where “the student can learn names of figures…” (Usiskin, 1982, p.4).  Similarly, the capability of identifying the diagonal of a rectangle is provided as an example of the capability “intellectual skill” by Gagné et al (1992, p.44) (R-40, p.44) which appears to have it’s equivalent in van Hiele’s Level 1 where students can understand that “rectangles have four right angles” (Hoffer, 1979, 1981) or that a rectangle “has two equal diagonals” (The Project Maths Development Team, 2014, p.32).

50 – Van Hiele and Piaget

Piaget (1953) (R-50) argues that children do not enter the formal operational stage until they are 14 years of age and that they cannot learn formal proofs before this period. Van Hiele (1985) (R-51) describes similar properties in his penultimate geometric level deduction although he does not specify which age pupils reach this level.  In Irish secondary schools, students generally don’t study formal proofs in geometry until second or third year when they are approximately 14 years old.  (R-04)

60 – Van Hiele, Vygotsky and Bruner

Van Hiele questioned the notions of growth being linked with biological maturation. Instead, in ways that have much in common with Vygotsky (1978), he saw development in terms of students’ confrontation with the cultural environment, their own exploration, and their reaction to a guided learning process. (p.112)

70 – Neuroscience and Teaching

What can neuroscience teach us about teaching? (Dr. William O’Connor)


80 – Implications for ICT and Instructional Design

Book (Principles of Instructional Design), Book (Michael Allen’s Guide to e-Learning) Software (GeoGebra).

Key References

Curran, S. (2014). Is The Van Hiele Model Useful in Determining How Children Learn Geometry? Munich: GRIN.

Gagné, R. M., Briggs, L. J., & Wager, W. W. (1992). Principles of Instructional Design. Fort Worth: Harcourt.

Piaget, J. (1953). The Origin of Intelligence in the Child. London: Routledge and Kegan Paul.

Project Maths Development Team (2015). Teacher Handbook First Year. Retrieved September 25, 2016, from  http://www.projectmaths.ie/documents/handbooks/firstyearhandbook2015.pdf

Usiskin, Z (1982). Van Hiele Levels and Achievement in Secondary School Geometry.  University of Chicago

Yazdani, M. A. (2008).  The Gagne – van Hieles Connection: A Comparative Analysis of Two Theoretical Learning Frameworks.  Journal of Mathematical Sciences & Mathematics Education, 3(1), 58-63.