MIP2601 Assignment 1 (601617)|COMPREHENSIVE DOCUMENT| - DUE 13 MAY 2026

MIP2601
Assignment 1
Unique NO: 601617

DUE: 13 MAY 2026

,MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics




UNIVERSITY OF SOUTH AFRICA
Department of Mathematics Education




ASSIGNMENT 1
MIP2601 – Mathematics for Intermediate Phase Teachers III

UNDERSTANDING AND APPLYING THE VAN HIELE FRAMEWORK

IN INTERMEDIATE PHASE MATHEMATICS EDUCATION




Student Name: ___________________________
Student Number: ___________________________
Module: MIP2601
Unique Assignment No.: 601617
Due Date: 13 May 2026
Lecturer: Dr PD Motseki




University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 1

,MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics



STUDENT DECLARATION


I, the undersigned, declare that:

1. I understand what plagiarism entails and am aware of the University's policy in

this regard.

2. This assignment is my own, original work. Where I used someone else's work,

whether a printed source, the internet or any other source, I give the proper

acknowledgement and include a complete reference list.

3. I did not use another current or previous student's work, submitting it as my

own.

4. I did not allow and will not allow anyone to copy my work with the intention of

submitting it as his or her own work.



Full Name: _______________________________________________


Student Number: _________________________________________


Signature: ______________________________________________


Date: ___________________________________________________




University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 2

,MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics



Table of Contents
STUDENT DECLARATION ........................................................................................ 2
SECTION A: Conceptual Understanding of the Van Hiele Framework ...................... 5
A.1 Origin and Historical Background of the Van Hiele Theory .............................. 5
A.2 Key Ideas of the Van Hiele Theory ................................................................... 6
A.3 The Five Van Hiele Levels with Detailed Examples ......................................... 7
Level 0: Visualisation .......................................................................................... 7
Level 1: Analysis ................................................................................................. 8
Level 2: Informal Deduction ................................................................................ 8
Level 3: Formal Deduction .................................................................................. 8
Level 4: Rigor ...................................................................................................... 9
A.4 Visual Representation: The Van Hiele Levels as a Staircase ........................... 9
SECTION B: Diagnostic Task Analysis .................................................................... 11
B.1 Design of the Diagnostic Assessment ............................................................ 11
Full Diagnostic Tasks (As Given to Learners) ................................................... 12
B.2 Interpreting Learner Responses ..................................................................... 13
SECTION C: Lesson Design and Application ........................................................... 15
C.1 Lesson Plan 1 – Van Hiele Level 0: Visualisation (Grade 4) .......................... 15
Phase 1: Introduction / Motivation (10 minutes) ................................................ 15
Phase 2: Teaching Activity – Shape Hunt and Sort (25 minutes) ...................... 16
Phase 3: Class Discussion and Shape Gallery (15 minutes) ............................ 16
Phase 4: Assessment (10 minutes) ................................................................... 17
C.2 Lesson Plan 2 – Van Hiele Level 2: Informal Deduction (Grade 6) ................ 18
Phase 1: Review and Activation (10 minutes) ................................................... 18
Phase 2: The Quadrilateral Hierarchy Challenge (25 minutes) ......................... 18
Phase 3: Gallery Walk and Peer Assessment (15 minutes) .............................. 19
Phase 4: Assessment Task (10 minutes) .......................................................... 20
SECTION D: Curriculum Integration – Van Hiele Theory and CAPS ....................... 22
D.1 The CAPS Geometry Curriculum in the Intermediate Phase ......................... 22
D.2 CAPS Alignment with Van Hiele Levels ......................................................... 22
D.3 Scaffolding Geometry Teaching Using the Van Hiele Framework.................. 23
1. Level-Appropriate Language and Questioning .............................................. 23
2. Concrete–Representational–Abstract (CRA) Progression ............................ 24
3. Collaborative and Inquiry-Based Learning .................................................... 24
D.4 Identifying Missed Opportunities in Current Practice ...................................... 24
SECTION E: Reflective Commentary ....................................................................... 26
E.1 Reflecting on My Own Understanding of Geometry ....................................... 26


University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 3

, MIP2601 – Assignment 1 | Van Hiele Framework in Intermediate Phase Mathematics



E.2 How the Van Hiele Framework Has Influenced My Teaching Approach ........ 26
E.3 Challenges and Areas for Further Growth ...................................................... 27
E.4 The Van Hiele Framework as a Lifelong Teaching Tool ................................. 28
REFERENCE LIST................................................................................................... 29




University of South Africa – Department of Mathematics Education | Unique No: 601617 | Page 4