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TMS3725 Assignment 2 (COMPLETE ANSWERS) Semester 1 2025 - DUE 18 June 2025; 100% correct solutions and explanations.

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TMS3725 Assignment 2 (COMPLETE ANSWERS) Semester 1 2025 - DUE 18 June 2025; 100% correct solutions and explanations. Questions from Tutorial Letter 501. Instructions for Assignments 02 Before attempting to do Assignment 03, you must read through units 1 to 6 of TMS3725. Ensure that you read and understand each section of these units. You may work with your peers when reading and discussing the work presented in units 1 to 6, but you are expected to present your assignments as your own work (individually attempted or written work). Copying from other students is not allowed. Students submitting identical copies of the assignments will be penalized severely. Before uploading your assignment, please ensure that you have completed and attached the honesty declaration form. [NB. Copying from the study guide and other materials is prohibited] QUESTION 1 [39] 1.1. Describe the theory of constructivism developed by Jean Piaget. (8) 1.2. Describe two general principles of constructivism that are largely based on Jean Piaget's principles. (6) 1.3 Rote learning is a construction, but the tools or ideas used for the construction of knowledge in rote learning are minimal. Name the weaknesses of the rote-learning approach. (6) 1.3 Van de Walle provides seven effective suggestions to empower mathematics teachers to teach developmentally. Name them. 1.4 Teachers write lesson plans to help them structure the envisaged learning for both them and their learners. Discuss how these lesson plans assist teachers in the (7) teaching and learning of Mathematics by providing six valid arguments. (12) [39] QUESTION 2 [29] 1.1 What is meant by a problem-centred approach in the teaching and learning of mathematics? Give a problem in FET Mathematics and indicate the teacher’s role in using a problem-centred approach. (6) 1.2 Given the exponential equation 10(

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,TMS3725 Assignment 2 (COMPLETE ANSWERS)
Semester 1 2025 - DUE 18 June 2025; 100% correct
solutions and explanations.
QUESTION 1


1.1 Describe the theory of constructivism developed by Jean
Piaget. (8)
Jean Piaget’s constructivist theory holds that children actively
construct their own understanding of the world through
interaction and cognition. Its key tenets are:
1. Stages of Cognitive Development
o Sensorimotor (0–2 years): Knowledge emerges

through physical interaction (e.g. object permanence).
o Preoperational (2–7 years): Symbolic thinking

develops (language, pretend play), but thinking is still
egocentric and intuitive.
o Concrete Operational (7–11 years): Logical

reasoning about concrete events appears; children
grasp conservation, classification, serial ordering.
o Formal Operational (11 years+): Abstract and

hypothetical thinking emerge, enabling systematic
problem‐solving.
2. Schemas
– Mental “building blocks” or frameworks that organize
experiences. Schemas evolve as children assimilate new
information into existing schemas or accommodate
schemas to fit new information.

, 3. Assimilation & Accommodation
– Assimilation: Integrating new experiences into existing
schemas (e.g. calling every four‐legged animal “dog”).
– Accommodation: Adjusting schemas when new
information cannot fit (e.g. distinguishing “cat” from
“dog”).
4. Equilibration
– A self-regulatory process balancing assimilation and
accommodation. Equilibration drives the progression
through developmental stages by resolving cognitive
conflict (disequilibrium) into a more stable understanding
(equilibrium).
5. Active, Discovery Learning
– Children learn best through hands-on exploration and
discovery rather than passive reception of facts. Knowledge
is constructed internally, not simply transmitted from
teacher to learner.
Through these mechanisms, Piaget showed that intellectual
development is a dynamic, self-regulated process in which
learners construct, test, and refine their understanding of
mathematical and scientific concepts.


1.2 Describe two general principles of constructivism that
are largely based on Piaget’s principles. (6)
While Piaget focused on individual cognitive development, two
broader constructivist principles for instruction are:
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