TMS3726 Assignment 3 (COMPLETE ANSWERS) 2024 (566030 ) - DUE 30 August 2024 ; 100% TRUSTED Complete, trusted solutions and explanations
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University of South Africa
Teaching Mathematics in Further Education and Trai
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TMS3725 Assignment
2 (COMPLETE
ANSWERS) 2024
(313968) - 19 June
2024; 100% TRUSTED
workings,
explanations and
solutions.
ADMIN
[COMPANY NAME]
,QUESTION 1 1.1 What is the difference between assimilation and
accommodation? (4) 1.2 Explain the difference between errors and
misconceptions in mathematics. Illustrate your answer with an
example. (6) 1.3 Discuss the benefits of a constructivist approach in
the teaching and learning of mathematics. (10) [20]
Question 1
1.1 What is the difference between assimilation and
accommodation? (4)
Assimilation and accommodation are concepts from Piaget's
theory of cognitive development:
• Assimilation: This process involves integrating new
information into existing cognitive schemas. When a person
encounters something new, they try to understand it by fitting
it into what they already know. For example, a child who
knows the concept of a "dog" might initially call all four-
legged animals dogs.
• Accommodation: This process requires changing existing
schemas or creating new ones to incorporate new information
that doesn't fit into existing schemas. It involves altering one's
understanding to accommodate new experiences or
information. For example, the same child will eventually learn
that cats and dogs are different animals and adjust their schema
accordingly.
In summary, assimilation is about fitting new information into
existing structures, while accommodation is about changing
structures to fit new information.
1.2 Explain the difference between errors and misconceptions in
mathematics. Illustrate your answer with an example. (6)
, Errors in mathematics are mistakes that occur due to a slip or
miscalculation and are usually random or occasional. These do not
indicate a fundamental misunderstanding of concepts.
Misconceptions, on the other hand, are consistent and systematic
misunderstandings of mathematical concepts. They reflect an
underlying issue in the learner's comprehension.
Example:
• Error: A student makes a mistake in a simple arithmetic
calculation, such as writing 7 + 5 = 11. This could be a result
of a momentary lapse in concentration.
• Misconception: A student consistently believes that when
multiplying two numbers, the product is always larger than
either of the original numbers, leading them to assert that
0.5×0.5=0.50.5 \times 0.5 = 0.50.5×0.5=0.5 because they think
multiplication can't result in a smaller number. This reflects a
deeper misunderstanding of multiplication, especially when
dealing with fractions or decimals.
1.3 Discuss the benefits of a constructivist approach in the
teaching and learning of mathematics. (10)
A constructivist approach to teaching and learning mathematics is
based on the idea that learners construct their own understanding
and knowledge of the world through experiencing things and
reflecting on those experiences. Here are several benefits of this
approach:
1. Active Learning: Students are actively involved in their
learning process, which helps them to better understand and
retain mathematical concepts. They engage in problem-
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