Exam (elaborations)
TMS3725 Assignment 2 (COMPLETE ANSWERS) 2024 (313968) - 19 June 2024
- Course
- TMS3725
- Institution
- University Of South Africa
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TMS3725Assignment 2
(COMPLETE
ANSWERS)
2024 (313968) -
19 June 2024
CONTACT: biwottcornelius@gmail.com
, 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]
1.1 Difference between assimilation and accommodation:
Assimilation and accommodation are terms introduced by Jean Piaget to describe processes
involved in cognitive development:
Assimilation refers to the process of taking in new information or experiences and
incorporating them into existing mental schemas or structures. In other words, it involves
fitting new information into pre-existing cognitive frameworks without changing those
frameworks substantially.
Accommodation, on the other hand, is the process of altering existing cognitive
frameworks to incorporate new information or experiences that do not fit into existing
schemas. It requires modifying or creating new schemas to adapt to the new information.
Example: Imagine a child who has a schema for birds. Initially, they may have a schema that all
birds are small and can fly (assimilation). However, when they encounter an ostrich (a large
flightless bird), they must accommodate this new information by either adjusting their bird
schema to include large flightless birds or creating a new schema specifically for ostriches.
1.2 Difference between errors and misconceptions in mathematics:
In mathematics education:
Errors are incorrect answers or steps in problem-solving that arise from computational
mistakes, misapplication of rules, or misunderstanding of procedures. Errors can be
corrected through feedback and further practice.
Misconceptions are more fundamental and persistent misunderstandings or flawed
beliefs about mathematical concepts, principles, or relationships. Misconceptions often
stem from faulty mental models or incomplete understanding of mathematical ideas and
may persist despite attempts to correct them.
Example: In division, a common error might be incorrectly subtracting instead of dividing in a
multi-step problem. A misconception, on the other hand, could be believing that multiplying
always results in a larger number than either of the factors.
1.3 Benefits of a constructivist approach in teaching and learning mathematics:
A constructivist approach in mathematics education emphasizes active engagement, exploration,
and sense-making by students. Here are some benefits:
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