This document contains workings, explanations and solutions to the TMS3725 Assignment 2 (QUALITY ANSWERS) 2024. For assistance call or us on 0.6.8..8.1.2..0.9.3.4....... 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 2 2.1 How would you describe what it means to “do” mathematics? (5) 2.2 Why is doing pencil-and-paper computations not “doing mathematics”? (3) 2.3 Give five weaknesses of the rote-learning approach. (5) 2.4 Discuss in your own words what “understanding” means in mathematics. (4) 2.5 Discuss two examples of understanding in mathematics. (6) [23] QUESTION 3 3.1 Describe conceptual knowledge and procedural knowledge of mathematics. Provide examples of each. (6) 3.2 What is reflective thought? Why is reflective thinking so important in the development of conceptual ideas in mathematics? (5) 3.3 Describe Vygotsky’s socio-cultural view of learning. What is the zone of proximal development? (4) 3.4 How can teachers use models incorrectly? (2) [17] QUESTION 4 4.1 Why is planning in the teaching of Mathematics important? Discuss by providing at least 5 valid arguments. (5) 4.2 What pre-knowledge concepts would a Grade 11 learner need to know before learning to sum to infinity (Sequences and Series)? (5) 4.3 In a recycling bin, the quantity of tin recovered during the 1st cycle is 300 kg, during the 2nd cycle it is 240 kg, during the 3rd cycle 129 kg and so on … 4.3.1 Show that the recycling process represents a geometric sequence. (2) 4.3.2 Calculate the total quantity of tin recovered during the geometric sequence. (3) 4.3.3 If the process is continually repeated, calculate the total mass of tin that would be recovered. (2) 4.3.4 In order for the process to be economical, at least 10 kg of tin must be recovered in a cycle. What is the greatest number of cycles for this process to be economical? (2) [19] QUESTION 5 There are three questions in this section: 1, 2 and 3. First read the guidelines below the question. Describe in detail the nature, characteristics and application of: 1. the problem-centred approach in mathematics education 2. modelling in mathematics education, and 3. the relationship between the two of them.
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