MTE1501 Assignment 2 (DETAILED ANSWERS) 2024 - DISTINCTION GUARANTEED

MTE1501 Assignment 2 (DETAILED ANSWERS) 2024 - DISTINCTION GUARANTEED Answers, guidelines, workings and references .......... Question 1 (10) Are the following statements true or false? Where the statement is false, make it to be true. 1.1 Euclid is the Pythagorean school and contributed to philosophy and the study of proportion, plane, and solid geometry. 1.2 Zeno of Elea proposed that a unit has magnitude and is infinitely divisible. 1.3 Base 100, the ancient Greek numeral system, was also known as the Attic or Herodianic numeral system. 1.4 Plato has one of his longest and clearest mathematical discussions in Phaedo. 1.5 In his works, Socrates dealt in some detail with mathematical questions in the early 4th century 300 BCE. Question 2 (10) Match each statement with the appropriate explanation or statement. Statement Appropriate explanations or statements 2.1 According to Plato, it is a rough characterisation of real mathematics. a. Someone who deals with abstract concepts. b. They were discovered before 1000 BCE with the operations of three basic operations including cube roots. 2.2 Socrates’ view of the ordinary arithmetician in Plato's Meno. c. Decimal place value number system. 2.3 Powers of 10 from 100 to a trillion were evoked in Mantras. d. Simplified Pythagorean theorem. 2.4 What school was founded by Thales, who discovered the five e. Ionian school – every triangle is a semicircle is a right-angle triangle. basic theorems in plane geometry? f. Mathematics makes sense when there is a connection structure and is independent of human thinking. 2.5 The Sulba sutras listed Pythagorean triples and provided a simplified Pythagorean theorem g. Numbers have an independent existence. Question 3 (40) Give a short response to the following question: 3.1 What are primary focus of mathematics as described in the passage below? (8) 3.2 Provide a brief answer to the question: How does Ziegler (2010) define mathematics according to the passage? Do not copy the definition but describe it according to your understanding. (8) 3.3 Give a concise response to the following question: What does the term "mathematics education" encompass according to section 2.3.2 in the study guide? (12) 3.4 Draw a table and give the differences or similarities between mathematics and mathematics education. (6) Mathematics education as a scientific discipline is considered here in a rather broad view as the study of how people learn and do mathematics of any kind, and of how this learning and doing can be influenced and fostered among others by teaching, by the use of media, by different representations, or by the social organisation of mathematical activity. Thus, the object of mathematics education clearly is a certain area of hu- man activities whose content, object and goal is mathematics at different levels and in different forms … the role (professional) mathematicians currently take in relation to mathematics education … they themselves consider as their main task to develop mathematical theories and/or to apply them in various contexts. This should/could give a reason for mathematics education to investigate the mathematical activity of mathematicians, its conditions, forms, means, goals, intentions, etc. 3.5 What are the key differences between constructivism and behaviourism in terms of the learning practices outlined in Table 2.3? Give them in your own words. Do not copy the responses in the study guide but use them to show your understanding of this question. (6) Question 4 (20) 4.1 According to Piaget, what are the three types of knowledge? Explain why it is important that teachers understand them. Refer to the section 2.11 in your study guide. Use your creativity to unpack the responses from the given figure. (4) 4.2 Why is concrete knowledge emphasised in the teaching of mathematics according to the passage? (3) 4.3 Discuss the connections between procedural and conceptual knowledge regarding the construction of relational understanding in mathematics. (5) 4.4 Determine if the following mathematical problems as routine or non-routine: (6) 4.4.1 Three x + 5 is = 17 4.4.2 Find the area of a rectangle with a length of eight units in the width of 3 units. 4.4.3 Explore the relationship between the Fibonacci sequence and the ratio concept. 4.5 Give a brief description of your responses in 4.4 above.