TMS3725 Assignment 3
(COMPLETE ANSWERS)
2023 (245380) - DUE 19
July 2023
, Question 1
1.1 Rote learning can never be used to replace high-level thinking. It is, however, crucial for achieving
high-level thinking.
1.1.1 When is rote learning necessary in mathematics? (2)
Rote learning is necessary in mathematics when learning basic facts or formulas that need to
be memorized in order to solve more complex problems. For example, in algebra, students
need to memorize the quadratic formula in order to solve quadratic equations. In geometry,
students need to memorize the formulas for calculating the area and perimeter of different
shapes.
1.1.2 Give TWO examples under the topic of probability where rote learning can be applied and
motivate your choice. (4)
Example 1: Rote learning can be applied in probability when calculating basic probabilities. For
example, students need to memorize the formula for calculating the probability of an event,
which is the number of favorable outcomes divided by the total number of outcomes.
Example 2: Rote learning can also be used in probability when learning the rules of
probability. For example, students need to memorize the rule of addition, where the
probability of the union of two non-mutually exclusive events is equal to the sum of their
individual probabilities.
1.2 Use one example from each type of knowledge to differentiate between conceptual knowledge
and procedural knowledge of mathematics. (6)
Conceptual knowledge refers to the understanding of mathematical concepts, principles, and
relationships. It involves the ability to explain and apply mathematical concepts in various
situations. Procedural knowledge, on the other hand, refers to the knowledge of how to carry
out mathematical procedures or algorithms. It involves the ability to perform mathematical
operations or solve problems using specific procedures.
Example 1: Conceptual knowledge in mathematics would involve understanding the concept of
fractions and being able to explain what a fraction represents, how to compare fractions, and
how to perform operations with fractions.
Example 2: Procedural knowledge in mathematics would involve knowing the step-by-step
procedure for adding fractions, multiplying decimals, or solving equations using the quadratic
formula. It focuses on the process or algorithm used to solve mathematical problems.
1.3 Van de Walle (2016) offers definitions that differentiate between drill and practice. Use these
definitions to explain how you will apply these concepts in your classroom. (NB: Do not define
the two concepts.) (6)
(COMPLETE ANSWERS)
2023 (245380) - DUE 19
July 2023
, Question 1
1.1 Rote learning can never be used to replace high-level thinking. It is, however, crucial for achieving
high-level thinking.
1.1.1 When is rote learning necessary in mathematics? (2)
Rote learning is necessary in mathematics when learning basic facts or formulas that need to
be memorized in order to solve more complex problems. For example, in algebra, students
need to memorize the quadratic formula in order to solve quadratic equations. In geometry,
students need to memorize the formulas for calculating the area and perimeter of different
shapes.
1.1.2 Give TWO examples under the topic of probability where rote learning can be applied and
motivate your choice. (4)
Example 1: Rote learning can be applied in probability when calculating basic probabilities. For
example, students need to memorize the formula for calculating the probability of an event,
which is the number of favorable outcomes divided by the total number of outcomes.
Example 2: Rote learning can also be used in probability when learning the rules of
probability. For example, students need to memorize the rule of addition, where the
probability of the union of two non-mutually exclusive events is equal to the sum of their
individual probabilities.
1.2 Use one example from each type of knowledge to differentiate between conceptual knowledge
and procedural knowledge of mathematics. (6)
Conceptual knowledge refers to the understanding of mathematical concepts, principles, and
relationships. It involves the ability to explain and apply mathematical concepts in various
situations. Procedural knowledge, on the other hand, refers to the knowledge of how to carry
out mathematical procedures or algorithms. It involves the ability to perform mathematical
operations or solve problems using specific procedures.
Example 1: Conceptual knowledge in mathematics would involve understanding the concept of
fractions and being able to explain what a fraction represents, how to compare fractions, and
how to perform operations with fractions.
Example 2: Procedural knowledge in mathematics would involve knowing the step-by-step
procedure for adding fractions, multiplying decimals, or solving equations using the quadratic
formula. It focuses on the process or algorithm used to solve mathematical problems.
1.3 Van de Walle (2016) offers definitions that differentiate between drill and practice. Use these
definitions to explain how you will apply these concepts in your classroom. (NB: Do not define
the two concepts.) (6)
