Teaching Mathematics in the Intermediate Phase
TMN3704
Assignment 2
, 2.1 Briefly discuss what learners' mathematical thinking involves. How can you, as the
teacher, support learners to express and clarify their own
Mathematical thinking is a unique process. Mathematical thinking involves the explanation and
collaboration of mathematics through problem-solving, reasoning and proof, communication,
connections, and representation. It is a whole way of looking at things, stripping them down to
their essentials, whether it’s numerical, structural or logical and then analyzing the underlying
patterns.
When we are teaching a mathematical method, we are showing something that happens all the
time, something that happens in general. Getting students to see these underlying structures,
whether it’s in a math problem, in society, or in nature, is one of the reasons that studying
mathematics is so worthwhile.
How can you, as the teacher, support learners to express and clarify their own
• Create an effective class opener. The first five minutes of the class period set the tone for the
entire lesson. ...
• Introduce topics using multiple representations. ...
• Solve the problems many ways. ...
• Show the application. ...
• Have students communicate their reasoning. ...
• Finish class with a summary.
2.2 Learners may begin to lose track of some numbers when they use the break-up
strategy to do calculations. Using brackets is helpful to show the grouping of
numbers and so help learners to keep track of what they are doing. Use the
distributive property to multiply (96 × 85) and check the reasonableness of the
answer. (The example on page 76 of the CAPS document provides guidance on how
to simplify this problem.)
96 x 85 = 96 x (80 +5)
= 96 x 80 + (96 x 5)
= 7680 + 480
= 8160
TMN3704
Assignment 2
, 2.1 Briefly discuss what learners' mathematical thinking involves. How can you, as the
teacher, support learners to express and clarify their own
Mathematical thinking is a unique process. Mathematical thinking involves the explanation and
collaboration of mathematics through problem-solving, reasoning and proof, communication,
connections, and representation. It is a whole way of looking at things, stripping them down to
their essentials, whether it’s numerical, structural or logical and then analyzing the underlying
patterns.
When we are teaching a mathematical method, we are showing something that happens all the
time, something that happens in general. Getting students to see these underlying structures,
whether it’s in a math problem, in society, or in nature, is one of the reasons that studying
mathematics is so worthwhile.
How can you, as the teacher, support learners to express and clarify their own
• Create an effective class opener. The first five minutes of the class period set the tone for the
entire lesson. ...
• Introduce topics using multiple representations. ...
• Solve the problems many ways. ...
• Show the application. ...
• Have students communicate their reasoning. ...
• Finish class with a summary.
2.2 Learners may begin to lose track of some numbers when they use the break-up
strategy to do calculations. Using brackets is helpful to show the grouping of
numbers and so help learners to keep track of what they are doing. Use the
distributive property to multiply (96 × 85) and check the reasonableness of the
answer. (The example on page 76 of the CAPS document provides guidance on how
to simplify this problem.)
96 x 85 = 96 x (80 +5)
= 96 x 80 + (96 x 5)
= 7680 + 480
= 8160
