PST201F/101/2/2018
Tutorial Letter 201/2/2018
MATHEMATICS AND MATHEMATICS TEACHING
PST201F
Semester 2
Department of Mathematics Education
This tutorial letter contains important information
about your module.
BARCODE
,PART B
Activity 1.1 Write a short paragraph on your experiences as a learner in a Mathematics class
when you were at school. Write at least one good experience and one bad experience.
There is no wrong or right answer.
Activity 1.2 (pictures 3 and 4)
(Some of the students’ opinions)
Picture 3: It looks like the old or traditional classroom set-up with many learners listening to
the teacher with fear.
Picture 4: This is a small group activity with manipulatives; learners are explaining to the
teacher.
Activity 1.3 No 2 Choose any three words and use each in a sentence to relate them to the
doing of Mathematics.
Examples:
The student will be able to calculate the area of a triangle.
The student will describe the properties of a square.
The student will list the disadvantages of rote learning.
Activity 1.6
Explain the following:
Assimilation: It occurs when new concepts fit into an existing network of ideas. The
new information expands the pre-existing network. It refers to the use of an existing
schema to give meaning to new experiences. Assimilation is based on learners'
abilities to notice similarities among objects and match new ideas to those they
already possess.
Accommodation: It takes place when new concepts do not fit into an existing network
of ideas. The brain has to revamp or re-organise the network to accommodate the
new concepts. It is also a process of altering existing ways of seeing things or ideas
that do not fit into an existing schemata.
Disequilibrium: When new knowledge and pre-existing knowledge do not match and
there is a need to modify the rearrangement of concepts and connections so as to
accommodate the new knowledge.
Reflective thought: A sift through the pre-existing ideas in order to find those that
seem related to the new knowledge and how they are related.
2
, PST201F/201/2/2018
Activity 1.7 (1a and 1b)
1. Four children had three boxes of Smarties. They decided to open all three boxes, to share
the Smarties fairly. There were 52 Smarties in each box. How many Smarties did each child
get?
Now look at two attempts from Grade 4 learners to solve this problem.
a. Explain in your own words how the two learners solved the problem.
b. What is an algorithm?
Michael: Got a total of 156 Smarties. Uses repeated subtraction as well as the division
to arrive to 39 Smarties each.
Romy: Got a total of 156 Smarties, then uses grouping and sharing to arrive to
39 Smarties. This implies that each learner will get 39 Smarties.
An algorithm is a step-by-step procedure that leads to the expected result.
Activity 1.9 (Bullets 4–6)
Read the section above about “rote learning”. Seven weaknesses are given at the end. Write
your own interpretation about each of these weaknesses (do not just repeat what is said here).
4. The facilitator pays little attention to the needs, interests and development of learners.
The teacher who uses this method is more concerned about getting through the work done,
and is not concerned about how students learn and if they are really learning.
5. Knowledge learned by rote learning is hardly connected to the learners’ existing ideas.
Learners using this method of learning are not encourage to link the new knowledge learned
to the pre-existing knowledge.
6. Rote learning will almost never contribute to a useful network of ideas.
Learners using this method of learning do not really build a useful network of ideas.
Activity 1.11 No 3
Explain what it means that understanding exists on a continuum from relational to instrumental
understanding. Give an example of a mathematical concept and explain how it might be
understood at different places along a continuum.
This question does not only require the definition of instrumental and relational
understandings, but also to explain what a continuum is in relation to these concepts.
Instrumental understanding is knowing how to use rules and procedures without
reference to previously learnt information, and not linking to explanations of why these
3
Tutorial Letter 201/2/2018
MATHEMATICS AND MATHEMATICS TEACHING
PST201F
Semester 2
Department of Mathematics Education
This tutorial letter contains important information
about your module.
BARCODE
,PART B
Activity 1.1 Write a short paragraph on your experiences as a learner in a Mathematics class
when you were at school. Write at least one good experience and one bad experience.
There is no wrong or right answer.
Activity 1.2 (pictures 3 and 4)
(Some of the students’ opinions)
Picture 3: It looks like the old or traditional classroom set-up with many learners listening to
the teacher with fear.
Picture 4: This is a small group activity with manipulatives; learners are explaining to the
teacher.
Activity 1.3 No 2 Choose any three words and use each in a sentence to relate them to the
doing of Mathematics.
Examples:
The student will be able to calculate the area of a triangle.
The student will describe the properties of a square.
The student will list the disadvantages of rote learning.
Activity 1.6
Explain the following:
Assimilation: It occurs when new concepts fit into an existing network of ideas. The
new information expands the pre-existing network. It refers to the use of an existing
schema to give meaning to new experiences. Assimilation is based on learners'
abilities to notice similarities among objects and match new ideas to those they
already possess.
Accommodation: It takes place when new concepts do not fit into an existing network
of ideas. The brain has to revamp or re-organise the network to accommodate the
new concepts. It is also a process of altering existing ways of seeing things or ideas
that do not fit into an existing schemata.
Disequilibrium: When new knowledge and pre-existing knowledge do not match and
there is a need to modify the rearrangement of concepts and connections so as to
accommodate the new knowledge.
Reflective thought: A sift through the pre-existing ideas in order to find those that
seem related to the new knowledge and how they are related.
2
, PST201F/201/2/2018
Activity 1.7 (1a and 1b)
1. Four children had three boxes of Smarties. They decided to open all three boxes, to share
the Smarties fairly. There were 52 Smarties in each box. How many Smarties did each child
get?
Now look at two attempts from Grade 4 learners to solve this problem.
a. Explain in your own words how the two learners solved the problem.
b. What is an algorithm?
Michael: Got a total of 156 Smarties. Uses repeated subtraction as well as the division
to arrive to 39 Smarties each.
Romy: Got a total of 156 Smarties, then uses grouping and sharing to arrive to
39 Smarties. This implies that each learner will get 39 Smarties.
An algorithm is a step-by-step procedure that leads to the expected result.
Activity 1.9 (Bullets 4–6)
Read the section above about “rote learning”. Seven weaknesses are given at the end. Write
your own interpretation about each of these weaknesses (do not just repeat what is said here).
4. The facilitator pays little attention to the needs, interests and development of learners.
The teacher who uses this method is more concerned about getting through the work done,
and is not concerned about how students learn and if they are really learning.
5. Knowledge learned by rote learning is hardly connected to the learners’ existing ideas.
Learners using this method of learning are not encourage to link the new knowledge learned
to the pre-existing knowledge.
6. Rote learning will almost never contribute to a useful network of ideas.
Learners using this method of learning do not really build a useful network of ideas.
Activity 1.11 No 3
Explain what it means that understanding exists on a continuum from relational to instrumental
understanding. Give an example of a mathematical concept and explain how it might be
understood at different places along a continuum.
This question does not only require the definition of instrumental and relational
understandings, but also to explain what a continuum is in relation to these concepts.
Instrumental understanding is knowing how to use rules and procedures without
reference to previously learnt information, and not linking to explanations of why these
3
