SUPPORT MATERIAL TO ASSIST IN WRITING ASSIGNMENT 1 FOR TMN 3704
Instructions: Read information in both Sections A and B
SECTION A
Question 1- 4: get information from the Mathematics Intermediate Phase CAPS document (Where to get
the policy document: Read page 5 of TUT Letter 501(TMN3704), just before activity 1.3
Questions 5-8 : Any relevant source and notes under section B
Questions 8-15: Check any mathematics textbooks for Intermediate and Senior Phases (Grade 4-9)
SECTION B(NOTES)
The notes in this section are sourced from: TUT letter 501/3/2019 and TUT letter 201/2/2019.
Mathematics and mathematics teaching (intermediate and Senior Phase) PST 201F. Department of
Mathematics Education. UNISA
1 MATHEMATICAL PROFICIENCY
Mathematically proficient people exhibit certain behaviours and dispositions as they are ―doing mathematics‖.
How will we, as teachers, recognise mathematical proficient learners?
Activity 1
What is your understanding of the concept ―mathematical proficiency‖?
Read the description of each of the following strands of mathematical proficiency. Explain in your own words
what does each mean and provide appropriate examples.
Conceptual understanding—an understanding of concepts, operations and relations. This frequently results in
students comprehending connections and similarities between interrelated facts.
Procedural fluency—flexibility, accuracy and efficiency in implementing appropriate procedures. Skill in
proficiency includes the knowledge of when and how to use procedures. This includes efficiency and accuracy in
basic computations. Being able to carry out mathematical procedures flexibly, accurately and efficiently
.
Strategic competence—the ability to formulate, represent and solve mathematical problems. This is similar to
problem solving. Strategic competence is mutually supportive with conceptual understanding and procedural
fluency.
Adaptive reasoning—the capacity to think logically about concepts and conceptual relationships. Reasoning is
needed to navigate through the various procedures, facts and concepts to arrive at solutions. Logical thought,
reflection, explanation and justification.
Productive disposition— To see mathematics as sensible, useful and worthwhile. positive perceptions about
mathematics. This develops as students gain more mathematical understanding and become capable of learning
and doing mathematics.
1|Page
, 2 A CLASSROOM ENVIRONMENT FOR DOING MATHEMATICS
As you work through the rest of this study unit, you will be challenged to rethink and reconstruct your own
understanding of what it means to know and do mathematics – so that learners with whom you work will have an
exciting and more positive vision of mathematics. Doing mathematics (mathematization) will be eventful,
compelling and creative.
Activity 2.1
Read the section, ―A classroom environment for doing Mathematics‖, and answer the following
questions as a way of reconstructing your own understanding of what it means to do Mathematics.
1 Name the words that you can relate to teaching and learning in a traditional Mathematics
classroom.
2 Think of the the verbs related to the ―doing of mathematics‖ in a mathematics classroom.
Use each of them in a sentence to relate them to the doing of mathematics.
3 Describe the role of the teacher and the learners in a classroom where they are doing
mathematics.
It is the job of the teacher to ensure that every child learns to do mathematics, but for this, the right environment is
important.
An environment for doing mathematics is one in which learners are allowed to engage in investigative processes
and where they have the time and space to explore particular cases (problems). Then they can move slowly
towards establishing, through discovery and logical reasoning, the underlying regularity and order (in the form of
rules, principles, number patterns, and so on).
Learners can create a "conjecturing atmosphere" in the classroom if the teacher gives appropriate tasks and
promotes learner thinking and discussion about these tasks. This atmosphere is one in which the rightness or
wrongness of answers is not the issue, but rather an environment that encourages learners to make conjectures
(guesses) about the regularity (sameness) they see and to discuss these conjectures with others without fear of
being judged wrong or stupid, to listen to the ideas expressed by others, and consequently, to modify their
conjectures.
The mathematical processes involved in doing mathematics are best expressed by action verbs. They require
reaching out, taking risks, testing ideas and expressing these ideas to others. (In the traditional classroom, these
verbs take the form of listening, copying, memorising, drilling and repeating – passive activities with very little
mental engagement, involving no risks and little initiative.)
The classroom must be an environment in which every learner is respected, regardless of their perceived
"cleverness", and, where they can take risks without fear that they will be criticised if they make a mistake. It should
be an environment in which learners work in groups, in pairs or individually, but where they are always sharing
ideas and engaged in discussion.
2|Page
Instructions: Read information in both Sections A and B
SECTION A
Question 1- 4: get information from the Mathematics Intermediate Phase CAPS document (Where to get
the policy document: Read page 5 of TUT Letter 501(TMN3704), just before activity 1.3
Questions 5-8 : Any relevant source and notes under section B
Questions 8-15: Check any mathematics textbooks for Intermediate and Senior Phases (Grade 4-9)
SECTION B(NOTES)
The notes in this section are sourced from: TUT letter 501/3/2019 and TUT letter 201/2/2019.
Mathematics and mathematics teaching (intermediate and Senior Phase) PST 201F. Department of
Mathematics Education. UNISA
1 MATHEMATICAL PROFICIENCY
Mathematically proficient people exhibit certain behaviours and dispositions as they are ―doing mathematics‖.
How will we, as teachers, recognise mathematical proficient learners?
Activity 1
What is your understanding of the concept ―mathematical proficiency‖?
Read the description of each of the following strands of mathematical proficiency. Explain in your own words
what does each mean and provide appropriate examples.
Conceptual understanding—an understanding of concepts, operations and relations. This frequently results in
students comprehending connections and similarities between interrelated facts.
Procedural fluency—flexibility, accuracy and efficiency in implementing appropriate procedures. Skill in
proficiency includes the knowledge of when and how to use procedures. This includes efficiency and accuracy in
basic computations. Being able to carry out mathematical procedures flexibly, accurately and efficiently
.
Strategic competence—the ability to formulate, represent and solve mathematical problems. This is similar to
problem solving. Strategic competence is mutually supportive with conceptual understanding and procedural
fluency.
Adaptive reasoning—the capacity to think logically about concepts and conceptual relationships. Reasoning is
needed to navigate through the various procedures, facts and concepts to arrive at solutions. Logical thought,
reflection, explanation and justification.
Productive disposition— To see mathematics as sensible, useful and worthwhile. positive perceptions about
mathematics. This develops as students gain more mathematical understanding and become capable of learning
and doing mathematics.
1|Page
, 2 A CLASSROOM ENVIRONMENT FOR DOING MATHEMATICS
As you work through the rest of this study unit, you will be challenged to rethink and reconstruct your own
understanding of what it means to know and do mathematics – so that learners with whom you work will have an
exciting and more positive vision of mathematics. Doing mathematics (mathematization) will be eventful,
compelling and creative.
Activity 2.1
Read the section, ―A classroom environment for doing Mathematics‖, and answer the following
questions as a way of reconstructing your own understanding of what it means to do Mathematics.
1 Name the words that you can relate to teaching and learning in a traditional Mathematics
classroom.
2 Think of the the verbs related to the ―doing of mathematics‖ in a mathematics classroom.
Use each of them in a sentence to relate them to the doing of mathematics.
3 Describe the role of the teacher and the learners in a classroom where they are doing
mathematics.
It is the job of the teacher to ensure that every child learns to do mathematics, but for this, the right environment is
important.
An environment for doing mathematics is one in which learners are allowed to engage in investigative processes
and where they have the time and space to explore particular cases (problems). Then they can move slowly
towards establishing, through discovery and logical reasoning, the underlying regularity and order (in the form of
rules, principles, number patterns, and so on).
Learners can create a "conjecturing atmosphere" in the classroom if the teacher gives appropriate tasks and
promotes learner thinking and discussion about these tasks. This atmosphere is one in which the rightness or
wrongness of answers is not the issue, but rather an environment that encourages learners to make conjectures
(guesses) about the regularity (sameness) they see and to discuss these conjectures with others without fear of
being judged wrong or stupid, to listen to the ideas expressed by others, and consequently, to modify their
conjectures.
The mathematical processes involved in doing mathematics are best expressed by action verbs. They require
reaching out, taking risks, testing ideas and expressing these ideas to others. (In the traditional classroom, these
verbs take the form of listening, copying, memorising, drilling and repeating – passive activities with very little
mental engagement, involving no risks and little initiative.)
The classroom must be an environment in which every learner is respected, regardless of their perceived
"cleverness", and, where they can take risks without fear that they will be criticised if they make a mistake. It should
be an environment in which learners work in groups, in pairs or individually, but where they are always sharing
ideas and engaged in discussion.
2|Page
