FMT3701 ASSESSMENT 2
Question 1:
Differentiation between concepts and examples:
1. Object counting: Object counting refers to the process of determining the quantity of
individual objects by assigning each object a unique number. It involves physically
touching or pointing to each object while assigning a number. For example, a child
counting the number of apples in a basket by touching and saying "one, two, three,
four."
2. Counting on: Counting on is a strategy used to determine a quantity by starting with
a known number and incrementing or adding more to it. It involves mentally moving
forward from the known number. For instance, to find the sum of 5 + 3, a student
might start with 5 and count on from there: "5, 6, 7, 8."
3. Counting backwards: Counting backwards involves determining a sequence of
numbers in descending order. It is the reverse of counting forwards. An example
would be counting down from 10 to 1: "10, 9, 8, 7, 6, 5, 4, 3, 2, 1."
4. Counting in multiples: Counting in multiples involves counting by a specific number
instead of counting by one. For instance, counting by twos would be: "2, 4, 6, 8, 10,
12, 14, 16, 18, 20." It allows for quicker determination of quantities and helps in
understanding patterns and skip counting.
5. Counting all: Counting all involves counting every individual item in a set, even if the
total quantity is already known or can be determined more efficiently using other
strategies. For example, counting each finger on one's hand to determine a total of
five, even though the number is known without counting.
Table comparing two major approaches to teaching mathematics:
Application in Mathematics
Approach Description Teaching
Emphasizes direct instruction, rote It can be used to introduce
Traditional memorization, and basic math facts,
such as addition and
Approach practice of algorithms. multiplication tables.
bashCopy code
, FMT3701 ASSESSMENT 2
| | However, it may limit conceptual understanding.
------------------- | ------------------------------------------------------- | ----------------
--------------------- Constructivist | Focuses on student-centered learning, problem-
solving, | It can be used to engage students in hands-on Approach | and discovery of
mathematical concepts. | activities, real-world problem-solving, and | | cooperative
learning to foster conceptual understanding.
To apply the traditional approach, I would incorporate drills and practice sessions to
reinforce basic mathematical facts and algorithms. For the constructivist approach, I
would design activities that encourage exploration, critical thinking, and problem-
solving, allowing students to discover mathematical concepts through hands-on
experiences and collaborative tasks. A combination of both approaches can create a
balanced mathematics teaching environment, catering to different learning styles
and promoting conceptual understanding alongside procedural fluency.
Question 2:
Three child development theorists and their applicability to teaching mathematics in
the Foundation Phase:
1. Jean Piaget: Piaget's theory of cognitive development emphasizes the importance of
a child's active construction of knowledge through experiences and interactions with
the environment. In teaching mathematics, educators can provide concrete materials
and hands-on activities to allow children to manipulate objects and explore
mathematical concepts. Piaget's theory supports the idea that children should
engage in activities that promote discovery and problem-solving, fostering their
understanding of mathematical concepts.
2. Lev Vygotsky: Vygotsky's sociocultural theory highlights the role of social interactions
and language in a child's cognitive development. In the context of mathematics
teaching, educators can promote collaborative learning environments where children
work together, discuss their ideas, and solve problems as a group. This approach
helps children internalize mathematical knowledge through interaction with their
peers and more knowledgeable others, such as teachers or classmates who have a
better understanding of certain mathematical concepts.
3. Jerome Bruner: Bruner's theory of cognitive development emphasizes the importance
of scaffolding, where more knowledgeable individuals provide support to learners as
they gradually acquire new skills and knowledge. In mathematics teaching, educators
can use scaffolding techniques to guide students through the learning process. For
example, a teacher may provide step-by-step explanations, offer prompts or cues,
and gradually decrease support as students gain mastery over mathematical
concepts and skills.
Question 1:
Differentiation between concepts and examples:
1. Object counting: Object counting refers to the process of determining the quantity of
individual objects by assigning each object a unique number. It involves physically
touching or pointing to each object while assigning a number. For example, a child
counting the number of apples in a basket by touching and saying "one, two, three,
four."
2. Counting on: Counting on is a strategy used to determine a quantity by starting with
a known number and incrementing or adding more to it. It involves mentally moving
forward from the known number. For instance, to find the sum of 5 + 3, a student
might start with 5 and count on from there: "5, 6, 7, 8."
3. Counting backwards: Counting backwards involves determining a sequence of
numbers in descending order. It is the reverse of counting forwards. An example
would be counting down from 10 to 1: "10, 9, 8, 7, 6, 5, 4, 3, 2, 1."
4. Counting in multiples: Counting in multiples involves counting by a specific number
instead of counting by one. For instance, counting by twos would be: "2, 4, 6, 8, 10,
12, 14, 16, 18, 20." It allows for quicker determination of quantities and helps in
understanding patterns and skip counting.
5. Counting all: Counting all involves counting every individual item in a set, even if the
total quantity is already known or can be determined more efficiently using other
strategies. For example, counting each finger on one's hand to determine a total of
five, even though the number is known without counting.
Table comparing two major approaches to teaching mathematics:
Application in Mathematics
Approach Description Teaching
Emphasizes direct instruction, rote It can be used to introduce
Traditional memorization, and basic math facts,
such as addition and
Approach practice of algorithms. multiplication tables.
bashCopy code
, FMT3701 ASSESSMENT 2
| | However, it may limit conceptual understanding.
------------------- | ------------------------------------------------------- | ----------------
--------------------- Constructivist | Focuses on student-centered learning, problem-
solving, | It can be used to engage students in hands-on Approach | and discovery of
mathematical concepts. | activities, real-world problem-solving, and | | cooperative
learning to foster conceptual understanding.
To apply the traditional approach, I would incorporate drills and practice sessions to
reinforce basic mathematical facts and algorithms. For the constructivist approach, I
would design activities that encourage exploration, critical thinking, and problem-
solving, allowing students to discover mathematical concepts through hands-on
experiences and collaborative tasks. A combination of both approaches can create a
balanced mathematics teaching environment, catering to different learning styles
and promoting conceptual understanding alongside procedural fluency.
Question 2:
Three child development theorists and their applicability to teaching mathematics in
the Foundation Phase:
1. Jean Piaget: Piaget's theory of cognitive development emphasizes the importance of
a child's active construction of knowledge through experiences and interactions with
the environment. In teaching mathematics, educators can provide concrete materials
and hands-on activities to allow children to manipulate objects and explore
mathematical concepts. Piaget's theory supports the idea that children should
engage in activities that promote discovery and problem-solving, fostering their
understanding of mathematical concepts.
2. Lev Vygotsky: Vygotsky's sociocultural theory highlights the role of social interactions
and language in a child's cognitive development. In the context of mathematics
teaching, educators can promote collaborative learning environments where children
work together, discuss their ideas, and solve problems as a group. This approach
helps children internalize mathematical knowledge through interaction with their
peers and more knowledgeable others, such as teachers or classmates who have a
better understanding of certain mathematical concepts.
3. Jerome Bruner: Bruner's theory of cognitive development emphasizes the importance
of scaffolding, where more knowledgeable individuals provide support to learners as
they gradually acquire new skills and knowledge. In mathematics teaching, educators
can use scaffolding techniques to guide students through the learning process. For
example, a teacher may provide step-by-step explanations, offer prompts or cues,
and gradually decrease support as students gain mastery over mathematical
concepts and skills.
