,HED4813 EXAM PREP 30 JAN 2025
HED4814 ASSIGNMENT 1 AND 2: EXAM PREPARATION
Question 1
1.1. In not more than 1500 words, critically discuss the relationship between
cognition and modelling, drawing from the cognitive modelling of the
learning process and the subjective perception of cognition. Furthermore,
investigate the role of modelling in the formulation of pedagogical content
knowledge, considering the perspectives presented in the textbook
'Elementary and Middle School Mathematics: Teaching Developmentally'
by Van De Walle, JA. (2013) and its impact on teacher knowledge and
learner learning.
Cognition refers to the mental processes involved in acquiring knowledge and
understanding. These include thinking, remembering, problem-solving, and
decision-making. Modelling, on the other hand, is a process of representing a
concept, phenomenon, or idea in a way that helps learners understand it better.
In the context of education, the relationship between cognition and modelling is
critical, as effective teaching depends on understanding how learners think and
process information. This essay critically discusses the connection between
cognition and modelling, drawing from cognitive modelling of the learning
process and the subjective perception of cognition. Additionally, it explores the
role of modelling in formulating pedagogical content knowledge, referencing Van
De Walle’s work, "Elementary and Middle School Mathematics: Teaching
Developmentally" (2013).
Cognitive Modelling of the Learning Process
,Cognitive modelling is a strategy used to understand and represent how learners
process information. According to Van De Walle (2013), cognitive modelling helps
teachers design instructional strategies that align with how students think. For
example, when solving a math problem, a teacher may verbalize their thought
process step-by-step, allowing learners to observe and internalize the approach.
This method bridges the gap between abstract concepts and concrete
understanding.
Cognition is a subjective process because it varies from one individual to another.
Each learner brings unique prior knowledge, experiences, and ways of thinking
into the classroom. Teachers must consider these differences when using
modelling as a teaching strategy. For instance, a learner who struggles with
multiplication might benefit from visual models, such as arrays or number lines,
which align with their cognitive preferences (Van De Walle, 2013).
Subjective Perception of Cognition
Subjective perception of cognition refers to how individuals interpret and make
sense of information based on their experiences, cultural background, and prior
knowledge. This perception significantly influences how learners engage with and
understand new concepts. Van De Walle (2013) emphasizes the importance of
recognizing learners' subjective cognition when designing models to teach
mathematical concepts.
For example, a learner’s cultural background might influence how they perceive
patterns or relationships in math problems. If a teacher introduces a word
problem involving money, the learner’s familiarity with the currency used can
affect their ability to solve the problem. Therefore, teachers need to create
inclusive models that consider diverse perspectives, ensuring that all learners can
relate to and understand the content.
The Role of Modelling in Pedagogical Content Knowledge
Pedagogical content knowledge (PCK) is the combination of subject matter
knowledge and teaching strategies that enables teachers to effectively deliver
content to learners. Modelling plays a crucial role in developing PCK because it
, helps teachers connect theoretical knowledge with practical teaching techniques.
Van De Walle (2013) highlights that modelling is not just about showing learners
how to solve problems but also about helping them understand the underlying
concepts and principles.
For instance, in teaching fractions, a teacher might use a pie chart to visually
represent parts of a whole. This model helps learners grasp the concept of
fractions more concretely. By using models, teachers can also anticipate common
misconceptions and address them during instruction. For example, learners often
struggle to understand that 1/4 is smaller than 1/3 because they focus on the
denominator rather than the size of the fraction. A teacher can use a visual model
to clarify this misconception, enhancing their PCK.
Impact of Modelling on Teacher Knowledge
Modelling not only benefits learners but also enhances teacher knowledge. When
teachers engage in modelling, they deepen their understanding of the subject
matter and refine their instructional strategies. Van De Walle (2013) explains that
modelling requires teachers to think critically about how to represent concepts in
ways that are accessible to learners. This process involves breaking down complex
ideas into simpler components, which helps teachers internalize the content more
thoroughly.
Additionally, modelling encourages teachers to reflect on their teaching practices.
For example, after using a model to teach multiplication, a teacher might assess
its effectiveness by observing learners’ responses and outcomes. If learners
struggle to understand the concept, the teacher can modify the model or try a
different approach. This reflective practice improves teacher knowledge and
fosters continuous professional growth.
Impact of Modelling on Learner Learning
HED4814 ASSIGNMENT 1 AND 2: EXAM PREPARATION
Question 1
1.1. In not more than 1500 words, critically discuss the relationship between
cognition and modelling, drawing from the cognitive modelling of the
learning process and the subjective perception of cognition. Furthermore,
investigate the role of modelling in the formulation of pedagogical content
knowledge, considering the perspectives presented in the textbook
'Elementary and Middle School Mathematics: Teaching Developmentally'
by Van De Walle, JA. (2013) and its impact on teacher knowledge and
learner learning.
Cognition refers to the mental processes involved in acquiring knowledge and
understanding. These include thinking, remembering, problem-solving, and
decision-making. Modelling, on the other hand, is a process of representing a
concept, phenomenon, or idea in a way that helps learners understand it better.
In the context of education, the relationship between cognition and modelling is
critical, as effective teaching depends on understanding how learners think and
process information. This essay critically discusses the connection between
cognition and modelling, drawing from cognitive modelling of the learning
process and the subjective perception of cognition. Additionally, it explores the
role of modelling in formulating pedagogical content knowledge, referencing Van
De Walle’s work, "Elementary and Middle School Mathematics: Teaching
Developmentally" (2013).
Cognitive Modelling of the Learning Process
,Cognitive modelling is a strategy used to understand and represent how learners
process information. According to Van De Walle (2013), cognitive modelling helps
teachers design instructional strategies that align with how students think. For
example, when solving a math problem, a teacher may verbalize their thought
process step-by-step, allowing learners to observe and internalize the approach.
This method bridges the gap between abstract concepts and concrete
understanding.
Cognition is a subjective process because it varies from one individual to another.
Each learner brings unique prior knowledge, experiences, and ways of thinking
into the classroom. Teachers must consider these differences when using
modelling as a teaching strategy. For instance, a learner who struggles with
multiplication might benefit from visual models, such as arrays or number lines,
which align with their cognitive preferences (Van De Walle, 2013).
Subjective Perception of Cognition
Subjective perception of cognition refers to how individuals interpret and make
sense of information based on their experiences, cultural background, and prior
knowledge. This perception significantly influences how learners engage with and
understand new concepts. Van De Walle (2013) emphasizes the importance of
recognizing learners' subjective cognition when designing models to teach
mathematical concepts.
For example, a learner’s cultural background might influence how they perceive
patterns or relationships in math problems. If a teacher introduces a word
problem involving money, the learner’s familiarity with the currency used can
affect their ability to solve the problem. Therefore, teachers need to create
inclusive models that consider diverse perspectives, ensuring that all learners can
relate to and understand the content.
The Role of Modelling in Pedagogical Content Knowledge
Pedagogical content knowledge (PCK) is the combination of subject matter
knowledge and teaching strategies that enables teachers to effectively deliver
content to learners. Modelling plays a crucial role in developing PCK because it
, helps teachers connect theoretical knowledge with practical teaching techniques.
Van De Walle (2013) highlights that modelling is not just about showing learners
how to solve problems but also about helping them understand the underlying
concepts and principles.
For instance, in teaching fractions, a teacher might use a pie chart to visually
represent parts of a whole. This model helps learners grasp the concept of
fractions more concretely. By using models, teachers can also anticipate common
misconceptions and address them during instruction. For example, learners often
struggle to understand that 1/4 is smaller than 1/3 because they focus on the
denominator rather than the size of the fraction. A teacher can use a visual model
to clarify this misconception, enhancing their PCK.
Impact of Modelling on Teacher Knowledge
Modelling not only benefits learners but also enhances teacher knowledge. When
teachers engage in modelling, they deepen their understanding of the subject
matter and refine their instructional strategies. Van De Walle (2013) explains that
modelling requires teachers to think critically about how to represent concepts in
ways that are accessible to learners. This process involves breaking down complex
ideas into simpler components, which helps teachers internalize the content more
thoroughly.
Additionally, modelling encourages teachers to reflect on their teaching practices.
For example, after using a model to teach multiplication, a teacher might assess
its effectiveness by observing learners’ responses and outcomes. If learners
struggle to understand the concept, the teacher can modify the model or try a
different approach. This reflective practice improves teacher knowledge and
fosters continuous professional growth.
Impact of Modelling on Learner Learning
