Early Numeracy: Mathematical and Pedagogical Content Knowledge Essay

This essay, submitted by Kellie Sciacca (Student number: 13894018) for EDC 145 SP4 Assessment 3, delves into the foundational aspects of early numeracy. It examines the significance of counting, sorting, and classification in children's initial understanding of numbers. The essay explores mathemat...Read More

Kellie Sciacca
Student number: 13894018
EDC 145 SP4
Assessment 3

Introduction
Early understanding of numeracy skills such as counting, sorting and
classification, is an integral skill that children need to have in order to
understand basic counting and numeracy (Beverley, Hughes & Hastings,
2020). It is a foundation for beginning numeracy, children should be able to
sort and classify the resources that they are counting, for example,
counters, blocks, animals, shapes.
This essay will discuss the basis of understanding early numeracy
composition. It will furthermore briefly discuss early numbers and place
value and the mathematical and pedagogical content knowledge relating to
these two numeracy skills. In conclusion the essay will outline various links
in the curriculum that supports the area of mathematics.
Early Number’s
Mathematical Content Knowledge (MCK)
Children start their learning mathematics before they start their elementary
school. The basic skills need to be enhanced between the children.
Mathematical content knowledge is very much essential in the fields of
teaching. As this helps in determining the best process that is needed for
teaching the children efficiently. It is important to ensure that the
mathematical concepts are made clear among the minds of each kid. The
most fundamental concept that is related to number is to understand the
whole concept of numeracy (Charalambous et al., 2019). It becomes
essential to understand the concept of numbers at an early stage
effectively so that it becomes easy to mathematical concepts. With the help
of proper mathematical knowledge it becomes easy to decide whether the
two set of numbers are same or not. Children need to be made aware
about the way maths needs to be calculated. This helps in shaping the
concept of numbers. The child must have the potential to perceive the
knowledge that has been taught to them. Once they gain complete
knowledge it becomes easy to count the sets of numbers. While teaching
the student regarding numeracy it is important to keep in mind the
important principles that are needed for carrying out the maths. This
includes one to one principle, stable order, and cardinal, abstraction, and
order irrelevance.
Pedagogical Content Knowledge (PCK)
Pedagogical content knowledge is referred to the integration of subject
expertise and skilled knowledge. Pedagogical content knowledge is
considered as an important factor while providing instructions in the
classroom. This includes understanding the approach with which the
numbers concepts are discussed with the members. The key steps that are
associate with providing proper teaching towards the children includes
encouraging the contact between the faculty members and students. With
a better communication between the students and staff it becomes easy to
clear the knowledge (Gess-Newsome et al., 2019). Early number concept
helps in providing better concept about the maths. With the help of
numbers several functions can be carried out. Thus it can be stated that
there is a need to ensure that the selected method is suitable for teaching
the children. Everyone should have clear knowledge regarding the

numbers. The pedagogical content knowledge helps in providing a better
understanding towards the subjects without any misunderstanding. This
ensures that the content is easily accessible by the students. Teaching
needs to be done properly so that it becomes easy to manage the
performance. This also offers a greater way of using the authentic
assessment approaches. Numbers needs to be identified at the early
stage so that it becomes easy to manage the mathematical.
There are several of features that are included in the pedagogical content
knowledge. All the features are developed for providing the students a
proper learning facility. One of the important feature is the combining
content and pedagogy (Iserbyt, Ward & Li, 2017). The pedagogical content
knowledge is considered as combination of the pedagogy and content. The
next feature is the understanding student perception. In this aspect the
pedagogical content knowledge needs a proper understanding regarding
the approach point of the student in reference with the subject being taught
to them. Another feature is deciding the difficulty of a subject. The teachers
who are having a good pedagogical content knowledge must be having
proper understanding of the subject regarding which parts are difficult and
which part are easy.
Place Value
Mathematical Content Knowledge (MCK)
The basic concept is that teachers should have adequate amount of knowledge in those content
areas for which they have been hired. They need to have a deep understanding especially in case of
mathematics that includes the procedures as well as the concepts. Mathematical content knowledge
is required to be able teach it to others. The knowledge of the content will help in clearing the
concepts of others. In case of mathematics, content knowledge includes the procedures, concepts
and the mathematical processes as well that are necessary to make use of mathematics. A teacher’s
capability to provide relevant solutions to various problems by making use of different methods
comes under the purview of this (Sears, 2016). The way a pedagogue adapts himself to different
contexts is evaluated in this. The ability of an individual to make use of reasoning and other proofs
for investigating conjectures as well as evaluating mathematical arguments are included in
mathematical content knowledge. Individuals should be able to make use of algebraic reasoning and
relate to various other topics in mathematics. In this context, understanding the concepts of place
value will provide the foundation for various operations with the number system specifically whole
numbers. The knowledge of the content of place value will help the teachers to explain the same to
the students. The basic concept of place value is that it is the value which is represented by a specific
digit in a number and this depends on the digit’s position in that number.
Pedagogical Content Knowledge
Pedagogical content knowledge includes a teacher’s ability to make use of content
knowledge. This knowledge requires a teacher to make use of his knowledge to properly unwrap
different topics of mathematics and present the same in such a way that students learn the same
properly. Pedagogical content knowledge also considers an individual’s capability to make use of his
content knowledge for accessing different representations along with the various methods that need
to be used for solving problems in mathematics (Keller, Neumann & Fischer, 2017). The ability of a
mentor to help the students link the concepts learned in one chapter with that of the concepts in

another comes under the purview of pedagogical content knowledge. The responsiveness of the
teachers to the questions asked by the students is also considered in pedagogical content
knowledge. The teachers should be able to understand the queries of the students and why they are
repeating some mistakes. The weak point of the students in mathematics should be recognized by
the teachers. The teachers should be capable enough to handle different questions of the students.
Their ability to satisfy the students with the answers should be enhanced with every passing day and
their experience in teaching (Oleson et al., 2018). This requires the teachers to conduct interactive
sessions with the students so that they can understand where the student is facing problem. The
interaction between the teacher and the student should be focussed on so that students feel free to
approach the teachers whenever they face any problem regarding concepts or methods in
mathematics.
Links to other areas of mathematics-How can these area’s support
other areas of mathematics
Mathematics aims at encompassing the growing variety and depth. With
the help of proper mathematical links it becomes easy to manage the
performance. Daily lives have a link with mathematic calculations. Thus it
becomes essential to ensure that proper link is maintained while
performing the activities. The major importance of proper mathematical
knowledge is that it helps in shopping, ensures that the foods are prepared
with calculating correct measures. Mathematics is used as a main support
in the fields of calculations. It becomes very much essential to have proper
knowledge. Maths is considered as an important element in managing the
money in banks and other areas. With the use of early numbering featuring
it becomes easy to identify whether a number is a real number, whole
number or a natural number. Almost everything is related to maths. Thus it
becomes essential to gain a better knowledge regarding the different fields
of maths (Young, 2018). This helps in having a better calculative
knowledge. Mathematics knowledge helps in preventing the life from
getting hampered by the problems. The key qualities that are needed for
becoming a better knowledge in the fields of maths are having a better
reasoning knowledge with proper creativity and abstract. In this aspect, it
can also help in mathematics by enabling the teacher so that they can
engage within a particular type of teaching tasks. Here, it can include how
accurately the mathematical ideas can be represented and it will be also
helping providing the mathematical explanations for common type of
procedures and rules for the understanding and examination process of
solution methods.
Conclusion (100 words)
From the above discussion it can be concluded that basic counting and
numeracy is important for the children and for appropriate numeracy skills
are important. In the current paper various aspect of the numeracy skills
has been discussed. Also, basic understanding of the early numeracy
composition has been discussed within this report. This paper includes an
important and a brief discussion on the mathematical content knowledge,
pedagogical content knowledge and mathematical content knowledge. In
this aspect link to other areas of mathematics has been discussed

thoroughly. Here, also the early numbers and the place value has been
discussed within this report.

References
Beverley, M., Hughes, J. C., & Hastings, R. (2020). Improving Essential Numeracy Skills in Primary
Schoolchildren Using a Brief Fluency-building Intervention.
Charalambous, C. Y., Hill, H. C., Chin, M. J., & McGinn, D. (2019). Mathematical content knowledge
and knowledge for teaching: exploring their distinguishability and contribution to student
learning. Journal of Mathematics Teacher Education, 1-35.
Gess-Newsome, J., Taylor, J. A., Carlson, J., Gardner, A. L., Wilson, C. D., & Stuhlsatz, M. A. (2019).
Teacher pedagogical content knowledge, practice, and student achievement. International
Journal of Science Education, 41(7), 944-963.
Iserbyt, P., Ward, P., & Li, W. (2017). Effects of improved content knowledge on pedagogical content
knowledge and student performance in physical education. Physical Education and Sport
Pedagogy, 22(1), 71-88.
Keller, M. M., Neumann, K., & Fischer, H. E. (2017). The impact of physics teachers’ pedagogical
content knowledge and motivation on students’ achievement and interest. Journal of
Research in Science Teaching, 54(5), 586-614.
Oleson, A., Mendez, C., Steine-Hanson, Z., Hilderbrand, C., Perdriau, C., Burnett, M., & Ko, A. J.
(2018, August). Pedagogical content knowledge for teaching inclusive design. In Proceedings
of the 2018 ACM Conference on International Computing Education Research (pp. 69-77).
Sears, R. (2016). Developing Preservice Teachers’ Mathematical Content Knowledge with
MyMathTest.
Young, N. D. (2018). Mathematical Content for Teaching: Solving the Student Achievement
Equation. Stars in the Schoolhouse: Teaching Practices and Approaches that Make a
Difference, 99.