The Early Years Learning Framework: Mathematics Teaching and Learning Experience

This discussion focuses on the early childhood learning and teaching experience, particularly in mathematics. It includes observations of learning, fostering numeracy, relational and instrumental learning, and mathematical reasoning and problem solving. The discussion is based on personal experience and the Australian Curriculum Mathematics.

Running head: THE EARLY YEARS LEARNING FRAMEWORK
THE EARLY YEARS LEARNING FRAMEWORK
Name of the Student:
Name of the University:
Author Note:

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Contents
Introduction:...............................................................................................................................2
Part 1:.........................................................................................................................................2
Discussion Topic 1: Observations of Learning......................................................................2
Discussion Topic 2: Fostering Numeracy Video...................................................................3
Part 2:.........................................................................................................................................5
Task 1: Rational and instrumental learning:..........................................................................5
Task 2: Mathematical reasoning and problem solving:.........................................................8
Conclusion:................................................................................................................................9
Reference list:...........................................................................................................................10

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Introduction:
The aim of the discussion is to understand the early childhood learning and teaching
experience. The discussion is based on both personal experience as well as the way
mathematics is taught to the children in the early childhood phase.
Part 1:
Discussion Topic 1: Observations of Learning
Answer 1: An experience of teaching mathematics
Once I got the chance of teaching maths to 5 children together who were at second
standard. The addition and subtraction were very new to 3 of them whereas 2 of them knew
how to do it. Although I was determined to teach afresh to each individual, there was some
kind of confusion among the 2 children who already new the method because I did not start
with direct calculation but I preferred using story sums to explain them the process in more
details. According to the Burns’ article, if we add words to mathematics, it becomes easier for
the children to understand the situation (Burns, 2003). This was indeed true, there was a clear
indication that all the children were finding it very interesting to work on numbers when they
were made understand in terms of a story. Thus, the class contained more talk and writing
was a part of the learning.
Answer 2: Linking the experience with The Australian Curriculum Mathematics
As mentioned that the children were in the second standard and they were in between
5 and 7 years old. As per The Australian Curriculum Mathematics, the children of this level
developed the understanding, fluency along with reasoning and problem solving. In fact,
these are the part of the mathematics curriculum that teaches about the number and algebra,
along with geometry and probability. It was made clear that the concept of addition and

THE EARLY YEARS LEARNING FRAMEWORK 3
subtraction was made clear only when texts or story was involved in the learning process. At
this level, the children showed the four proficiencies and those were understanding, fluency,
problem solving ability and at the same time reasoning. It was clear that by the means of
working on the numbers by reading and understanding the text, the level of problem solving
and reason can be easily interpreted among the learning children.
Discussion Topic 2: Fostering Numeracy Video
The video talks about numeracy and its importance in learning among the children.
According to Bragg, numeracy is the process of communicating, understanding and applying
the mathematical concepts and information. Numeracy gives the ability to make connection
and to understand the mathematics in the world that can be a demand of any moment at
school, home or any other broader community. It is largely related to the logical reasoning
and the idea of mathematics. Children have been found to show much interest when it comes
to numbers and mathematics and numeracy can be used to solve major issues related to
measurement, counting and also to compare between two objects.
The key idea shared in the video is that we should focus on teaching numeracy to the
students rather than forcing them to work on mathematics. In this way, we shall be able to
make the students understand the basic concepts of calculation and counting. Our day to day
life activities involve measurements and geometry and thus, numeracy ill help in creating
understanding among the students. We can either explain the students by the means of
numbers or pictures and numeracy can help the children to understand the mathematics
around them.
The similar approach can be used for teaching students in future and shall
incorporate the same while teaching students in future. It might happen that there arise few
instances where I might face challenges in teaching the student. For example, students from

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different socio-economic backgrounds are likely to face challenges to understand the concept
because certain barriers like language or communication might not be proper and the student
might not be able to understand what has been taught. The sequence of learning might not be
understood properly and as a result of which there can be significant outcome of the teaching.
As mentioned that the numeracy requires detailed discussion with the learners, students who
have different dialects might face certain issues in understanding and coping up with the
studies. The teachers have to be versatile and undertake the perspective of the students who
learns in different language so that right communication is done and the children will be able
to receive the best out of it.
Language and dialect can be the key issues to consider while addressing numeracy
needs of diverse learners. People from different background will have different language
proficiency and thus, if they are taught by using pictures and other materials, there would not
be language barrier. In fact, students can be exposed to other process like explaining the
height by showing a video of a Koala jumping from a tree. This way, their problem solving
skills can also be improved and they can relate the daily activities with mathematics. It has to
be understood that different children has different understanding and thus, the teaching
procedure should be different as well. Often children should be treated considering their
background and other factors like their disabilities or related factors.

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Part 2:
Task 1: Relational and instrumental learning:
In the article, Skemp has built upon the fact that one gets faux amis while dealing
with the different types of learning and relational behaviour because the teaching and
learning are not same throughout the world. We might often come across such situation
where a person could come across different cues due to the difference in their language,
country or the way of learning (Skemp, 2006). It is during this point of time there are certain
factors that acts accordingly. These approach of a person has been characterised by calling
them, ‘relational understanding’ and ‘instrumental understanding’. For example, a similar
word can mean different in different language, but the meaning of the same word can be
determined by understanding the context where the word has been used. When a reader or a
learner takes the approach of dealing with certain materials like books in order to read and
understand the concept, it is usually referred to as instrumental learning. In such situation, the
ability of thinking rationally or with reasons reduces because the reader considers what is
written in the particular material and tries to incorporate the same as a part of the learning and
tries to establish a relationship with the word and the context and thus, a relational
understanding is established. All these perspectives depend on the diverse needs of the
children coming from different socio-economic background or someone with physical
disabilities (Skemp, 2006). One can be able to comprehend the topic properly by reading and
understanding the examples used in the text and thirdly, the concepts can be really useful for
others to a reference.
Skemp is of the opinion that the relational and the instrumental thinking and learning
needs to be filled simultaneously in order to make sure that the student receive the written
knowledge and at the same time has developed the rational idea behind the particular

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concept. It is depended on the ability of a person to interpret a situation and align it with the
understanding gained from the instrumental learning. It is only when one will be able to link
up his relational with the instrumental learning, the idea of proper learning can be establish.
Adding to the importance of the rational learning, Skemp gave the example of playing sports
like football (Skemp, 2006). He explained easily that one needs to understand the relational
part of the game rather than the instrumental part because when it comes to actually act at the
particular ground, it completely depends on the relationship of the person with other players
and not on what achieved as a part of the instrumental learning. Similar thing happens when
student are being asked to work on particular formulas or examples in mathematics. If we ask
the children to give proper evaluative answers to particular formulas, it might become
challenging for the children to answer as the concept of the particular formula might not be
clear to the student. Likewise, if a judgement was given to the student and was asked to
answer the particular sum, the student could easily apply the concept and could have
answered it easily (Skemp, 2006).
It has been much criticised that whatever is taught today in the modern mathematics is
merely instrumental and not relational and that there is huge scope in bringing improvement
to the existing learning procedure. Instrumental learning can be really easy to explain and
understand but a relational knowledge will bring better knowledge that would prove effective
in life not only for mathematics but while teaching other subjects as well. In order to improve
the learning process, it has been highly recommended to use innovative means to
accommodate the learning. One needs to come up with the idea that would make the children
understand the concepts of developing a relational attribute rather than focusing on the
existing things in the books and other reading materials.
Discussion on the idea to build relational as opposed to instrumental understanding in
early childhood setting:

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Ladhams, J. (2005). Teaching children to understand operations in early
childhood. Australian Primary Mathematics Classroom, 10(4), 19.
In the above mentioned article, the author aimed to underline the concept of Skemp in
distinguishing between the relational and the instrumental understanding of the student. The
educators are found to use the connections between addition, subtraction, multiplication and
division and related to the relational thinking of the students. The Western Australian State
Government focused on the relational and the instrumental learning of the children so that
they understand the reason behind the calculation and the operation. It has been commonly
observed that the learning mechanism depends on the particular student and his ability to
make the connection between the concept and the understanding. Once the student justifies
the thinking ability, the choice or the method of the calculation can be done accurately
(Ladhams, 2005). It is also true that most students lacks the basic concept of understanding
and find it difficult to give reasons behind the learning and one has to understand the relation.
It depends on the ability of the student to fill the deficiency with their understanding.
However, there should always be a rational approach of learning in order to make sure that
the particular problem can be solved easily.
In order to develop the understanding among the children, it is important to
understand that the learner have adequate knowledge on the numbers and operations. It has
been pointed out that unless a particular mathematical model is understood completely
rationally and the relation is understood, there cannot be any other means by which a student
would be able to understand the context. Thus, the role of relational thinking plays here rather
than the instrumental concept (Ladhams, 2005). In fact, it has also been pointed out that the
relational thinking not only develops by the means of study and education but our day to day
life activities also teaches us many things that the books or the other learning means could not
provide us. There are various ways of teaching numbers to the students and the use of

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physical materials like marbles can be used to teach those numbers, when they are able to
understand the relation between different objects and numbers. In fact, the students will get a
more in-depth knowledge and can make the evaluation of the findings more properly.
Task 2: Mathematical reasoning and problem solving:
Problem solving has been defined as the process of reaching out a solution by
working through the issue in details. There can be various means of problem solving and one
can use the approach of mathematical or systematic operation and at the same time can utilise
the critical thinking ability in order to solve a particular issue (Ladhams, 2005).
Reasoning has been defined as the process of drawing out the conclusion or the
inference by the means of a use of a particular reason. In such case, we use the information
and try to compare it with our understanding.
The difference between problem solving and reasoning can be stated as the reasoning
is a logical and practical part that arises at any point of time while dealing with any kind of
situation. However, reasoning is an important factor that cannot be take place at any point of
time but requires deliberate effort to overcome the particular point (Haylock & Cockburn,
2013). Reasoning is also accompanied by one’s own ability to overcome the particular issue
and think of better ways.
Children are often found to compare their part of things with others. Like they
compare how much water is filled in a bottle or who has received a bigger piece of the cake.
These are the few examples of the reasoning that requires numerical knowledge as well and
the students are learning such things which developing the capability of logical reasoning
(Ladhams, 2005).
Discussion prompts:

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Q1. Which would be heavier, one kilogram of iron or one kilogram of cotton?
Q2. If today is Wednesday, which day comes after 7 days?
Q3. How much is 4 multiply by 3?
Conclusion:
The above discussion highlighted the various aspects of learning and teaching as
described in the Australian curriculum. It has been found that the curriculum focuses on the
reasoning and the rational judgement of the students and not merely only on the written and
instrumental concept stated in the books.

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Reference list:
Arthur, L., Beecher, B., Death, E., Dockett, S., & Farmer, S. (2017). Programming and
Planning in Early Childhood Settings with Student Resource Access 12 Months.
Cengage AU.
Bragg, L., Muir, T., Livy, S., Clark, J., Wells, J., & Attard, C. (2017). Engaging with
mathematics through picture books.
Burns, M. (2003). 10 big math ideas. Scholastic Instructor, 113, 16-19.
Clarke,D.M Clarke.D.J & Sullivan P. 2012 Reasoning in the Australian Curriculum:
Haylock, D., & Cockburn, A. D. (2013). Understanding mathematics for young children (4th
ed.). London, England: Sage Chapter 1, 'Understanding Mathematics'
Jimenez. B.A., & Kemmery M. (2013) Building the early numeracy skills of students with
moderate interllectual disability, Education and training in Autism and developmental
disabilities 48(4) 479-490
Ladhams, J (2005) Teaching children to understand operations in early childhood Australian
Primary Mathematics Classroom 10(4) 19-26
Laureate Education (Producer). (2014b). What is numeracy? [Video file]. Baltimore, MD:
Author.
McLachlan, C., Fleer, M., & Edwards, S. (2018). Early childhood curriculum: Planning,
assessment and implementation. Cambridge University Press.
Merkley, R., & Ansari, D. (2016). Why numerical symbols count in the development of
mathematical skills: Evidence from brain and behavior. Current Opinion in
Behavioral Sciences, 10, 14-20.

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Peers, C., & Fleer, M. (2014). The theory of ‘belonging’: Defining concepts used within
belonging, being and becoming—The Australian early years learning
framework. Educational Philosophy and Theory, 46(8), 914-928.
Pitt, C. Luger. R.. Bullen A Phillips P & Geiger M (2013) Helping children learning
mathematics (1st Australian ed) Brisbane, Australia, Wiley. Chapter 2 helping children
learn mathematics with understanding
Reys, R. E., Lindquist, M., Lambdin, D. V., Smith, N. L., Rogers, A., Falle, J., Frid, S., &
Bennett, S. (2012). Helping children learn mathematics (1st Australian ed.). Brisbane,
Australia: Wiley.
Skemp, R. R. (2006). Relational understanding and instrumental understanding. Mathematics
teaching, 77(1), 20-26.