Portfolio of Mathematics Projects

This portfolio covers various topics related to mathematics, including contextualising maths experiences, assisting parents to support children's mathematical understanding, mathematical conversations, intentional teaching of mathematical concepts, and resourcing an early childhood program for mathematical enquiry based learning.

Portfolio of
Mathematics Projects

Table of Contents
INTRODUCTION...........................................................................................................................3
MAIN BODY...................................................................................................................................3
Contextualising maths experiences with babies, toddlers and pre-schoolers.........................3
Assisting parents to support children’s mathematical understanding....................................5
Mathematical conversations...................................................................................................6
Intentional teaching of mathematical concepts......................................................................7
Philosophical position statement on mathematics..................................................................9
Resourcing an early childhood program for mathematical enquiry based learning.............10
CONCLUSION..............................................................................................................................10
REFERENCES..............................................................................................................................11

INTRODUCTION
The concept of mathematics covers several topics and some of them are listed to the
hundreds of articles and the concerning templates to the right which is undertaken in the
alphabetical lists for the mathematical articles. The concepts bring together the similar content in
the organised manner which is better suited for the browsing. The concepts of mathematics cover
various basic topics like advanced mathematics, integrals, general concepts, reference tables and
mathematical objects (Yashin and et. al., 2018). While entering in the school, children begin to
develop their basic skills and mathematics makes it possible for the students in terms of solving
the simple number based issues. Children become intensely involved during their paly by
considering their own purpose and also leads to tackle issues which are challenging for them.
The nature of learning children is sticking with the problem, puzzling over it and approaching it
in the different manner that lead towards the powerful learning.
MAIN BODY
Contextualising maths experiences with babies, toddlers and pre-schoolers
In mathematics, contextualisation is important that leads to develop the direct link among
the maths and real life situations and scenarios through the imagination of students. The children
also get proper vision towards the maths as they are learning by using it in terms of recognising
and understanding the context. Therefore, most of the children prefer learning through real life
examples or digital classes as traditional methods are not promoted in modern era.
Toddlers: It include the age group of 6 months to 2 years that include several teaching
methods to toddlers which are really easy. Toddlers learn through their daily activities and also
by exploring their surroundings. The learning experience of toddlers include the counting cars,
pointing towards the colour, counting their jumps, pointing towards the different shapes, looking
for the numbers on newspapers, magazines or mail boxes (Criscuolo and et. al., 2021). Giving
toddlers the real life experience of math concepts such as numbers, measurement and shapes is
considered as the great way to get them thing learn effectively.

Babies: It include the age group of 2 to 4 years that undertake different and unique
teaching concepts to the children which is easy for them. Babies develop the concept of maths
and skills very early in their life. Children learn from their everyday experiences and also
through several interactions with trusted adults. Babies use math concepts in order to make sense
of their world (Ngoko, Cérin and Trystram, 2019). For instance, when babies want more food
then more is considered as the concept to make sense of the world. Moreover, during the early
age, babies learn mathematical concepts through shapes, sizes of things, drawing, verbally and
many more.
Pre-schoolers: Counting help children in terms of learning their number in sequence as
they need to develop the basic understanding of numbers first. It includes the age group of 4 to 6
years that include number concept activities and counting through everyday objects like the
count of buttons of shirt, the oranges put in the grocery bag, the forks needed to set the table and

many more. The pre-school children prefer to learn several mathematical concepts by paper,
notebooks, visual learning method.
Assisting parents to support children’s mathematical understanding
It is broadly recognised that families and parents plays the essential role for the primary
educator of children and also responsible for laying down the intellectual foundations for the
effective learning and development. Parents need to support the resources of schools that are
available and also permit teachers to organise effective workshops for the parents in their own
schools. It includes effective guide, leaflets for the parents, workshop plan and so on. There is a
great potential in the home and family of children’s mathematics learning (Bodnar and et. al.,
2020). In terms of understanding things in several ways that are used in mathematics out of the
school can help in order to enhance the attitude of children towards mathematics and also help
them in understanding the value and relevance in the variety of contexts.
Further, parents do not need extensive mathematical knowledge to support their children’s
learning. Discussion of interesting questions and also talk regarding various ways in which math
can help in everyday activities that can be more useful instead of knowing the correct process
and answer. Parents and wider family is also motivated to explore that mathematics which is
involved in family and activities and also leads to share it with children. Also, children need
continuous support in terms of recognising the mathematics in the world around them as parents
are the best people to provide this support (Demir, Cynthia and Başboğaoğlu, 2018). Parental
involvement is positively interlinked with the achievement of their informal and incidental
things. Parents also need to focus on the effective achievement but the stakes that do not have to
be high and their involvement can be more relaxing, contextualised and collaborative with
natural events.

Mathematical conversations
It is considered as the central idea in terms of developing the accuracy, efficiency and
flexibility with the numbers. It includes the inquiry in which the teacher leads to facilitate the
math conversations and include various steps to enhance the number sense. It is the harmonic
measure that leads to relate with any boundary function and its harmonic extension, as it is also
able to hit the probability of the boundary for moving inside the domain (Arribas and et. al.,
2019). This conversation is important among the students and children as it is the essential
approach in which the students provide effective information which is needed for the
mathematics lesson that include the teacher simply by telling students about what they need to
know.
It is the thoughtful approach for the student engagement that leads to motivate the productive
conversation. In terms of engaging students in the productive mathematics discussion, it is
essential to learn about the whole environment. Students need to be encouraged in terms of using
the problem-solving, communication skills, reasoning etc. to explore their own ideas and
approaches by finding out the relevant solution to the routine and non-routine mathematics
issues. The conversation includes:
 Students and teachers acknowledging and discussing suitable errors and the reasons
behind them to help students for developing great understanding.
 Students questioning each other regarding the use of mathematics arguments to develop
the correctness of solutions.
 Students also reach and justify the conclusions which are based on their own mathematics
understanding and knowledge without relying over the authority of teachers.

 Children are motivated to use the variety of approaches to convey their solution and
knowledge strategies considering the oral presentations, physical, graphical, written
explanation and so on.
 Most of the students also engage within the “productive struggle” with suitable scaffolds
for support.
Intentional teaching of mathematical concepts
Intentional teaching is an active process and the significant way of relating things to
children that tends to embraces and develop on their strengths, ideas, needs and interests. It
requires teachers to be purposeful in their actions and decisions as teachers use the range and
balance of strategies to provide and promote the learning of children (Shmatko, Gokhberg and
Meissner, 2020). Here, educator need to be deliberate, purposeful and thoughtful in their overall
decisions and actions. Intentional teaching is the opposite of teaching and also continuing with
traditions simply due to few things that have been done in an effective manner.
For instance, a group of five children came into the room in which A and B welcomed
them. They had to set out the tubs of polygons in the several varieties of shapes and sizes. From
this, polygons were available four time over the course and in which B student came to the
polygon centre and sat on the floor while selecting some 2D shapes. He set two red triangles into
the form of a square (Shown below).
After some discussion, student A came and said by pointing out the triangles that “it’s a square”.
Further, put two small blue equilateral triangles collectively.

After figuring it out, “it seems like different shaped triangle” student B said by pointing out the
sides of equilateral. Further, student A found two small yellow obtuse, isosceles triangles by
thinking that it leads to shape square or not.
Student B pointed to the yellow hexagon in the designs that was in the same colour as the yellow
triangles. After sometime, student A held up the two large yellow squares and put them
collectively to make the long square.
One of them sat bac and watched the whole process. Student B changed the design and also
contain a long column of yellow squares that aligned with the column of green rhombuses filling
with the space.

Philosophical position statement on mathematics
The philosophy of mathematics education is an interdisciplinary area of study and the
effective research which is based on the intersection of the several fields of mathematics
education and the philosophy of math that consider the inclusive sense to consider
multidisciplinary theories regarding mathematics. In regard of this, there are several theories for
the mathematics learning that include the elements of constructivist theories of learning and also
can be tracked back to the antiquity (Woolcott and et. al., 2020). Further, the philosophy of
mathematics has the range of suitable perspective which is termed as “absolutist”. Through this
theory, it exceeds the intended scope, absolutism that suggests the sanctioned image of
mathematics in terms of rigidity, fixed, logical, absolute, cold, objective, pure, abstract and so
on.
Apart from that, Fallibilism consider mathematics as the result of social processes that
include the knowledge which is being understood as the eternal factor for the revision both in
terms of the proofs and concepts. It tends to view to embrace the practices of mathematicians
considering the human culture, issues for values, education and so on. The view of Fallibilist
does not reject the role of structure and logic in mathematics considering the notion that there is
something unique and permanent enduring the hierarchical structure (Pareja Roblin and et. al.,
2018). Fallibilism does not reject the absolutist image of mathematics as the pure body and
perfect abstract knowledge which exists among the superhuman. Mathematics is associated with

the set of social practices with its history, institutions and social locations and so on. hence, it is
essential make difference among the Fallibilist or absolutist epistemology of math by considering
the nature of mathematics.
Resourcing an early childhood program for mathematical enquiry based learning
Learning is an approach that leads to support student centred methods of teaching that
include students regarding their overall development for own learning. As it seems like inquiry
based instruction has not been employed broadly in the subject area of mathematics as it leads to
conduct the study focusing on the young children (Graham, Jaki and Harbron, 2020).
Kindergarten children depict the shapes through several levels from which the first one is
recognition level in which children tends to recognise the subset of shape’s considering the
visual characteristics. Children at the age of five years old have the difficulty in describing
shapes through which the language which is used in terms of describing the shapes is gradually
developed.
Moreover, the primary description of children includes several terms and attributes that is
based on the effective description in comparison with the specific representation of shapes. The
kindergarten classroom is the place where the intervention took place and the students are
classified into some categories considering the cultivating the conditions for the math discussion.
Therefore, the obstacles lead to cause the shortage of inquiry based instructions which is being
employed widely in the subject area of mathematics and the shortage of studies which is being
conducted by focusing over the young children.
CONCLUSION
From the above discussion, it has been summarised that effective learning of mathematics
concept is essential for the overall development of students. The experience of mathematics is
quite different for each and every stage of children like toddlers, babies and pre-schoolers. For
this, teachers also use different approaches for the children of different stage to make them
understand the learning theories for their development.

REFERENCES
Books and Journals
Arribas, I and et. al., 2019. Negative screening and sustainable portfolio
diversification. Enterpreneurship and Sustainability Issues, 6(4), pp.1566-1586.
Bodnar, T and et. al., 2020. Statistical inference for the expected utility portfolio in high
dimensions. IEEE Transactions on Signal Processing, 69, pp.1-14.
Criscuolo, P and et. al., 2021. The sequence effect in panel decisions: Evidence from the
evaluation of research and development projects. Organization Science.
Demir, M., Cynthia, A.T. and Başboğaoğlu, U., 2018. Comparative investigation of alternative
assessment methods used in Turkey and United States elementary 4th grade
mathematics curriculum. International Journal of Educational Administration and
Policy Studies, 10(7), pp.72-82.
Graham, E., Jaki, T. and Harbron, C., 2020. A comparison of stochastic programming methods
for portfolio level decision-making. Journal of biopharmaceutical statistics, 30(3),
pp.405-429.
Ngoko, Y., Cérin, C. and Trystram, D., 2019. Solving SAT in a distributed cloud: a portfolio
approach. International Journal of Applied Mathematics and Computer Science, 29(2).
Pareja Roblin, N and et. al., 2018. Exploring shifts in the characteristics of US government-
funded science curriculum materials and their (unintended) consequences. Studies in
Science Education, 54(1), pp.1-39.
Shmatko, N., Gokhberg, L. and Meissner, D., 2020. Skill-sets for prospective careers of highly
qualified labor. Handbook of labor, human resources and population economics, pp.1-
14.
Woolcott, G and et. al., 2020. The re-emergence of spatial reasoning within primary years
mathematics education. In Research in Mathematics Education in Australasia 2016–
2019 (pp. 245-268). Springer, Singapore.
Yashin, S.N and et. al., 2018, April. Anti-crisis cluster innovation strategy risk management with
usage of real put option. In International Conference Project “The future of the Global
Financial System: Downfall of Harmony” (pp. 987-1001). Springer, Cham.