Mathematical Concepts: Approach to Learning

Critical Reflection on my Professional Experience Placement

Annotated Photographs

Photograph 1: Annotated Photograph for PMC Learning Experience One

• The PMC learning purpose is an abstraction, and the key resources are powder, opaque lid, and bowl.
• The photograph above indicates a child measuring playdoe products, which are in a semi-solid state, otherwise referred to as powder form.
• The child measures the powder in various proportions.
• The bowl was initially covered with an opaque lid, meaning that the child could not see what was inside the bowl or determine whether it was empty.
• When the bowl was uncovered, the child noted that the bowl had nothing in it.
• When instructed to transfer the powder to the bowl, the child notes that its volume changes gradually, and this is a quantitative change.

Photograph 2: Annotated Photograph for PMC Learning Experience Two

• The PMC learning purpose is mathematical thinking, and the key resources are wooden rings.
• The child was required to identify how many wooden rings were present in the formed Caterpillar.
• Each wooden ring was therefore placed at an equidistant interval. Thus, there was a wooden ring an estimated four centimeters over the Caterpillar’s length.
• After forming the Caterpillar, the child was required to count all the rings and assign wooden numbers to them.
• The Caterpillar had a total of nine rings and was an estimated thirty-seven centimeters.
• The child’s first assessment was counting the rings from 1 to 9.

Critical Reflection

Photograph 1 provides detailed information on the powder measurement and quantitative observation activity, whereas Photograph 2 illustrates Caterpillar activity to promote mathematical thinking. The focus children engaged with the experience proactively and with great interest. The PMC learning of quantity, magnitude, and measurement could be observed during the activity, which reflected abstraction, mathematical thinking, and generalization. Both children were in the transforming phase of learning due to the ability to abstract and generalize. On the basis of the observation data, it can be concluded that the learning experience was successful, but some improvements can be made in the future. The main change would be to make the measurement of the powder more structured, intuitive, and precise to invoke interest in accuracy. Since the measuring process was complicated for the child, it impacted the activity negatively by confusing the learner in the process. However, no significant issues with a potential for improvement were present in the Caterpillar exercise. The spatial-temporal relationship was planned next to support the two focus children after the initial implementation. The reason is that the given attribute is essential to developing mathematical concepts.

My understanding of PMC learning developed through the experience profoundly. The main way the latter occurs is direct observation of how children think about the attributes with increasing precision. In my own future knowledge development, I will focus on learning more about the specific attributes which contribute to the development of mathematical concepts the most. It is important because delivering the most comprehensive and effective learning exercise packages can further facilitate engagement as well as mathematical improvement among learners.

In the case of reflection on each individual child, my first experience with focus learner A prompted me to think of supplementary ways which I can use to interact with early childhood learners on the PMCs, which I was exploring. While the learner answered questions with ease, I observed that she was sometimes confused, particularly when I gave questions that were not necessarily predictable, such as instructing her to add two spoonfuls of powder and, in quick succession, requesting her to add seven spoonsful. Based on the engagement of the child with the experience, Child A showed hesitance when carrying out the instructed task. For example, the child had to pause for a second to determine the correct way of handling the unpredictable task, such as in the case of adding seven spoons instead of the typical three. The behavior places this child in the developing phase of PMC learning, meaning she is mastering the skills of dealing with unpredictable questions. For child A, she successfully mastered the art of answering unpredictable questions, and her speed in executing tasks was improved.

Centering on the children’s response towards the PMC learning, Learner B showed easier understanding when the comparison method of learning was applied. My role in training this child was to ensure the compared material represents the real things in the child’s surroundings. Nevertheless, this child implied in the phase of transforming as his learning capability changed to an exemplary one. The core achievement in this type of learning is that children can be exposed to objects in our environment through the comparison without harming them. However, the items used in the comparison process need to reflect accuracy to impose a valid knowledge in the child’s mind. The next PMC learning that I can use for the child is Disney learning, where I expose him to Disney comics that manifest major themes in the current world. Unequivocally, the comparison method has made me understand that a lookalike object can be a valuable source of knowledge among children.

Developing an Advocacy Resource

Rationale

Advocacy in early childhood refers to speaking about and subsequently influencing actions, policies, and plans which are important to the learning process in early childhood. Children in the early years of education could face unfamiliar environments and have difficulties fitting into typical classrooms, among other factors (Reikerås, 2020, p. 704). Early Childhood Australia (ECA) has a number of tenets that guide early childhood practices. The ECA stands for a number of priorities, which in turn influence the provision of education among children. ECA collaborates and champions equality in Australia’s early childhood education. Advocacy in early childhood education is important as it influences how children’s voices are perceived in education (McCluskey, Mulligan, and Van Bergen, 2018). We should be advocating on children’s behalf to illuminate their problems by manifesting them in actions, policies, and plans. We share important information about children’s learning through structured communication with parents, communities, and policymakers.

Precursor learning has a critical role since it develops foundational skills. The key elements include children’s communication needs, positive and constructive communication methods, and the usefulness of email. My thinking was shaped in relation to the resource that I have developed because the most effective communication format is email, while I expected it to be something more advanced. The interviewee is a staff member, and one can refer to this person as JA.

Advocacy and Communicating with Staff

The staff member shared feedback on the most crucial aspects discussed below. The staff member highlighted the essence of communication in supporting the provision of quality education to children. When teachers interact with their learners effectively, they are able to highlight learners’ strengths, weaknesses, opportunities, and threats in learning. Therefore, the teachers can act accordingly and support the delivery of efficient education to the learners. The staff member emphasized the importance of communication among staff members involved in early childhood education. Effective communication therein bolsters collaboration and cooperation. The interviewee remitted that collaboration is crucial in informing best practices in instruction and helping early childhood learners achieve learning objectives (Thomas and Jones, 2021, p. 218). Such staff members can share methods and strategies which are most effective in interacting with early childhood learners. The interviewee stated that the Variety of communication tools is important for diversity in the provision of early childhood education.

Effective communication in the workplace is founded on a number of values, proportions, and strategies, as will be subsequently discussed. Effective communication is first informed by certain values, which can be seen as rules or guidelines. Effective communication ought to be founded on context and content (Hynes-Berry, Chen, and Abel, 2021). Context, in this case, refers to how information is passed in the workplace. For instance, some workplaces prefer using emails to communicate with their staff members, while others could, for instance, prefer physical meetings (Mevawalla and Hadley, 2012). Content refers to what is contained in a piece of communication. For instance, in a memo sent out to early childhood teachers in a school, it would be more practical if the information contained therein is restricted to the learner demographic unit as opposed to information that could be deemed as more applicable to higher levels of learning (Ilic, 2014, p. 17). For communication to be effective, messages ought to be founded on the applicable precincts of both content and context.

Communication in the workplace is effective if it has all the required complementary or supplementary materials. For instance, communicators ought to attach secondary or tertiary materials which are appropriate in making the messages passed therein comprehensible. Further on, effective communication ought to be founded on a two- or multi-way passage format. To this effect, workplaces ought to provide opportunities to pass feedback. Feedback is crucial as it enables the communication recipients to state their feelings about messages as well as encourages reciprocity (Thompson, 2018). Feedback supports collaboration among staff members and promotes a sense of belonging among the human resources. It is crucial that workplaces also illustrate the dedication to acting on feedback (Van den Heuvel-Panhuizen, Van Den Boogaard, and Doig, 2009). In instances where they do not find feedback tenable, they ought to reach out to their human resources and explain the rationale for such dismissals.

Communication shapes advocacy practices used by leaders in a manner where such actions translate into direct and organized plans or policies, as referred to in the section above. The elements of effective communication indicated previously are applicable to early childhood education through deliberate responses to emerging issues (Thompson, 2018). Effective communication is based on accurate content and context. Thus, leaders involved in advocacy must know what to communicate and in what ways.

Presenting the Resource

The PMCs and mathematical thinking that I am focusing on are quantity, magnitude, and measurement. As noted in the first segment of this paper, the learners were supposed to demonstrate their ability to distinguish volumes and sizes, which are essentially quantity, magnitude, and measurement of PMC activities. I developed a video resource to support staff understanding of effective communication, and it is shaped by the interview as it seeks to illustrate the essence of the subject in early childhood learning. The video draws from and reflects on information from the unit reading of building skills with an open-ended approach (Southey, 2015). The interview additional substantiates the latter statement by adhering to a wide range of communication tools. The access will be provided through a direct cloud link, and it uploading on YouTube is an option as well. The key features that will support staff to build their understanding of particular aspects of the subject are how early childhood learners’ abilities ascertains quantity, magnitude, and measurement. Therefore, the resource will highlight the essence of effective communication, particularly as it relates to staff members’ interactions with stakeholders involved in the education process (Ilic, 2014, p. 19). The resource communicates the ways in which the staff can support the children’s development, and it is focused and reflected on PMC and communication, as shown in the following list:

• Ways of interacting with early childhood education learners on children’s precursor mathematics concept learning.
• The essence of effective communication in supporting children’s precursor mathematics concept learning.
• Rules of effective communication in supporting early childhood education precursor mathematics concept learning.

Communicating with Staff

The video resource developed will be used to communicate with staff as described in the previous sections. The interview revealed that communication is critical not only to identify key children’s needs but additionally to provide good quality care and education for children in the service. One of the ways that teachers can use to help early childhood learners gain mathematical knowledge is by using mathematics games. Mathematics games are unique games where children gain mathematical knowledge with minimal instruction (Reikerås, 2020, p. 705). Thus, children could discover essential information on their own as it relates to mathematics. Such games include puzzles and wooden block games. Such games help learners associate with mathematical knowledge in a paced fashion, where they gradually gain knowledge on how to interact with numbers (Garner, Bender, and Fedor, 2018, p. 380). Mathematics games are essential in bolstering creativity and problem solving among learners.

Reference List

Garner, P. W., Bender, S. L., and Fedor, M. (2018) ‘Mindfulness‐based SEL programming to increase preservice teachers’ mindfulness and emotional competence’, Psychology in the Schools, 55(4), pp. 377-390.

Hynes-Berry, M., Chen, J. Q., and Abel, B. (2021) Precursor math concepts: the wonder of mathematical worlds with infants and toddlers. New York: Teachers College Press.

Ilic, T. (2014) ‘Extending children’s thinking through schemas: a professional responsibility?’, Early Education, 55, pp. 16-20.

McCluskey, C., Mulligan, J., and Van Bergen, P. (2018) ‘Noticing mathematical pattern and structure embodied in young children’s play’, Mathematics Education Research Group of Australasia, 8, pp. 535-542.

Mevawalla, Z., and Hadley, F. (2012) ‘The advocacy of educators: perspectives from early childhood’, Australasian Journal of Early Childhood, 37(1), 74-80.

Reikerås, E. (2020) ‘Relations between play skills and mathematical skills in toddlers’, ZDM – Mathematics Education, 52(4), pp. 703-716.

Southey, S. (2015) ‘Building mathematical skills though design play’, Educating Young Children – Learning and Teaching in the Early Childhood Years, 21(3), pp. 43-44.

Thompson, N. (2018) Effective communication: a guide for the people professions. Heidelberg: Springer.

Van den Heuvel-Panhuizen, M., Van Den Boogaard, S., and Doig, B. (2009) ‘Picture books stimulate the learning of mathematics’, Australasian Journal of Early Childhood, 34(3), pp. 30-39.