Mathematical concepts among toddlers rely on the Early Years Learning Framework (EYLF), which entails the concepts and processes essential in shaping young children’s mathematical development during their years of education (Ortlipp et al., 2011). This strategy relates to mathematical thinking skills, learning dispositions, and mathematical terminologies. EYLF framework guides education stakeholders with children education for children from birth to five years of age. This paper will focus on a case study of Levi, the 2.5 years child who made a zoo using stacking blocks. The paper will examine the various mathematical skills, learning dispositions, and mathematical terminologies used in the video and conduct critical analysis.
Mathematical Skills
Levi’s case is connected to EYLF as there is evidence of mathematical thinking skills. Levi showcases a wide range of cognitive abilities through reasoning, problem-solving and engaging in mathematical concepts (Knaus, 2017). Levi can recognise various patterns. For instance, he explicitly demonstrated pattern understanding when he picked up a rectangular block and tossed it aside, as it is not a part of his structure, being square blocks only. This skill is critical in the cognitive development of children through identifying recurring patterns in their environment. Also, this skill helps lay the foundation for mathematical skills and problem-solving. Toddlers can begin by identifying simple visual patterns of shapes and colours (Knaus, 2017). Levi can determine the various shapes and colours he uses to fill his object in his games, like square bits and orange colours.
Furthermore, there are aspects of object patterns where toddlers may notice patterns in objects. For instance, Levi is seen arranging objects based on size and colour. Additionally, children gain mathematical skills by sorting and grouping objects based on their unique features, such as colour and shape. Levi is seen comparing the rectangular block to his square block; he then tosses it aside, resulting in him sorting the blocks Various studies show that pattern recognition in children can be done through engaging in playful activities, toys, and their engagement with their caregivers, which boosts their cognitive development. Pattern development sets a foundation for other cognitive development and learning among toddlers.
Moreover, mathematical skills are evident as children develop logical reasoning in mathematical concepts, which lays a foundation for cognitive skills and understanding mathematical concepts and problem-solving skills (Cohrssen & Niklas, 2019). Young children demonstrate their engagement in logical reasoning by appreciating their environment. This strategy can be demonstrated through spatial reasoning, where toddlers engage in spatial activities by fitting shapes into matching spaces and stacking blocks to create stable structures. Levi demonstrates his spatial reasoning by successfully matching the spaces and stacking the blocks to create a stable structure that invokes his mathematical skills. Also, he said, “9 more bits to go”, showing his understanding of logical reasoning of numbers. Likewise, mathematical skills are evident in Levi’s case through the skills observed in problem-solving (Cohrssen & Niklas, 2019). Levi uses blocks to develop a complete structure that demonstrates problem-solving skills developed through pattern recognition. Finally, the concepts of matching and sorting are critical in developing mathematical skills in toddlers, as is evident in Levi’s video. Toddlers demonstrate logical reasoning when matching and sorting objects based on unique features like colours, shapes and sizes. Therefore, there is a need to encourage and support logical reasoning in mathematical concepts for toddlers, which can be done through engaging in gaming activities. According to scholars, toddlers should be provided opportunities for exploration, problem-solving and interactive experiences with various shapes and objects to nurture their logical thinking skills.
Additionally, the concept of learning through play is evident in Levis’s case. The EYLF highlights the importance of play in early childhood education. Various researchers claim that play-based learning allows children to apply mathematical thinking skills in their environment (Cohrssen et al.,2013). When children engage in play, children can develop a deeper understanding of mathematical concepts and help to develop a connection between mathematical concepts and their environment. Levi showcases his mathematical skills through the play of arranging objects by identifying patterns around them and arranging them as they are supposed. Finally, in mathematical skills, there is intentional teaching where caregivers provide children with resources that would trigger their mathematical thinking skills and ask open-ended questions and encourage problem-solving skills (Cohrssen & Niklas, 2019). Levi has been provided with blocks, and his mother is heard asking him questions and encouraging him to complete the task. Thus intentional teaching practices support children’s mathematical development and curiosity.
Learning Disposition
Dang & Keamy (2022 state that learning disposition refers to concepts relating to children’s attitudes, learning methodology and temperaments towards mathematics. These concepts’ attitudes include curiosity, perseverance, creativity, and readiness to take risks and explore new ideas. Curiosity is a critical aspect that seeks a distinctive desire to examine and seek knowledge about various concepts (Chen, 2003). Curiosity plays a critical role in learning mathematical concepts in their cognitive, social and emotional growth. Levi is seen as a curious child when constructing his zoo using square blocks to cover the surface area of his orange board. He has completed two rows that can fit 4 square blocks. As he moves onto his third row, he picks up another square block from the Lego box, says, “I need this block now, ” and places it in its spot. Furthermore, Levi demonstrated his creativity and imagination through his engagement in the curious activity, which steers him to explore new ideas and engage in imaginative play by constructing a zoo using blocks.
Moreover, based on EYLF, there is a need for learning environments as a way of creating a supportive and diverse learning environment to promote and enhance a solid mathematical foundation (Maxwell, 2001). Levi’s case involves the utilisation of learning through the provision of the learning blocks to make a zoo which positively enhances his mathematical skills through enhancing creativity, problem-solving skills and curiosity.
Mathematical Terminology
Artigue (2002) states that mathematical terminology refers to the explicit language and vocabulary used in mathematics as children engage in mathematical activities. EYLF encourages the use of mathematical terminologies to reinforce mathematical concepts and knowledge. Levi’s activity demonstrated the use of mathematical terminologies. Levi has used size terms related to mathematical knowledge when using words such as big and short. He says, “I see that these blocks are smaller and these ones are bigger,” showing practical use of mathematical terminologies. Also, Levi demonstrates his understanding of counting numbers with the objects as he calls out “one” and “nine,” showing his understanding of numbers.
Observation further explored measurement through the objects acting as a non-standard unit of measure (Sarama & Clements, 2009). This strategy is shown a few times when Levi identifies how many more “bits” he needs to complete his row and board, referring to his square blocks. Furthermore, toddlers like Levi use shapes to describe the forms of the objects they are playing. For instance, Levi claims he is using his square bits. Likewise, Levi understood the various numerals as Levi observed numerically before placing his blocks in his structure, demonstrating the use of mathematical terminologies. Finally, toddlers use basic mathematical actions, demonstrating an understanding of mathematical concepts, as Levi uses stacking when claiming he is making a zoo.
Conclusion
Levi’s playful game of arranging bits into a zoo structure allows him to develop a mathematical foundation. This strategy is demonstrated through mathematical skills demonstrated through patterns, sorting and grouping objects based on their unique features, logical reasoning, and spatial reasoning. Also, Levi has demonstrated the use of learning disposition through curiosity, active participation, and adopting a diverse learning environment, which triggers his cognitive ability and boosts mathematical concepts. Finally, Levi has adopted various mathematical terminologies by comparing words, understanding counting numbers, identifying various shapes, and using mathematical actions and terms.
Recommendations
Regarding future recommendations, Levi should be engaged in play-based block games, which would help him foster his comparing skills. Also, the mother should consider reading a book to him about counting and ensure that the content is based on his interest which would help him sharpen his one-to-one correspondence skills. Alternatively, the mother should introduce play counting games using blocks, toys or fingers to help Levi understand more about counting numbers. Furthermore, I recommend future engagement to incorporate a focus on numbers as students’ motivation is internal, and they will engage in activities that satisfy their needs. Additionally, the square blocks can be numbered as they act as guidance and question the child, which would be a source of guidance for a more knowledgeable and make the activity enjoyable. Likewise, more take relating to the building blocks should often be adopted to trigger awareness and understanding of concepts like stacking and balancing. Similarly, Levi should be engaged in activities that make him recognise common and simple shapes by providing those shapes. Finally, Levi can be engaged in number songs and rhymes, counting simple arithmetic such as in songs like “three blind mice.”
References
Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers For Mathematical Learning, pp. 7, 245–274. DOI:10.1023/A:1022103903080
Chen, C. T. (2003). The Development of Computerized Mathematical Learning Dispositions Scale for Elementary School Children. In 8th Asian Technology Conference in Mathematics. Chung Hua University, Hsin-Chu, Taiwan. https://atcm.mathandtech.org/EP/2003/2003C502/fullpaper.pdf
Cohrssen, C., & Niklas, F. (2019). Using mathematics games in preschool settings to support the development of children’s numeracy skills. International Journal of Early Years Education, 27(3), 322-339. https://doi.org/10.1080/09669760.2019.1629882
Cohrssen, C., Church, A., Ishimine, K., & Tayler, C. (2013). Playing with maths: Facilitating the learning in play-based learning. Australasian Journal of Early Childhood, 38(1), 95-99. https://doi.org/10.1177/183693911303800
Dang, S., & Keamy, R. K. (2022). Learning dispositions in the Early Years Learning Framework: two VET teachers’ experiences of walking the learning dispositions talk. International Journal of Training Research, 20(1), 26-42. https://doi.org/10.1080/14480220.2021.1944273
Knaus, M. (2017). Supporting early mathematics learning in early childhood settings. Australasian Journal of Early Childhood, 42(3), 4–13. https://doi.org/10.23965/AJEC.42.
Maxwell, K. (2001). Positive learning dispositions in mathematics.
Ortlipp, M., Arthur, L., & Woodrow, C. (2011). Discourses of the early years learning framework: Constructing the early childhood professional. Contemporary Issues in Early Childhood, 12(1), 56–70. doi:10.2304/ciec.2011.12.1.56
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge.
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