Mathematics in Early Childhood Part 6 (Shape)

A child playing with shapes.

In this article, Shape will be discussed.

Shape is everywhere in the world, though in mathematics, they are mainly two-dimensional and three-dimensional, so the classroom’s block corner is ideal in helping children explore shapes (Brownell, Chen, Ginet, & Hynes-Berry, 2013). Children and teachers can look around their physical classroom and discover that there are endless shapes. However, in mathematics, these are often the ones that share similar attributes and not random blobs.

The Big Ideas for Shape are, firstly, shapes are defined and classified by their attributes, secondly, the flat shapes of three-dimensional shapes are two-dimensional shapes, and thirdly, shapes can be composed or decomposed to create new shapes (Brownell, Chen, Ginet, & Hynes-Berry, 2013).

Firstly, shapes are defined and classified by their attributes.

Shapes have rules that make each shape, such as a triangle having three sides or a square with four equal sides, so teachers should craft activities that highlight these important rules (Brownell, Chen, Ginet, & Hynes-Berry, 2013). Using these rules, it is easy to identify or even create shapes from loose parts. The rules also ensure correction because though a rectangle and a square have the same number of sides, only the square has four equal sides.

Secondly, the flat shapes of three-dimensional shapes are two-dimensional shapes.

Children can explore and discover that two-dimensional shapes are found on the faces of three-dimensional shapes (Brownell, Chen, Ginet, & Hynes-Berry, 2013). Concrete materials are great at illustrating this rule, as children rotate common household items like toilet roll cores or a box, they can discover there are hidden shapes everywhere.

Thirdly, shapes can be composed or decomposed to create new shapes.

As children gain opportunities to rotate, combine, and compare shapes, they will realise how shapes have part and whole relationships, where there are shapes within shapes (Brownell, Chen, Ginet, & Hynes-Berry, 2013). They can break apart a shape into different shapes, or even use shapes to create a different shape. The possibilities are endless.

So what does the role of the teacher look like? There is a wide variety of student profiles in a classroom, so teachers need to cater instruction for all students, such that the different dimensions of diversity are covered, including: Gender, culture and ethnicity, socioeconomic status, experiences, language, delays or disabilities, and developmental level (Chaillé, 2021). The lessons and classroom environment should never be a one-size-fits-all approach, but rather be sensitive to the different learning profiles of children.

Teachers understand that manipulatives help children to learn abstract mathematical concepts, but they do not contain mathematics for children to learn and are only helpful in guiding children to think in problem-solving, and one example to teach shape is using tangrams for spatial reasoning though teachers should not help them too much that causes them to lose opportunities to think, and if a child faces frustration it is better to provide an easier activity (Kamii, Lewis, & Kirkland, 2001). While concrete materials are often used for illustrative purposes, the main benefit of them is to allow children to self-discover and problem-solve on their own terms. Teachers should think critically about the types of materials found in the classroom, and never intervene when unnecessary.

Instruction and construction differ in that instruction is classroom practices the teacher carries out to provide knowledge with objectives and systematic systems, whereas construction is about how children learn through a process to actively build their skills and concepts, and in modern classrooms, both exist together (Chen, 2014). As teachers build the learning environment, children can construct knowledge and problem-solve.

Thus, the topics and Big Ideas of mathematics have been elaborated through this series of six articles.

 

References

Brownell, J., Chen, J.-Q., Ginet, L., & Hynes-Berry, M. (2013). Big Ideas of Early Mathematics. US: Pearson Education.

Chaillé, C. (2021). ECE314 Facilitating children's mathematical thinking (study guide). Singapore: Singapore University of Social Sciences.

Chen, J.-Q. (2014). Intentional Teaching: Integrating the Processes of Instruction and Construction to Promote Quality Early Mathematics Education. Early Mathematics Learning, 257-274. doi:10.1007/978-1-4614-4678-1_16

Kamii, C., Lewis, B. A., & Kirkland, L. (2001). Manipulatives: when are they useful? Journal of Mathematical Behavior, 20, 21-31. doi:https://doi.org/10.1016/S0732-3123(01)00059-1

 

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