Mathematics in Early Childhood (Part 2)

Sets and number sense.

Previously, it has been mentioned that these are the topics of mathematics: Sets, number sense, counting, number operations, pattern, measurement, data analysis, spatial relationships, and shape. The Big Ideas stem from each of these topics. For part 2 of this series of articles, the topics of Sets and Number Sense will be elaborated.

Traditional classrooms use a behaviourist approach towards teaching numbers, with the main teaching strategy being direct instruction, whereby questions asked only have a correct answer, and the teacher gives the information and rewards children for answering accurately (Chaillé, 2021). While this method is better for children with special needs, it is better to use a constructivist approach for mainstream children. Mathematics can also be integrated into the classroom throughout the daily routine, during children’s play, and in the curriculum (Chaillé, 2021).

Whereas with a constructivist approach, the teacher creates a rich mathematical environment but gives little direct instruction and instead allows children to explore mathematics in their own ways (Chaillé, 2021). This requires a higher level of skill from the teacher, as the environment must be constructed to allow children to acquire math skills organically, and the teacher does not interfere with their learning.

The teacher is also observant of children’s mathematical explorations and caters for materials in response to that, such as by placing images of buildings of different heights when children are using blocks to create buildings (Chaillé, 2021). Intentional teaching directly contrasts rote learning and occurs in a supportive play environment, because children learn mathematical concepts when play and intentional teaching are combined, so for educators, they have to overcome their fear or lack of confidence in teaching mathematics (Knaus, 2017). The role of the teacher is to be a facilitator and observe children during play.

Many educators still believe that mathematics should only be taught in formal schooling years rather than during early childhood, though there has been research done to show that these experiences are crucial for children’s later development, so educators must understand that mathematics is for every early learner, and that it is beyond shapes and numbers (Knaus, 2017).

Next, the topics of Sets and Number Sense will be introduced.

Teaching Sets

Sets mean using attributes to create collections, with the same collection able to be sorted in different categories, and they can be compared and organised (Brownell, Chen, Ginet, & Hynes-Berry, 2013). For instance, a child may sort some beads by size or colour, and thus has created sets.

Three Big Ideas on sets are that attributes are used to group collections into sets, a single collection can be sorted in a variety of ways, and that sets can be ordered and compared (Brownell, Chen, Ginet, & Hynes-Berry, 2013). The concept of sorting is defined as unique from matching, as it is about reorganising an entire collection or set into at least two subsets (Brownell, Chen, Ginet, & Hynes-Berry, 2013). For instance, a box of marbles is sorted into blue or green.

Big Idea #1 of Sets

Find my match.

What's my rule?

Firstly, the use of attributes to help children sort collections into sets will be explored. The teacher can guide the child to use different attributes, like colour, shape, or similar objects, or even increase the difficulty of the activity by adding more attributes or objects to the collection, and inviting children to figure out which object is taken away (Brownell, Chen, Ginet, & Hynes-Berry, 2013). There is a wide variety of methods to be used with just a simple box of small manipulatives. In the first image, the teacher uses all stars in the activity, and gets the child to find the exact colour to match the star. The game "What's my rule?" requires children to take out objects that share an attribute that the rest of the objects do not have.

Big Idea #2 of Sets

People sort activity.

Secondly, a single collection can be sorted in a variety of ways. This is a more difficult concept, but children can learn it through self-discovery during play, where they understand that there are many ways a collection can be sorted (Brownell, Chen, Ginet, & Hynes-Berry, 2013). If a child has sorted a box of crayons by colour, the crayons can also be sorted by size. In the People Sort activity, children understand that there are so many ways to sort objects.

Big Idea #3 of Sets

Thirdly, sets are able to be ordered and compared. This involves comparing sets to find out which is better, though it is more often about quantity, so children need to explore more to understand the concept (Brownell, Chen, Ginet, & Hynes-Berry, 2013). Children will naturally count the objects of each set during play and conclude that one of them has a higher quantity.

Teaching Number Sense

Moving on to Number Sense, which is about developing a purposeful sense of quantity, and the Big Ideas include learning that numbers are used in different mathematical or non-mathematical ways, knowing that quantity symbolises an attribute for a set of objects with numbers being used to name quantities, and lastly, the quantity of a small collection can be understood without counting (Brownell, Chen, Ginet, & Hynes-Berry, 2013).

Big Idea #1 of Number Sense

Firstly, learning that numbers are used in different mathematical or non-mathematical ways. Numbers are not just used to describe quantity or order, as they can become identifiers like a name, and people normally do not think about all the other numbers that precede it (Brownell, Chen, Ginet, & Hynes-Berry, 2013). Hence, just like finding the classroom 105 does not require children to start from 1, numbers may sometimes have a different function.

Big Idea #2 of Number Sense

Secondly, knowing that quantity symbolises an attribute for a set of objects, with numbers being used to name quantities. Numbers are sometimes used as attributes, but other attributes must be ignored to understand them, as quantity is a mental image when a child understands the relationships between sets (Brownell, Chen, Ginet, & Hynes-Berry, 2013). Usage of this Big Idea thus involves the child having prior knowledge of sets in order to compare two collections of objects.

Big Idea #3 of Number Sense

Thirdly, the quantity of a small collection can be understood without counting. Subitising is being able to tell “how many” in collections of objects quickly, without counting (Brownell, Chen, Ginet, & Hynes-Berry, 2013). Children who have developed in their mathematical thinking can tell how many dots a face of a die has without physically counting each of them.

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.

Knaus, M. (September, 2017). Supporting Early Mathematics Learning in Early Childhood Settings. Australasian Journal of Early Childhood, 42(3), 4-13. doi:https://doi-org.suss.remotexs.co/10.23965/AJEC.42.3.01

 

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