Mathematics in Early Childhood Part 5 (Data Analysis and Spatial Relationships)

Data Analysis and Spatial Relationships.

In this article, Data Analysis and Spatial Relationships will be discussed.

How do children do data analysis?

Data Analysis is about asking questions and finding out the answers, so activities may include complicated graphs and charts, but it can also be as simple as writing down a list of items (Brownell, Chen, Ginet, & Hynes-Berry, 2013). Data can be collected through these tasks.

The Big Ideas for Data Analysis are firstly that the purpose of gathering data is to answer questions when answers are not available immediately, secondly, data needs to be represented to be analysed, and the questions frame how data is gathered and organised, and thirdly, parts of data should be compared, and data as a whole can be concluded (Brownell, Chen, Ginet, & Hynes-Berry, 2013).

Big Idea #1 of Data Analysis

Firstly, the purpose of gathering data is to answer questions when answers are not available immediately.

Children realise that data analysis helps in answering questions and thus they are motivated to understand it more, and teachers need to know that, for problem-solving to happen, a real problem must be present for children to solve by guiding them step-by-step, and children should do data analysis like how survey experts do, where the answers are attained only after analysis (Brownell, Chen, Ginet, & Hynes-Berry, 2013). It may be tempting to give the answers to children right away, but doing so deprives them of the opportunities to self-discover and problem-solve.

Big Idea #2 of Data Analysis

Secondly, data needs to be represented to be analysed, and the questions will frame how data is gathered and organised.

When children gain experience and feel empowered, they can follow steps to gather and represent data, and the teacher is present to guide them through (Brownell, Chen, Ginet, & Hynes-Berry, 2013). This allows them to learn and imitate the process when they are older.

Big Idea #3 of Data Analysis

Thirdly, parts of the data can be compared, and the data as a whole can also be concluded.

Adults typically guide children to understand that data can be compared in parts and concluded as a whole, so a new concept can be learned as questions are answered through the data (Brownell, Chen, Ginet, & Hynes-Berry, 2013). For instance, a huge bag of sweets can be counted, but also the different types of sweets within it.

What is spatial reasoning?

Spatial reasoning is an early phenomenon in children, where they have mental understanding and physically transform objects, and these are the five key areas: firstly, symmetry, secondly, transforming, thirdly, composing and decomposing 2D images and 3D objects, fourthly, locating, orienting, mapping and coding, and lastly, perspective-taking (Novakowski, 2018), and even from birth, infants are already learning about spatial relationships, as they reach for objects around them or move from place to place (Brownell, Chen, Ginet, & Hynes-Berry, 2013).

Symmetry is about when one of two shapes matches the other shape, and transforming is understanding what an object can look like after being flipped or rotated (Novakowski, 2018). These can be achieved by using blocks or paper.

Composing and decomposing 2D images and 3D objects is about identifying shapes within shapes or creating a new shape from two or more smaller ones (Novakowski, 2018). Children can learn to use 2D images and craft 3D figures, or use 3D figures to make 2D drawings. Different shapes can also be used during play for children to form new shapes.

Locating, orienting, mapping, and coding are about understanding the location of objects within a space to learn the relationships between positions, and also includes how 2D objects look in 3D, and the sequence of numbers and symbols to show an action or instruction, while perspective-taking is learning to see things from a different perspective or knowing the changes in perspectives (Novakowski, 2018).

The Big Ideas for Spatial Relationships are, firstly, that the relationships between places and objects are described with mathematical accuracy, secondly, that a person’s experiences of space and two-dimensional representations of space only show a certain perspective, and thirdly, spatial relationships are visualised and manipulated mentally (Brownell, Chen, Ginet, & Hynes-Berry, 2013).

Big Idea #1 of Spatial Relationships

Firstly, the relationships between places and objects are described with mathematical accuracy.

Children know that when they talk, draw, write, or create models, they can show movement and direction, so teachers can use photos to show spatial relationships and encourage discussions, and use language that describes space or movement games to show movement in certain directions (Brownell, Chen, Ginet, & Hynes-Berry, 2013). Common phrases used can include “below the table” or “on top of the shelf” to symbolise spatial relationships.

Big Idea #2 of Spatial Relationships

Secondly, a person’s experiences of space and two-dimensional representations of space only show a certain perspective.

Children learn that when seen through other perspectives, spatial relationships look very different, so they need to listen to how others are seeing something through organic self-discovery (Brownell, Chen, Ginet, & Hynes-Berry, 2013). A garden can look very different when seen from a bird’s eye view or from a taller angle than a child’s eye level.

Big Idea #3 of Spatial Relationships

Thirdly, spatial relationships are visualised and manipulated mentally.

Young children may struggle to imagine spatial relationships, but they can learn through concrete or pictorial experiences, and for children who have mastered mental images, they do not need concrete materials to create solutions (Brownell, Chen, Ginet, & Hynes-Berry, 2013). Mathematics has to be taught progressively and according to the developmental stages of children, which teachers are capable of understanding as they observe children.

The role of teachers

To understand if children are learning mathematics, teachers use observation, documentation, and formal assessments (Chaillé, 2021). Observations are how teachers observe children during activities or play, and analyse their behaviour. Documentation can include work samples, written observations, or photographs of children engaged with activities. Formal assessments include portfolios or checklists to gauge the development of children.

Therefore, data analysis and spatial relationships are both complicated topics with challenging Big Ideas, but these are not impossible for children to attain through guidance from teachers and self-discovery.

 

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.

Novakowski. (2018). Spatial Reasoning.

 

 

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