Outcomes of Early Childhood Mathematics Learning

This article discusses the outcomes of early childhood mathematics learning and the importance of numeracy and problem-solving skills. It provides teaching approaches and practices for children aged birth to 8 years, including learning to understand concepts of size, pattern, and shape, forward and backward counting, recognition of numerals, and one-to-one correspondence. It also covers number sense, representation, spatial sense, measurements, estimation, patterns, and problem-solving. The article further explores cognitive and developmental aspects of mathematical concepts and provides assessment and teaching pedagogies.

Running Head: OUTCOMES OF EARLY CHILDHOOD MATHEMATICS LEARNING
Outcomes of Early Childhood Mathematics Learning
Name
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Outcomes of Early Childhood Mathematics Learning 2
Introduction
The main objective of STEM is to interpret the relationship between Science, Technology,
English, and Mathematics (HongHaekyung, 2014, p. 168). For example, through STEM,
mathematical concepts such as classification, measurements, and comparison are used to
implement problems in science and engineering fields. Similarly, mathematical and engineering
problems require skills in the science field. Learning mathematics is important at early
childhood development age because it helps the children to gain effective foundation for future
understanding of mathematical concepts and solving various life problems (Al Hafiz &
Nopriandi, 2019, p. 212). Numeracy helps to solve problem, use shapes to measure their spatial
awareness, and create and describe patterns. Learning mathematics also helps the children to
develop competent reasoning skills thus; improving their levels of confidence (Aunio, 2019,
p. 718). This paper outlines the approaches and teaching practices for children in the age bracket
between birth to 8-years mathematics.
Learning outcomes for children between Birth- 2 years
 Learning to understand the concepts of size, pattern, and shape
 Both forward and backward verbal counting
 Recognition of numerals
 Understanding one-to-one correspondence such as identification of groups, and matching
the sets.
Number Sense

Outcomes of Early Childhood Mathematics Learning 3
This represents the ability of the child to accurately count both forward and backward. The child
should also learn the relationship between numbers, for example, addition and subtractions
(Brillante, 2017, p. 87).
Representation
The child learns how to represent mathematical ideas using pictures, symbols, words, and objects
such as blocks (Farland-Smith, 2019, p. 97).
Spatial Sense
This is also called geometry, however, for children between birth and 2 years, it is called spatial
sense (Grenier, 2014, p. 438). The child is introduced to various ideas such as size, space, shape,
position, movement, and direction.
Measurements
Helping the child to find the length, height, and objects’ weight for example, showing the child
how to the measuring cup with water, or sugar (HongHaekyung, 2014, p. 168). The child can
also be introduced to measurement of time.
Estimation
Since this is a very difficult task especially for young children in this age bracket, the child is
introduced to basic knowledge such as understanding the meaning of words like bigger, smaller,
more than, and less than (Lee, 2014, p. 35).
Patterns

Outcomes of Early Childhood Mathematics Learning 4
The child is introduced to numbers, images, and shapes in repeated sequences to improve their
abilities to predict occurrences, logical creation of connections, and using reasoning and
competent skills (Menzer & Winsler, 2018, p. 195).
Problem-solving
The child is introduced to the concept of using the past knowledge and logical thinking to
provide a solution to a problem (Méndez, Hammer, Lopez, & Blair, 2019, p. 258).
Mathematical Concepts of Learning Experience
Exposing the child to stories, songs, use of repletion, rhymes, and numbers.
Cognitive and Development of Mathematical Concepts
Grasping and releasing objects, using sensorimotor approach and mental representation to
manipulate internal depictions such as pictures, concepts, spaces and grouping of objects. The
children falling between 10-12 can also use analogical techniques of solving problems
(HongHaekyung, 2014, p. 168),
Children between 2-3 years
Learning Outcomes
Learning outcomes for the children in this age bracket is similar to those between birth and 2
years (Méndez, Hammer, Lopez, & Blair, 2019, p. 196) such as;
 Learning to understand the concepts of size, pattern, and shape
 Both forward and backward verbal counting
 Recognition of the numerals

Outcomes of Early Childhood Mathematics Learning 5
 Understanding one-to-one correspondence such as identification of groups, and matching
the sets.
Number Sense
This represents the ability of the child to accurately count both forward and backward. The child
should also learn the relationship between numbers, for example, addition and subtractions.
Representation
The child learns how to represent mathematical ideas using pictures, symbols, words, and objects
such as blocks.
Spatial Sense
This is also called geometry, however, for children between birth and 2 years, it is called spatial
sense. The child is introduced to various ideas such as size, space, shape, position, movement,
and direction.
Measurements
Helping the child to find the length, height, and objects’ weight for example, showing the child
how to the measuring cup with water, or sugar. The child can also be introduced to measurement
of time.
Estimation

Outcomes of Early Childhood Mathematics Learning 6
Since this is a very difficult task especially for young children in this age bracket, the child is
introduced to basic knowledge such as understanding the meaning of words like bigger, smaller,
more than, and less than.
Patterns
The child is introduced to numbers, images, and shapes in repeated sequences to improve their
abilities to predict occurrences, logical creation of connections, and using competent reasoning
skills.
Problem-solving
The child is introduced to the concept of using the past knowledge and logical thinking to
provide a solution to a problem.
Cognitive and Development of Mathematical Concepts
Mathematical Concepts of Learning Experience
 Playing with the shape-sorters: conversing with the child regarding each shape, counting
and describing patterns, developing skills of different shapes, and giving directional
instructions, for instance, instructing a child to jump on a circle (Resnick, Newcombe, &
Jordan, 2019, p. 428).
 Counting and Sorting: gathering small toys, pebbles, and buttons then counting them with
the child. Sorting the collected items on the basis of their sizes, colors, and their functions
(Sun, 2017, p. 98).
 Recognition of numbers and sizes: helping the child to locate their room following the
series of house arrangements, and introducing the child to phone numbers. Noticing the

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sizes of objects around the child and asking the child to compare his/her size with that of
the object (Sun, 2017, p. 77).
 Nature walk: this gives the child opportunities to compare, assess, note the similarities,
differences and patterns, and categorize them based on property differences. Estimation
of the distance covered, for example, in terms of far or close, and counting the steps made
to reach a certain destination (Sun, 2017, p. 80).
 Picture time: using hourglass, and stopwatch to time activities to help the child in
developing timing skills and appreciating why activities are longer than the others
(Verkerk, Jeukens-Visser, Van Wassenaer-Leemhuis, Kok, & Nollet, 2014, p. 188).
 Shaping up: identification of shapes and colors observed daytime
 Reading and singing numbers: singing repeated songs reinforce their understanding of
patterns, practice language, and foster social skills Verkerk, Jeukens-Visser, Van
Wassenaer-Leemhuis, Kok, & Nollet, 2014, p. 190).
 Playground math: instruct the child to play while changing instructions based on; height,
position, and size (Verkerk, Jeukens-Visser, Van Wassenaer-Leemhuis, Kok, & Nollet,
2014, p. 186).
Cognitive and Development of Mathematical Concepts
Grasping and releasing objects, using sensorimotor approach and mental representation to
manipulate internal depictions such as pictures, concepts, spaces and grouping of objects
(Aunio, 2019, p. 718). The children falling between this age bracket can use advanced
analogical techniques of solving problems,

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Children between 3-5 years and primary school children
Learning outcome
 Understand the characteristics of various shapes.
 Having improved and comprehensive number sense.
 Counting out a collection of up to 20 items
 Conducting addition and subtraction of simple arithmetic
 Identifying the larger number in a given set
 Understanding the meaning of words used to relate position such as under and behind.
 Learning to sequence events chronologically and telling time.
 Sorting of objects based on more than one features.
Numbers
Leaning the use of teen to accurately count numbers such as 20, 30,,,,,,. Figuring the use of
repeating patterns count numbers up to 200. Determining the quantities of items in a group of up
to 20 items by counting one-to-one, naming numbers after certain numbers up to 200 without
prompting numbers in the preceding sequence, verbally counting the numbers up to 200
(Wallace, 2019, p. 387). Understanding the terms that are related to estimation such as about,
near, between, closer to, and a little less than. Using mental number line to identify the relative
proximity of four digit numbers. Writing numbers upto ten in words and symbols. Understanding
the meaning of abbreviations such as 2nd, 3rd, 4th
Operation of numbers

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Determine the sum and subtractions of numbers up to five, using informal knowledge to estimate
addition and subtraction of word problems, using concrete counting techniques to solve word
problems, application of advanced and abstract counting methods to identify solution to word
problems with sums up to 20, using the available and reasoning skills to accurately find the
addition and subtraction of unknown values up to 20 and their subtraction counterparts.
Understanding the concept of place values of numbers up to 100. Developing a mental procedure
of carryout addition and subtraction (Wallace, 2019, p. 278).
Geometry and Spatial Sense
Learning to name the variations of circles, triangles, rectangles, and squares, learning to describe
a two-dimensional shape, putting together complex shapes, making pictures by using shapes
(Wallace, 2019, p. 487), finding hidden shapes in the overlapping shape arrangements, using
words to represent the physical relations or positions, placing objects in the relative position.
Measurement
Learning to name, discuss, and develop a language describing the various attributes such as small
and big. Comparing attributes of different objects, developing sense of time, understanding that
numbers would remain constant unless some are either subtracted or added (Wallace, 2019,
p. 548), measuring of lengths, measuring the area by covering the surface to be measured using a
given unit, and making informal comparisons and estimations.
Patterns, Reasoning, and Algebra
Understanding the sequence of events, identification of the core of simply repeated pattern,
understanding the growing pattern resulting from counting, recognizing the concept of even and

Outcomes of Early Childhood Mathematics Learning 10
odd numbers (HongHaekyung, 2014, p. 168), using letters to represent the core of a repeating
pattern, summarize the ideas of additive identity, and subtractive identity using natural language.
Statistics and probability
Understanding the importance of statistics to analyze phenomenon, organizing and describing
data, develop necessary skills and interpreting real graphs, determine the frequency at which
events occur (HongHaekyung, 2014, p. 174).
Mathematical Concepts of Learning Experience
 Addressing questions, and making prediction, conducting simple experiment to determine
the probability of every player winning a game, asking the most common color in a
family, drawing pictures, making trials, and adjusting (HongHaekyung, 2014, p. 158),
working backwards to solve algebraic problems, estimating collection of different
quantities, using patterns to solve addition and subtraction problems, figuring the missing
child by considering the children present, using rulers to take measurements, and using
class names to classify and sort, modelling.
Cognitive and Development of Mathematical Concepts
Using intentional means and sequences of actions to solve problems, demonstrating the ability to
conserve (Aunio, 2019, p. 718). The tasks of conservation include; weight, mass, liquid, and
numbers. Using logical, flexible, organized, and reasoning skills to solve problems.
Assessment and Teaching Pedagogies
Using continuum K-10 to carry out the assessments. Curriculum assessment at this stage includes
gathering data and reflecting on the data for future planning and learning. The three major

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purposes of assessments are assessment of learning, assessment for learning, and assessment as
learning (Aunio, 2019, p. 718). The pedagogical principles of assessment at this stage is
framework assessment for learning. Summative assessment (assessment of learning) and
formative assessment (assessment for learning) helps the learning facilitator (educator) to record
the learning progresses of the child, and sent the feedback to the parents. On the other hand,
formative assessment (assessment for learning) helps the educator to document and analyze the
children’s progresses and plan for future activities of learning (Resnick, Newcombe, & Jordan,
2019, p. 428). The contemporary techniques of documenting the children’s learning experiences
include drawings, photographs, videos, audio, samples, and sketches. Anecdotal, running record,
story learning, jottings, work sample, language samples, and daily diaries are examples of the
types of documents that the educator can use to make learning visible and interesting. The
educator can also use checklist when assessing many children and when testing the children’s
IQ. EYLF is the best technique of assessing children at early stages of mathematical learning
developments, while NSW syllabus is used for the children in primary school levels (Resnick,
Newcombe, & Jordan, 2019, p. 428).

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