What is a mathematics concept?
What are mathematics processes?
Sometimes we hear about mathematical concepts and processes but what are they?
Analogies are always helpful so we will use a tree to assist in our explanation.
Mathematical Concepts
Concepts are the nouns of mathematics e.g., 2D shape, line, length, partitioning, area, capacity, etc. If mathematics is the tree itself, the concepts can be thought of as the leaves. Conceptual understanding is knowing that there are many types of leaves - dark green, light green, spiny etc, all representing what we think of as plant appendages. They are related but can look different.
Mathematical conceptual understanding, then, is knowing there are many ways to think of and represent mathematical concepts. For example, lines can be straight or curved and have different orientations like horizontal and vertical. They are all still 1-dimensional figures that continue endlessly in both directions.
Mathematical Processes
Processes are the adjectives of mathematics, e.g. counting, locating, playing, measuring, reasoning, problem-solving, communicating, and explaining. They are the interconnected thinking and doing actions undertaken when learning or applying mathematics concepts to solve problems.
In terms of the tree, if my problem is to get to the end of a particular branch, I would have to think about and choose the actions I might use to get there. These may include using a range of processes like lifting, reaching and balancing. It is the combination of these along with my conceptual understanding of length, height, positioning and climbing trees that helps me solve this problem.
Early Years Learning Framework v2.0
There are processes and concepts in the new EYLF2.0 (AGDE, 2022) that specifically mention mathematics or appear to be associated with mathematics concepts based on aligned educator-implementation advice.
For more detail, click on the picture to link to our Mathematics in the EYLF2.0 page.
The mathematical concepts highlighted by their inclusion in these indicators are: patterns, counting, length, volume, capacity, 3D, time, data The mathematical processes mentioned are: noticing, observing, sorting, classifying, ordering, comparing, organising, identifying, naming, recording, communicating, predicting, explaining, discussing, reasoning, generalising, representing, and modelling.
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Australian Curriculum: Mathematics v9
The Australian Curriculum: Mathematics [AC;M] (ACARA, n.d.) is organised into content areas under 6 interrelated strands: Number, Algebra, Measurement, Space, Statistics, Probability.
If we look at the concepts embedded in these strands from school entry to Year 6, they are presented with different levels of complexity as:
Number: counting, subitising, counting collections, partitioning quantities, adding, subtracting, grouping and equal sharing, place value, multiplication, division, fractions, decimals, percentages, properties of numbers
Algebra: repeating patterns, growing patterns, equivalence
Measurement: length, capacity, mass, time, angles, perimeter, area
Space: 3D, 2D, spatial reasoning, symmetry, cartesian plane
Statistics: data, graphs
Probability: chance
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The mathematical processes through which this content is addressed include thinking, reasoning, communicating, problem-solving and investigating. Problem solving and investigation processes are further explicated as mathematical modelling, computational thinking, statistical investigation, probability experiments and simulations.
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Mathematical proficiency is defined in the AC:M as "increasingly sophisticated knowledge and understanding of mathematical concepts, fluency in representations and procedures, and sound mathematical reasoning and problem-solving skills". Proficiency involves a combination of understanding, fluency, reasoning and problem solving skills in mathematics.
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