Mathematics & Numeracy: Counting and Place Value

Comprehensive vocabulary flashcards covering the definitions of mathematics and numeracy, counting principles, developmental stages of counters, historical contexts, and educational frameworks.

Mathematics

The study of numbers, shapes, and space using reason and usually a special system of symbols and rules for organising them (Cambridge University Press, 2024).

Numeracy

The knowledge, skills, behaviours and dispositions that students need to use mathematics in a wide range of situations (ACARA, 2017).

Stable Word Order

A principle of counting where the list of number names always occur in the same order: one, two, three…

One-to-one principle

The process of assigning one, and only one, distinct counting word to each of the items to be counted.

Cardinal principle

The principle where the number name allocated to the final object in a collection represents the total number of items in that collection.

Order irrelevance

The concept that the order in which items are counted is irrelevant to the final total.

Abstract principle

The concept that counting principles can be applied to any collection of objects, whether they are tangible or not (Gelman & Gallistel, 1978).

Facile

A state of being easily accomplished, attained, or comprehended with ease.

Emergent counter

A child in the earliest stage of learning who cannot yet consistently count a collection and struggles with one-to-one correspondence.

Perceptual counter

A learner who can only count items that they can directly see, touch, or hear, and cannot yet solve math problems mentally.

Figurative counter

A stage where a person can determine the total of hidden objects by mentally visualising them but must count from the number $1$.

Counting-on

A stage where a student counts a collection by starting from one of the numbers instead of starting from $1$ (e.g., starting at $8$ then counting $9, 10, 11$).

Base $10$

A system where ten is the value that determines a new collection; it is represented by the numeral $10$ and uses ten digits, $0$ through $9$.

Place-Value System properties

The four properties of this system are positional, base-ten, additive, and multiplicative.

Number and Algebra

A content strand for what is being taught, dealing with patterns, equations, and quantitative calculations.

Measurement and Geometry

A content strand involving the study of size, shape, position, and spatial reasoning.

Statistics and Probability

A content strand involving the interpretation and critical analysis of data to understand chance.

Proficiency Strands

The 'how' students engage with mathematical content, consisting of Understanding, Fluency, Problem-Solving, and Reasoning.

Fractals

Broken shapes and numbers found in nature, such as a river delta, veins, and trees.

Ethnomathematics

The study of how mathematics relates to different cultures.

Subitising

The skill to 'instantly see how many' are in a group, such as recognizing the dots on a die without counting.

CPA Framework

A framework developed by Jerome Bruner consisting of three stages: Concrete, Pictorial, and Abstract.

Concrete (C)

The stage of using tactile objects and manipulatives, such as counters, blocks, or dice.

Pictorial (P)

The stage where students can see objects in drawings or pictures but cannot physically move them.

Abstract (A)

The stage of imagining concepts in the mind and using symbols and numbers, such as the symbol $6$.

Rote Counting

The ability to recite numbers in the correct order from memory through nursery rhymes, books, or videos.

Partitioning

The strategy of taking numbers apart, such as breaking $59$ into $50+9$.

Compensation

A strategy where a student adjusts one number by rounding up or down to make a calculation easier (e.g., $48+34 = 50+32 = 82$).

Quipu

Colored knotted cords used by the Incans for mathematical and recording purposes.

Rekenrek

A mathematical resource used for mental addition and subtraction.

Trading

The process of grouping or exchanging values, such as trading $10$ ones for $1$ ten.

SENA

Formal assessments known as the Schedule for Early Number Assessment ($SENA1$ and $SENA2$).

National Numeracy Learning Progressions (NNLP)

A sequence of observable indicators used by teachers to assess students, track growth, and plan teaching goals.