# Numeracy glossary

This page includes definitions used in the Mathematics Teaching Toolkit relating to numeracy.

For detailed definitions and examples of mathematical vocabulary see: the Victorian Curriculum Mathematics Glossary

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## A

### Additive

Additive strategies are the use of known addition facts to solve addition problems.

### Algebra

Algebra involves a study of pattern and the prediction of further outcomes.

### Algorithms

Algorithms are a well-defined set of instructions designed to perform a particular task or solve a type of problem.

### Authentic tasks

Authentic tasks are activities that require the application of knowledge, skills and resources to respond to everyday contexts and situations.

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## C

### Chance (Probability)

Chance refers to exploring the likelihood of events using experimental and theoretical approaches. Probability refers to the attribution of a numeric value to an outcome.

### Coding

Coding is the syntax that allows a certain script or program to work.

### Cognitive load

Cognitive load refers to how much information can be processed at any one time.

### Collaborative learning

Collaborative learning occurs when students work together in small groups with everyone participating in and contributing to the learning task.

### Commutative

Commutative operations yield the same result regardless of the order of two elements. For example, a+b=b+a and a x b = b x a

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## D

### Developing number sense

Number sense refers to the ability to understand numbers and the relationships between numbers; enabling the solving of mathematical problems.

### Differentiated learning

Differentiated teaching extends the knowledge and skills of every student at their starting point. It recognises student differences and provides appropriate challenge for all students.

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## E

### Early Years Planning Cycle

The Early Years Planning Cycle refers to a model that early childhood professionals use to collect and interpret evidence that contributes to a detailed, up-to-date, strengths-based picture of children’s learning and development to inform planning and practice decisions.

### Explicit teaching

Explicit teaching involves showing students what is required, explaining what is to be learnt, using examples, and providing opportunities for practice and mastery of new knowledge.

### Exploring patterns and relationships

Patterns and relationships refer to the ability to identify a pattern and recognise the properties that created that pattern in order to extend or create new patterns.

### Exploring chance and data

Exploring chance and data refers to the process of understanding likelihood, probability and the representation and analysis of data.

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## F

### Feedback

Feedback is the exchange of information that captures and informs progress towards a learning goal.

### Fluency

Fluency describes the choosing of appropriate procedures; carrying out procedures flexibly, accurately, efficiently and appropriately; and recalling factual knowledge and concepts readily.

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## G

### Geometry

Geometry refers to the study of the properties of objects in space.

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## H

### High Impact Teaching Strategies

High Impact Teaching Strategies provide teachers and teams with the opportunity to observe, reflect, and improve classroom practice.

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## I

### Inquiry-based learning

Inquiry-based learning is an open-ended approach that focusses on a solving a particular problem or answering a central issue through questions, research, and curiosity.

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## M

### Mathematics

Mathematics is the study of function and pattern in number, logic, space and structure, and of randomness, chance, variability and uncertainty in data and events.

### Measurement

Measurement refers to the study of quantities, choosing appropriate metric units of measurement and building an understanding of the connections between units.

### Metacognitive strategies

Metacognitive strategies are methods, processes and routines used to assist students understand the way they learn.

### Modelling

Mathematical modelling involves using various approaches to represent real-world situations in such a way that reduces a problem to its essential characteristics.

### Multiple exposures

Multiple exposures offers students multiple opportunities to access new knowledge and concepts over time to promote deep learning. Multiple exposures are planned, sequential and utilise different activities and practice.

### Multiplicative thinking

Multiplicative thinking is an ability to recognise and work flexibly with the concepts, strategies and representations of multipication (and division) as they occur in a wide range of contexts.

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## N

### Number

Number refers to the way in which we quantify, measure and label our environment.

### Numeracy

Numeracy refers to the knowledge, skills, behaviours and dispositions that students need in order to use mathematics in everyday situations.

### Numeracy focus

Numeracy focus involves the application of mathematical ideas to interpret the world around you.

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## P

### Play-based learning

Play-based learning refers to a context for learning through which children organise and make sense of their social worlds, as they actively engage with people, objects and representations.

### Problem-based learning

Problem-based learning (PBL) is a teaching method that provides a structure for discovery that helps students internalise learning through exploring problems.

### Problem-solving

Problem-solving is the ability of students to apply existing strategies to seek solutions and verify that the answers are reasonable.

### Proficiencies

Programming is the logical use of tools/steps to achieve an outcome.

### Programming

Programming is the logical use of tools/steps to achieve an outcome.

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## Q

### Questioning

Questioning probes learning and promotes interest and curiosity by generating dialogue aimed at extending and refining understanding.

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## R

### Reasoning

Reasoning refers to students developing a capacity for logical thought and action and an ability to explain their thinking.

### Reflective prompt

A reflective prompt is a question or instruction requiring a person to revisit past actions and make judgements about those experiences.

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## S

### Sequencing

Sequencing, in coding terms, is the process of putting algorithm steps in the correct order.

### Setting goals

Goal setting involves the application of prior knowledge to differentiate learning, set the learning purpose and explain what success will look like.

### Statistics

Statistics is a branch of mathematics dealing with the collection, organisation, analysis, interpretation and presentation of data.

### Structuring lessons

Structuring lessons are specific steps and routines to optimise time on task, maintain engagement, and make clear connections between goals and assessment.

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## T

### Teaching and Learning Cycle

The Victorian teaching and learning cycle consists of five major components: Use student data; Identify learning goals; Plan; Teach; Assess. It encourages collaboration among principals, school leaders, teachers, students and parents/carers in effective learning communities to improve learning outcomes for students.

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## U

### Understanding

Mathematical understanding refers to students ability to identify the relationship between the ‘why’ and the ‘how’ of mathematics and the ability to describe their thinking.

### Understanding and using geometric properties and spatial reasoning

Understanding and using geometric properties and spatial reasoning involves visualising, describing and analysing the way shapes and objects are combined and positioned in the environment for different purposes.

### Understanding, estimating, and using measurement

Understanding, estimating, and using measurement refers to the ability to make appropriate choices when quantifying the world, including the choice of units, accuracy and understanding the relationships between measures.

### Using proportional reasoning

Using proportional reasoning involves operating with decimals, fractions, percentages, ratios and rates, and interpreting and moving fluently between the different representations.

### Visualisation

Visualisation involves creating images of the situation that is being discussed in order to make sense of it.

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## W

### Worked examples

Worked examples refers to the demonstration of the steps required to successfully approach a learning task. Worked examples support the learning of new knowledge and independent practice.

Last Update: 26 September 2019