1 May 2023© NSW Department of Education | Numeracy

NUMERACY SKILLS FRAMEWORK Nagla JebeileNumeracy AdvisorNSW Department of Education

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1 May 2023© NSW Department of Education | Numeracy

WHAT IS NUMERACY?THE DEPARTMENT NUMERACY K-12 POLICY

https://detwww.det.nsw.edu.au/policies/curriculum/schools/numeracy/PD20070365_i.shtml?level=Schools

• To be numerate is to use mathematical ideas effectively to participate in daily life and make sense of the world.

• It incorporates the use of numerical, spatial, graphical, statistical and algebraic concepts and skills in a variety of contexts and involves the critical evaluation, interpretation, application and communication of mathematical information in a range of practical situations.

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1 May 2023© NSW Department of Education | Numeracy

WHERE IS NUMERACY?GENERAL CAPABILITY IN THE NSW SYLLABUSES

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1 May 2023

WE LISTENED TO TEACHERS - NSW SCHOOL CONSULTATIONS

© NSW Department of Education | Document title Page 4

quae.

1 May 2023© NSW Department of Education | Document title

HOW WAS THIS DOCUMENT DEVELOPED?

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1 May 2023© NSW Department of Education | Numeracy

WHAT IS THE NUMERACY SKILLS FRAMEWORK?

• provides teachers with the numeracy skills required by students at each stage of development across all syllabuses

• supports the successful integration of numeracy across the curriculum

• a range of numeracy skills from preschool to year 10

• allows teachers to identify stage skills

• allows teachers to assess students’ prior learning

• strategies for the successful integration of numeracy within each key learning area

• information essential for devising lessons with appropriate differentiation strategies

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1 May 2023© NSW Department of Education | Numeracy

NUMERACY IS EVERY TEACHERS RESPONSIBILITY

The key to successfully addressing numeracy across the curriculum:

- is for teachers to understand the mathematical demands of the work they set students

- the potential difficulties of the numeracy aspects students may experience

- knowledge of various strategies to assist students with numeracy concepts and skills

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1 May 2023© NSW Department of Education | Numeracy

NUMERACY IS EVERY TEACHERS RESPONSIBILITY

While the majority of the responsibility for the enhancement of mathematical skills lies within the mathematics classroom, numeracy skills can only be developed when numeracy is implemented across the curriculum and across a range of contexts.

This involves a whole school focus, with numeracy skills explicitly taught through every syllabus and by every teacher.

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THE NUMERACY SKILLS FRAMEWORK CONSISTS OF FIVE FOCUS AREAS: Focus Area 1: Mental computation and numerical reasoning A student identifies mathematical information, understands numbers, calculates, estimates and solves problems.

Focus Area 2: Patterns and algebraic reasoning A student identifies patterns, develops algebraic reasoning and makes generalisations.

Focus Area 3: Spatial visualisation, geometric reasoning and mapping A student understands and applies concepts of 2D shapes and 3D objects, angles and position.

Focus Area 4: Measurement and time calculations A student applies measurement strategies and understands time.

Focus Area 5: Graphical representation and data analysis A student represents and interprets data in graphs, tables and diagrams.

FOCUS AREAS CONSIST OF VARIOUS ASPECTS OF NUMERACY WITH KLA APPLICATIONS AND CONSIDERATIONS

Public Schools NSW

EACH FOCUS AREA LISTS THE NUMERACY SKILLS FOR EACH STAGE OF SCHOOLING FROM PRESCHOOL TO YEAR 10

1 May 2023© NSW Department of Education | Numeracy

BUILDING CAPACITY IN NUMERACYOUR PRIORITY IS TO CATER FOR ALL STUDENTS

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Differentiate learningWorking mathematicallyCustomise learning forEALD learnersLearning difficultyGifted and talented students Unpack languageVisualise problemsProvide range of strategiesCommunicate the strategies

1 May 2023© NSW Department of Education | Numeracy

THE POWER OF MAKING MISTAKES STANFORD UNIVERSITY PROFESSOR OF MATHEMATICS EDUCATION – JO BOALER

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“…the brain sparks and grows when we make a mistake, even if we are not aware of it, because it is a time of struggle; the brain is challenged and the challenge results in growth”

Making mistakes is a great thing, they are

opportunities for learning and for brains to grow

https://www.youcubed.org/think-it-up/mistakes-grow-brain/

1 May 2023© NSW Department of Education | Numeracy

BUILDING CAPACITY, WHAT IS KNOWN ABOUT NUMERACY IN THE BRAIN?

• Numeracy is created in the brain through biology and experience, numerical abilities become much more sophisticated with education

• Genetically-destined structures alone cannot support numeracy• Neural structures not genetically specified for numeracy gradually customise

for numerical function Dehaene (1997) • Mathematical abilities are distributed in different parts of the brain, very

simple numerical operations require the co-ordination of multiple brain structures –e.g. multiplying two digits requires the collaboration of millions of neurons distributed in many areas of the brain.

UNDERSTANDING THE BRAIN: THE BIRTH OF A LEARNING SCIENCE , OECD 2007

Harvard University

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1 May 2023© NSW Department of Education | Numeracy

PROMOTE EFFECTIVE NEURAL PATHWAYS• Teachers provide multiple means of method of representation and assessment -

importance of providing flexible pathways to mathematical knowledge to cater for student• Ability in a certain mathematical skills is not predictive of ability in another – raising

questions about ability grouping and the fact that a student may excel at an advanced skill and struggle with a prerequisite, hence placed in a lower ability group and held back

• Learning new mathematical knowledge can dramatically alter brain activity patterns (Delazer et al., 2003, 2004), the changes that occur seem to be a function of both the content and method of instruction

e.g. two children may both answer that 10 plus 10 equals 20, one child has memorised this fact while the other is applying the strategy of double-digit addition, the students are engaging distinct neural circuitryUNDERSTANDING THE BRAIN: THE BIRTH OF A LEARNING SCIENCE, OECD 2007

Harvard University

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1 May 2023© NSW Department of Education | Document title

PROCESS FOCUSED ASSESSMENTS PROVIDE MORE ACCURATE REPRESENTATION OF BUILDING CAPACITY FOR NUMERACY

Important implications for assessment being focused on learning pathways

- More sensitive measures are required to assess underlying understanding

- Stevenson and Stigler (1992) identified approaches that Asian teachers use involving ongoing assessment which describes the process of learning in rich detail

- The focus is on the learning pathways as opposed to the identification of right/wrong answer

- Assessment which distinguishes between knowledge encoded as a fact and knowledge encoded through strategy

- Process focused assessments provide more accurate representation of knowledge and the building of numeracy

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1 May 2023© NSW Department of Education | Numeracy

LEARNING BY DRILL VERSUS BY STRATEGY Delazer et al. (2005) found:

• learning by drill, which involved learning by heart, was encoded in a different neural substrate than learning by strategy

• that strategy learning resulted in greater accuracy and transferability than the drill condition

• these results suggest that the neural pathway underlying drill learning is less effective than the neural pathway underlying strategy learning

• teaching by strategy leads to more robust neural encoding of mathematical information than teaching by drill

• different instructional methods can lead to the creation of neural pathways that vary in effectiveness, hence the crucial role of instruction

UNDERSTANDING THE BRAIN: THE BIRTH OF A LEARNING SCIENCE, OECD 2007

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Website

Numeracyskills.com.au

WebsiteNumeracyskills.com.au

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VIDEO OF STUDENTS SOLVING PROBLEMS View a video

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ELEMENTS OF THE MODEL

COMPARATIVE LANGUAGE NEEDS TO BE DEVELOPED

Comparative language and polarised termsWell known difficulties students often face in dealing with the language in which numeracy tasks are written, is in the

use of comparatives and polarised terms (opposites) such as:

More, lessmore than, the same as, least

longerdriest

wettesttimes heavier

tallestshortest

most commonlytwice as much ashalf as much as

three times as muchhalf as tall as

one third as tall as

NSW Public Schools

SIGNIFICANT SMALL WORDS ………TO, BY, OF, FROM

The temperature increased to 5 degrees. The temperature increased by 5 degrees.

The temperature increased from 5 degrees.

• Most familiar texts and language is full of redundant information, this allows us to understand by skim reading or gain information using keywords, however with Mathematics is different.

• Mathematics is lexically dense this means that few words are used which are all essential to the meaning. Consequently, as part of the literacy demands of mathematics, word order is very important.

• Otherwise insignificant small words become vitally important for making sense in mathematics.

ARE YOU SURE YOUR STUDENTS ARE THINKING WHAT YOU ARE THINKING?

Find the volume.

Everyday meaning versus mathematical meaning

Draw a square

Square three

Square root of 932

√9

1 May 2023© NSW Department of Education | Numeracy

NUMERACY FOCUS POINTS

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Prior knowledge and skills assessed

Provide a range of representations and strategies

Identify Student Numeracy Skills and Concepts

Assess Numeracy skills and content within a context Provide authentic

numeracy activities for students to engage in and think about