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Numeracy across the Curriculum

PPN Assignment 2, M.Teach. Yr1.
by

Gary Topham

on 13 March 2016

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Transcript of Numeracy across the Curriculum

What is Numeracy?
- 'Numeracy is the intelligent practical mathematical action in context.
(Willis & Hogan, 2002).

- Numeracy is a critical awareness which builds bridges between mathematics and the real world, with all its diversity.
(Johnston, 1994).

- "being numerate," as possessing an at-homeness with numbers and an ability to use mathematical skills to cope confidently with the practical demands of everyday life.
(Cockcroft, 1982).
Why Numeracy?
It all counts in the end...and not just the Math
Who Is Responsible for Numeracy?
As far back as 1997, Numeracy Education Strategy Development Conference, produced the report 'Numeracy = everyone's business.' (DEETYA, 1997).

One of its four "common understandings" reported is the cross-curricular nature of numeracy. It also highlights the fact that "all teachers in all subject areas accept responsibility for the development of numeracy" (p.88).

Wait, there is more....
'Furthermore,
numeracy
equips
students for life beyond school, in
providing access to further study
or training, to personal pursuits
and to participation in the world of
work and in the wider community.
(DEECD 2009, p.2).
Numeracy In Context

The New Literacy for a Data Drenched Society
'
To develop an informed citizenry and to support a democratic government, schools must graduate students who are numerate as well as literate.'

(Steen, 1999. p.8.)
Numeracy in ICT
Our data drenched society.

At a recent International EDUsummIT in the Hague (2011), a key action point proposed was:

'
To establish a clear view on the role of ICT in 21st Century learning, and its implications for formal and informal learning.
'

Supported by Anderson (2008) who discussed ICT literacy, specifically an Information Literacy Domain; relating to the capacity to access, evaluate and use information. In essence to be Numerate (
Numeracy
).
Numeracy In ICT
(counting the digits)
Numeracy
is not as simple as counting 1,2,3.....
The concept of numeracy was created from the 1959 Crowther report and defined as the 'mirror image of literacy,' but requiring quantitative thinking. A form of thinking essential to human life (Opfer & Siegler).

This 'quantitative' aspect of thinking was further enhanced by Steen (2001) who discusses Quantitative Literacy: the capacity to deal with quantitative aspects of life.

Steen proposed certain inclusions into his working definition of Quantitative Literacy, and they are.........
Steen's Quantitative Literacy Inclusions......

1- Mathematical Confidence
2- History & Nature of Maths in Society
3- Logical Thinking & Decision Making
4- Mathematics in everyday context $$$$$
5- Number & Symbol sense
6- Data Interpretation
7- Mathematical Knowledge & Tools

Calculus, Algebra, Trigonometry is the property of specific mathematical subjects!
Numeracy and Mathematics is Conceptually different....... (AMT, 2012).
Numeracy vs Mathematics

Numeracy = ability to comprehend the daily significance of numerical issues in everyday existence.

Such would be cash, percentage, cost per unit, quantity and banking; as examples.
Mathematics = study of order, relation and pattern (ACARA, 2012) and similary the 'study of patterns' (Steen 1988).
Numeracy within the Context of the Australian Curriculum.....

Numeracy encompasses the knowledge, skills, behaviours and dispositions that students need to use mathematics in a wide range of situations (ACARA, 2012, .......)
Numeracy within VELS
Learning mathematics creates opportunities for and enriches the lives of all Australians. The Australian Curriculum: Mathematics provides students with essential mathematical skills and knowledge in Number and Algebra, Measurement and Geometry, and Statistics and Probability. It develops the numeracy capabilities that all students need in their personal, work and civic life, and provides the fundamentals on which mathematical specialties and professional applications of mathematics are built (VELS...)
Life After School
Can we count on mathematics?...No!...but we do need to be numerically minded.......
Numeracy is.....
Critical Numeracy
3-Tier Hierarchy (Watson, 2010).
Critical social numeracy, or the ability to read, interpret, analyze, and use information presented in graphic and tabular form, is an important citizen competency.
3-Tier Model of Critical Thinking in relation to Numeracy (Watson, 2008).
Don't count on it.......
Tier 1 - Numeracy terminology
Knowing the language and recognising the numeracy in the situation
Tier 2 - Terminology in context
How is the language of numeracy used in the given situation?
Tier 3 – Critical numeracy
How is the numeracy used to illuminate or hide the thinking? What questions are needed to reflect critically about the situation?
Cross Curriculor Learning Continuums are easily adapted to facilitate other Curriculum subjects, hence the start of:

Numeracy across the Curriculum

Much of the work on numeracy in Australia has and is being led by people with mathematics backgrounds (Moroney, Hornton & Thornton, 2004).
Cross Curriculor Numeracy

"...every teacher is a teacher of mathematics (Steen, 2007).

Every teacher, of every subject, is at sometime presented with the opportunity to enhance students numeracy through the general delivery of their subject.

Consider the following, for instance:
Timelines
Carbon-dating
Early trading
Coinage
Mathematicians
Flight
Pyramids of Giza
Demographics of War
Dates
Time-frames
Chemistry
Volume
Concentration
Molecular Measurement
Temperature
Reaction Time
pH
Chemical Equations
Dosage
Art
Perspective
Shading
Scaling
Dimensions
Area
Quantity
Time
Abstract Concepts
Form & Shape
Cost
Materials
...and of course
MATHEMATICS

Dimensions
Linear Algebra
Matrices
Indices
Numbers
Fractions
Trigonometry
Calculus
&
The Multitude of various branches of MATHEMATICS.
Numeracy in the 21st Century
The age in which we live is witness to many major changes brought about by the rapid trend towards an interconnected, global society (Hean, 2000)
The advancement in technology has created a changing philosophy within educational teaching. Instead of the emphasis on computational mathematics, like during the pass industrial age, educationalists now promote the more 'higher order thinking.'
Computers, calculators, smart-phones, iPads and the Internet have caused a paradigm shift in the way students will develop newer levels and styles of thinking. The possibility of NEW numeracies emerging is an option (Zevenbergan, 2001), and indeed we live in an age where our students may experience technology of tomorrow today. An ever changing horizon of technology requiring ever changing numerical skills.
A New Era is Dawning

Zevenborg (2001) discusses three new numeracies:

1. Technological
2. Statistical
3. Business
&
4.
Personal Financial Literacy
is a recommended addition (Moroney et al, 2004).
In addition supported by ACARA, 2011, p.23.
A Numeracy Framework
(Hogan, 2000).
'numeracy requires more than routine facility with basic mathematical procedures' (Thornton, 2XXX, p.3).

It requires 3 abilities:
Mathematical-real quantitative problem solving
Conceptual-understanding the problem's context
Strategic-ability to comprehend the problem
(Hogan, 2000).

Hogan also states that these 3 abilities need to be supported by 1 of 3 roles:
Fluent operator-mathematically competent
Learner-learn what is needed
Critical Mathematician-Critical Mathematical Use
Numeracy Audit

The Numeracy Audit is a process through which teachers can collect information about numeracy within the school in order to plan improvement strategies.

.
Mathematical
Conceptual
Strategic
+
Fluent Operator
Learner
The Critic
=
NUMERATE
(Hogan, 2000)
Findings: Why Numeracy Should Be Across The Curriculum
NAPLAN
National Testing
NAPLAN can help schools to set broad directions for curriculum Planning, directions for Teaching Practices and indicate areas requiring Professional Development
(DEECD, 2009)
'we must ensure that we are teaching our students for numeracy attainment: mathematics skills and procedures alone are insufficient for students to have the capabilities needed to be numerate at school, home, at work, in the community and in civic life, let alone to be successful on an assessment genre designed to assess numeracy in a pen and paper test.' (Perso, 2011).
CONCLUSIONS:
A 'count' ability....
-
Numeracy
matters - Literacy, in any form, advances a person's ability to effectively and creatively use and communicate information (Jones-Kavalier, Barbara, Flannigan & Suzanne, 2008).
-
Numeracy
is NOT just mathematics, there is a difference between Numeracy and Mathematics (AMT, 2012). Numeracy is an 'aspect' of mathematics and EQUALLY important within the subject of mathematics.....preparing students for 21st Century learning & living
-
Numeracy
is embedded in all subjects & hence should be active across the curriculum, (Human Capital Working Group, Council of Australian Governments, 2008, p.7.)
-
Numeracy
needs a framework of operation within the curriculum for inclusion in all KLA's. 'What we need is a team-effort — but mathematics teachers can be leaders in meeting this challenge!' (Gough, 2007).
- Lastly,
Numeracy
needs to become a a consistent common denominator and one that has the students learning reflecting 21st Century pedagogical content.

NUMERACY needs not to be just the tip of the ice-berg, but rather a 'numerical' beacon to lead the way within the mathematics curriculum, across the curriculum and in all KLA... ...for numbers are the fundamental building blocks of NUMERACY.
Sometimes the whole 'is' greater than the sum of its parts.......
I attempted several similar tests online, United Kingdom teaching authority and various others I was able to source. The average score I achieved was 75-80%. I then decided to take the test online, as I concluded that my numeracy was of an acceptable standard to commence the test.
I started the test and immediately felt pressured because of the imposed time-frame. The tests that I used for practice also had time frames, but psychologically I interpreted this as not relevant. This sense of pressure started to manifest itself as anxiety, and I felt somewhat overwhelmed. I became so focused on time and the anxiety I was feeling that I incorrectly completed the task, submitting it before actually completing the total test.
On reflection I realised three critical factors which contributed to my incorrect attempt at the test, and the subsequent poor score.
1. The anxiety I experienced was due to a high level of expectation within myself. This was due to returning to studies and a overwhelming desire to score high, for my personal motivation for the course is very strong.
2. My mathematical knowledge and experience is with high order complex mathematics. I have concluded that this level of mathematics and my personal ability with mathematical processing does not actually prepare or provide for numeracy. Numeracy is its own 'subject' within mathematics.
3. A realisation that numeracy is its own subject, and cannot be immediately factored within Mathematics.
Therefore I have undertaken to educate myself more within the field of numeracy, and every opportunity I am presented with to develop this skill I embrace with a positive attitude. I routinely read, analyse and evaluate all material for numerical presentation, accuracy and interpretation. My recent teaching placement reinforced my evaluation of personal numeracy when discussing simple mathematical principles; familiarity breeds contempt.
This concludes the 'Numeracy across the Curriculum presentation.
Thank you for your attention and for using your numeracy and literacy skills; which sadly so many don't have.......
So, is numeracy = mathematics?.............NO!!!!!!!!!!
NO!
Being Numerate involves having those concepts of mathematics that are required to meet the demands of everyday life. And being numerate in today's world also requires the capacity to make sense of and be critical of presented numerical information
(Department of Education, Tasmania, 2002)
.
YES!!
History
Mathematics Domain clearly indicates that students are to:
- Demonstrate useful mathematical & numeracy skills for successful general employment & functioning in society.
-be empower through knowledge of mathematics as numerate citizens, able to apply this knowledge critically in societal and political contexts.
-solve practical problems with mathematics, especially industry and work-based problems.
-see mathematical connections and be able to apply mathematical concepts, skills and processes in posing and solving mathematical problems.
-be confident in their personal knowledge of mathematics, to feel able both to apply it, and to acquire new knowledge and skills when needed.
(VCAA, 2008)
Numberacy
'a kind of everyday number sense mixed with computation skill - which neglect other aspects of numeracy.' (Mathematics itself is much more than just arithmetic.) (Gough, 2007)......Gough indicates numeracy arises from areas such as:

- probability, will I win Powerball?
- spatial thinking, will that couch fit into my lounge?
- logical reasoning, Labour will not get back in, too many people blaming them!
- reading & interpreting graphs, tables and other forms of data, my gas use seems more this winter, am using less water but why am I paying more for it.
Numeracy is properly contained within the larger curriculum of school mathematics (set theory terminology) (Gough, 2007)
(Gough, 2007)
Gough (2007) states that numeracy is more than the Third 'R,' as in reading, righting & rithmetic!

He states that 'numeracy includes not only number sense, but also other aspects of mathematical knowledge and thinking....'

INCLUDING
Numeracy > Numberacy
Using number skills in applied measurement situations
Applied Measurement
Volume, Capacity, Quantity, Space, Area....
Length, Distance, Counting, Money, Measurements....
Time, Numbers, Ratio, Percent, Fraction, Parts....
algebraic and pattern related thinking....
Differences, Seperation, Value, Degree, Mixture, Interference...
Pattern, Organisation, Arrangement, Logic
Banking, Finances, Rent, Lay-by, Sales, Lease
Geometric & Spatial Thinking...
3D-Design, Angles, Shapes, Perspective, Wire-frames, Scale...
Direction, Bearings, Co-ordinates, Directions, Latitude, Longitude......
Variation, Density, Compaction, Capacity.....
Data-Handling (Statistics & Graphing)
Averages, Trends, Increments, Fluctuations, Proportions, Change, Results, Predictions, Norms, Finances, Patterns,
Figuring the Odds of Events...
Prediction, Guessing, Approximation, Assumptions, Chance, Optimising......
plus
Gambling & Risk Evaluation
Logical Analysis & Argument
Ability to read financial statements, bills, data presented and interpret the data in a logical fashion, so as to be understood....

'Was the Mad Hatter mad, or just simply Confused?'
Problem Solving
Strategic skills are important, such as knowing that mathematics might help, adapting mathematics to the context, knowing how accurate to be, and knowing if the result makes sense in context.
(DEECD, 2009. p24)
One step further along the numeracy line, this skill may be called "critical numeracy", defined as "being able to critique or make critical interpretations of mathematical information (Stoessier, 2002, p. 19).
The Importance of Numeracy in the Learning Area
Numeracy, along with literacy, have been recognised as two domains essential for a students success at school (COAG, 2008). Numeracy is the effective use of mathematics to meet the general demands of life at home, in paid work, and for participation in community and civic life (MCEETYA, 1997). Furthermore, numeracy is a fundamental component of learning, discourse and critique across all areas of the curriculum (AAMT, 1998). This component is the capacity to use mathematics to 'better understand' knowledge, data or information in the context of the presented domain of usage; to be numerically competent and hence a better understanding of numeracy. Mathematics that people use in context is better understood than mathematics taught in isolation (Carraher, Carraher and Schliemann 1985; Zevenbergen and Zevenbergen 2009). With this ability a person's life and well-being can be positively maintained and an active participation within society achieved.

The curriculum is a collection of many subjects, all of which have embedded in them opportunities to enhance numeracy. Steen (2001) states that for numeracy to be useful to students, it must be learned in multiple contexts and in all school subjects; not just mathematics. Hence it is important that Numeracy becomes an inclusive practice across all key learning areas (KLA). Willis (1998a, p. 33) has categorised the varying perspectives that school students must be capable of to be considered numerate in three ways: numeracy in terms of the mathematics itself, numeracy in terms of the context operating and numeracy in terms of strategic processes needed to choose and use mathematics. It has been recognised that numeracy is simply not the responsibility of the primary school teachers and the high school mathematics teachers. This requires a cross-curricular commitment and is not just the responsibility of the Mathematics Department (Miller 2010). The report, 'Numeracy=everyone's business' (NESDC, 1997) clearly indicates the cross-curricular nature of numeracy and that 'all teachers, in all subject areas accept responsibility for the development of numeracy (p.88). Stating, 'all teachers need to recognise the numeracy demands within learning areas and subjects and deal appropriately with them by taking opportunities to develop and enhance student's numeracy within the learning area and subjects.'

Education is essential in promoting and improving student learning across the curriculum in order to equip students for life post school. In addition it has been stated that 'poor numeracy' is a primary reason for students dropping out of school. The ever increasing technological developments further highlights the importance of numeracy ability. This ability is more required for the interpretation of the vast amount of information this technology now provides daily; the Internet. In addition, the operation of a socially aware and democratic society is greatly enhanced with increased numeracy, and its logical development into a critical thinking numeracy awareness model (Watson, 2005).

Numeracy provides a common core across the curriculum, essential in all key learning areas; to prepare students for post-school life.
Compare to Steen's 7 Quantitative Inclusions, discussed previously...Gough's 'Numberacy' reflects the
Numeracy Audit contd.......
Numeracy Audit provides teachers with information,
which enables them to respond to the following questions.
1. What is numeracy and numerate behaviour?
2. What is the school doing with regard to numeracy?
3. How well are our students developing numerate behaviour?
4. How effective are current practices for developing students’ numeracy.
Numeracy within Mathematics: hence across the curriculum
Mathematics is just the tip of the ice-berg....

'Numeracy has a significant role in realising the goals set out in the Melbourne Declaration on Educational Goals for Young Australians (MCEETYA 2008) that all young people in Australia should be supported to become successful learners, confident and creative individuals, and active and informed citizens.'
A recurring concern across both survey responses and submission was that numeracy focus less on Mathematical content and more on what it means to be numerate (incorporating elements such as authentic contexts and dispositions, choosing mathematical processes and use of tools such as rulers and beakers). Several submissions recommended that financial literacy feature in a more focused way.

There was a consistent view that the numeracy continuum is too similar to the content in Mathematics and does not provide sufficient support for the application of numeracy as a general capability in all learning areas. It was seen to privilege mathematical knowledge and skills over other essential elements of numeracy such as positive dispositions, critical orientation and use of tools.
Consultation findings for each general capability
(ACARA, 2011)
NUMERACY is there, just below the surface....across the 'whole' curriculum...it waits...
Numeracy is conceptualized as the application of mathematical skills and thinking in the context of everyday problems and usage. Information and communication technologies, or ICT, are an essential part of this process (Kilderry, Yelland, Lazardiris & Dragavic, 2003)
- To collect information about the numeracy demands across the curriculum which will enable the school to make judgements about the extent to which numeracy requires action, and where the action should be directed.

- To develop the skills of teachers to recognise numeracy demands in their classroom and their curriculum.

- To extend teacher's knowledge of a range of strategies to develop students' numeracy.
(Kemp & Hogan, 2000)
'students believe that mathematics is a relatively uncreative subject, which is not essential for succeeding in life, but it is a necessary stepping stone for most students for future study or careers; that is, it is useful but more in an instrumental than practical way' (Brinkworth & Truran, 1998).
..this attitude makes student's less likely to develop numeracy ability
(Kemp & Hogan, 2000)
the mathematics underpinning the actions in the situation might be
‘hidden’—this has been referred to as the ‘black box’ (Williams & Wake, 2007);
'the methods used in life and work situations are often not the way similar and connected ideas and techniques are taught in school mathematics.'
(Resnick, 1987).
(Lake, 2002)
Why Numeracy in Mathematics should be extended across the Curriculum: Numeracy (mathematics) is in all Key Learning Areas (KLA).
Reflection of Numeracy Competency Test.
Mathematics should lead the way for Numeracy across the Curriculum, not just in Mathematics !
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