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ETL 421 Teaching the Curriculum / Integrating Numeracy

Daniel_ Sameena_ s256688_ ETL421 Assignment 1

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Assignment 1: Curriculum through Numeracy

This document will attempt to illustrate the developments of numeracy and establish how

mathematical activities in a classroom are acquired and applied within an International

Baccalaureate context.

Documentation

What is numeracy?

The definition of numeracy has certainly evolved considerably over time; it has changed

from being similar, if not identical to literacy, to now being quite diverse and viewed as a

‘multifaceted.... cultural, social, emotional and personal aspects of each individual context

(Maguire & Donaghue 2002, cited in American Institutes for Research, 2006,p.6 in

COAG,2008). The Australian Association of Mathematics Teachers (AAMT) (1997,p.15 in

Perso) describes numeracy, ‘is to use mathematics effectively to meet the general demands

of life at home, in paid work, and for participations in community and civic life.’ This

definition mirrors many other professional literatures like Perso’s, who concurs with the

AAMT and suggests; that being numerate is having the ‘disposition and capacity to use

mathematics to function effectively and fully at home and in society’. Steen (2007,p.17

cited in Westwood)also suggests that ‘numeracy has no special content of its own but

inherits its content from its context’. Moreover, Mason and Johnston-Wilder claim that the

‘kinds of powers that are relevant for learning mathematics are innate’. (Mason et al,2006).

These claims broadly state that it is the ability of an individual to use numbers and

mathematics effectively in everyday life through positive attitude; mathematical skills and

thinking, concepts and numerical strategies that deem them as numerate. These views

later led to further diversification by looking at what type of numeracy would be required



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for those in certain communities or occupations and showed that numeracy would indeed

be different for everyone; which led to numeracy being applied to different contexts and

termed as ‘multiple numeracies’- ‘community numeracy’, ‘critical numeracy’ and ‘consumer

maths’ (Westwood, 2008) as just a few examples. With these aspects in mind and claims

from professional literature; it is evidently becoming apparent that we must acknowledge

the importance of ‘multiple numeracies’ in everyday life and therefore necessary for

schools to embrace and adopt learning skills required for participation in the wider

community or civic life (see fig 1).

Fig.1. Teaching Numeracy

Students Innate

Ability /

Positive Disposition

Problem Solving

Student Interest

Teachers Knowledge /

Strategies



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Moreover, throughout the readings, Perso, Westwood and Ginsburg et al talk about ‘the

affective component of numeracy includes beliefs, attitudes and emotions that contribute

to a person’s ability and willingness to engage in...mathematical thinking and

learning’(Ginsburg et al, cited in Westwood, 2008,p.10). Perso like other scholars also

agree that ‘numeracy is different from mathematics’ and this relationship is sometimes not

well understood by some teachers- ‘resulting in an imbalance in their approach’ (Perso,

2006a;2007 cited in Westwood) and consequentially focusing on computational methods

of teaching mathematics (Perso,2006). Steen (2007,p.18 cited in Westwood) also believes,

that ‘numeracy is often characterised as watered-down mathematics’. However,

DEETYA,(1997) states, ‘all numeracy is underpinned by some mathematics; hence school

mathematics has an important role in the development of young people’s numeracy’

(Westwood,2008,p.9) (fig.2). Gough (2007) proposes that: ‘the content of numeracy is

represented by most of what comprises the typical primary school mathematics course’.

Obviously, this basic introduction to simple arithmetic is essential to further

understanding. The acquisition and application of numeracy is now quite subjective to the

individual and their circumstances, but continues to refer to the effective use of

mathematics and numbers in a given situation.



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Fig 2.

Inter-relationship between Mathematics and Numeracy

Learning

through

actions and

experiences

Basic

Mathematical

Skills

Specialised

mathematical

knowledge

Ability to

use

mathematics

in everyday

situations

Ability to

understand

further

mathematical

concepts

Further mathematical

learning

Knowledge gained

through necessary

activities

Broader mathematical

knowledge base adaptable

to many situations

Adapting knowledge

to real life situations

NUMERACY

MATHEMATICS



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Analysis

As a reference point this document will use a Grade 2 class from an International school in

Singapore. The Canadian International School (CIS) consists of expatriates from all over the

globe and is a large school that follows the International Baccalaureate Primary Years

Programme. The IBPYP program follows a constructivists approach to how children learn.

It is an inquiry based student-led learning process. The PYP curriculum follows a

transdisciplinary model and these themes cross the confines of traditional subject areas

(International Baccalaureate, 2009).

Grade 2 class comprises of 21 students which include:

4 ELL students of varying levels of English abilities

13 students are bi-lingual

10 countries are represented (9 from Eastern and Western Europe, 6 North

America, 6 Asia)

The students are at various stages of the IB continuum as they are not streamed

upon ability.

Teaching Numeracy within IB

Mathematics in the Primary Years Programme (PYP) at an IB school is very different to

mathematics in a traditional school. Following the constructivist approach, mathematics is

taught to children through a transdisciplinary programme (International Baccalaureate,

2013) (see fig.3). The work of Askew et al, suggests that teachers of numeracy tend to

reflect one of three possible orientations; connectionist-linking prior knowledge to new

knowledge; transmissionist-teach explicit information and discovery-learners discover

mathematical concepts for themselves (cited in Westwood,2008,p.36). It is very interesting



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to see how the IB also reflects the connectionist orientation with some elements of

discovery to their practices of teaching.

Fig.3 International Baccalaureate –How children learn mathematics

However, there is a realisation that not all students will be at the same part of the cycle at

the same time. The curriculum is designed on the recognition that the learning of

mathematics is a developmental process, which is not always age-related or linear. With

that in mind, the curriculum is based on phases or a continuum (International

Baccalaureate,2013). This does not mean there are not goals set for the grade levels. What

it does mean is teachers at CIS receive the grade level curriculum for their grade as well as

a grade below and a grade above. This allows the teacher to better tailor activities that are

inclusive to all abilities in the classroom. Vygotsky, suggests ‘optimum learning occurs

when tasks or problems are correctly tailored to be just a shade above a child’s current

Transferring meaning

Apply with

understanding

Constructing meaning



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level of ability but which a child can handle successfully with some support or guidance

from an adult’(cited in Westwood, 2008,p.29).

The Grade two mathematic curriculums are broken down into five sections:

Number benchmarks (50%)

Algebra –patterns and function benchmarks (10%)

Measurement (15%)

Statistics & Data handling (15%)

Shape and space (20%)

Although Number benchmarks and Algebra are separate sections they really go hand in

hand. Recognizing the patterns in maths, help the student create strategies to help them

with more complex problems. These segments coincide with Ginsburg et al (2006) views,

in such, that they suggest that ‘courses should be organised around four key strands:

number and operations sense; patterns, functions and algebra; measurement and shape

and data, statistics and probability (Westwood, 2008,p.7).

According to the IBPYP philosophy; it believes that ‘wherever possible, mathematics

should be taught through relevant, realistic context of the units of inquiry (UOI)...to help

students make connections between the different aspects of the curriculum’ (International

Baccalaureate,2012).

However, there are some points not clearly addressed in the IB Mathematics Scope and

Sequence curriculum; one being; teachers’ ability in numeracy and the other being; student

engagement. Perso emphasises the need for students to know how and when to apply

different types of mathematics or technology to solve problems and suggests that this is

best taught through a ‘task-centred’ approach. This is also highlighted through the

Annenberg Media entitled Mathematics: What's the Big Idea? (1997) where collaboration of



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student activity is encouraged in order to facilitate student engagement and hence aide

student learning. It is important for teachers to feel confident and competent about

teaching numeracy.

Inequalities

Being an independent international school in an affluent community, financial inequalities

are not prevalent, nor does the school lack funding or resources. However, inequalities are

apparent at the school and take shape in certain areas such as-language and culture

principally. The international school in Singapore uses English as its primary teaching

language and is made up of both local and international students, making it very transient.

As a result, there are several ELL learners; this can nevertheless cause complexities as the

classroom will inevitably have different abilities of spoken English which can create divide

and isolation. Also many students at CIS come from different cultures with little or no

knowledge of ‘western’ culture, this too can prove to be an issue for learners who are not

accustomed to ‘Canadian/Western’ culture as they may find it difficult to blend in; and

most teachers employed at the school are from a western background, who may have little

or no knowledge of different cultures of their learners which can lead to further

differences.

In addition, students experiencing this teaching approach for the first time may struggle

with group discussions, which can be a cause for concern for both students and parents

who come from more conventional traditional educational backgrounds, where education

culture is competitive and therefore difficult to appreciate and understand. Students from

traditional cultures or authoritative teacher led classes may have difficultly in the

cooperative learning and questioning approach. They may need time to learn and



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understand IB concepts. For many students the concept of thinking how to do something,

instead of being told is very foreign to them.



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Connecting theory to practice within IB

NUMERACY

EVERYDAY LIFE MATHEMATICAL

PROCESSES & SKILLS

WORK

CULTURAL COMMUNITY

EMOTIONAL RECREATIONAL

NUMBERS

SPATIAL ALGEBRA

DATA &

STATISTICS

SHAPE & SPACE

NUMERICAL

STRATEGIES

TEACHERS

UNDERSTANDING

COMPETENCE &

CONFIDENCE

DISPOSITION

TASK-CENTRED

APPROACHES

IB

TRANSDISCIPLINARY

INNATE ABILITY MULTIPLE NUMERACIES

CRITICAL NUMERACIES CONSUMER NUMERACIES

COMMUNITY NUMERACIES

MATHEMATICAL

KNOWLEDGE

CRITICAL THINKING

PROBLEM SOLVING

ETL 421 Teaching the Curriculum 2 Integrating Numeracy


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Consolidation

The following is a broad outline of two rich inter-related activities that have been designed

for a Grade 2 class at CIS.

The activities will be outlined using the Learning by Design pedagogy.

Learning Focus__________________________________________________________________________________

To inquire into the following Transdisciplinary Theme:

UOI – Sharing the Planet

Central idea - Share resources with other people and with other living things.

Learning level audience – Professional colleagues and grade two students.

Learning outcomes-Grade Two Mathematics Continuum (International Baccalaureate

2013)

Collecting and displaying data in a range of graphs, and interpreting the results.

Using appropriate mathematical vocabulary and symbols.

Selecting and explaining appropriate methods for solving problems.

Finding a unit of a fraction by using halving or repeated halving.

Task 1: ‘Develop a community in the forest’. (Brief outline)

Students are given a forest to build a community and told that there will be 25 people, (all

different ages and gender) which they have to divide into appropriate families. Then they

must build a community (1 bedroom house =cut down 10 trees etc). Also, within the forest,

there are living things (birds, fish, rabbits, trees) and natural resources, every living thing



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that they eliminate to build will cost them etc. The idea is to build a community with the

smallest amount of loss.

Ex

pe

rie

nci

ng

Known Experiencing their own community (nature parks, forests etc). Looking at their individual families & how they are made up. Gathering learners’ prior knowledge about environment and purpose

New How does it relate to what they see in real life? Listening and responding to texts Illustrate dividing up of families as a graph.

Co

nce

ptu

ali

sin

g

Naming Through connection, sorting and

classifying. Thinking routine ‘think, pair, share’(TPS) to

discuss their representations and what it

shows

Theory What do living & non living things need to survive? Show data results in form of graph

An

aly

sin

g Functionally

Demonstrate the link between developing a community and

how many living things & natural resources are lost

Critically What purpose does it serve?

Group discussion about how much was lost building a community?

show data in form of graph

Ap

ply

ing

Appropriately Gather post data of how many living & non living things were impacted by building a community

Creatively How can we build a community and share (divide) resources? Devise problem solving strategies



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Task 2-(Brief outline)

‘If the Earth was an apple’- incorporate with International Year of Mathematics of Planet

Earth (IYMPE).

Start by asking ‘What is a fraction? Gather data and show results in the form of a graph.

Students are given an apple and told that if ¾ was water how much would be left? And

then it gets divided further and further, so the students have to work out fractions and see

what how much soil is left to grow the earth’s food consumption.

Ex

pe

rie

nci

ng

Known Gathering learners’ prior knowledge about fractions, environment and purpose?

New How does it relate to what they see in real life? Listening and responding to texts

Co

nce

ptu

ali

sin

g

Naming

Through connection, sorting and classifying. Thinking routine ‘think, pair, share’ to discuss

their representations and what it

shows

Theory How to slice apple in ½ ¾ etc. Show data results in form of fractions

An

aly

sin

g Functionally

Watching video- ‘If the earth was an apple’. What does it tell us?

Further T.P.S discussion

Critically What purpose does it serve?

Group discussion about how much we have left to grow, show data in

form of graph

Ap

ply

ing

Appropriately Gather post data and create pie chart

Creatively How can we connect to IYMPE? How does it help our understanding?



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Redirection Whilst working through the IB Mathematics teaching philosophy, I noticed how it mainly

centres its approach to task-centred activities; but should they also incorporate direct

instruction, for those who have little or no knowledge of English, e.g. ELL learners? And

how does the IB compare along traditional concepts of teaching mathematics? Is inquiry

based learning really the way forward to teach mathematics?

Furthermore, I have also noticed that there is very little mention of technology in the IB

curriculum. ICT is only first mentioned in the Grade 2 curriculum benchmark guide. Would

a calculator not give those struggling in maths a voice in mathematical discussions? Or are

calculators and other technologies a hindrance to a child’s learning, to their thinking

process? What impact does technology have on mathematics in elementary students?

Word count 2180



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References:

Annenberg Media (1997). Mathematics: What's the Big Idea? USA: Author.

Retrieved 10/08/13 from: http://www.learner.org/resources/series98.html#

Council of Australian Governments 2008, National Numeracy Review Report,

Commonwealth of Australia, Barton, ACT

International Baccalaureate. (2009). Making PYP Happen: A curriculum framework

for International Primary Education. International Baccalaureate (revised edition ed.).

Cardiff, Wales: Antony Rowe.

International Baccalaureate. (2013). Primary Years Programme: Mathematics Scope and

Sequence. Canadian International School, Singapore

Kalantzis, M., & Cope, B. (2012). Literacies. Melbourne: Cambridge University

Press.

Mason, J. & Johnston-Wilder, S. (2006). Designing and Using Mathematical Tasks.

Milton Keynes: The Open University

Perso, T. (2006). Teachers of Mathematics or Numeracy?. amt 62(2), 36-40.

Retrieved 07/08/13 from

http://web.ebscohost.com.ezproxy.cdu.edu.au/ehost/pdfviewer/

pdfviewer?sid=d55ec1fa-53d3-45cb-b42df4b297f23633%

40sessionmgr10&vid=2&hid=28

Westwood, P. (2008). What teachers need to know about Numeracy. Victoria: ACER

Press

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ETL 421 Teaching the Curriculum / Integrating Numeracy ...samdanielteachingportfolio.weebly.com/uploads/1/9/3/2/19321115/... · ETL 421 Teaching the Curriculum / Integrating Numeracy