Numeracy Across Learning

East Lothian

October 2009

Aims and programme• Possible misconceptions about NAL

• What is Numeracy and why NAL?

• Approaches to Numeracy

• Working with Numeracy Es and Os

• NAL within depts and whole school

• Sharing emerging practice

• National Maths/Numeracy Glow Group

N.A.L.

Workshop : Possible misconceptions within NAL

In small groups:

• discuss each statement given and record any key points.

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Why is numeracy important?

• Some 44% of men & 37% of women living in Scotland had left full-time education by the time they were 16 - early exit increased to over 6 in 10 men with SCQF Level 2 or 3 numeracy (SG, 2008) • About two-thirds of the juvenile offenders screened had under-developed basic skills eg subtraction, measure, fractions, decimals, percentages, volume, area, graphs and timetables (NRDC, 2005)

• .. the NRDC study showed that “while the impact of low level literacy and low level numeracy is substantial, low numeracy has the greater negative effect” (DIUS, 2008)

What is numeracy?

Number literacy ~ number based skills needed by everyone regularly as they go about their

daily lives

These areas featured on all lists:

• Time and its management

• Finance and its management

• Interpretation of data (analysis and decision-making)

• Communicating numerically

• Computer use for numerical data handling

• Application of mathematics in a range of occupational areas.

London South Bank University

Numeracy Strategies?

Workshop : In cross-learning working groups:• discuss and record the strategies you use to solve the type of problems given.• rotate to next station, discuss and add comments on the strategies suggested • repeat once more• as you work discuss emerging noteworthy issues

Numeracy Strategies?

Workshop : In cross-learning working groups:• 40 – 29• 3000 – 2457• 6000 – 1998• 8hrs 24min – 6 hrs 52 min

What does it mean to be numerate?

How are the numeracy experiences and outcomes structured?

Mathematics is not my specialism. How will I contribute to the development of numeracy skills?

What are the features of effective learning and teaching in numeracy?

How can I promote progression in children and young people’s development of numeracy skills? How do I know which numerical skills I should develop and that they are at an appropriate level?

Have we raised the bar in the expectations for numeracy?

What are broad features of assessment in numeracy?

Numeracy across learning

Principles and practice

Numeracy is a skill for life, learning and work. Having well-developed numeracy skills allows young people to

be more confident in social settings and enhances enjoyment in a large number of leisure activities. For

these and many other reasons, all teachers have important parts to play in enhancing the numeracy skills

of all children and young people. 

Numeracy across learningPrinciples and practice

Mathematics is not my specialism.

How will I contribute to the development of numeracy skills?

• where does numeracy play a part in my curriculum area?

• to what extent do you already provide numeracy experiences?

• does your programme involve estimating, calculating, measuring, using and managing time, carrying out money calculations?

• does it involve analysing information from charts and tables or explaining consequences of actions?

Numeracy ‘Organisers’(Subset of mathematics Experiences & Outcomes)

• Estimation & Rounding• Number & number Processes• Fractions (aspects of), Decimal Fractions and Percentages• Money• Time• Measure• Data Analysis (aspects of)• Chance & Uncertainty

Numeracy across learningPrinciples and practice

I am mathematics teacher.

How will I exploit contexts provided within other curriculum areas to enhance the development of numeracy skills?

 

Numeracy across LearningThe main way in which interdisciplinary learning can support

numeracy is by cross-referencing within everyday learning across curriculum areas. This can takes two forms:

• Exploiting knowledge, skills, contexts and applications introduced in other subjects (and especially soon after their introduction)

• Promoting the integration, reinforcement and application of numeracy skills and concepts within relevant contexts within other disciplines. This reinforces important aspects of prior learning and it focuses attention on the transferable ideas and skills.

Numeracy Across Learning Some key Messages:

Contexts and activities:– Natural, authentic and relevant to learners– Is bi-directional– Applies to a manageable number of related Es and Os– Promotes consistency and opportunities to declutter– Can be daily & include opportunities for rich activities

Numeracy ‘Organisers’(Subset of mathematics Experiences & Outcomes)

• Estimation & Rounding• Number & number Processes• Fractions (aspects of), Decimal Fractions and Percentages• Money• Time• Measure• Data Analysis (aspects of)• Chance & Uncertainty

Working with Experiences and Outcomes

Workshop : In small working groups:• get to know the numeracy Es and Os

Working within an appropriate line(s) of development:

• look for progression across levels • identify how you will support and develop numeracy in your classroom• share with others these ways in which you can support the development of numeracy within your subject

Contexts and activities for NAL

Estimating and Rounding

• Olympic Games

• Supermarket

•Dimensions for decorating

• Money – costings/budget

• The ‘rough joiner’

• Machine parts

• Flat pack furniture – fitted kitchen

Working with Experiences and Outcomes

Workshop : Working within an appropriate line(s) of development:

• identify possible authentic contexts and activities for NAL

Contexts and activities for NAL

Fractions, Decimal Fractions and %

• Paint/wallpaper paste

• Solutions for hair products/dry cleaning

• Fruit juice concentrates

• Catering

• Transport – fuel consumption

• Literacy – reading instructions

Contexts and activities for NAL

Money

• Wages – different jobs/minimum wage

• Renting/buying houses

• Enterprising activities eg ‘Doghouse’

• Costing activities

• Inflation/depreciation

• Foreign Exchange

Contexts and activities for NAL

Time

• Time management

• Working week

• Rates of activities

• Journey times – bus/taxi fares

• Opening hours/TV schedules

• Catering/industrial processes

Contexts and activities for NAL

Measure

• Buying furniture

• Design

• Minimising waste - fabrics

• Car tyres

• Car models eg Corsa 1.3

• Stopping distances – ferry charges

• Car park restrictions

Contexts and activities for NAL

Data & Analysis

• Sports statistics

• Elections and polls

• Personal interests – Google Search

• Robust sources

• Online shopping

• Personal Information/identity

• Best buys – online evaluation

• Informed choices eg HWB

Contexts and activities for NAL

Chance & Uncertainty

• Buying a house – flooding/settlement

• Smoking and drinking

• Probability - consequences

• Driving accidents

• Self harm

• Staring a successful business

• Job security

Auditing opportunities for NAL

I can work collaboratively, making appropriate use of

technology, to source information presented in a

range of ways, interpret what it conveys and discuss whether I believe the information to be

robust, vague or misleading. MNU 3-20a

To help me develop an informed view, I am learning about the techniques used to influence opinion and how to

assess the value of my sources, and I can recognise

persuasion. LIT 3-08a

Linkages across

Outcomes

Numeracy across LearningRelated experiences and outcomes:

I am developing the skills and attributes which I will need for learning, life and work. I am gaining understanding of the relevance of my

current learning to future opportunities. This is helping me to make informed choices about my life and learning. HWB 3-19a

The Kennel ClubProposals:Activity which involves students developing numeracy and craft skills through research, enterprise and collaboration between mathematics and CDT.

Skills/concepts:• Purchase a medium sized dog kennel.• Inventory each part.• Measure all components.• Cost each component.• Measure, cut, and assemble kennel.• Hire extra skills

Interesting practice in NAL:

I can round a number ....... MNU 3-01a

By applying my knowledge and skills of science and mathematics ....... TCH 2-12a/3-12a

I can solve problems by carrying out calculations......... MNU 3-07a

I can solve practical problems by applying my knowledge of measure ....... MNU 3-11a

By using problem solving strategies and showing creativity .......

TCH 3-14a

In a business environment, I explore and use data handling......

TCH 3-06a

Family of

related Es and Os

The Kennel Club (Mathematics & CDT)

• Additional certification via qualifications in two SQA National Certificate (half) modules at SCQF level 4:

- Construction Numeracy 1 , module number 0091048- Construction Crafts: Carpentry & Joinery Techniques, number DM82 10.

• .

Construction Numeracy 1 is designed to enable the student who is interested in, or employed within, the construction industry. It provides the student with a series of basic mathematical/numerical tools sufficient to operate effectively at craft level in construction.

The student should:1.carry out basic calculations;2.calculate perimeters, areas and volumes of rectilinear shapes;3.apply simple costing methods

Construction Crafts: Carpentry and Joinery Techniques

1200 mm

end elevationHousing joint detail

10mm deep

OUTCOME 1Select, use and maintain basic carpentry and joinery tools and equipment.OUTCOME 2Erect a prefabricated timber assembly.OUTCOME 3Replace a designated timber panel.

Carpentry and joinery skills and techniques:

• Selecting and using appropriate tools.

• Cutting and fitting

• Placing and securing

• Framing and jointing

• Testing eg a plumb line

• Servicing and storing tools

• Health & safetysawed off

The Finished Article

NAL : Climate ChangeNumeracy AimsThe development of a consistent cross-school or cross-departmental approach to numeracy skills, in particular, those related to measurement, graph and chart work or basic number processes eg

Representation of numbers including decimal places and rounding leading to scientific notation, standard form and significant figuresUse of averages, percentages, decimals and fractionsUse of bar charts, histograms and line graphsPercentages, decimals and fractions

Project AimsWithin the ‘Processes of the Planet’ section, allow students to learn about climate change as a natural process in time as well as the result of human activity.

Working in collaboration, the project will require students toFind and analyse historical weather dataDraw conclusions about changes in the weather over the time these data exhibitRelate these findings to our understanding of climate change, including global warming.

Key Experiences and OutcomesCarry out Geographical enquiry to assess the impact and possible outcomes of climate change on a selected region and can propose strategies to slow or reverse the impact (Soc Studs SOC 4-12b)Evaluate and interpret raw and graphical data using variety of methods, comment on relationships I observe within the data and communicate my findings to others. (Numeracy MNU 4-20a) In order to compare numerical information in real life contexts, I can find the mean, mode, and range of sets of numbers, decide which type of average is most appropriate to use and discuss how using an alternative type of average could be misleading. (Mathematics MTH 4-20b)I enhance my learning by applying my ICT skills in different learning contexts across the curriculum. (TCH 3-04a)

NAL: Enterprising Numeracy - Bridge Building

Key Experiences and Outcomes

• Numeracy MNU3-01a, MNU3-10a, MNU3-07a, MNU3-07c, MNU3-09a, MNU3-12a• Technology TCH3-01a, TCH3-03a, TCH3-04a, TCH3-07a, TCH3-07b, TCH3-12a, TCH3-13a, TCH3-14a• Social Subjects SOC3-10a

Project Description

The class will be given Brief to build a bridge over a river, some basic specifications, and a map of the river to work from. The class will be split into groups which will form the Companies. Each group will decide their company name and roles for each member of their team. Teacher led lessons will include; map reading, scale measurement, bridge design, structure shapes, basic forces and guidance on model building.

Each ‘Company’ is given a standard components list and pricelist to work from. Fines and bonuses can be applied by the teacher as appropriate. This project opens the possibility of interdisciplinary work with the following departments; Geography, Design Technology, Science, Mathematics Business Education and ICT.

Recommendations and Resources

Project requires continuity of planning across departmentsResources supporting this project can be found at various locations including websites operated by GLOW, LTS, google images, www.technologystudent.com, www.technologyinthemearns.net

NAL: Health & WellbeingProject Aims

• Within the ‘Biological Systems’ section to understand what a healthy diet is and relate it to fitness and health.• Within ‘food and health’ section to understand what a healthy diet is and to make healthy food choices by analysing their own diet.Within ‘physical wellbeing’ to use their knowledge of the human body to maintain and improve their well being.Relate these findings to our understanding of health and fitness. Analyse and draw valid conclusions from data. Identify and collect appropriate data. To record relevant measurements and observations in appropriate formats.Key Experiences and Outcomes

• To learn about the structure and function of organ systems, explore the role of technology in monitoring health and improving quality of life (SCN 3-12a, 3-12b) Having researched food and health policy and dietary legislation pupils can explain the impacts on individuals, relate current healthy eating advice and make links between energy nutrients and health (HWB 3-30a, 3-31a, 3-34a, 3.36a, 4-30a, 4-34a) Develop and build on physical competences and improve aspects of fitness (HWB 3-15a, 4-15a, 3-22a, 4-22a, 3-24a, 4-24a, 4-25a)Evaluate and interpret raw and graphical data using variety of methods, comment on relationships I observe within the data and communicate my findings to others. (MNU 4-20a)To enhance pupils learning by applying my ICT skills in different learning contexts across the curriculum. (TCH 3-04a).

NAL: School PolicyProject Aims

To develop a consistent approach to basic numeracy techniques across departmentsTo develop a common understanding of basic numeracy skills by all staffTo ensure that a common approach is taken by all departments in teaching and consolidation of basic numeracy skillsTo promote improved transferability of numeracy skills by pupils

Project Description The development of a whole school numeracy policy for staff, pupils and parents. This is to allow the consistent teaching and then practising and consolidation of basic numeracy skills across all departments using numeracy skills.

Recommendations and Resouces• Project requires continuity of planning across departments - Mathematics, Sciences, Technologies, Social Subjects and others as appropriate.Develop a numeracy ‘glossary of terms’, see Stromness Academy for an exemplar at:http://www.stromnessacademy.orkney.sch.uk/school_xcurr_page.htm

Document knowledge expectations at various levels in each involved departmentDocument terminology / links / applications used by the different subject departmentsResources supporting this project can be found at various locations including: Getting to Grips with Graphshttp://www.ase.org.uk/htm/book_store/detail.php?SIID=1

Collaboration on Measurement, Scale Diagrams and Maps:

• Mathematics Es & Os contains “measurement” , “proportion” , “shapes”, “transformation”

• In Science, measurement, accuracy and rounding are important in most areas of experimentation, units are important in all quantitative calculations, graphs require handling of scales and estimation when interpolating or extrapolating

• In Technologies, there is reference to estimation and measurement and to graphical techniques; scale?

• In Social Studies (geog) there is reference to maps and “geographical information systems”

 

Cross-department and whole-school implementation

Discuss and share emerging practice in:

• Possible forms of leadership or coordination?• Supporting collaborative planning and working?• Possible implications for practice?• Evidence of NAL in action?• Any other important issues?

NAL

Audit into Action Interesting PracticeAudit into Action Interesting Practice

Mathematics / Numeracy Teachers

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Glow Group

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Where am I ?

• Navigate using the tabs at the top of the screen

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So how do I log on ?

• All teachers should be able to access the group through a Glow username and password

How to access the group

1. Go to the National Site homepage2. Look for the section on National Glow Groups3. Click on Click on “Staffroom groups” link

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Go to the National Site homepage

How to access the group

4. Two sections• “Glow groups”• “Staffroom Glow Groups you are not a member

of”

5. In the first instance you will click on the second option above to navigate to the Mathematics / Numeracy Teachers Group

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If the screen below appears enter the following and click on

“I would like access to the Mathematics / Numeracy Teachers Glow Group. Could this please be organised. Thank you , A Teacher, Any School, Any Council”

How to access the group

6. On your next login Maths/Numeracy teachers group will appear under “My Glow Groups”

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How to access the group: Summary … 1. Go to the National Site homepage2. Look for the section on National Glow Groups3. Click on Click on “Staffroom groups” link4. Two sections

• “Glow groups”• “Staffroom Glow Groups you are not a member of”

5. In the first instance you will click on the second option above to navigate to the Mathematics / Numeracy Teachers Group

6. On your next login Maths/Numeracy teachers group will appear under “My Glow Groups”