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K EEPING IT REAL : C ONNECTING NUMERACY WITH VOCATIONAL CONTEXTS Beth Marr – Adult Numeracy Consultant bethmarr@westnet.com.au

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W ORKSHOP O UTLINE Introduction Presenter background Aims of workshop Participant contexts Activities, reflection & discussion Questions

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K EEPING IT REAL Background in vocational numeracy: TAFE vocational mathematics subjects TAFE bridging courses for women National Automotive Industry Language and Literacy coordination unit Training needs analyses Printing Industry Training Board Food Industry Training Board NCVER workplace numeracy research project Manufacturing & despatch - small and large business Aged care Workplace numeracy training Ministry of Finance – East Timor

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K EEPING IT REAL Aims of this activity based workshop: Asked to do a workshop that focuses on relating numeracy to students vocational needs Also will introduce Activity Models Simple ideas for activity formats you can adapt for your students and their vocational needs

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K EEPING IT REAL Participant vocational contexts: TAFE subject for specific vocational groups? TAFE subject for mixed groups? Workplace training? Numeracy within literacy program? Other? Anyone at ACAL conference workshop?

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K EEPING IT REAL Activity – What maths do you need to...? ‘Brainstorm’ model In pairs – 2-3 minutes What numeracy was involved in you getting to this conference?

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K EEPING IT REAL Put the topic ‘getting to the conference’ in centre of the circle and brainstorm

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T EASING OUT THE NUMERACY Examples: Did it involve thinking about money? Did it involve thinking about time? Did it involve thinking about any other kind of measurement? Did you have to use graphs, charts or tables? Did anyone have to consult a map or street directory? Were any rates, formulae or rules for calculating things involved?

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T EASING OUT THE UNDERPINNING NUMERACY SKILLS Examples: What was involved in the money calculations? Numbers? – what kind? – how big? Decimals? Fractions? +, -, x, ÷ ? Did you do exact calculations or estimates? What was involved in the time calculations? exact or estimates?

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L EARNER VERSION What mathematics is needed in this ( budget) department? What mathematics is needed by.... Builders? Hairdressers? Butchers? Nurses? Fishermen?.... Try to pair up students with similar interests or jobs If they do not know then send them out to interview, shadow, chat to people in the job

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L EARNER VERSION If learners do not know then ask them out to go and interview, shadow, chat to people in the job Get examples if possible All kinds of interesting shortcuts can emerge Can be shared with class Teacher can also investigate Talk to trade and vocational teachers or people in the jobs

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L EARNER VERSION Final step - involve learners in the topic planning decisions eg Prioritise – write down three things from our list you would most like to learn about Encourage self awareness of existing skills eg rate your current knowledge of the numeracy skills we have teased out What are you already good at What you need a bit more help with What you need a lot of help with

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K EEPING IT REAL Discussion of the rationale for this activity with reference to results from two projects: NCVER research Thinking Beyond Numbers: Learning numeracy for the future workplace - Beth Marr & Jan Hagston Interviews with teachers for Rethinking Assessment: Strategies for holistic adult numeracy assessment – Beth Marr & Sue Helme

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F ROM WORKPLACE NUMERACY RESEARCH Invisibility of maths in the workplace Numeracy related tasks in the workplace dependent on the context embedded within workplace routines no longer resemble ‘mathematics’ from school not appreciated or ‘recognised’ as mathematics or numeracy Need to tease out and ask detailed questions Spending time ‘shadowing’ and chatting is useful

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F ROM WORKPLACE NUMERACY RESEARCH Workers interviewed - negative feelings about school maths Most about seeming irrelevance of high school maths - as one young woman said: “the teacher couldn’t relate it to real life”. she enjoyed percentages, but hated algebra because she saw it as useless for life “I only did maths to year 10, I couldn’t stand it - fractions and all that stuff - I didn’t pay attention. But I did do accounting - didn’t mind that.”

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R ETHINKING A SSESSMENT - TEACHER INTERVIEWS H OLISTIC C OMPETENCE - I DENTITY AS N UMERATE P ERSON Autonomy & Independence Transfer & Application Confidence Awareness Skills & Knowledge Task Process Cycle Personal Connections

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P ERSONAL C ONNECTIONS & LEARNING Touches on emotional relationship to learning Connections to students’ own lives & interests linking it with the familiar & informal seeing it as useable now for example, confidence to give correct change when selling ‘Footy Record’ “Sometimes it is the ability to see their learning as useable, applicable to their life outside the classroom, that indicates real learning taking place: making connections between what they do outside and what’s happening.”

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P ERSONAL C ONNECTIONS & LEARNING “... after we had done the practical measuring in class one of the students said he had helped his brother build a shed … the brother didn’t know where to put the end of the tape measure, like where the nought was and they kept getting this little bit wrong. ‘I told him it was because he was measuring from the wrong part’ … Something that was real knowledge that had happened in the class.”

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P ERSONAL C ONNECTIONS & LEARNING Connections to their reasons for studying -seeing it a useable later: “Competence is inextricably tied up with what the student wants to achieve.. They are not going to learn anything unless they have a purpose” Adult TAFE student in an interview: “ I won’t use any of this stuff (area calculations linked to painting & building) … I would learn better if I could see how it connects with things I might use in the office”

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P ERSONAL C ONNECTIONS & L EARNING Asked about the numeracy courses in the factory most preferred a direct relationship or ‘connection’ to their work: Frank – “When they did the course here they worked in centimetres which we never do on the factory floor” Elaine - “I would rather have done something useful.. it was mainly the men’s stuff ” Asked how they preferred to learn workers said: Learning on the job from supervisors or peers Hated reading through big manuals or work folders Some short courses OK if related directly to work

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K EEPING IT REAL C REATING CONNECTIONS Workplace research – skills transfer not automatic Methods, language/terminology often different Learners need help to ‘transfer’ skills from classroom to workplace

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K EEPING IT REAL C REATING CONNECTIONS One suggestion After skills /knowledge lesson eg percentage Turn brainstorm model around How are percentages used in your work ? in the building trade? Help students explore the connections Particular application eg diff % relevant in diff deps in Finance Ministry - ) special methods, language

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N UMERACY – WHAT WORKERS USED Calculations by all +, -, x daily Fractions – rarely Decimals frequently Division avoided - eg “say we have an order for 120 parts and I’ve got 18 sheets of metal available to cut them from. If I know that each sheet gives me 16 parts then I calculate 18 x 16 to see if it’s enough” Estimation common ‘in head’ or paper and pencil.. “because calculators have a way of straying”

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N UMERACY – WHAT WORKERS USED Measurement daily huge variety of tools extremely contextual Visual estimation common particularly for OH&S judgments re lifting and storage through familiarity Estimation of time – for planning tasks common

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N UMERACY IN THE W ORKPLACE Important in the workforce to have a sense of Number Size Timing The messages told by charts and graphs Understand the big picture Consequences of errors - expense

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S ENSE OF METRIC MEASUREMENTS ‘Guess, estimate and measure’ Model Cubic metre estimation Everyone should be able to visualise a cubic metre Very important in some work areas Task for individuals then pairs

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‘ G UESS, ESTIMATE AND MEASURE M ODEL Important for gaining sense of measurements Lengths using hands and arms Closed hand (10cm or 100mm) Handspan stretched (20cm or 200mm) Finger width (1cm or 10mm) Arm length (1 metre) Volume & weights using common objects as references or benchmarks Litre of milk ( 1 litre – 1 kg) References Mathematics: a new beginning Breaking the maths barrier

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‘ G UESS, ESTIMATE AND MEASURE M ODEL Using specific vocationally related references or benchmarks is even better Cubic metre related to typical sized packing cartons for warehouses and despatch areas Eg customs department in East Timor important to be aware of likely cargo coming in How many of these would fit in a cubic metre? in a small shipping container?

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S ENSE OF PERCENTAGES ‘Matching’ Model - Numeracy in our lives Small group task Explores existing knowledge of relevant percentages Explores understanding of ‘percentage’ in words and pictures Can adapt to specific, current vocationally related percentages Or general, current work related percentages eg – GST; tax rates; levees; unemployment rate......

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M ATCHING MODEL Easy to create Many possible uses Match words to pictures, diagrams or objects, graphs to stories Match maths symbols to expressions, definitions Match equivalent amounts 25% to ¼ to 0.25 1/10 to 0.1 to 10%

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M ATCHING MODEL Include some blanks for learners to make their own cards Encourages them to look carefully at the definitions, explanations, language used in the other sets eg look at other stories about the graphs in order to write their own – makes them really examine the features and their understanding References: Breaking the maths barrier Numeracy on the line

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S ENSE OF PERCENTAGES – SHORT CUTS ‘In the head’ methods or short cuts Used for exact calculations of common quantities eg percentages 10%, 20%, 30% etc 5%, 15% 50%, 25%, 75% These ‘benchmarks’ or references can be used to estimate other calculation results Individually empowering Useful for checking calculator results

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S HORT CUT PERCENTAGES Good to practice in the head calculations Demonstrates power of two simple initial calculations 10% (divide by 10) and 50% (halve) Top half: start with 10% and work all others from that draw an arrow from one bubble to the other and write the calculation you did to get there Bottom half: start with 50% and work all others from that

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T RUE OR F ALSE A CTIVITY MODEL In pairs or small groups discuss these statements and decide whether they are true or false If you think a statement is false then write a true one Best done in pairs or small groups to encourage discussion and shared thinking Asks students to use/share what they know to make judgements Good to introduce a topic or start a lesson Also good as revision device

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S AMPLE OF A T RUE OR F ALSE A CTIVITY M ODEL - T OPIC : A REA AND V OLUME Try this with a partner: Decide whether the following statements are more likely to be : Always true Sometimes true False If a statement is false – write a replacement statement that you think is true. 1. The capacity of a kitchen cup is approximately a quarter of a litre. 2. To buy paint for his lounge room Stephen will calculate its volume.

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S AMPLE OF A T RUE OR F ALSE A CTIVITY M ODEL - T OPIC : A REA AND V OLUME 3. The formula Volume = length x width x height can be used to find the volume of any three dimensional (3D) shape. 4. One litre (1 L) of water weighs exactly one kilogram (1 Kg). 5. A cubic centimetre is the same as a square centimetre. 6. The length around the outside of any flat shape is called its circumference. 7. John carried a cubic metre of soil in his wheelbarrow.

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T RUE OR F ALSE A CTIVITY MODEL Tease out learners understandings Can also be used to highlight and discuss common misconceptions eg ¼ = 0.4 T or F? Can use from 2 to 8 questions depending on how long a discussion you want Variations Always true, sometimes true, never true For estimations of calculations: Reasonable or not Good or No good

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