KEEPING IT REAL: CONNECTING NUMERACY WITH VOCATIONAL CONTEXTS

Beth Marr – Adult Numeracy Consultant

bethmarr@westnet .com.au

WORKSHOP OUTLINE

Introduction Presenter background Aims of workshop Participant contexts

Activities, reflection & discussion

Questions

KEEPING 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

KEEPING 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

KEEPING 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?

KEEPING 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?

KEEPING IT REAL

Put the topic ‘getting to the conference’ in centre of the circle and brainstorm

TEASING 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?

TEASING 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?

LEARNER 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

LEARNER 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

LEARNER 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

KEEPING IT REAL

Discussion of the rationale for this activity with reference to results from two projects:

NCVER researchThinking 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

FROM 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

FROM 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.”

RETHINKING ASSESSMENT - TEACHER INTERVIEWSHOLISTIC COMPETENCE - IDENTITY AS NUMERATE PERSON

Autonomy& Independence

Transfer & Application

Confidence

Awareness

Skills & Knowledge

TaskProcessCycle

Personal Connections

PERSONAL CONNECTIONS & LEARNING

Touches on emotional relationship to learning

Connections to students’ own lives & interests linking it with the familiar & informalseeing it as useable nowfor 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.”

PERSONAL CONNECTIONS & 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.”

PERSONAL CONNECTIONS & LEARNINGConnections 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”

PERSONAL CONNECTIONS & LEARNING

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 peersHated reading through big manuals or work

foldersSome short courses OK if related directly to

work

KEEPING IT REAL CREATING CONNECTIONS

Workplace research – skills transfer not automatic

Methods, language/terminology often different

Learners need help to ‘transfer’ skills from classroom to workplace

KEEPING IT REAL CREATING CONNECTIONS

One suggestionAfter skills /knowledge lesson eg

percentageTurn brainstorm model aroundHow are percentages used

in your work ? in the building trade?

Help students explore the connectionsParticular application eg diff % relevant in diff deps in Finance

Ministry - )special methods, language

NUMERACY – 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”

NUMERACY – WHAT WORKERS USED

Measurement daily huge variety of toolsextremely contextual

Visual estimation common particularly for OH&S judgments re lifting and storagethrough familiarity

Estimation of time – for planning tasks common

NUMERACY IN THE WORKPLACE

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

SENSE 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

‘

GUESS, ESTIMATE AND MEASURE MODEL

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

‘

GUESS, ESTIMATE AND MEASURE MODEL

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?

SENSE 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 ......

MATCHING 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%

MATCHING 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

SENSE 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

Persentajen uza Dalan Korta (short cut) “iha Kakutak Laran”

“In the head” Percentage using short cuts.

15 %

5 %

40 %

20 %

30 % 10%

60 %

50 %

25 %

$.

75 %

80 %

SHORT 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

TRUE OR FALSE ACTIVITY 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

SAMPLE OF A TRUE OR FALSE ACTIVITY MODEL - TOPIC: AREA AND VOLUME

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.

SAMPLE OF A TRUE OR FALSE ACTIVITY MODEL - TOPIC: AREA AND VOLUME

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.

TRUE OR FALSE ACTIVITY 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