Literacy + Mathematics + Language = Numeracy? Dave Tout, ACER tout@acer.edu.au

Literacy + Mathematics + Language = Numeracy?

Dave Tout, ACER

tout@acer.edu.au

Literacy + Mathematics + Language = Numeracy?

What is numeracy? How does it relate to literacy? How does it relate to mathematics? And how does it relate to language? What does it mean for teaching numeracy?

Literacy + Mathematics + Language = Numeracy?

The equation L + M + l = N, how else can we look at it?

Should we start with the subject of the equation - numeracy? N = L + M + l

So what is this thing Numeracy?

So what is this thing Numeracy?

So what is this thing Numeracy?

So what is this thing Numeracy?

Numeracy counts too

And in workplaces they use: Measurement, including of areas

and volumes Numbers in all forms – whole,

fractions, decimals, percentages Quantities – rates, $/m, $/m3 etc Statistics – tables, graphs,

averages Geometry and shapes And yes, they do use algebra!!

So what is this thing Numeracy?

And yes, algebra is used!

Key points – Parts MethodThere are three steps involved in calculating the ’actual’ binder application rate.Step 1: Convert volume from ‘hot’ to ‘cold’ using the following formula:

Step 2: Calculate the residual binder using the formula:

Step 3: Calculate the ‘actual’ binder application rate using the formula:

MultipliersprayedbitumenofVolumeC015atVolume

00 15at Volumecutter)bitumen (ofParts

bitumenofPartsC15atbinder Residual

)(m Area

(L)binder ResidualC15at raten applicatiobinder Actual

2

0

So, what is numeracy?

Numeracy is the bridge between mathematics and the real world

Numeracy is about making meaning of mathematics and therefore maths is seen as a critical tool to be used efficiently and effectively – and it can be low level maths through to high level maths

Numeracy is about using maths for social purposes (personal, community, work, further education)

Lynn A. Steen, probably the most articulate spokesperson for “Quantitative Literacy”, states that:

"...numeracy is not the same as mathematics, nor is it an alternative to mathematics. Today's students need both mathematics and numeracy. Whereas mathematics asks students to rise above context, quantitative literacy is anchored in real data that reflect engagement with life's diverse contexts and situations.

What is numeracy?

Is there a numeracy problem?

Gender (Oz):

47.5% of males are at levels 1 or 2

57.6% of females are at levels 1 or 2

A difference of over 10%!

Is there a numeracy problem?Age

• After an initial dip, age and skills are inversely related.• Generally highest performing age groups are from the early 20s to early 30s.• What are schools teaching students?• If you don’t use it, you lose it. Importance of lifelong learning?

Solving a real numeracy problem

Joe measures the depth of a road to be filled with asphalt. It is 225 mm deep (= the compacted thickness).He knows that the loose thickness needs to be 20% more than the compacted thickness. How high must the “loose” asphalt be prior to compacting by the roller?How did you work it out? What did you need to do to solve the problem?

Loose thickness Compacted

thickness

20%

Solving a real numeracy problem

And how did you calculate the 20%? Loose

thickness Compacted thickness

20%

20100 X

2251

Solving a numeracy problem

Step 1: Understanding the problem – reading the real world - reading/listening/watching – a literacy activity. Step 2: Doing the maths – calculating / estimating / measuring / acting in some wayStep 3: Putting it back into the real world to make it work, interpreting the maths and communicating it to others. More literacy.So there is some L in N!And now to the M?

The mathematics

The mathematics

The M is central to the numeracy equation N = L + M + l. You need M to be N.

Is mathematics a problem?Who’s a L teacher?Who’s a M teacher?Who’s a l teacher?Who’s a N teacher?Who’s all? Do you teach VET!?

The mathematics

How do you feel about maths?

0

Hate it

4

Love it

1 2 3

The mathematics

Were you good at maths at school? In Primary school? In High school?

0

Hopeless

4

Bloody good

1 2 3

The Blame game

The mathematics

The mathematics

The mathematicsTrends in International Mathematics and Science Study (TIMSS) (Hollingsworth, Lokan & McCrae, 2003), an international study based on videos of mathematics classroom practice. As reported in this study, McIntosh describes a typical Australian Year 8 mathematics lesson as:

The teacher talks a lot, the students mainly reply with very few words, most of the time the students work, using only paper and pencil, on a repetitive set of low level problems, most presented via the board or textbooks or worksheets; discussion of solutions is mainly limited to giving the right answer or going through the one procedure taught. There is little or no opportunity for students to explain their thinking, to have a choice of solution methods or to realise that alternative solution methods are possible, and very few connections are drawn out between mathematical ideas, facts and procedures.

(McIntosh, 2003, p. 108).

So we (should) know what Not to do!

The mathematics

But do we know what we should do?

Yes, for example, Jo Boaler’s research. The main benefits for the students (aged 13 to 16) that came from the “non-text book” school included: Positive attitudes to maths—lack of mathematics anxiety, and

students enjoyed their maths. Transferability of mathematics skills. These students

understood and could apply their mathematics inside and outside the classroom.

Skills remained with them. Little or no underachievement or anxiety for girls. Still successful academically on tests.

The l – language? Where does it come in?

But where does the language come in?Let’s look at some “sums” and see how we do them and see what we can learn about doing “maths” and what role language plays.

The mathematics - some sums

Work with the person next to you to work out how or why the learners got the following sums wrong:

657 – 329 = 3321/2 + 1/4 = 2/6

And the CHALLENGE question:225 ÷ 5 = 177

The mathematics - some sums

And the CHALLENGE question:325 ÷ 5 = 145

Or7235 ÷ 5 = 2775

The lessons:The language and words are crucialA context provides meaningUnderstanding crucial – and a need for

unlearning too!

The lowest common denominator (LCD) is the denominator which contains a representative of factors of each of the denominators. To include all factors take the highest power of each different prime factor present.

The language of mathematics

Interviewer: Do you know what volume means?Child: YesInterviewer: Could you explain to me what it

means?Child: Yes, it’s what is on the knob on the

TV set.

The language of mathematics

LW

H

The language of mathematics

Maths words are crucial to the understanding and learning of mathematics, but often language use and meaning is not addressed, nor are teachers aware of the important role language plays.Words can be difficult to understandWords can be misunderstood, confusing

and misleading.

Literacy + Mathematics + Language = Numeracy?

So does the equation work?

Literacy + Mathematics + Language = Numeracy?

Should language, literacy, VET teachers teach numeracy?Yes – with support for the maths contentShould maths teachers teach numeracy?Yes – with support for the language, literacy (and VET) content

Teach in context – connect to the real world – use real texts and real situations

Use a problem solving, investigative, open-ended approach Start from where students are at – allow for different levels,

different ways of doing Use different strategies and activities – cater for different

learning styles Scaffold and model – support the learners Make the maths skills explicit Use individual, small and whole group activities Connect language and maths – crucial Build confidence – have fun and success!

Teaching numeracy

Questions?

Some references Australian Bureau of Statistics, (2007) Adult Literacy and Life Skills Survey: Summary results, Australia

(cat. no. 4228.0), Australian Bureau of Statistics, Canberra Bynner, John & Parsons, Samantha (2005) Does numeracy matter more?, National Research and

Development Centre for Adult Literacy and Numeracy (NRDC), London Bynner, John & Parsons, Samantha (1997) Does numeracy matter? Evidence from the National Child

Development Study on the impact of poor numeracy on adult life, Basic Skills Agency, London FitzSimons, G., Mlcek, S., Hull, O. & Wright, C. 2005, Learning numeracy on the job: A case study of

chemical handling and spraying, NCVER, Adelaide. Gleeson, Lynne, 2005, Economic returns to education and training for adults with low numeracy skills,

NCVER, Adelaide. Hartley, Robyn & Horne, Jackie, (2006) Social and economic benefits of improved adult literacy:

Towards a better understanding, National Centre for Vocational Education Research (NCVER), Adelaide

Marr, Beth & Hagston, Jan, (2007) Thinking beyond numbers: Learning numeracy for the future workplace, NCVER, Adelaide.

Marr, Beth; Helme. Sue & Tout, Dave, (2003) Rethinking assessment: strategies for holistic adult numeracy assessment. A resource book for practitioners, policy-makers, researchers and teachers, Language Australia, Melbourne 2003

Tout, Dave, (1991) ‘Language and Maths’ in Marr, Beth; Helme. Sue & Tout, Dave, Breaking the Maths Barrier, Department of Employment, Education and Training, Canberra

Tout, Dave & Motteram, Gary, (2006) Foundation Numeracy in Context, ACER Press, Camberwell, Victoria