Numeracy – a Numeracy – a matter of life and matter of life and

deathdeathSteve ThorntonSteve Thornton

s.thornton@griffith.edu.aus.thornton@griffith.edu.au

Quantitative literacy Quantitative literacy (Steen)(Steen)

Quantitative literacy empowers Quantitative literacy empowers people by giving them tools to think people by giving them tools to think for themselves, ask intelligent for themselves, ask intelligent questions and confront authority.questions and confront authority.

Critical mathematical Critical mathematical literacy (Frankenstein)literacy (Frankenstein)

Understanding the mathematicsUnderstanding the mathematics Understanding the mathematics of Understanding the mathematics of

political knowledgepolitical knowledge Understanding the politics of Understanding the politics of

mathematical knowledgemathematical knowledge Understanding the politics of Understanding the politics of

knowledgeknowledge

NUMBER (THOUSANDS)

CATEGORY

(1) 101,400 Employed full-time

(2) 19,000 Employed part-time, want part-time work

(3) 4,000 Employed part-time, want full-time work

(4) 5,600 Not employed, looked for work in last month, not on temporary layoff

(5) 1,100 Not employed, on temporary layoff

(6) 400 Not employed, want a job now, looked for work in last year, stopped looking because discouraged about prospects of finding work

(7) 1,400 Not employed, want a job now, looked for work in last year, stopped looking for other reasons

(8) 3,800 Not employed, want a job now, have not looked for work in the last year

(9) 60,700 Not employed, don’t want a job now (adults)

An Australian example: An Australian example: boys’ educationboys’ education

““FALLING BEHIND”FALLING BEHIND”

Key facts from the federal parliamentary Key facts from the federal parliamentary report into the education of boys:report into the education of boys:

Year 3 and 5 literacy tests show boys perform up Year 3 and 5 literacy tests show boys perform up to five percentage points worse than girlsto five percentage points worse than girls

Average NSW Tertiary Entrance Score for boys Average NSW Tertiary Entrance Score for boys was 19 percentage points worse than for girls in was 19 percentage points worse than for girls in 19961996

80 percent of suspensions from schools were boys80 percent of suspensions from schools were boys

(Canberra Times 22 October 2002)(Canberra Times 22 October 2002)

Situated cognition (Lave)Situated cognition (Lave)

The context shapes the mathematics The context shapes the mathematics usedused

The importance of mathematics The importance of mathematics varies from context to contextvaries from context to context

It is impossible to separate cognitive It is impossible to separate cognitive activity, context and the personactivity, context and the person

Numeracy (Willis)Numeracy (Willis)

To be numerate is, at the very least, To be numerate is, at the very least, having the competence and the having the competence and the disposition to use mathematics to disposition to use mathematics to meet the general demands of life at meet the general demands of life at home, in paid work, and for home, in paid work, and for participation in community and civic participation in community and civic life.life.

A numeracy frameworkA numeracy framework

Being numerate involves a blend of Being numerate involves a blend of three types of knowledge:three types of knowledge:

ContextualContextual knowledge knowledge MathematicalMathematical knowledge knowledge StrategicStrategic knowledge. knowledge.

Contextual knowledgeContextual knowledge

1.1. Clarify the outcomes of the task and recognize Clarify the outcomes of the task and recognize when and where mathematics might help.when and where mathematics might help.

2.2. Understand the mathematical ideas and Understand the mathematical ideas and techniques as embedded in the context or that techniques as embedded in the context or that might be applied in the situation.might be applied in the situation.

3.3. See what interpretations make sense in the See what interpretations make sense in the setting, apply and adapt the mathematics to fit setting, apply and adapt the mathematics to fit the constraints of the situation and in a way that the constraints of the situation and in a way that makes sense in the setting. makes sense in the setting.

4.4. Make decisions about how accurate you need to Make decisions about how accurate you need to be.  be.  

5.5. Interpret the outcome(s) in the context and Interpret the outcome(s) in the context and evaluate the mathematics used.evaluate the mathematics used.

Mathematical knowledgeMathematical knowledge

1.1. Understand the mathematical ideas Understand the mathematical ideas and techniques required in the and techniques required in the situation.situation.

2.2. Use the mathematical ideas and Use the mathematical ideas and techniques. techniques.

Strategic knowledgeStrategic knowledge

1.1. An orientation or disposition to use mathematics An orientation or disposition to use mathematics in a situation.in a situation.

2.2. Know what mathematics is and isn’t and what it Know what mathematics is and isn’t and what it can and can’t do in order to judge and question can and can’t do in order to judge and question the appropriateness of its use in particular the appropriateness of its use in particular situations. situations.

3.3. Judge or question the validity or reasonableness Judge or question the validity or reasonableness of the use of mathematics in situations.of the use of mathematics in situations.

4.4. Understand the mathematical idea used in one Understand the mathematical idea used in one setting and see how it could be used in other setting and see how it could be used in other contexts. contexts.

A cautionary taleA cautionary tale

Jack the RipperJack the Ripper

30/9 30/9

8/11 31/8

Mary Kelly’s body was found at flat 1326 Dorset Street

Another woman, Martha Tabram, was also found murdered on 6/8/1888.She was killed by 39 stab wounds.

THE JUWES ARE THE THE JUWES ARE THE MEN THAT WILL NOT MEN THAT WILL NOT

BE BLAMED FOR BE BLAMED FOR NOTHINGNOTHING

1 3 5 7 9T E T B OH T W L TE H I A HJ E L M IU M L E N2 4 6 8W E N D GE N O FS T T OA H B RR A E N

9 4 6 8 2 3 1 7 5E E T B TN N D W T H L WT O F E H E A I

O H T O S E J M LT A B R A M U E LH E N RING

The numeracy momentThe numeracy moment

1.1. Notice the ‘moment’Notice the ‘moment’

2.2. Decide how crucial the moment is to Decide how crucial the moment is to deal withdeal with

3.3. Decide on when to deal with itDecide on when to deal with it

4.4. What are the student numeracy issues or What are the student numeracy issues or possibilities?possibilities?

5.5. Identify the strategy you will useIdentify the strategy you will use

6.6. Talk to the studentsTalk to the students

Implications for the Implications for the teacherteacher

Capture the numeracy in the momentCapture the numeracy in the moment Be aware of possible numeracy demands when Be aware of possible numeracy demands when

planningplanning Allow students to work it outAllow students to work it out Support student numeracy learning by questioningSupport student numeracy learning by questioning Diagnose student numeracy by listening purposefullyDiagnose student numeracy by listening purposefully Debrief the numeracyDebrief the numeracy PracticePractice Promote critical use of mathematicsPromote critical use of mathematics Teach the framework to the studentsTeach the framework to the students Share information on student numeracy with othersShare information on student numeracy with others

A final quote: whose A final quote: whose mathematics?mathematics?

““There is no future in denying some successes in the There is no future in denying some successes in the

science and technology developed following the science and technology developed following the

Greek style. We will surely not be able to build Greek style. We will surely not be able to build

faster jets and more powerful missiles using the faster jets and more powerful missiles using the

male and female triangles of the Xingu male and female triangles of the Xingu

ethnomathematics.ethnomathematics.

But maybe the male and female triangles could help But maybe the male and female triangles could help

us us notnot build the missiles and the jets carrying the build the missiles and the jets carrying the

bombs.” (Ubi d’Ambrosio)bombs.” (Ubi d’Ambrosio)

The ACT MYNRP WebsiteThe ACT MYNRP Website

http://activated.det.act.gov.au/MYNRP/http://activated.det.act.gov.au/MYNRP/index.htmindex.htm

ReferencesReferences Frankenstein, M. (2001). “Frankenstein, M. (2001). “To read the world: To read the world:

goals for a critical mathematical literacygoals for a critical mathematical literacy”. Paper ”. Paper presented at AAMT conference, Canberra 2001presented at AAMT conference, Canberra 2001

Lave, J. (1988). Lave, J. (1988). Cognition in PracticeCognition in Practice. Cambridge . Cambridge University PressUniversity Press

PISA (2001). PISA (2001). Knowledge and skills for lifeKnowledge and skills for life. Paris: . Paris: OECDOECD

Steen, L. (2001). Steen, L. (2001). Mathematics and democracy: Mathematics and democracy: the case for quantitative literacythe case for quantitative literacy. National . National Council on Education and the DisciplinesCouncil on Education and the Disciplines

Willis, S (1992). Being numerate: Whose right? Willis, S (1992). Being numerate: Whose right? Whose left? Whose left? Literacy and Numeracy ExchangeLiteracy and Numeracy Exchange