Vera Frith, Robert Prince, Jacob Jaftha,

Pam Lloyd, Sheena Rughubar-Reddy,

Kate Le Roux, Duncan Mhakure

Numeracy Centre, ADP

Centre for Higher Education Development, University of Cape Town

Numeracy Centre Research: A journey over a decade. 

Goals of the Numeracy Centre

1. To assist the university with ensuring that students and graduates are quantitatively literate in a manner that is appropriate for their course of study and intended role in the community.

2. To promote access to and foster success in quantitatively demanding programmes of study.

Overview of Numeracy Centre research 

 What is academic QL and how can it be promoted? 

    Some considerations about the use of technology 

Questions for further investigation

Outline of presentation

Some reflections

Defining the domain of Academic Numeracy (Quantitative Literacy) practice

A brief overview of the Numeracy Centre’s research

An overview of the Numeracy Centre research

Academic numeracy (quantitative literacy) is a social practice in which people : 

 - manage situations or solve problems in real disciplinary contexts, 

 - by  responding to quantitative (mathematical and statistical) information (which may be presented verbally, graphically, in tabular or symbolic   form). 

 - It requires the activation of a range of enabling knowledge, behaviours and  processes

 - and can be observed when it is expressed in the form of a communication, in written, oral or visual mode.

Refs: International Lifeskills Survey; Lave, 1988; Street, 2005; Street and Baker, 2006; Johnson, 2007; Yasukawa, 2007

Definition of academic numeracy (quantitative literacy) practices

EducationalOur

Practices

Disciplinary Academic Numeracy (QL) Practices

Nature of QL

Framework

School

Academ

ic 

development

Graduateness

Postgraduate

Affect

Technology

Feedback

Testing

Framework for a Quantitative Literacy Test

1+ 1- 2+ 2- 3+ 3- 4+ 4- n Actual %

Specified %

VocabularyRepresentations of numbers and operationsConventions for visual representations Using representations of dataComputing (and estimating?)

ConjecturingInterpretingReasoningRepresenting quantitative informationDescribing quantitative relationships

nActual %

Specified %

Acting, interpreting, communicating

Competence area

Knowing Applying routine procedures in familiar

contexts

Applying multistep procedures in a variety

of contexts

Reasoning and reflecting

Comprehending: identifying or locating

Framework for a Quantitative Literacy Test cnt.

1+ 1- 2+ 2- 3+ 3- 4+ 4- n Actual %

Specified %

Quantity, number and operations

Shape, dimension and space

Relationships, pattern, permutation

Change and rates

Data representation and analysis

Chance and uncertainty

n

Actual %

Specified %

Reasoning and reflecting

Mathematical and statistical ideas

Competence area Knowing Applying routine procedures in familiar

contexts

Applying multistep procedures in a variety

of contexts

Some initial results across the Higher Education sector

3055

6125

3022

0

1000

2000

3000

4000

5000

6000

7000

Total

QUANTITATIVE LITERACYNBT Benchmark Levels, February 2009

Basic

Intermediate

Proficient

Some initial results across the Higher Education sector cnt.

596

136

563

78

590

142

599

1807

77

1265

292

673

212

1235

1392

4

921

179121

29

669

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Commerce Education Engineering Health Humanities Law Science

QUANTITATIVE LITERACYNBT Benchmark Levels, February 2009

Basic

Intermediate

Proficient

EducationalOur

Practices

Disciplinary Academic Numeracy (QL) Practices

Nature of QL

Framework

School

Academ

ic 

development

Graduateness

Postgraduate

Affect

Technology

Feedback

Testing

Marco Polo:

“To distinguish the other cities’ qualities, I must speak of a first city that remains implicit. For me it is Venice.”

Kublai Khan: “You should then begin each tale of your travels from the departure, describing Venice as it is, all of it, not omitting anything you remember of it.”

Invisible Cities, Italo Calvino

“We will seek opportunities within existing curricula to strengthen the basic ‘literacies’ – academic, quantitative and information – both as a means of improving learning capacity and as a contribution to informed citizenship.” 

Concept Paper ‘Enhancing the quality and profile of UCT graduates’ (2009)

Fundamental research questions for the Numeracy Centre:

•What does it mean for a student to be quantitatively literate?

•What curriculum changes are needed to “strengthen” quantitative literacy?

Quantitative literacy for higher education curriculum

Health and Rehabilitation Studied in first year Speech and Hearing Science

Psychology – first year

Psychology

Extract from judgement in: Government of South Africa v Grootboom 2001 (1) SA 46(CC)(studied in first year Constitutional Law course)

“The housing shortage in the Cape Metro is acute. About 206 000 housing units are required . . .  the number of shacks in this area increased by 111% during the period 1993 to 1996 and by 21% from then until 1998. . . . The scope of the problem is perhaps most sharply illustrated by this: about 22 000 houses are built in the Western Cape each year while demand grows at a rate of 20 000 family units per year. The backlog is therefore likely to be reduced … only by 2 000 houses a year.

Law

Elaboration of the competencies involved in QL practice1. Know Know the meanings of quantitative terms and phrases (verbal representations). 

Know the conventions for the symbolic representation of numbers, measurements, variables and operationsKnow the conventions for the representation of quantitative information in tables, charts, graphs, diagrams and objects. (visual representations).

2. Identify  Identify connections and distinction between different representations of quantitative conceptsIdentify the mathematics to be done and strategies to do itIdentify relevant and irrelevant information in representations

3. Derive meaning

Understand a verbal description of a quantitative concept/situation/processDerive meaning from representations of data in contextDerive meaning from graphical representations of relationshipsDerive meaning from diagrammatic representations of spatial entitiesTranslate between different representations

4. Apply  Use mathematical techniques - calculating, estimating, measuring, ordering, modelling, applying algebraic or graphical techniques etc.

5. Think Synthesise information or ideas from more than one sourceReason logicallyConjectureInterpret, reflect and evaluate.

6. Express quantitative concepts

Represent quantitative information using appropriate representational conventions and languageDescribe quantitative ideas and relationships using appropriate language

So what difference does this knowledge make?

Disciplinary context

Extract from statement of outcomes for QL in first year MBChB

Content Contexts used “Reasoning/thinking”

Understand and work with percentiles (including median, quartiles) of a distribution.

Read off values for the percentiles of a distribution from a cumulative curve.

Distribution of body weights and heights in a normal population, Body Mass Index

Make conceptual links between different representations of the same concepts 

Generalise ideas from specific cases 

Understand, calculate and work with the statistical measures for central tendency; mean and median

Body weights and heights, Body Mass Index

Reason about distributions - data and uncertainty

Questions relating to choice of contexts for QL courses

Do they serve our purposes for teaching QL? 

Should contexts be familiar to students? 

What is the appropriate balance between context and content in QL courses?

Ref: Frith, V. et al (2010) Tensions between content and context in a quantitative literacy course for university students. In preparation: Mathematics Education and Society conference

Purposes for teaching quantitative literacy

Tertiary study

Professional life and work

Everyday life

Citizenship

Social justice

Ref: Frith, V. et al (2010) Tensions between content and context in a quantitative literacy course for university students. In preparation: Mathematics Education and Society conference

Unit 2: Xenophobia in South Africa In this unit we will read extracts from reports about xenophobia and refugees in South Africa.

Activity 1:Group discussion1(a) What is meant by xenophobia?1(b) What do you consider to be the main beliefs about foreigners that lead to xenophobia in South Africa? 2. Read the following extract from the report by Danso, R and McDonald, D.A. (2004) Writing Xenophobia: Immigration and the Press in Post-apartheid South Africa and then discuss the answers to the questions below.

In mid-1997 and late-1998, SAMP conducted two nation-wide surveys on the attitude of South Africans towards immigrants and immigration. . . Firstly, it is apparent that South Africans on the whole carry strong anti-immigration sentiments, with fully 25% of the population calling for a complete ban on migration into the country and approximately half (45% in 1997 and 53% in 1998) calling for a “strict limit on the number of foreigners allowed into the country”. Only 6% of the 1997 survey said that the government should “let anyone in who wants to enter”, a figure that dropped to 2% in 1998. . .

(a)Is it true to say that more South Africans in 1998 than in 1997 called for a ‘strict limit on the number of foreigners allowed into the country’? What information in the text leads one to make this statement?

. . .

Curriculum extract

Contexts in the curriculum

“I found like that first section of the course … quite tedious in a way. Uhm, it didn’t really seem to justify getting up so early in the morning to, to like get to university … the stuff that you could sort of just blag my way through ….”

“… the first 3 units … I found them very useful in terms of that they really made you think and analyse something differently ….they kind of like made you look beyond the surface meaning and even go deeper … it was something that I thought, wow, I could actually use this in the future when I am working . . .”

“… I just thinked the course was very difficult because I did maths and so the whole writing and analysing sentences and all it was like, oh my word. …  I was like oh my what am I going to have to write so long and all …”

In 2009, we are administering computer-based learning materials to approximately   1800  students:

Numeracy Centre courses for Law and Humanities:  ~ 400Psychology:  ~850Sociology:  ~200Health Sciences:  ~350

Use of computers

Spreadsheets as a productivity tool

Computer technology in QL

Project to conduct a survey that either confirms or disproves that Cape Town’s youth is indulging in risky behaviour (first year QL students in the psychology major stream)

A mini research project in a course (MAM1016S)

Student answers saved

Conduct survey

Save data

database

Analyse own data

Retrieve data 

Submit tutorial

Write report

Complete tutorial

Tutorial feedback

Nature 

Features 

Aspects we have exploredAffective issuesTeaching and Learning issues

(tutorial) Learning environment

VF,JJ,RP: Interactive Excel Tutorials in a Quantitative Literacy Course for Humanities Students in Integrating Technology in Higher Education (Eds) M.O. Thirunarayanan & Aixa Pérez-Prado, 2005

AD,JJ,DH:Customising Microsoft Office to develop a tutorial learning environment BJET 35(2), 2004

VF,JJ,RP: Interactive Excel Tutorials for learning Mathematics and Statistics, ICMI, 2005VF,JJ,RP: Evaluating the effectiveness of interactive computer tutorials for an undergraduate mathematical literacy course, BJET 35(2), 2004

Aspects of feedback

Affective issues

Learning environment design

Technology in QL: Quo Vadis?

Motivation and relevance

Fear and loathingStatements like: “I came to do Law especially because I never wanted to have to do any maths again!”

QL not “proper maths”

Stigma

EducationalOur

Practices

Quantitative disciplinary practices

Nature of QL

Framework

School

Academ

ic 

development

Graduateness

Motivation

Technology Fe

edback

Testing

Transfer

Language

See our posters!

Or e-mail:Vera.frith@uct.ac.zaRobert.prince@uct.ac.za.Jacob.jaftha@uct.ac.za

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