oecd march 07 jim ridgway, james nicholson and sean mccusker child’s play - reasoning with...

OECD March 07 Jim Ridgway, James Nicholson and Sean McCusker

Child’s Play - Reasoning with Multidimensional Data

Jim Ridgway, James Nicholson and

Sean McCusker

[email protected]

University of Durham

www.dur.ac.uk/smart.centre/

mailto:[email protected]


Child’s Play – Reasoning with Multi-Dimensional Data

• Play therapy– Alcohol, Fast Birds, and Sexually Transmitted Infections

• Research– Testing smart 9 and 13 year olds – they can reason with

multidimensional data

– Generalising to representative students – they can do it too

• What don’t we know• The threat of education• What are we doing about it all


Child’s Play

• Sexually Transmitted Infections

• Alcohol

• Fast Birds

– http://www.ic.nhs.uk/pubs/alcoholeng2006/alcoholtables/file – www.hpa.org.uk/infections/topics_az/hiv_and_sti/epidemiology/datatables200

5.htm

In collaboration with CCEA, QCA and The Information Centre

http://www.ic.nhs.uk/pubs/alcoholeng2006/alcoholtables/file

http://www.hpa.org.uk/infections/topics_az/hiv_and_sti/epidemiology/datatables2005.htm

http://www.hpa.org.uk/infections/topics_az/hiv_and_sti/epidemiology/datatables2005.htm


Child’s Play - Research

• Oxygen

• Testing smart 9 and 13 year olds

• Generalising to representative students


From Watson and Callingham


Paper Based

Most Difficult 5

Computer Based

.

. OXY1_4 .

. .4

. . .

. .

3 OXY2_2 B3.2_3 RF3_3 . OXY3_4 B4._1/B3.1_3 . B2.2_3

M7CH_4 . B4.1_1 RF4_2_2 HSE3_2 . OXY1_3 B1.2.2_1 BW2.2_2 SP11_2 . OXY3_3

2 BW2.1_2 .

M7CH_3 M8QU_2 . . B3.1_2/B3.2_2 . OXY2_1/OXY3_2 B2.2_2 BW2.3_2

HSE1_2 . RF2.2_3 MPDifG_2 1 OXY1_2 WF2.4_2 RF3_2 SP10 . B1.2.1_2 BW2.2_1/BW3.3_1 WF2.3_2

HSE2_2 M7CH_2 . HSE3_1 .

. B2.2_1 BW3.2_1 WF2.2_1 RF2.2_2 SP9/SP7 . RF4_1 0 B3.1_1

M8QU_1 . OXY3_1 BW2.1_1 WF2.4_1 SP11_1 . B3.2_1 BW3.1_1 WF2.3_1 SP8 . B1.2.1_1 BW2.3_1 RF2.2_1

HSE2_1/HSE1_1 . . RF3_1

-1 OXY1_1 M7CH_1 . SP6 . BW1_1

. WF1_1 RF2.1_1 MPDifG_1 . .

-2 WF2.1_1 .

. . . RF1_1

TRV2/TRV5 . -3 .

. TRV3 .

. . TRV1_1 -4

. . .

. .

Least Difficult -5


The Threat of Education

• Condorcet le savoir liberateur and all that…

• UK students are taught 1930s statistics (Ridgway et al, 06)

– the 1930s principle was fine – ‘take something of interest and mathematise it’


Child’s Play – What don’t we know?

What do/can people understand from multivariate data – in an emerging field?

What can people learn as they interact with data?


Some Heuristics for Playing

• Critique the quality of the data

• Describe and explore before you model and explain

• Check that the effect size is a lot bigger than the likely measurement error

• Look for interactions, and think about ‘data surfaces’

• Think about possible confounding variables

• Disaggregate data – are the patterns the same?

• Be cautious about ‘causality’ – especially in observational data


Our Current Work

• Interface design– Generic shells as freeware– Empirical studies on difficulty

• Curriculum development– Modelling disease spread– Risk taking by young people

• Drugs, sex, obesity, alcohol abuse

• Conceptual analyses– What is worth knowing?– What develops?– How?

• Collaborating! - http://www.dur.ac.uk/smart.centre


Child’s Play - Reasoning with Multidimensional Data

Jim Ridgway, James Nicholson and

Sean McCusker

[email protected]

University of Durham

www.dur.ac.uk/smart.centre/

mailto:[email protected]


Levels of Statistical Literacy

1. Idiosyncratic Tautologies, one-to-one counting, read cells

2. Informal Intuitive non-statistical beliefs (3 is lucky), one-step calculations

3. Inconsistent Limited appreciation of content and context without justification; qualitative ideas.

4. Consistent Non-critical

Straight-forward engagement with context; means, simple probabilities and graphs.

5. Critical Questioning engagement; appreciation of variation; qualitative interpretation of chance.

6. Critical Mathematical Questioning critical engagement with context, proportional reasoning, subtle language.


-2

-1

0

1

2

3

4W

F1

WF

2.1

WF

2.2

WF

2.3

WF

2.4

RF

1

RF

2.1

RF

2.2

RF

3

RF

4

B1.

2.1

B1.

2.2

B2.

2

B3.

1

B3.

2

B4.

1

B4.

2

OX

Y1

OX

Y2

OX

Y3

BW

1

BW

2.1

BW

2.2

BW

2.3

BW

3.1

BW

3.2

BW

3.3

T2X

2

TR

V1

TR

V2

TR

V3

TR

V4

TR

V5

TR

V6

HS

E1

HS

E2

HS

E3

M7C

H

M8G

R

M8Q

U

SP

6

SP

7

SP

8

SP

9

SP

10

SP

11

MP

DifG

Item

Ave

rag

e S

core

Upper Third Lower Third

Computer Based Paper Based


OxygenN=161

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10

Score

Count

Oxygen


From AQA 3 (a) A sample of people, who commute regularly from a town in Surrey into London, was

asked for an estimate of the time taken on their most recent journey. The replies are summarised below.

Time

(minutes) Frequency

35 - 12

45 - 54

55 - 68

65 - 41

85 - 105 23

Calculate estimates of the mean and the standard deviation of these times. (5 marks) (b) A sample of people who commute regularly from a town in Essex into London was also

asked for an estimate of the time taken on their most recent journey. Their replies had a mean of 64 minutes and a standard deviation of 21 minutes. Compare, briefly, the journey times estimated by commuters from the two towns. (2 marks)

(c) Give two reasons why the data presented in parts (a) and (b) may not adequately represent typical commuting times from the two towns. (2 marks)


From AQA

3(a) Class mid-mark Frequency 40 12 50 54 60 68 75 41 95 23

x = 63.2 s = 15.2

M1

A2 A2

5

Allow m1A1 for mean and s.d. if method shown. 63.2 (63.1 63.3)

15.2 (15.0 15.3)

(b) Journeys from Surrey have similar duration, on average, but are less variable than those from Essex.

E1 E1

2

(c) People asked may not be representative. Times are estimated not measured.

E1 E1

2

Or any other sensible comments e.g. journey time not defined , weather conditions may be extreme etc

Total 9


ALL National Exams (2004) ‘Technique’ as % of Exam

Exam Board

S 1 S 2 S 3 S 4

AQA 75 80 75 77

OCR 76 71 69 86

CCEA 88 77

Edexcel 73 75 77

WJEC 97 72 79

OCR (MEI)

75 69 72 78


Average Score/Maximum Score

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1W

F1

WF

2.1

WF

2.2

WF

2.3

WF

2.4

RF

1

RF

2.1

RF

2.2

RF

3

RF

4

B1.

2.1

B1.

2.2

B2.

2

B3.

1

B3.

2

B4.

1

B4.

2

OX

Y1

OX

Y2

OX

Y3

BW

1

BW

2.1

BW

2.2

BW

2.3

BW

3.1

BW

3.2

BW

3.3

T2X

2

TR

V1

TR

V2

TR

V3

TR

V4

TR

V5

TR

V6

HS

E1

HS

E2

HS

E3

M7C

H

M8G

R

M8Q

U

SP

6

SP

7

SP

8

SP

9

SP

10

SP

11

MP

DifG

Item

Ave

rag

e S

core

/Max

imu

m s

core

Upper Third Lower Third

Paper BasedComputer Based

oecd march 07 jim ridgway, james nicholson and sean mccusker child’s play - reasoning with...

Documents