Kwok-cheung Cheung, Pou-seong Sit, Man-kai Ieong &

Soi-kei Mak,

Educational Testing and Assessment Research Centre,

University of Macau, Macao

Predicting academic resilience with

mathematics learning and demographic

variables: Comparing Macao, Hong

Kong, Korea, Japan, Canada, Estonia

and Finland

Paper presented at the 2014 European Conference on Educational Research(ECER) in Porto, Portugal, 2-5 September, 2014

Synopsis

• Mathematics is the major domain of literacy

assessment in PISA 2012.

• Based on the impact of the Economic, Social, and

Cultural Status (ESCS) of the student on mathematical

literacy performance, the equity of the participating

education systems is also assessed.

• This study analyzes data of selected mathematics

learning variables for the seven high-performing high-

equity economies (i.e. Macao, Hong Kong, Korea,

Japan, Canada, Estonia, and Finland).

• Special attention is paid to the ESCS-disadvantaged

students who are academically resilient in spite of

being in an unfavorable condition.

• Logistic regression is run to identify the predictive

learning mathematics and demographic variables.

• Across the seven economies under study, demographic

variables like gender, family structure, immigration

status, attending kindergarten and grade repetition, as

well as the four self-regulatory learning mathematics

variables, are found to differentiate within the group of

ESCS-disadvantaged between the academically

resilient and non-resilient students.

• The key finding is that across the seven economies

primary attention needs to be paid to students’

mathematics self-efficacy and familiarity with

mathematics concepts. Another two alterable

variables mathematics self-concept and mathematics

anxiety are also verified to affect particular

economies to different extents.

• After accounting for the effects of the demographic

variables, interesting patterns of effects are

discernible when the high-performing and high-

equity East Asian economies (Macao, Hong Kong,

Japan and Korea) are contrasted with that of the non-

East Asian counterparts (Canada, Estonia and

Finland).

Hypothesis of study

This study examines links between

resilience (and non-resilience) of the

ESCS-disadvantaged students with

pertinent learning mathematics variables

while controlling for the demographic

characteristics of the seven high-

performing high-equity economies in

PISA 2012.

Across the seven high-performing and high-

equity economies in PISA 2012, the self-

regulatory learning mathematics variables (i.e.

familiarity with mathematical concepts,

mathematics self-efficacy, mathematics self-

concept and mathematics anxiety), after

controlling for the effects of the demographic

covariates, have differential effects on the

classification of academic resilience in

mathematical literacy within the group of

ESCS-disadvantaged students.

Method

Sample

• This study utilizes data drawn from PISA 2012 in

which the seven economies Macao, Hong Kong,

Korea, Japan, Canada, Estonia and Finland

ranked amongst the top positions in the league

table of mathematical literacy performance, and at

the same time, bottom positions regarding the

impact of ESCS on student mathematical literacy

performance.

Dependent Variable

• The research interest lies with the academic resilience in

mathematical literacy within the subgroup of ESCS-

disadvantaged students in connection with the resilience

classification by four self-regulatory learning mathematics

variables, using the demographic variables as covariates.

• The difference between disadvantaged non-resilient and

disadvantaged resilient student regarding the effects of the

learning mathematics in the prediction of the resilience

class membership is examined in this study.

• The dependent variable corresponds to the two

classifications of the resilient and non-resilient students in

the subgroup of ESCS-disadvantaged students.

Method

Dependent Variable

• There are three steps in the identification of resilient students.

First, students located at the bottom quarter of the PISA index of

ESCS within their own economies are identified as

disadvantaged students.

• Second, literacy performance scores as assessed in PISA are

regressed on student ESCS across all participating economies to

find out the international ESCS-performance relationship.

• Third, student residual performance is obtained by comparing

the actual performance of each student with the performance

predicted by the international ESCS-performance relationship.

• Resilient student is identified as those whose residual

performance is amongst the top quarter of student residual

performance from all economies.

Method

Identification of disadvantaged resilient (DRS),

disadvantaged non-resilient (DNR) and

non-disadvantaged students (NDS) in Macao

0

200

400

600

800

1000

-4 -3 -2 -1 0 1 2 3

ESCS

Mathematical Literacy Score

Table 1: Percentage of students by resilience

classification

Economy Resilience classification (%) Total sample size

(N) NDS DNR DRS

Macao 75.0 8.0 17.0 5,335

Hong

Kong

75.0 6.7

18.3 4,670

Korea 75.0 12.2 12.8 5,033

Japan 75.0 13.6 11.4 6,351

Canada 75.0 16.6 8.4 21,544

Estonia 75.0 15.3 9.7 4,779

Finland 75.0 16.7 8.3 8,829

Note: NDS=Non-Disadvantaged Student; DNR=Disadvantaged Non-Resilient

student; DRS=Disadvantaged Resilient Student

Independent Variables

• Gender (X1): female=0; male=1.

• Family structure (X2): mixed or single family=0; nuclear

family=1. Students in nuclear family refer to those who are

living with both parents, whereas students in mixed or

single family are not.

• Immigration status (X3): first or second generation=0;

native=1.

• Years of attendance of kindergarten (X4): 0= one year or

less; 1= more than one year.

• Grade repetition (X5): 0=not repeated; 1= has repeated one

time or more in primary or secondary grades.

Method

Independent Variables

• Familiarity with mathematical concepts (X6)

• Mathematics self-efficacy (X7)

• Mathematics self-concept (X8)

• Mathematics anxiety (X9)

Method

Pearson correlation of the learning mathematics variables with

mathematical literacy performance in PISA 2012

Economy Familiarity

with

mathematical

concepts (X6)

Mathematics

self-efficacy

(X7)

Mathematics

self-concept

(X8)

Mathematics

anxiety

(X9)

East Asian economy

Macao .474 .513 .371 -.321

Hong

Kong .405 .553 .355 -.319

Korea .610 .622 .424 -.202

Japan .477 .580 .217 -.206

Non-East Asian economy

Canada .420 .553 .441 -.411

Estonia .320 .524 .439 -.470

Finland .434 .553 .516 -.445

OECD

Average .432 .529 .400 -.366

Analysis Strategies

• First, the sample characteristics (i.e. the demographic,

self-regulatory learning mathematics characteristics)

for the DRS versus DNR in each of the seven

economies are examined.

• Second, logistic regression is carried out for the DRS

vs DNR student classification, as a function of the

demographic and self-regulatory learning

mathematics characteristics.

Results

Sample Characteristics of the Seven

High-performing High-Equity

Economies

Sample characteristics of the DRS vs NDR

classification for Macao, Hong Kong, Korea and Japan Variables Macao Hong Kong Korea Japan

DRS DN

R

Total S.S DRS DN

R

Total S.S DRS DN

R

Total S.S DRS DN

R

Total S.S

Demographic characteristics (%)

Gender (X1)

0 = Female

1 = Male

65.9

68.6

34.1

31.4

100

100

71.7

73.1

28.3

26.9

100

100 *

49.5

52.5

50.5

47.5

100

100 *

40.4

49.4

59.6

50.6

100

100 *

Family structure (X2)

0= mix or single

family

1 = nuclear family

68.2

68.0

31.8

32.0

100

100

74.9

72.6

25.1

27.4

100

100 *

56.5

52.7

43.5

47.3

100

100 *

45.0

46.7

55.0

53.3

100

100 *

Immigration status

(X3)

0= first or second

generation

1 = native

70.8

58.2

29.2

41.8

100

100 *

74.2

70.7

25.8

29.3

100

100 * -- -- --

15.6

45.3

84.4

54.7

100

100 *

Attend kindergarten

(X4)

0 = one year or less

1 = more than one

year

54.1

69.9

45.9

30.1

100

100 *

61.9

73.5

38.1

26.5

100

100 *

45.3

52.6

54.7

47.4

100

100 *

27.1

46.0

72.9

54.0

100

100 *

Grade repetition (X5)

0 = not repeated

1 = repeated in

primary/secondary

85.3

48.1

14.7

51.9

100

100 *

77.3

53.9

22.7

46.1

100

100 *

51.7

30.1

48.3

69.9

100

100 * -- -- --

*p<.05; S.S. = Statistical significance (Chi-square/t-test)

Sample characteristics of the DRS vs NDR

classification for Macao, Hong Kong, Korea and Japan

Variables Macao Hong Kong Korea Japan

DRS DNR Total S.S DRS DNR Total S.S DRS DNR Total S.S DRS DNR Total S.S

Learning mathematics and problem solving characteristics (group mean)

Familiarity with

mathematical

concepts (X6) .751 -.001 .497 * .388 -.334 .192 * .492 -.097 .188 * .352 -.194 .058 *

Mathematics self-

efficacy (X7)

.235 -.580 -.025 * .242 -.820 -.076 * -.362 -1.206 -.765 * -.245 -1.189 -.775 *

Mathematics self-

concepts (X8) .072 -.418 -.086 * -.001 -.415 -.106 * -.175 -.781 -.460 * -.068 -.450 -.274 *

Mathematics anxiety

(X9) .078 .541 .227 * .056 .418 .149 * .285 .546 .409 * .258 .548 .415 *

*p<.05; S.S. = Statistical significance (Chi-square/t-test)

For Macao, Hong Kong, Korea and Japan, the

following findings are summarized:

• The Chi-square test of independence between gender and

resilience classification is statistically significant for Hong

Kong, Korea and Japan.

• The Chi-square test of independence between family structure

and resilience classification is statistically significant for Hong

Kong, Korea and Japan.

• The Chi-square test of independence between immigration status

and resilience classification is statistically significant for Macao,

Hong Kong, and Japan.

• The Chi-square test of independence between attend

kindergarten and resilience classification is statistically

significant for Macao, Hong Kong, Korea and Japan.

• The Chi-square test of independence between grade

repetition and resilience classification is statistically

significant for Macao, Hong Kong, and Korea.

• For familiarity with mathematical concepts,

mathematics efficacy, mathematics self-concepts, and

mathematics anxiety the DRS mean is statistically

significantly different from that of DNR (p<0.05).

Noteworthy is that the mean mathematics anxiety for

DNR is higher than that of DRS, whereas it is the

other way round for the other three learning

mathematics variables.

Sample characteristics of the DRS and NDR classification for

Canada, Estonia and Finland

Variables Canada Estonia Finland

DRS DNR Total S.S DRS DNR Total S.S DRS DNR Total S.S

Demographic characteristics (%)

Gender (X1)

0 = Female

1 = Male 29.8

36.9

70.2

63.1

100

100

* 38.0

39.2

62.0

60.8

100

100

31.4

33.6

68.6

66.4

100

100

*

Family structure (X2)

0= mix or single family

1 = nuclear family 35.4

34.0

64.6

66.0

100

100

* 43.2

38.3

56.8

61.7

100

100

* 31.9

34.8

68.1

65.2

100

100

*

Immigration status (X3)

0= first or second

generation

1 = native

33.0

34.3

67.0

65.7

100

100

* 22.5

40.3

77.5

59.7

100

100

* 13.4

34.2

86.6

65.8

100

100

*

Attend kindergarten (X6)

0 = one year or less

1 = more than one year 32.1

35.7

67.9

64.3

100

100

* 45.3

36.4

54.7

63.6

100

100

* 30.0

35.1

70.0

64.9

100

100

*

Grade repetition (X5)

0 = not repeated

1 = repeated in

primary/secondary

36.8

13.4

63.2

86.6

100

100

* 40.3

9.9

59.7

90.1

100

100

* 35.2

3.7

64.8

96.3

100

100

*

*p<.05; S.S. = Statistical significance (Chi-square/t-test)

Sample characteristics of the DRS and NDR classification for

Canada, Estonia and Finland

Variables Canada Estonia Finland

DRS DNR Total S.S DRS DNR Total S.S DRS DNR Total S.S

Learning mathematics characteristics (group mean)

Familiarity with

mathematical

concepts (X6)

.301 -.288 -.089 * .411 .098 .213 * -.189 -.769 -.580 *

Mathematics self-

efficacy (X7)

.365 -.479 -.203 * .073 -.471 -.260 * -.057 -.833 -.572 *

Mathematics self-

concepts (X8)

.571 -.105 .127 * .251 -.273 -.061 * .409 -.444 -.150 *

Mathematics

anxiety (X9)

-.277 .331 .124 * -.497 .246 -.052 * -.654 -.014 -.232 *

*p<.05; S.S. = Statistical significance (Chi-square/t-test)

For Canada, Estonia, and Finland, the following

may be summarized:

• The Chi-square test of independence between

gender and resilience classification is statistically

significant (p<0.05) for Canada and Finland.

• The Chi-square test of independence between

family structure and resilience classification is

statistically significant (p<0.05) for Canada,

Estonia and Finland.

• The Chi-square test of independence between

immigration status and resilience classification is

statistically significant (p<0.05) for Canada,

Estonia, and Finland.

• The Chi-square test of independence between

attend kindergarten and resilience classification is

statistically significant (p<0.05) for Canada,

Estonia, and Finland.

• The Chi-square test of independence between

grade repetition and resilience classification is

statistically significant (p<0.05) for Canada,

Estonia, and Finland.

• For familiarity with mathematical concepts,

mathematics efficacy, mathematics self-concepts,

and mathematics anxiety the DRS mean is

statistically significantly different from that of DNR

(p<0.05).

• Noteworthy is that the mean mathematics anxiety

for DNR is higher than that of DRS, whereas it is

the other way round for the other three self-

regulatory learning mathematics variables.

Logistic regression analysis of the

resilience classification (i.e. DRS vs

DNR) as a function of the

demographic and learning

mathematics variables

The following findings are

summarized for the five demographic

variables:

• Grade repetition (X5) is found predictive of the

resilience classification (except Japan where this

variable is not applicable to this education system).

• X5 is most predictive for Finland. The logistic

regression coefficient is -2.775 and the odds ratio is

0.062. This shows that when the other predictor

variables are held constant the chance that an ESCS-

disadvantaged student who have repeated in

primary/secondary grades is an academically resilient

student is 0.062 times of those who have not repeat

grades at all.

• Immigration status (X3) is found most predictive

of the resilience classification for Macao, Canada,

Estonia and Finland.

• X3 is most predictive for Finland. The logistic

regression coefficient is 1.182 and the odd ratio is

3.262. This shows that when the other predictor

variables are held constant the chance that an ESCS-

disadvantaged Finnish native student is academically

resilient is 3.262 times of the first or second

generation peers.

• Attend kindergarten (X4) is found predictive for Macao and

Estonia, but in different direction.

• In the case of Macao, The logistic regression coefficient is

0.612 and the odds ratio is 1.844. This shows that when the

other predictor variables are held constant the chance that an

ESCS-disadvantaged Macanese student who has attended more

than one year of kindergarten education is academically

resilient is 1.844 times of peers who attend one year or less.

• In the case of Estonia, The logistic regression coefficient

is -0.471 and the odds ratio is 0.625. This shows that when the

other predictor variables are held constant the chance that an

ESCS-disadvantaged Estonian student who has attended more

than one year of kindergarten education is academically

resilient is only 0.625 times of those who attend one year or

less.

• Gender (X1) is predictive only for Canada.

• The logistic regression coefficient is 0.226 and the

odds ratio is 1.254. This shows that when the other

predictor variables are held constant the chance that

an ESCS-disadvantaged Canadian male student is

academically resilient is 1.254 times of a female

peer.

• Family structure (X2) is not predictive in the

logistic regression analyses of the seven high-

performing high-equity economies of PISA 2012.

The following findings are

summarized for the four learning

mathematics variables:

• Mathematics efficacy (X7) is a powerful predictor of

the resilience classification for all the seven

economies under study.

• X7 is most predictive for Japan. The logistic regression

coefficient is 0.911 and the odds ratio is 2.486. This shows that

when the other predictor variables are held constant the chance

that an ESCS-disadvantaged Japanese student whose

mathematics efficacy increases one scale unit is academically

resilient is 2.486 times of peers who haven’t increased in

mathematics efficacy.

• Across the seven economies, higher level of mathematics

efficacy is found associated with better chance of academic

resilience, and this phenomenon is especially prominent in most

East Asian (i.e. Hong Kong, Korea and Japan; except Macao)

than the Non-East Asian economies (i.e. Canada, Estonia and

Finland).

• Familiarity with mathematics concepts (X6) is also

predicting the resilience classification very well.

The coefficients of X6 are statistically significant

for all the four East Asian and two of the three

East Asian economies (except Estonia).

• X6 is most predictive for Korea. The logistic regression

coefficient is 0.960 and the odds ratio is 2.610. This shows that

when the other predictor variables are held constant, the chance

that an ESCS-disadvantaged Korean student whose familiarity

with mathematics concepts increases one scale unit is

academically resilient is 2.610 times of his/her peers who

haven’t increased in familiarity with mathematics concepts.

• Across the six economies (except Estonia), higher level of

familiarity with mathematics concept is found associated with

better chance of academic resilience.

• Mathematics anxiety (X9) is able to make a contrast

between the East Asian economies and non-East

Asian economies regarding the prediction of the

resilience classification.

• For Canada, Estonia and Finland, the regression coefficients of

X9 are -0.175, -0.409 and -0.366 respectively, and the

corresponding odds ratios are 0.839, 0.664 and 0.694. The three

regression coefficients just mentioned are all statistically

significant (p<0.05), whereas those of the four East Asian

economies are not.

• Across the three non-East Asian economies, higher level of

mathematics anxiety is found statistically significantly

associated with lesser chance of academic resilience.

• Mathematics self-concept (X8) is able to make a

contrast between the East Asian economies (except

Macao) and non-East Asian economies regarding

the prediction of the resilience classification.

• For Canada, Estonia and Finland, the regression coefficients of

X8 are 0.429, 0.377 and 0.553 respectively, and the

corresponding odds ratios are 1.536, 1.458 and 1.739. The

three regression coefficients just mentioned are all statistically

significant (p<0.05), whereas those of the four East Asian

economies except Macao are not.

• Across the three non-East Asian economies, higher level of

mathematics self-concept is found statistically significantly

associated with higher chance of academic resilience, and the

only East Asian economy has this similar phenomenon is

Macao.

Implications of study

East Asian Economies

• Macao, Hong Kong, Korea and Japan have the largest

share of resilient students in their ESCS-disadvantaged

population, respectively amounting to 68%, 73%, 51%

and 46% of their 15-year-old cohort of secondary

students.

• The research evidence of this study show clearly that

ESCS-disadvantaged students who have attended

kindergarten more than one year, and who have not

repeat education in primary and/or secondary grades,

stand higher chances of beating the odds against them

and being identified as academically resilient than their

counterparts.

• This study establishes that the two learning

mathematics variables familiarity with mathematical

concepts and mathematics self-efficacy are not only

educational quality indicator variables, but also from

the resilience in learning perspective educational equity

indicator variables.

• Educationally and psychologically, students who are

more familiar with mathematical concepts and equipped

with higher degrees of mathematics self-efficacy attain

higher in mathematics literacy performance, and

importantly if they are ESCS-disadvantaged then they

stand higher chances to beat the odds against them to

become academic resilient students in their home

country/economy.

Non-East Asian Economies

• Canada, Estonia and Finland have a not small share of

resilient students in their ESCS-disadvantaged

population, amounting to 34%, 39%, and 33% of the 15-

year-old cohort of secondary students.

• The research evidence of this study show clearly that

ESCS-disadvantaged students who are male, native, and

who have not repeat education in primary and/or

secondary grades, stand higher chances of beating the

odds against them and being classified as academically

resilient than their counterparts.

• Apart from familiarity with mathematical concepts and

mathematics self-efficacy, this study establishes that there are two

other learning mathematics variables mathematics self-concept

and mathematics anxiety which are not only educational quality

indicator variables, but also from the resilience in learning

perspective educational equity indicator variables applicable

to the non-East Asian economies in this study.

• Educationally and psychologically, students who are less anxious

and equipped with higher degrees of mathematics self-concept

attain higher in mathematics literacy performance, and

importantly if they are ESCS-disadvantaged stand higher chances

to beat the odds against them to become academic resilient

students in their home country.

Conclusions

• Seven economies, four East Asian and three non-East Asian, are

considered as high-performing and high-equity in mathematical

literacy in PISA 2012.

• One hypothesis applicable to these seven economies is that

academic resilience of the local ESCS-disadvantaged students

helps raise academic performance and as a result of this

contributes to educational equity.

• Through logistic regression of the resilience classification this

study establishes a number of demographic and self-regulatory

learning mathematics characteristics that can predict whether an

ESCS-disadvantaged student is likely academically resilient or

not.

• Amongst the five demographic characteristics, grade repetition

and immigration status of student are important predictors for

both East Asian and non-East Asian countries, whereas

kindergarten attendance and gender of student predict certain

economies in unique local ways.

• Amongst the four learning mathematics characteristics, it is found

that when an ESCS-disadvantaged student is familiar with

mathematical concepts in the school curriculum and his/her

degree of mathematics self-efficacy in the tackling daily-life

mathematical tasks is high he/she is more likely an academic

resilient student.

• This conclusion is valid whether the student concerned comes

from the East Asian or non-East Asian economies or not.

• However, when an ESCS-disadvantaged student whose

degree of mathematics self-concept is high and at the same

time his/her mathematics anxiety is low, he/she is more likely

an academic resilient student.

• This conclusion is valid when the student concerned comes

from the three non-East Asian economies, i.e. Canada,

Estonia and Finland. It is also valid for mathematics self-

concept in the case of Macao, an economy with serious

problem of grade repetition.

Stakeholders can make reference of the findings

of this study to tailor pedagogy and psychology

of learning to improve quality and equity in

mathematics education in their own

countries/economies.

Thank you