PISA results: affirming for mathematics learning in the Hong Kong early childhood setting?
Dr Wong Kwok Shing, RichardDept. of Early Childhood Education,
Hong Kong Institute of Education,Hong Kong-China
What do Hong Kong (HKG) early childhood practitioners teach and what types of activities do they employ in the classroom?
Do HKG teachers help young children build a solid foundation for future maths learning?
Aims of this presentation
Past century: Asia has looked to the West （超英趕美 , literally ‘surpass Britain, catch up
with the US’） The latest PISA results in Mathematics: the
top three economies/ countries are all in Asia.
Background
Economy or country Mean SDShanghai-China 613 101Singapore 573 105Hong Kong-China 561 96The United Kingdom 494 95The United States 481 90OECD (the average) 494 92
Looks reaffirming But greater variation across students in the
top-performing economies or countries Equity issue:
◦ A higher proportion of students scoring at level 5 or above in the top-performing economies/ countries
◦ What does this imply?
Data Interpretation
Past studies: ◦ Greater intellectual capacity of Asian students?◦ Superior mathematics education in Asia? (see
Leung, 2000)◦ More demanding parents in Asia (See Chen &
Stevenson, 1995; Kwok & Lytton, 1996; Leung, 1999)
◦ Learners hold high standards for themselves (See Chen & Stevenson, 1995; Kwok & Lytton, 1996)
What is left to be explored...???
Issues for exploration
What applies to the primary school setting may not apply to the kindergarten setting
How do HKG preschool teachers help to lay a solid foundation for young children to learn mathematics?◦ What methods do they use in teaching maths?◦ Do they teach the skills that are critical for
children’s future maths abilities?◦ What is the content covered at different age levels?◦ How much do they believe in nurture in contributing
to a child’s maths ability?
What I want to investigate…
Particulars Frequency Percent
Groups* BEd Yr 1 25 27.2
BEd Yr 2 23 25.0
BEd Yr 3 20 21.7
PGDE Yr 1 24 26.1
Academic qualifications Higher Diploma in ECE 62 67.4
Degrees (non-ECE) 25 27.2
Others 5 5.5
Level of the children taught 2-3 yrs old 14 15.2
3-4 yrs old 30 32.6
4-5 yrs old 21 22.8
5-6 yrs old 27 29.3
92 Participants
* Years of teaching experience: 4.41 years (SD = 4.6)
Demographic information 17 items focusing on three types of
activities: child-centered, teacher-centered, activities favoured by psychologists
36 items: specific maths content Other items: teachers’ motivation in
learning maths, teachers’ beliefs, etc.
Tool: A self-developed questionnaire
Mean (0-4) SDForward counting 3.18 0.76Teacher-centred demonstration
2.88 0.80
Homework 2.67 0.93Statistics 2.66 0.94Relate to real life 2.5 0.91Puzzles 2.24 1.09Backward counting 2.08 1.14Games 2.05 1.04Self-exploration 1.99 0.90Group-exploration 1.98 1.01Patterns 1.97 1.07Use of story 1.84 0.88Use of picture books 1.72 0.95Missing numbers 1.4 1.05Forward digit span 1.36 0.99Analogical reasoning 1.07 0.94Backward digit span 1.01 1.05
Results
Emphasis of teacher educators
Drilling? ‘Traditional’ approach
Emphasis of dev.
psychologists
Factorial analysis of variance (p < .05) No main effect for group except for group
exploration No main effect for age of the children
except for homework, backward counting, statistics, patterns and missing number
No interaction between group and age of the children
Between-group differences
Items 2-3 yrs old
3-4 yrs old
4-5 yrs old
5-6 yrs old
Counting from 1 to 10 100 - - -
Counting from 11 to 20 50 63.33 100 -
Counting from 21 to 30 21.43 33.33 95.24 88.89
Counting from 31 to 50 7.14 16.67 80.95 92.59
Counting from 51 to 100 0 6.67 42.86 77.78
Arabic numbers: 1 to 10 100 96.67 100 -
Arabic numbers: 11 to 30 21.43 30 95.24 92.59
Arabic numbers: 31 to 100 0 0 52.38 88.89
Odd and even numbers 7.14 10 71.43 100
Prime numbers 0 0 14.29 14.81
Chinese numbers 57.14 43.33 90.48 88.89
English numbers 92.86 76.67 95.23 88.89
Maths Content: Number (%)
Items 2-3 yrs old 3-4 yrs old 4-5 yrs old 5-6 yrs old
Set 5 28.57 20 80.95 100
Set 10 21.43 3.33 42.86 100
Set 15 0 0 4.76 44.44
Set 20 0 0 0 29.63
Set 21 or above 0 0 0 11.11
Maths content: Sets (%)
Items 2-3 yrs old
3-4 yrs old
4-5 yrs old
5-6 yrs old
3 + 5 7.14 13.33 47.62 100
12 + 6 0 0 4.76 40.74
3 + 2 +2 0 0 0 66.67
12 + 10 + 2 0 0 0 14.81
5 - 3 0 0 19.05 96.30
12 - 3 0 0 4.76 33.33
10 - 2 - 3 0 0 0 48.15
20 - 10 - 2 0 0 0 14.81
Maths content: addition and subtraction (%)
Items 2-3 yrs old 3-4 yrs old 4-5 yrs old 5-6 yrs old
Date 100 93.33 100 -
Size 100 100 - -
Quantity 92.86 100 - -Location: front and back 100 100 - -Location: middle and beside 64.29 83.33 90.48 100Location: right and left 57.14 73.33 85.71 92.59
Direction 0 6.67 4.76 48.15
Grid reference 0 3.33 4.76 44.44
Simple shape 100 - - -
Complex shape 28.57 6.67 33.33 85.19
3D shape 14.29 13.33 52.38 77.78
Maths content: location, shape and others (%)
Mean (1-7)
SD
Self-perceived maths ability 4.17 .98
Past motivation in learning maths
3.7 1.47
Contribution of nurture 5.59 .85
Contribution of nature 5.17 1.12
Other results
Note 1: No differences across groups (F-test, p < 0.05)Note 2: Significant difference between the scores for nurture and nature (t-test, p < 0.01)
Relatively inexperienced teachers… Not so motivated in learning maths
themselves… Not much time spent teaching maths… (18
minutes on average) Certainly NOT experts But believing in hard work!! Bad news for teacher educators but good
news for developmental psychologists! PISA results: really affirming???
Discussion
What is the role of tutorial centres (colloquial term: 雞精班 , literally ‘class serving chicken extract’) in Asia?
A case study: school versus tutorial centre
Further issue for exploration
At School
Addend turn around: 5 + 6 = 11 and 6 + 5 = 11
Addition and subtraction: up to 24 3 addends Pattern: sequence, complete a pattern Match patterns: visual skills Right & left Mental rotation Combine figures 3-D shape
What does the same child learn in the tutorial centre? Same concepts but in English!
Concepts that are learnt at school are re-introduced through a foreign language
A lot of practice: many practice items Memorization (automacy): no need to
compute the answers Visual skill training Logical reasoning
Contribution of tutorial centres
The mother said, ‘If you’re a failure, better not live in Asia because you will be trampled on. The system here only helps the “winners”. If you have problems, study abroad or just go abroad-the system there is more protective and caring.’
Hidden cost: pressure
Asian parents?
System is geared towards examination success but to the detriment of play
Do children have a happy childhood? Or is their childhood being cut short? (Further research)
My own experience…
Conclusion
Short-term predictors (beginning to the end of kindergarten): counting, quantity discrimination, and number naming (Jordan, 2010)
Long-term predictors (beginning of kindergarten to the end of grade three): foundational number sense supports computation and applied problem solving (Jordan et al., 2010)
Appendix A: What do scholars recommend?
Quantitative pathway Linguistic pathway Spatial pathway
=> A learner excels in one area of mathematics but not in another area
Underlying Pathways (LeFevre et al.)
