1

Mathematics & Science Priority Area:

Findings

Fourth Education Ministerial Meeting

Lima, Peru June 2008

2

Economies Included in Study

• Australia• Canada• China (math only)• Chinese Taipei• Korea• Japan

• Hong Kong• Malaysia• New Zealand• Singapore• Thailand (math only)• United States of America

Number of Economies

Math Science

Grade Span # Grade Span #

1-6, 7-9 12 1-4, 7-10 10

10-12 11 5-6 9

Biology 5

3

A Single National Set

of Required Math &

Science Courses

Multiple Sets of

Nationally Required

Courses for Different

Diplomas

Multiple Sets of

Provincially

Required

Courses

Indonesia

( Comp=12)

Chinese Taipei

( Comp=12)

Chile ( Comp=12)

China ( Comp=9)

J apan ( Comp=LS)

New Zealand

( Comp=11)

Canada

( Variable)

U.S. ( Comp=11) *

Central Government and Provincial Governments' Roles in Setting Math & Science

Course Requirements

Note: Comp = Compulsory, LS = Lower Secondary*At U.S. grade 11, a majority of states with course requirements

require at least 3 years of mathematics for graduation.

4

The Common Core of Math and Science

• Primary Level:

Content from corresponding grade level standards• Lower & Upper Secondary Levels:

Content from required courses and courses taken by 50% or more of students

Content addressed by 67% or more of participating APEC Economies

5

Math Common Content Core: Sample of Topics Included in All Grade Spans

MAJOR MATH AREASSub-topics

Grade Span 1-6

(12 economies)

Grade Span 7-9

(12 economies)

Grade Span 10-12

(11 economies)

GEOMETRY: POSITION, VISUALIZATION & SHAPE Points, lines, segments, half-lines, & rays

Circles & their properties75% (9/12)

100% (12/12)92% (11/12) 92% (11/12)

82% (9/11) 82% (9/11)

FUNCTIONS, RELATIONS, & EQUATIONS

Substituting into or rearranging formulas 67% (8/12) 67% (8/12) 73% (8/11)

DATA REPRESENTATION

Representing data

Interpreting tables, charts, plots, graphs100% (12/12) 100% (12/12)

92% (11/12) 92% (11/12)

82% (9/11) 82% (9/11)

6

Sample of Math Topics: Grade Span 1-6

% of Economies Including Topic Data Strand Topics

100% • Representing data• Interpreting tables, charts, plots,

graphs

67% • Measures of central tendency

0-20% • Prediction and inferences from data

7

Average Representation of Math Strands across Grade Spans

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Grades 1-6 Grades 7-9 Grades 10-12

Elementary Analysis

Data Representation,Probability, & Statistics

Functions, Relations, &Equations

Proportionality

Geometry: Symmetry,Congruence & Similarity

Geometry: Position,Visualization & Shape

Measurement

Numbers

8

Representation of Math Strands across Grade Spans

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Grades 1-6 Grades 7-9 Grades 10-120%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Grade 4 Grade 8 Grade 12

Other Content

Validation & Structure

Elementary Analysis

Data Representation,Probability, & Statistics

Functions, Relations, &Equations

Proportionality

Geometry: Symmetry,Congruence & Similarity

Geometry: Position,Visualization & Shape

Measurement

Numbers

JAPAN: National Standards USA: Assessment Framework

9Note: No answer from Canada and ChileNote: GR = Graduation Rate

Lin Eq Quad Eq Log Eq Trig Eq Geo PlnGeo.

AnalyStat Calc

China 100 100 100 100 100 100 100 100

Chinese Taipei ( GR=100%)

100 100 100 100 100 100 100 0

Indonesia ( GR=90%)

100 100 100 100 100 100 100 100

J apan ( GR=100%)

100 100 87 87 79 87 87

N.Z. ( GR=75%)

100 100 100 100 100 100 100 100

U.S. ( GR=75%)

95 68 68 10 75 8 13

Percent of Upper Secondary Graduates Who Take the Following Mathematics Courses

10

USA State Mathematics Requirements: November 2004 to June 2008

Number of states by the number of math courses they require

Number of states by the specific math courses they require

Number of Courses

November 2004

June 2008

Specified Courses

November 2004

June 2008

Four Courses 5 17 Algebra II 3 19

Three Courses

24 22 Geometry 9 6

Two Courses 13 7 Algebra I 8 5

No Courses Required

8 4 No Courses Specified

30 20

11

Integrated Sequenced

China

J apan

Canada

Chile

New Zealand

Chinese Taipei

U.S.

Math and Science Topics Taught as Parallel Or Sequenced Programs

Comparing Standards Show Differences in Approaches to Instruction

Year of School

Alg

ebra

Geo

met

ry

Sta

tistic

s

Trig

onom

etry

Cal

culu

s

Grade 8 X X XGrade 9 X X XGrade 10 X X XGrade 11 X X XGrade 12

Example: JapanTopics Covered in a Typical Math Sequence (Integrated Approach)

Specialized Elective

Year of School

Alg

ebra

Geo

met

ry

Sta

tistic

s

Trig

onom

etry

Cal

culu

s

Grade 8 XGrade 9 XGrade 10 XGrade 11 XGrade 12 X X

Example: USTopics Covered in a Typical Math Sequence (Sequential Approach)

13

Can

ada

Ch

ile

Ch

ina

Ind

on

esia

Jap

an

New

Z

eala

nd

Ch

ines

eT

aip

ei

Un

ited

S

tate

s

Lack of

Interestn n n n

Lack of Qualified

Teachersn n n n n n

Inadequate

Foundationn n n n

Weak Conceptual

Understandingn n

Challenges to Mathematics Improvement

14

Summary of Math Findings

Common Content Core:

• Substantial agreement on the common core; even more so at elementary and lower secondary levels

• Considerably different balance of strands across grade spans

Qualified Teachers

• Too few

• Uneven distribution

15

Average Representation of Science Strands in Common Core across Grade Spans

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Grades 1-4 Grades 5-6 Grades 7-10

Nature of Science

Environmental & ResourceIssues

History of Science &Technology

Science, Technology &Mathematics

Physical Sciences

Life Sciences

Earth Sciences

16

Science Common Content Core: Very Few Topics Included in All Grade Spans

MAJOR SCIENCE AREASSub-topics

Grades 1-4

Grades 5-6

Grades 7-10

EARTH SCIENCES:Weather & climate 80% (8/10) 78% (7/9) 70% (7/10)

PHYSICAL SCIENCES:Classification of matter

Heat & temperaturePhysical changes

90% (9/10)90% (9/10)70% (7/10)

78% (7/9)89% (8/9)78% (7/9)

90% (9/10)80% (8/10)80% (8/10)

ENVIRONMENTAL ISSUES:Material & Energy Resource

Conservation 70% (7/10) 78% (7/9) 80% (8/10)

17

Science Common Core Topics:A Limited Number of Topics Addressed by Almost All Economies Within a Grade Span

Grade Span 1-4 Grade Span 5-6 Grade Span 7-10• Heat & Temperature

• Physical Properties

• Classification of Matter

• Chemical Properties

• Heat & Temperature

• Dynamics of Motion

• Electricity

• Diversity, Organization, Structure of Living Things

• Life Cycles

• Habits & Niches

• Nature of Science

• Resource Conservation

• Energy types, conversions, sources

18

Science Common Core Topics:Excluded by Most Economies

Grade Span 1-4 Grade Span 5-6 Grade Span 7-10• Land forms

• Competition among organisms

•Types of motion/describing motion

•Effects of natural disasters

•Genetic engineering

•Exo-Endothermic Reactions

•Frames of Reference

19

Science Findings

Common Content Core:

• Very few topics repeat across all three grade spans• Somewhat greater emphasis on Physical Science across all

grade spans as compared to other strands• Wide range of topics covered in common core

20

Can

ada

Ch

ile

Ch

ina

Ind

on

esia

Jap

an

New

Z

eala

nd

Ch

ines

eT

aip

ei

Un

ited

S

tate

s

Lack of

Interestn n n

Lack of Qualified

Teachersn n n n n

Inadequate

Foundationn n n

Weak Conceptual

Understandingn n

Obstacles to Upper-SecondaryScience Improvement

21

Commonality of Math and Science Topics Addressed in Standards in the Common Core

Math

Grade 1-6

Average

Grade 7-9 Average

Grade 10-12 Average

76%Range:

71%-89%

68%Range:

59%-85%

34%Range:

28%-55%

Science

Grade 1-4 Average

Grade 5-6 Average

Grade 7-10 Average

Biology Average

35%Range:

22%-53%

43%Range:

31%-53%

67%Range:

56%-82%

81%Range:

72%-91%

22

Similarities & Differences: Math & Science

• Greater consistency on topics taught across economies in lower grades in math and in upper grades in science

• Coverage of topics in common core is narrow and focused in math, but wide-ranging in science

Math & Science: Policy & Practice Leverage Points

• Course Requirements

• Course Content

• Topic Scheduling: Integrated vs. Sequential

• Teacher Quality