Research on Mathematics Education

Grover J. (Russ) Whitehurst, Ph.D.

Director

Institute of Education Sciences

United States Department of Education

Archived Information

Achievement

0

20

40

60

80

4th Grade 8th Grade 12th Grade

Proficient Below Basic Below Basic Af Am

NAEP 2000 Proficiency

TIMSS Math 1995

0

20

40

60

80

4th Grade 8th Grade 12th Grade

U.S. rank order

0

1

2

3

4

5

6

7

8

9

1995-96 1999-2000

Life SciEngineerPhy SciMath

Declared Major

4-year colleges

%

Tracking and Grouping

Assessment for Instruction

Structured Peer Feedback

The Math Wars

Constructivist Approaches Skills-based Approaches

Knowledge is constructed Knowledge is imparted

Children should develop their own understanding

Children should master standard facts & concepts

Authentic problems Skill-relevant problems

Intrinsically motivated Extrinsically motivated

Conceptual Understanding

Decimal Fractions

509 > 7

.509 < .7

Decimal Fractions

0.509

____________________ 0 1

?

Checks on Constructivism

• Many routes to understanding

• Limits on working memory

• Inefficiency of discovery

• Role of work in learning

220

260

300

340

380

420

460

500

540

580

620

660

700

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6

Average on liking mathematics scale

Ave

rage

mat

hem

atic

s sc

ore Japan

South Africa

U.S.

Curriculum

Constructivist Math – 3 States

0

20

40

60

80

100

% o

f po

ssib

le p

oint

s

IL Grd 3 IL Grd 5 MA Grd 4 WA Grd 3 WA Grd 4

Constructivist Business-as-usual

Implementation

0

10

20

30

40

50

60

7080

exam

sco

re

weak implement strong implement

Af. Am. White

Alignment

4th Grade Math Gains: 1992 to 2000

024

68

1012

14161820

Nation Texas North Carolina

NAEP

Elements of State Math Reforms

• State-wide standards

• Linked state-wide assessments

• Accountability for results

Putting It Together

Classroom-based assessment +

Structured peer feedback +

Tracking -

Understanding +

Direct instruction + - ?

Discovery + - ?

Authentic problems + - ?

Work and practice +

Curriculum ?

Implementation +

System alignment +