Mathematics Learning Goal

Proficiency with addition and

subtraction of whole numbers.

Ability to identify and represent

fractions and decimals, and compare

them on a number line or with other

common representations of fractions

and decimals.

Proficiency with multiplication and

division of whole numbers. Proficiency

with comparing fractions and decimals

and common percents, and with the

addition and subtraction of fractions

and decimals. Ability to solve problems

involving perimeter and area of

triangles and all quadrilaterals having

at least one pair of parallel sides

(i.e., trapezoids).

Proficiency with multiplication and

division of fractions and decimals.

Proficiency with all operations involving

positive and negative integers.

Ability to analyze the properties of

two-dimensional shapes and solve

problems involving perimeter and area,

and analyze the properties of threedimensional shapes and solve problems

involving surface area and volume.

Proficiency with all operations involving

positive and negative fractions. Ability

to solve problems involving percent,

ratio, and rate and extend this work

to proportionality. Familiarity with the

relationship between similar triangles

and the concept of the slope of a line.

Grade Level

(by the end of)

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Benchmarks

The benchmarks set forth by the Panel should help to guide

classroom curricula, mathematics instruction, textbook

development and state assessments that will lead to

proficiency with whole numbers and fractions, and

competence with certain aspects of geometry and

measurement.

The National Mathematics Advisory Panel

http://www.ed.gov/MathPanel

For electronic copies of the Math Panel’s final report

and the report of the task groups and subcommittees,

please visit www.ed.gov/mathpanel

or order copies at http://edpubs.ed.gov/,

by e-mail at edpubs@inet.ed.gov and

by phone at 1-877-433-7827 (TDD/TTY 1-877-576-7734).
About the National

Mathematics Advisory Panel

For students to compete in the

21st-century global economy,

knowledge of and proficiency in

mathematics are critical. Today’s

high school graduates need to have

solid mathematics skills—whether

they are headed to college or to the

workforce. To help ensure our nation’s future competitiveness

and economic viability, President George W. Bush created

the National Mathematics Advisory Panel (National Math

Panel) in April 2006. The Panel was charged with reviewing the

best available scientific evidence and making recommendations

on improving mathematics education with a focus on readiness

for and success in algebra.

The National Math Panel’s final report, Foundations for

Success: The Final Report of the National Mathematics Advisory

Panel, was issued on March 13, 2008. It contains 45 findings

and recommendations on numerous topics, including curricular

content, learning processes, instructional practices and

materials, teachers, assessments and future research priorities.

Highlights of the findings and recommendations are

briefly summarized below. For a complete discussion of

these topics, the public may read the final report as well

as the reports of the task groups and subcommittees

by visiting www.ed.gov/mathpanel or by ordering copies at

http://edpubs.ed.gov/, by e-mail at edpubs@inet.ed.gov and

by phone at 1-877-433-7827 (TDD/TTY 1-877-576-7734).

Core Principles of Math Instruction

The areas to be studied in mathematics from pre-kindergarten

through eighth grade should be streamlined and a well-defined

set of the most critical topics should be emphasized in the early

grades. Any approach that revisits topics year after year without

bringing them to closure should be avoided. Other important

findings and recommendations for mathematics instruction are:

Critical Foundations. Proficiency with whole numbers,

fractions, and certain aspects of geometry and measurement

are the critical foundations of algebra.

Fractions. Knowledge of fractions is the most important

foundational skill not currently developed among

American students.

Conceptual understanding, computational and procedural

fluency, and problem-solving skills are equally important

and mutually reinforce each other. Debates regarding the

relative importance of each of these components of

mathematics are misguided.

Automaticity. Students should develop immediate recall of

arithmetic facts to free the “working memory” for solving

more complex problems.

Major Topics of School Algebra include Symbols and

Expressions; Linear Equations; Quadratic Equations;

Functions; Algebra of Polynomials; and Combinatorics

and Finite Probability. More students should be prepared

for and offered an authentic algebra course in Grade 8.

Other Key Findings

Effort matters. A focus on the importance of effort will

improve outcomes. If children believe that their efforts to

learn make them “smarter,” they show greater persistence

in mathematics learning and their performance improves.

Most children develop considerable knowledge of

mathematics before they begin kindergarten. Children

from families with low incomes and low levels of parental

education and those of single parents often have less

mathematical knowledge when they begin school than do

children from more advantaged backgrounds. This tends to

hinder their learning for years to come. There are

promising interventions to improve the mathematical

knowledge of these young children before they enter

kindergarten.

Teachers’ mathematical knowledge is important for

students’ achievement. The preparation of elementary

and middle school teachers in mathematics should be

strengthened. Teachers cannot be expected to teach what

they do not know.

Teachers who consistently produce significant gains in

students’ mathematics achievement should be

recognized. When students are taught by a series of

effective teachers, the positive outcomes on their

mathematics learning are compounded.

Teachers’ regular use of formative assessment improves

their students’ learning, especially if teachers have

additional guidance on using the assessment to

individualize instruction.

Explicit instruction with students who have mathematical

difficulties has shown consistently positive effects on

performance with word problems and computation.

More research is needed. The nation must continue

to build the capacity for more

rigorous research in mathematics

education to more effectively

inform policy and practice.

Next Steps

The findings and recommendations

of the Panel are a first step in the

process toward fixing the delivery

system in mathematics education in this country.

The United States has genuine opportunities to improve

mathematics education, but these improvements can be

realized only if educators, policymakers, researchers and

parents all work together to ensure that our students master

the mathematical foundations that are so critical for

achievement in algebra and beyond.

The National Mathematics Advisory Panel

24 expert panelists, including a number of leading

mathematicians, cognitive psychologists and

mathematics educators, reviewed more than 16,000

research studies before preparing a final report

containing policy advice on how to improve mathematics

achievement for all students in the United States.