Students enter grade 3 with an interest in
learning mathematics. Nearly three-quarters of U.S. fourth graders report liking
mathematics, seeing it as practical and important. If mathematics continues to
be seen as interesting and understandable, students will remain engaged. If
learning becomes simply a process of mimicking and memorizing, students'
interest is likely to diminish.

Interwoven through the Content Standards for
grades 3–5 are three crucial mathematical themes--multiplicative thinking,
equivalence, and computational fluency. The focus on multiplicative reasoning
develops knowledge that students build on as they move into the middle grades,
where the emphasis is on proportional reasoning. As a part of multiplicative
reasoning, students in grades 3–5 should build their understanding of fractions
as a part of a whole and as division.

The concept of equivalence helps students learn
different mathematical representations and offers a way to explore algebraic
ideas. Students should develop computational fluency-- efficient and accurate
methods for computing that are based on well-understood properties and number
relationships. For example, 298 42 can be thought of as (300
42) – (2 42), or 41 16 can be computed by multiplying 41
8 to get 328 and then doubling 328 to
get 656. When these three themes are emphasized, the expectations for grades 3–5
reinforce two major objectives of mathematics learning: making sense of
mathematical ideas and acquiring the skills and understandings needed to solve
problems.

In grades 3–5, algebraic ideas emerge and are
investigated by children. For example, students in these grades are able to make
a general statement about how one variable is related to another variable. If a
sandwich costs $3, you can figure out how many dollars any number of sandwiches
cost by multiplying that number by 3. In this case, students have developed a
model of a proportional relationship: the value of one variable is always 3
times the value of the other, or C = 3 n.

Given their central role in shaping the
mathematics learning of students in these grades, teachers must recognize the
need to develop mathematical expertise. Some elementary schools identify a
"mathematics teacher-leader," who can support other teachers in their
instruction and professional development. Other schools use "mathematics
specialists" at the upper elementary grade levels, who assume primary
responsibility for teaching mathematics to larger groups of students. Each of
these models needs to be explored to enhance the mathematics education of
students in grades 3–5.