The study took place in elementary schools in 12 districts across 10 states, including Connecticut,
Florida, Kentucky, Minnesota, Mississippi, Missouri, Nevada, New York, South Carolina, and
Texas. Of the 12 districts, three were in urban areas, five were in suburban areas, and four
were in rural areas.
Following district and school recruitment and collection of consent from all teachers in the
participating grades, 111 participating schools were randomly assigned to one of four curricula:
(a) Investigations in Number, Data, and Space®, (b) Math Expressions, (c) Saxon Math, and
(d) Scott Foresman–Addison Wesley Mathematics. Blocked random assignment of the schools
was conducted separately within each district. In each district, participating schools were
grouped together into blocks of four to seven schools based on characteristics such as Title I
eligibility, free or reduced-price lunch eligibility status, grade enrollment size, math proficiency,
and proportion of White and Hispanic students. Two districts had an additional blocking variable
(magnet school status in one district and year-round school schedule in another district).
One district required that all schools that fed into the same middle school receive the same
condition. Schools in each block were randomly assigned among the four curricula. On average,
11 students were randomly sampled from each participating classroom for assessment.
One school with three teachers and 32 students assigned to Math Expressions withdrew from
the study and did not permit follow-up data collection.
The analysis sample included a total of 110 schools, 461 first-grade classrooms, 4,716 first
graders, 328 second-grade classrooms, and 3,344 second graders. In the first grade sample,
on average, 27 schools, 116 classrooms, and 1,180 students were assigned to each condition.
In the second grade sample, on average, 18 schools, 82 classrooms, and 835 students were
assigned to each condition.
Seventy-six percent of the schools in the study were eligible for Title I funding. Approximately
half of the students in the sample were eligible for free or reduced-price lunch. Among students
in the sample, 39% were White, 32% were non-Hispanic Black, 26% were Hispanic, 2% were
Asian, and 1% were American Indian or Alaskan Native.
Students in the intervention group used Scott Foresman–Addison Wesley Mathematics as
their core math curriculum. Study authors reported about nine out of 10 teachers self-reported
completing at least 80% of the curriculum.
The study included three comparison groups: (a) Investigations in Number, Data, and Space®,
(b) Math Expressions, and (c) Saxon Math. Each curriculum was implemented by comparison
teachers for 1 school year.
Investigations in Number, Data, and Space® is published by Pearson Scott Foresman. It uses
a student-centered approach that encourages reasoning and understanding and draws on
constructivist learning theory. The lessons build on students’ existing knowledge and focus on
understanding math concepts rather than simply learning computational methods. The curriculum
is organized in nine thematic units, each lasting 2–5.5 weeks. Study authors reported
that about four out of five teachers self-reported completing at least 80% of the curriculum.
Math Expressions is published by Houghton Mifflin Harcourt and uses a blend of student-centered
and teacher-directed instructional approaches. Students using the curriculum question and
discuss mathematics and are explicitly taught problem solving strategies. There is an emphasis
on using multiple specified objects, drawings, and language to represent concepts, and on
learning through the use of real-world situations. Students are expected to explain and justify
their solutions. Study authors reported that about nine out of 10 teachers self-reported completing
at least 80% of the curriculum.
Saxon Math is published by Houghton Mifflin Harcourt and uses a teacher-directed approach
that offers a script for teachers to follow in each lesson. It blends teacher-directed instruction
of new material with daily practice of previously learned concepts and procedures. The
teacher introduces concepts or efficient strategies for solving problems. Students receive
instruction from the teacher, participate in guided practice, and then undertake individual
practice. Frequent monitoring of student achievement is built into the program. Daily routines
are extensive and emphasize practice of number concepts and use of methods (such as the
use of number lines, counting on fingers, and diagrams) to represent mathematical concepts.
Study authors reported that about six out of seven teachers self-reported completing at least
80% of the curriculum.
Mathematics achievement was measured using the mathematics assessment developed for
the ECLS-K class of 1998–99. The assessment is individually administered, nationally normed,
and adaptive. The assessment meets accepted standards of validity and reliability. Scale scores
from an item response theory (IRT) model were used in the analysis. The test was administered
in the fall of the implementation year (within 4 weeks of the first day of classes) to assess students’
baseline math achievement. The test was also administered in the spring—that is, from
1–6 weeks before the end of the school year of program implementation. For a more detailed
description of the outcome measure, see Appendix B.
Support for implementation
Teachers in all four groups were provided training by the curriculum publisher. Teachers
assigned to Scott Foresman–Addison Wesley Elementary Mathematics received 1 day of initial
training in the summer before the school year began. Follow-up training was offered about
every 4–6 weeks throughout the school year. Follow-up sessions were typically 3–4 hours long
and held after school. Teachers assigned to Investigations in Number, Data, and Space® (comparison group 1) were provided 1 day of initial training in the summer before the school year began. Follow-up sessions were typically 3–4 hours long and held after school. Teachers assigned to Math Expressions (comparison group 2) were provided 2 days of initial training in the summer before the school year began. Two follow-up trainings were offered during the school year. Follow-up sessions typically consisted of classroom observations followed by short feedback sessions with teachers.
Teachers assigned to Saxon Math (comparison group 3) were provided 1 day of initial training
in the summer before the school year began. One follow-up training session, tailored to meet
each district’s needs, was offered during the school year.