Setting
One hundred ten elementary schools in 12 districts participated in the study. The districts were located across the following 10 states: Connecticut, Florida, Kentucky, Minnesota, Mississippi, Missouri, New York, Nevada, South Carolina, and Texas. These districts are located in urban, suburban, and rural areas, and each district had at least four Title I schools (a study eligibility requirement). In total, 76% of participating schools were eligible for Title I support.
Study sample
The study sample included first- and second-grade students. Thirty-seven percent of students in participating schools were non-Hispanic White, 33% were non-Hispanic Black, 27% were Hispanic, 2% were Asian, and 1% were American Indian or Alaska Native. Just over half of the sample (52%) was male, and about half of the students were eligible for free or reduced-price lunch (51%).
Intervention Group
Math Expressions is a curriculum for students in prekindergarten through sixth grade that aims to build students’ conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such as drawings and manipulatives, multiple approaches to solving problems, and opportunities for students to explain their mathematical thinking.
Students in the intervention group used Math Expressions (published by Houghton Mifflin Harcourt) as their core math curriculum. Cohort 1 used the 2005 copyright edition, and Cohort 2 used the 2008 copyright edition. Each day began with a set of routines led by students involving the calendar, money, a number chart, counting, and time. In general, the math lesson occurred later in the day and typically began with a quick fluency activity. Afterward, the teacher provided whole-class instruction and encouraged students to discuss and demonstrate the mathematical ideas taught. Visual learning supports were used to help students link their knowledge to formal mathematical concepts. Finally, students practiced the new mathematics skill or concept in pairs, small groups, or individually by completing worksheets. Math homework was assigned daily to students. Teachers in the intervention group reported using Math Expressions as their core math curriculum and provided, on average, 5.0 to 5.5 hours of math instruction per week. Most teachers (84% in first grade and 80% in second grade) reported completing at least 80% of Math Expressions lessons.
Comparison Group
The comparison group included students using three curricula: Investigations, Saxon, and SFAW.
1. Investigations (published by Pearson) is a mathematics curriculum for students in kindergarten through fifth grade organized into units that last 2 to 5 weeks. Within each unit, the curriculum is built around two or more investigations, each providing different contexts for students to explore mathematical problems through hands-on activities, written activities, and class discussions. Classroom activities vary depending on the length and type of investigation. Teachers begin by introducing the investigation to the class through large-group, hands-on activities, and over the following days students work in smaller groups to explore the concept through in-depth problems or by playing mathematical games. At the end of the investigation, the teacher and students discuss the work completed during the investigation. Schools used the first and second editions of the textbook. Teachers provided, on average, 2.7 to 3.1 hours of math instruction per week in each grade. Additionally, most teachers (72% in first grade and 80% in second grade) reported completing at least 80% of the lessons from Investigations.
2. Saxon (published by Houghton Mifflin Harcourt) is a curriculum for students in kindergarten through fourth grade that includes scripted lesson plans for teachers. It includes explicit instruction, practice, mathematical conversations, and hands-on activities. The curriculum includes five daily activities: morning routines, fact practice, an explicit lesson, guided class practice, and homework. Morning routines are extensive and designed to reinforce the previously learned skills and lay the foundation for building new skills. In the lesson, teachers conduct a whole-class activity to introduce a new concept, using manipulatives, worksheets, or overhead transparency masters. At the end of each lesson, the teacher asks a few students to summarize for the whole class what they learned that day. Teachers provided, on average, 6.1 to 6.9 hours of math instruction per week in each grade. In addition, most teachers (87% in first and second grades) reported completing at least 80% of the lessons from Saxon.
3. SFAW (published by Pearson) is a curriculum for students in prekindergarten through sixth grade that uses a consistent daily structure. Each lesson includes six activities: a spiral review (a brief review of previously learned material), investigating the concept (hands-on exploration of a new concept), a warm-up (a brief activity to activate prior knowledge and connect it to the new lesson), teach (direct instruction of the new concept), independent practice (students practice using worksheets or manipulatives), and assessment (a concluding activity to check for understanding of the new concept). Teachers provided, on average, 5.3 to 5.5 hours of math instruction per week in each grade. Additionally, most teachers (92% in first grade and 88% in second grade) reported completing at least 80% of the lessons from SFAW.
Support for implementation
After completing random assignment, the study team connected school staff to publishers of their assigned curriculum. Research funds were used to support teacher training. The study team did not specify implementation criteria that schools needed to be meet or maintain to be included in the study after participation began.
Teachers assigned to Math Expressions received 2 days of initial training in the summer before the school year began. Two follow-up trainings took place during the school year, once in the fall and again in the spring. Follow-up sessions typically consisted of classroom observations followed by short feedback sessions with teachers.
Teachers assigned to Investigations received 1 day of initial training in the summer before the school year began. Trainers offered group training sessions before the start of each unit (about every 4 to 6 weeks). The follow-up sessions were typically 3 to 4 hours long and held after school.
Teachers assigned to Saxon received 1 day of initial training in the summer before the school year began. One follow-up training session was tailored to meet each district’s needs and took place during the school year.
Teachers assigned to SFAW received 1 day of initial training in the summer before the school year began. Follow-up training was offered about every 4 to 6 weeks throughout the school year. The follow-up trainings were typically 3 to 4 hours long and took place after school.