Math curricula and interventions

Before making investments in math curricula and interventions, city and county leaders should ensure this strategy addresses local needs.

The Urban Institute and Mathematica have developed indicator frameworks to help local leaders assess conditions related to upward mobility, identify barriers, and guide investments to address these challenges. These indicator frameworks can serve as a starting point for self-assessment, not as a comprehensive evaluation, and should be complemented by other forms of local knowledge.

The Urban Institute's Upward Mobility Framework identifies a set of key local conditions that shape communities’ ability to advance upward mobility and racial equity. Local leaders can use the Upward Mobility Framework to better understand the factors that improve upward mobility and prioritize areas of focus. Data reports for cities and counties can be created here.

Several indicators in the Upward Mobility Framework may be improved with investments in high-quality math curricula and interventions. To measure these indicators and determine if investments in this strategy could help, examine the following:

• Effective public education: Average per-grade change in English Language Arts achievement between the third and eighth grades. These data are available from Stanford University’s Education Data Archive.
• Preparation for college: Share of 19- and 20-year-olds with a high school degree. These data are available from the Census Bureau’s American Community Survey.

Mathematica's Education-to-Workforce (E-W) Indicator Framework helps local leaders identify the data that matter most in helping students and young adults succeed. Local leaders can use the E-W framework to better understand education and workforce conditions in their communities and to identify strategies that can improve outcomes in these areas.

Several indicators in the E-W Framework may be improved with investments in high-quality math curricula and interventions. To measure these indicators and determine if investments in this strategy could help, examine the following:

• 6th grade on track: Percentage of students in grade 6 with passing grades in English language arts and math, attendance of 90 percent or higher, and no in- or out-of-school suspensions or expulsions.

• 8th grade on track: Percentage of students in grade 8 with a GPA of 2.5 or higher, no Ds or Fs in English language arts or math, attendance of 96 percent or higher, and no in- or out-of-school suspensions or expulsions.

• 9th grade on track: Percentage of students in grade 9 with a GPA of 3.0 or higher, no Ds or Fs in English language arts or math, attendance of 96 percent or higher, and no in- or out-of-school suspensions or expulsions.

• Math and reading proficiency in grade 3: Percentage of students in grade 3 who meet grade-level standards in reading/English language arts and math as measured by state standardized tests.

• Math and reading proficiency in grade 8: Percentage of students in grade 8 who meet grade-level standards in reading/English language arts and math as measured by state standardized tests.

• Math and reading proficiency in high school: Percentage of tested students who meet grade-level standards in reading/English language arts and math, as measured by state standardized tests.

• Successful completion of Algebra I by 9th grade: Percentage of first-time grade 9 students who complete Algebra I or an equivalent course by the end of their 9th-grade year.

• Intensive interventions taught 30 minutes per day, 3 days per week: While some interventions in Tiers II and III are delivered during a portion of the normal math period, many take place during elective or designated intervention periods during the school day. Experts advise that high-quality programs typically include at least thirty minutes of intervention time with an instructor, at least three days per week, with asynchronous or group work that is paired on alternate days.

• Individualized instruction in earliest grades, followed by small groups: Experts note that one-on-one instruction may yield the best outcomes for grades K-2. In later elementary and middle school, however, students start to benefit from working in groups and hearing the ideas and questions asked by their peers. For these grades, group sizes should be kept smaller than five students per instructor.

• Delivered by trained, compensated instructors: High-quality math interventions may be delivered by teachers, trained tutors, special educators, or other staff. Importantly, evaluations of several program models have found that interventions outside of core classroom instruction remain effective even when delivered by instructors that do not have a formal teacher certification. High-quality programs tend to seek tutors or instructors who can demonstrate math content knowledge, relational skills, and an ability to follow the intervention protocol. High-quality programs provide significant synchronous training for instructors and tutors prior to the start of a school year, during regular professional development sessions in addition to asynchronous skill-building opportunities.

• Focus on most critical, grade-level content: When delivered as a supplemental intervention to the core math class, interventions should choose to focus on the concepts that are most critical for students to advance at grade-level. In grades K-3 this is generally numeracy and whole numbers, before developing into rational numbers in grades 4-6 and algebraic reasoning in late middle and high school. It is important that the curricula closely aligns to that of the student’s regular math class and mirrors the vocabulary and terminology the student is expected to use in class.

• Intentional scaffolding of key concepts: For all tiers of interventions, experts emphasize the importance of explicit, systematic and schema-based instruction–or introducing “bite-sized” components of concepts individually and slowly building to full understanding by the student through teacher modeling, repetition, guided practice, and intentional feedback.

• Ongoing evaluation of virtual interventions: While many evaluations confirm the results of interventions delivered in-person, initial results from interventions delivered virtually via a live video conference between the instructor and students indicate that for older students, virtual tutoring or programs may be comparable in effectiveness. Ongoing evaluations work to confirm these findings.

• Use data to identify which students may need support: Many high-quality interventions rely on academic data, including grades and assessments, to identify which students are academically at-risk and may benefit from intervention. Doing so reduces the risk that unintentional biases on the part of teachers or other school staff come into play when identifying students who may need support.

• Support the learning of foundational content: Some students, including recent immigrants or students from under-resourced communities, may not have had the opportunity to learn crucial background content, like foundational numeracy or skills related to the process of learning and attending school. Programs should incorporate time for students to learn this critical knowledge.

• Ensure access to grade-level content: Expert practitioners note a common challenge faced in delivering math interventions is that teachers, tutors, or other instructors tend to overemphasize remedial concepts, and in doing so, unintentionally withhold access to learning grade-level content. Doing so may further prevent students most in need of support from progressing with their peers, exacerbating gaps. High-quality programs tend to address this concern via instructor training, yet experts note it may still require close monitoring to ensure this doesn’t occur.

• Provide language support: English-language learners may require language support in tandem with math curricula in order for them to effectively learn math vocabulary and navigate the language of math. Experts advise that equitably accounting for language may mean providing support in the student’s primary language to allow them to access math content, while also supporting their growth in the language that they’ll be expected to use in their normal math class. Ideally, interventions are flexible enough that a lack of English fluency is not prohibitive in participating.

• Hire instructors who reflect the students’ communities: Research suggests that students benefit from receiving instruction from teachers, tutors, or other staff who are similar to students and come from similar communities or cultural backgrounds. Programs should prioritize recruiting instructors who possess cultural competency that allows them to understand the experiences and circumstances of students.

• Be mindful of digital fluency and technology access: Some interventions, like asynchronous, online tutoring programs, can exacerbate equity gaps because they are more likely to be used by highly-resourced students who have access to technology and caregivers with digital fluency. Educators should consider methods for increasing access for all students by making technology available to students via the school library or loan programs, among other methods.

• Teachers: Math teachers and special education teachers are crucial in helping identify curricular needs, administering initial assessments, and supporting the overall learning of students. Experts note that tier two interventions tend to be most successful where there is teacher buy-in and interventions are viewed as supporting teachers in achieving their goals versus replacing them. Teacher support may also help in cases where the teachers union must approve changes to workload of expectations.

• Site coordinators and other school staff: Site coordinators play a particularly essential role in implementing tier two interventions that require coordinating student schedules with teachers, providing building access for external partners, organizing tutors, and other operational activities. These activities take significant time, and experts caution that without dedicated staff who are responsible for them, interventions are less likely to succeed.

• District leadership and principals: In many districts, decision-making authority related to curricula and the implementation of other interventions lies with district leadership. They have the ability to allocate district funding and approve partnerships with external program providers. They also may advocate to leaders in high levels of government for increased funding or support for needed interventions.

• Community-based or external education partners: In many cases, schools may bring in third party organizations to implement tier two interventions like high-dosage tutoring. These partners may bring crucial expertise and capacity needed to implement interventions and become critical collaborators in the overall educational approach of the school.

• State legislators and other government officials: Elected or appointed officials can support math-related interventions by elevating math educational achievement as a policy priority and advocating for public funding for evidence-based interventions. Officials within the state Department of Education may also have the ability to influence funding or curricular decisions related to state standards.

• Engage teachers to align curricula selection to student needs and state standards: Prior to selecting curricula, conduct a needs assessment to understand what types of features a curriculum should include, such as specialized programming for students with diverse needs or English Language Learners. Curricula should also be scored against metrics for rigorous research to ensure sufficient alignment.

• Equip teachers and tutors to deliver curricula with fidelity: Many curricula and related interventions provide robust training for teachers to deliver the model, along with ongoing professional development, and, in some cases, a credential. Ensuring that educators are sufficiently trained and well-versed in curricula materials will ensure greater implementation fidelity, a key factor in increasing impact.

• Partner with teacher colleges and higher education institutions to recruit instructors: Many high-quality programs have reported success in recruiting tutors or other instructors for Tier II interventions by partnering with higher education institutions to hire aspiring teachers, school counselors, social workers, or other aligned professions.

• Equip teachers with measurement tools: Evidence-based practices that can support math development include progress monitoring (tracking individual student performance against curriculum-specific benchmarks) and error analysis (documenting and reviewing individual errors to identify student- and class-wide trends). By equipping teachers with appropriate validated measurement tools and dedicated work time for measurement and analysis activities, they can better refine instruction.

• Foundational skills assessment: An assessment of student math attainment and knowledge tends to be the primary metric by which students are identified as in need of support and progress is measured. Most programs pair a series of formal assessments–typically at the beginning, middle points, and end of the school year–with brief, informal skills checks on a weekly basis. Formal assessments can be used to identify students in need of support, while the more frequent informal checks can help uncover sticking points in the curricula and help instructors tailor their focus with a particular student.

• Grades: Class grades or other measures of student performance may improve over the course of participating in an intervention.

• Attendance: Students attending and arriving on time can be an important indicator of the accessibility of an intervention and how successfully it engages students.

• Need for ongoing intervention: Ideally, Tier II and III interventions are designed to bring a student to grade-level, enabling them to engage with the core instruction with the rest of their class. Student response to the intervention may be an indicator that the intervention is not being delivered with fidelity, that there may have been a mismatch between student needs and the intervention, or that the student’s learning needs require more intensive support.

• Tutor or instructor hiring and attrition: Experts note that instructor vacancy rate and attrition of tutors can be an indicator of various aspects of program health, including adequacy of training and site culture.

• Incidence of behavioral issues: Experts note that sometimes behavioral issues during class are a result of a student not understanding classroom instruction. Teachers may notice that behavioral incidents decrease when students receive necessary academic supports.