Essential Questions for Middle Grade Math: Teaching and Learning

Math teachers across all grade levels operate as a “math team”, collaborating on annual, unit and lesson planning, connecting concepts across grades and meeting students’ needs. These structures are often called “Professional Learning Communities” (Education-to-Workforce).

Recent research consistently demonstrates teacher use of high-quality instructional materials (HQIM) boosts student achievement in reading and math. However, the curriculum alone is not enough; teachers’ craft and skillful use of materials are critical to achieving the full impact of HQIM. (CCSSO, A Nation of Problem-Solvers).

Research indicates professional learning experiences that help teachers use their specific curriculum to make informed decisions for their students can result in transformational changes in teaching and learning. (CCSSO, A Nation of Problem-Solvers).

Research documenting the potential impact of professional learning (RPPL).

Incentivize district partnerships with high-quality professional learning providers. Teachers require high-quality learning experiences that connect directly with the curriculum they use in their daily practice. Research shows that more than half of the potential impact of adopting a stronger curriculum is lost if it is not accompanied by a corresponding shift in teaching practices that specifically support the new materials. (CCSSO, A Nation of Problem-Solvers).

High-quality professional learning experiences are curriculum-based and directly applicable to teachers’ everyday work. Effective curriculum-based professional learning (CBPL) should include initial training aligned with specific curricular materials, regular collaborative planning opportunities for teachers such as unit and lesson internalization, lesson rehearsal, student work analysis and ongoing observation and feedback. (CCSSO, A Nation of Problem-Solvers).

Some states, including Colorado and Louisiana, are making strides by incentivizing the use of curriculum-based professional learning (CBPL). To ensure meaningful impact, professional development must focus on concrete concepts, connect directly to daily lessons and provide pedagogical strategies with clear, practical examples for use in the classroom. (CCSSO, A Nation of Problem-Solvers).

State chiefs can vet and curate a list of high-quality CBPL providers for districts. (CCSSO, A Nation of Problem-Solvers).

State chiefs can provide grant funding to incentivize districts to choose providers from the state-curated list. (CCSSO, A Nation of Problem-Solvers).

State chiefs can convene state-approved professional learning partners quarterly to monitor progress using common data collected and ensure alignment with the state’s vision. (CCSSO, A Nation of Problem-Solvers).

State chiefs can establish common contracts that ease procurement barriers, making it easy for districts to purchase from providers on the state list. (CCSSO, A Nation of Problem-Solvers).

State chiefs can audit all existing state training offerings to ensure they focus on CBPL practices. (CCSSO, A Nation of Problem-Solvers).

State chiefs can train regional education service centers (ESCs) to provide district materials selection and implementation support and ongoing, embedded professional development aligned to the state’s vision for CBPL. (CCSSO, A Nation of Problem-Solvers).

State chiefs can create guidance for districts to ensure that core instructors, special educators, interventionists and supplemental instructors all participate in professional learning. (CCSSO, A Nation of Problem-Solvers).

In 2022, Alabama passed the Alabama Numeracy Act, which required the state to convene a task force focused on math. In addition to reviewing HQIM for core instruction and intervention, the task force provides a continuum of hiqh-quality professional learning opportunities centered on foundational math knowledge with funding and support for educators.  (CCSSO, A Nation of Problem-Solvers).

The Alabama Numeracy Act requires the task force to monitor the implementation of intensive professional development for full support and limited support schools. The department regularly gathers data (e.g., usage data, surveys, site visits) on professional learning, the use of instructional materials, state-provided resources and technical assistance. Recent reports highlight Alabama’s commitment to mathematics, recognizing it as one of the only states where average student achievement exceeds pre-pandemic levels in math. (CCSSO, A Nation of Problem-Solvers).

Nebraska is increasing access to HQIM and training for educators through partnerships and incentive programs. Nebraska’s Instructional Materials Collaborative (NIMC) provides tools and resources for districts related to HQIM and curriculum-based professional learning. (CCSSO, A Nation of Problem-Solvers).

The NIMC math materials selection process provides districts with a three-phase process to select instructional materials and plan for the necessary professional learning aligned to the selected materials, as well as other required actions for successful implementation. (CCSSO, A Nation of Problem-Solvers).

Nebraska incentivizes the effective use of high-quality materials through the Nebraska Instructional Materials: Professional Learning Innovation Network Fellowship. This fellowship is designed to prepare districts and Educational Service Unit (ESU) teams to select quality materials, prepare to implement those materials and support teaching and professional learning aligned to the effective use of the materials and the vision for instructional excellence. (CCSSO, A Nation of Problem-Solvers).

Nebraska is partnering with regional ESUs and proven vendors, such as Zearn, which show evidence of a positive impact on math performance for elementary and middle school students. More than 50 percent of elementary and middle school students have access to HQIM in math. Additionally, more than two-thirds of elementary students of color and students from low-income families have access to HQIM in math, which has increased significantly from 2019, when the number was less than 5%. More broadly, the percentage of Nebraska students in grades 3-8 who tested proficient on the state math assessment rose by double digits from 2021-2022 to 2022-2023. (CCSSO, A Nation of Problem-Solvers).

A study by Kathleen Lynch, Kathryn E. Gonzalez, Heather C. Hill, and Ramsey Merritt looked at math and science PD focusing on teacher knowledge (content and pedagogical content knowledge) and classroom instruction (practices within the classroom, including how teachers engage students, manage class time, and apply content-specific instructional strategies). The study found that professional development that emphasized both teacher content knowledge and instructional practice in concert had the largest positive effects on classroom instruction. The findings suggest that while gains in teacher content knowledge alone don’t directly boost student achievement, PD focused on boosting teachers’ math and science content knowledge and improving classroom instruction has the greatest effect on students’ math and science achievement. (NCTQ, Professional development that delivers).

A study by Heather C. Hill, Brian Rowan, and Deborah Loewenberg Ball with the University of Michigan found that teachers’ mathematical knowledge was significantly related to student achievement gains in both first and third grades after controlling for key student- and teacher-level covariates. This finding provides support for policy initiatives designed to improve students’ mathematics achievement by improving teachers’ mathematical knowledge. In particular, the study showed that a teacher’s mathematical knowledge for teaching (i.e. their classroom explanations, representations, and interactions with students’ mathematical thinking) and not simply a teacher’s computational facility or course taking, is positively related to student achievement (Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement).

Schools’ contributions to student outcomes, including achievement, attendance, social-emotional learning, college enrollment, and earnings, using value-added models. Note that value-added and other growth models require linking schools to student outcome data (such as test scores from two or more academic years, so growth can be measured). In places that do not already calculate value-added or similar measures, framework users should consult with experts to implement this indicator, as there are different approaches to computing value-added that have different technical and practical considerations. In practice, many states use other approaches to incorporating student growth data as part of their school accountability systems, which vary in validity and comparability as measures of schools’ contributions to student outcomes. Users should also carefully consider the results of value-added measures so as not to reinforce existing inequalities by “explaining away” inter-group differences that might be addressed by system conditions or interventions (Education-to-Workforce Framework).

Prioritize, support, and invest in results-driven initiatives to transform low-performing schools into high-quality teaching and learning environments in which all children, including those from low-income families and high-poverty neighborhoods, are present, engaged, and educated to high standards (Annie E. Casey Foundation).

Students demonstrate growth on math assessments from beginning of the year to the end of the year.

The percentage of students across a district, school and classrooms who meet their annual growth targets in math.

Percentage of instructors demonstrating above average contributions to student learning, as measured by student growth on state standardized tests or other outcomes (for example, using value-added models or student growth percentiles). Note that value-added and other growth models require linking instructors to student outcome data (such as test scores from two or more academic years, so growth can be measured). The Education-to-Workforce Framework cautions against using value-added data as the only measure of teaching effectiveness and recommends also including measures based on classroom observation and student survey data. When used for high-stakes accountability, measures of teachers’ contributions to student learning may have unintended consequences (for example, leading to practices such as “teaching to the test”) (Education-to-Workforce Framework).

Schools’ contributions to student outcomes, including achievement, attendance, social-emotional learning, college enrollment, and earnings, using value-added models. Note that value-added and other growth models require linking schools to student outcome data (such as test scores from two or more academic years, so growth can be measured). In places that do not already calculate value-added or similar measures, framework users should consult with experts to implement this indicator, as there are different approaches to computing value-added that have different technical and practical considerations. In practice, many states use other approaches to incorporating student growth data as part of their school accountability systems, which vary in validity and comparability as measures of schools’ contributions to student outcomes. Users should also carefully consider the results of value-added measures so as not to reinforce existing inequalities by “explaining away” inter-group differences that might be addressed by system conditions or interventions (Education-to-Workforce Framework).

Collective teacher efficacy: The collective belief of teachers in their ability to positively affect students. The effect size (1.57) demonstrates a strong correlation to student achievement (Hattie).

Teachers prepare problems and use them in whole-class instruction (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers include both routine and non-routine problems in problem-solving activities (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers ensure that students will understand the problem by addressing issues students might encounter with the problem’s context or language (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers consider students’ knowledge of mathematical content when planning lessons (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers assist students in monitoring and reflecting on the problem-solving process (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers provide students with a list of prompts to help them monitor and reflect during the problem solving process (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers model how to monitor and reflect on the problem-solving process (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers use students’ thinking about a problem to develop students’ ability to monitor and reflect (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers teach students how to use visual representations (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers select visual representations that are appropriate for students and the problems they are solving (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers use think-alouds and discussions to teach students how to represent problems visually (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers show students how to convert the visually represented information into mathematical notation (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers expose students to multiple problem-solving strategies (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers provide instruction in multiple strategies (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers provide opportunities for students to compare multiple strategies in worked examples (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers ask students to generate and share multiple strategies for solving a problem (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers help students recognize and articulate mathematical concepts and notation (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers describe relevant mathematical concepts and notation, and relate them to the

problem-solving activity (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers ask students to explain each step used to solve a problem in a worked example (What Works Clearinghouse, Improving Mathematical Problem Solving).

Teachers help students make sense of algebraic notation (What Works Clearinghouse, Improving Mathematical Problem Solving).

Space learning over time. Arrange to review key elements of course content after a delay of several weeks to several months after initial presentation. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Identify key concepts, terms, and skills to be taught and learned. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Arrange for students to be exposed to each main elements of material on at least two occasions, separated by a period of at least several weeks—and preferably several months. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Arrange homework, quizzes, and exams in a way that promotes delayed reviewing of important course content. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Interleave worked example solutions and problem-solving exercises. Have students alternate between reading already worked solutions and trying to solve problems on their own. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Have students alternate between reading already worked solutions and trying to solve problems on their own. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

As students develop greater expertise, reduce the number of worked examples provided and increase the number of problems that students solve independently. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Combine graphics with verbal descriptions. Combine graphical presentations (e.g., graphs, figures) that illustrate key processes and procedures with verbal descriptions. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Use graphical presentations (e.g., graphs, figures) that illustrate key processes and procedures. This integration leads to better learning than simply presenting text alone. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

When possible, present the verbal description in an audio format rather than as written text. Students can then use visual and auditory processing capacities of the brain separately rather than potentially overloading the visual processing capacity by viewing both the visualization and the written text. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Connect and integrate abstract and concrete representations of concepts, making sure to highlight the relevant features across all forms of the representation. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Use quizzing to promote learning. Use quizzing with active retrieval of information at all phases of the learning process to exploit the ability of retrieval directly to facilitate long-lasting memory traces. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Prepare pre-questions, and require students to answer the questions, before introducing a new topic.  (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Use quizzes for retrieval practice and spaced exposure, thereby reducing forgetting.  (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Use game-like quizzes as a fun way to provide additional exposure to material. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Help students allocate study time efficiently. Assist students in identifying what material they know well, and what needs further study, by teaching children how to judge what they have learned. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Conduct regular study sessions where students are taught how to judge whether or not they have learned key concepts in order to promote effective study habits. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Teach students that the best time to figure out if they have learned something is not immediately after they have finished studying, but rather after a delay. Only after some time away from the material will they be able to determine if the key concepts are well learned or require further study. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Remind students to complete judgments of learning without the answers in front of them. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Teach students how to use these delayed judgments of learning techniques after completing assigned reading materials, as well as when they are studying for tests. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Use quizzes to alert learners to which items are not well learned. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Provide corrective feedback to students, or show students where to find the answers to questions, when they are not able to generate correct answers independently. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Teach students how to use delayed judgment of learning techniques to identify concepts that need further study. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Use tests and quizzes to identify content that needs to be learned. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Help students build explanations by asking and answering deep questions. Use instructional prompts that encourage students to pose and answer “deep-level” questions on course material. These questions enable students to respond with explanations and supports deep understanding of taught material. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Encourage students to “think aloud” in speaking or writing their explanations as they study; feedback is beneficial. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Ask deep questions when teaching, and provide students with opportunities to answer deep questions, such as: What caused Y? How did X occur? What if? How does X compare to Y? (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Challenge students with problems that stimulate thought, encourage explanations, and support the consideration of deep questions. (What Works Clearinghouse, Organizing Instruction and Study to Improve Student Learning).

Encourage students to develop a deeper understanding of algebra. Although proficiency in arithmetic operations is important to becoming proficient in algebra, instruction should move students beyond superficial mathematics knowledge and toward a deeper understanding of algebra. This includes encouraging students to make connections between algebraic concepts and the procedures present in problems, and helping students recognize how the placement of the quantities relative to the operations in problems impacts the solution strategy. Teachers can prompt students to consider: What am I being asked to do in this problem? What do I know about the form of this expression or equation? What are the relationships between the quantities in this expression or equation? How can I check that my solution is correct? (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Promote process-oriented thinking. Instruction should move beyond a primary focus on the correct final answer to algebra problems to also promoting the understanding of the processes by which one arrives at an answer. For example, teachers could encourage students to consider questions such as the following: What decisions did you make to solve the problem? What steps did you take to solve the problem? Was this a good strategy? Why or why not? Are there other ways to solve the problem? Can you show (through manipulatives, pictures, or number-lines) how you solved the problem? (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Encourage precise communication. Teachers should provide frequent opportunities for students to reason with and talk about mathematical concepts, procedures, and strategies using precise mathematical language. This communication plays a key role in helping students develop mathematical understanding. For example, teachers could ask students: How would you describe this problem using precise mathematical language? How would you describe your strategy for solving this problem using precise mathematical language? (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Use solved problems to engage students in analyzing algebraic reasoning and strategies. Compared to elementary mathematics work like arithmetic, solving algebra problems often requires students to think more abstractly. Algebraic reasoning requires students to process multiple pieces of complex information simultaneously, which can limit students’ capacity to develop new knowledge. (Such reasoning is sometimes described as imposing high cognitive load or challenging working memory, which can interfere with students’ ability to learn.) Solved problems can minimize the burden of abstract reasoning by allowing students to see the problem and many solution steps at once—without executing each step—helping students learn more efficiently. Analyzing and discussing solved problems can also help students develop a deeper understanding of the logical processes used to solve algebra problems. Discussion and the use of incomplete or incorrect solved problems can encourage students to think critically. (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Have students discuss solved problem structures and solutions to make connections among strategies and reasoning. Create opportunities for students to discuss and analyze solved problems by asking students to describe the steps taken in the solved problem and to explain the reasoning used. (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Select solved problems that reflect the lesson’s instructional aim, including problems that illustrate common errors. (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Use whole-class discussions, small-group work, and independent practice activities to introduce, elaborate on, and practice working with solved problems. (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Teach students to utilize the structure of algebraic representations. Structure refers to an algebraic representation’s underlying mathematical features and relationships, such as: the number, type, and position of quantities, including variables; the number, type, and position of operations; the presence of an equality or inequality; the relationships between quantities, operations, and equalities or inequalities; the range of complexity among expressions, with simpler expressions nested inside more complex ones. Paying attention to structure helps students make connections among problems, solution strategies, and representations that may initially appear different but are actually mathematically similar. (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Promote the use of language that reflects mathematical structure. (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Encourage students to use reflective questioning to notice structure as they solve problems. (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Teach students that different algebraic representations can convey different information about an algebra problem. (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Teach students to intentionally choose from alternative algebraic strategies when solving problems. A strategy involves a general approach for accomplishing a task or solving a problem. Unlike an algorithm, which contains a sequence of steps that are intended to be executed in a particular order, a strategy may require students to make choices based on the specifics of the problem as well as their problem-solving goals. A strategy might also include alternative approaches that consider variations of a problem or unexpected results a student might encounter while implementing the steps of the solution. Strategies are general and broadly applicable, making them useful in solving a variety of problems.  (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Teach students to recognize and generate strategies for solving problems. Provide students with examples that illustrate the use of multiple algebraic strategies. Include standard strategies that students commonly use, as well as alternative strategies that may be less obvious. Students can observe that strategies vary in their effectiveness and efficiency for solving a problem. (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Encourage students to articulate the reasoning behind their choice of strategy and the mathematical validity of their strategy when solving problems. Have students describe their reasoning while analyzing the problem structure, determining their solution strategy, solving a problem, and analyzing another student’s solution. Describing their reasoning helps students understand the choices they make and goals they set when selecting a strategy. Students should communicate their reasoning verbally and through written work. (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Have students evaluate and compare different strategies for solving problems. Encourage students to compare problem structures and solution strategies to discover the relationships among similar and different problems, strategies, and solutions. Begin comparison activities after students understand one strategy, so that students are able to identify similarities and differences between the familiar strategy and the newly learned strategy. (What Works Clearinghouse, Teaching Strategies for Improving Algebra Knowledge).

Prioritize, support, and invest in results-driven initiatives to transform low-performing schools into high-quality teaching and learning environments in which all children, including those from low-income families and high-poverty neighborhoods, are present, engaged, and educated to high standards (Annie E. Casey Foundation).

Teacher evaluation systems that use Value-Add Measures to determine the impact a teacher has on student learning.

Students’ perceptions of their teacher’s effectiveness, using a survey instrument such as the Pedagogical Effectiveness subscale of the Panorama Student Survey, the Tripod Student Survey, the Ambitious Instruction and Supportive Environment domains of the 5Essentials Survey, or the Elevate survey’s Feedback for Growth, Meaningful Work, Student Voice, Teacher Caring, Learning Goals, Supportive Teaching, and Well-organized Class scales (Education-to-Workforce Framework).

Teachers encourage students to view intelligence and mathematical ability as qualities that can be developed through effort and perseverance. Research indicates that when teachers adopt a growth mindset, student achievement improves, particularly among girls, English language learners, and economically disadvantaged students. Sharing neuroscience findings about brain plasticity and emphasizing that mistakes are opportunities for learning can help students embrace challenges and persist through difficulties (Crawford, 2018).

Classroom Engagement: The classroom environment facilitated by the teacher encouraged students to generate ideas, questions, conjectures, and/or propositions that reflected engagement or exploration with important mathematics and science concepts. (UTeach Observation Protocol for Mathematics and Science).

Classroom Interactions: Interactions reflected collegial working relationships among students (e.g., students worked together productively and talked with each other about the lesson). (UTeach Observation Protocol for Mathematics and Science).

Classroom On-Task: The majority of students were on task throughout the class.(UTeach Observation Protocol for Mathematics and Science).

Classroom Management: The teacher’s classroom management strategies enhanced the classroom environment.(UTeach Observation Protocol for Mathematics and Science).

Classroom Organization: The classroom is organized appropriately such that students can work in groups easily and get to lab materials as needed, and the teacher can move to each student or student group.(UTeach Observation Protocol for Mathematics and Science).

Classroom Equity: The classroom environment established by the teacher reflected attention to issues of access, equity, and diversity for students (e.g., cooperative learning, language-appropriate strategies and materials, attentiveness to student needs). (UTeach Observation Protocol for Mathematics and Science).

Lesson Importance: The structure of the lesson allowed students to engage with and/or explore important concepts in mathematics or science (instead of focusing on techniques that may only be useful on exams). (UTeach Observation Protocol for Mathematics and Science).

Lesson Assessments: The structure of the lesson included opportunities for the instructor to gauge student understanding. (UTeach Observation Protocol for Mathematics and Science).

Implementation Questioning: The teacher used questioning strategies to encourage participation, check on skill development, and facilitate intellectual engagement and productive interaction with students about important science and mathematics content and concepts. (UTeach Observation Protocol for Mathematics and Science).

Implementation Involvement: The teacher involved all students in the lesson (calling on non-volunteers, facilitating student–student interaction, checking in with hesitant learners, etc.). (UTeach Observation Protocol for Mathematics and Science).

Implementation Connections: The instructional strategies and activities used in this lesson clearly connected to students’ prior knowledge and experience. (UTeach Observation Protocol for Mathematics and Science).

Content Relevance: During the lesson, it was made explicit to students why the content is important to learn. (UTeach Observation Protocol for Mathematics and Science).

Content Societal Impact: During the lesson, there was discussion about the content topic’s role in history, current events, or relevant “real-world” problems. (UTeach Observation Protocol for Mathematics and Science).

States and districts implement a validated student perception survey, such as Panorama or Tripod, to systematically collect student feedback. The data gathered informs continuous improvement efforts and integrates into teacher, leader, school, and district accountability frameworks.

Percent of multilingual learners who are (or have ever been) classified as English language learners (Californians Together).

Percent of multilingual learners who are classified as Long-Term English language learners (LTELs) (Californians Together).

Percent of multilingual learners who are classified as “At-Risk” Long-Term English language learners (AR-LTELs) (Californians Together).

Percent of multilingual learners who had been classified as English Language Learners but are now reclassified as Fluent English Proficient (RFEP) (Californians Together).

Percent of English Language Learners who make progress towards English language proficiency.  The California Schools Dashboard has a measure called the English Learner Progress Indicator (ELPI) which determines whether an English Language Learner has made adequate progress, as measured by the English Language Proficiency Assessment for California (ELPAC) (Californians Together).

Percent of multilingual learners who participate in a Dual Language Immersion or Developmental Bilingual Programs (Californians Together).

Percent of students who participate in programs leading to proficiency in two or more languages (Californians Together).

Percent of multilingual learners who are chronically absent (Californians Together).

Percent of multilingual learners who have a breakfast meal before school. (Tracked through student response surveys like the California Healthy Kids Survey) (Californians Together).

Percent of multilingual learners who have access to expanded learning opportunities (Californians Together).

Percent of multilingual learners who have a caring adult relationship at school. (Tracked through student response surveys like the California Healthy Kids Survey) (Californians Together).

Percent of multilingual learners who experience chronic sadness or hopelessness in school (tracked through student response surveys like the California Healthy Kids Survey) (Californians Together).

Number of bilingual teacher preparation programs at state-approved education preparation programs (Californians Together).

Percent of teachers who have access to a supportive school environment and high-quality professional learning that includes designated and integrated English Language Development strategies (Californians Together).

Extra support for English language learners to help them master the language and content, including extra time for individualized instruction and materials that are relevant. (Annie E. Casey Foundation)

School and system schedules provide the appropriate amount of time for language instruction educational program (LIEP) services such as bilingual education or English language development (ELD) programs and services. This may or may not be state or locally mandated. (Instruction Partners)

All young children are capable of learning two languages. Becoming bilingual has long-term cognitive, academic, social, cultural, and economic benefits. Bilingualism is an asset. (Annie E. Casey Foundation)

Young multilingual learners require systematic support for the continued development for their home language. (Annie E. Casey Foundation)

Loss of the home language has potential negative long-term consequences for the multilingual child’s academic, social, and emotional development, as well as for the family dynamics. (Annie E. Casey Foundation)

Teachers and programs can adopt effective strategies to support home language development even when the teachers are monolingual English speakers. (Annie E. Casey Foundation)

Dual-language programs are an effective approach to improving academic achievement for multilingual children, while providing benefits to native English speakers. (Annie E. Casey Foundation).

Scheduling regular peer-assisted learning opportunities. English language learners of varying language proficiency should work together several times a week on structured academic tasks. (NCTQ Teacher Prep Review)

Capitalizing on students’ home language, knowledge, and cultural assets. This instruction could include providing a preview of content in a child’s home language, reading stories in the child’s home language, offering definitions of vocabulary in the home language, helping children learn cognates for English words (for example, asking Spanish-speaking students to identify cognates like “mysterioso” and “mysterious”), and connecting key concepts with children’s prior knowledge. (NCTQ Teacher Prep Review)

Providing visual and verbal supports to help students understand core content. These could include instructional videos, visuals, and graphic organizers. English learners benefit more than their English-proficient peers from the teacher providing students with information rather than engaging them in the creation of information. (NCTQ Teacher Prep Review)

Policymakers can ensure that ELs have fair opportunities to access Dual-language immersion programs by locating them in schools with significant EL populations, reserving seats for native speakers of non-English languages, and expanding the number of available DLI seats by investing in growing programs to train more bilingual teachers (The Century Foundation).

State leaders, including legislators, state agencies, and boards set clear statewide goals for multilingual learner outcomes and track progress towards these goals (Californians Together).

States improve tracking and reporting of public data regarding multilingual students and their outcomes. This includes high school graduation and outcomes for Reclassified Fluent English Proficient (RFEP) students, equitable access to rigorous coursework, access to bilingual programs, and teacher supply and attrition (Californians Together).

States invest in the expansion of Bilingual Pathways and programs (Californians Together).

States invest in community schools and initiatives that support the whole child. This includes ensuring that investments center the needs of ELs, support bilingualism and multilingualism, and are aligned to state goals for multilingual student achievement (Californians Together).

States support legislation that address the bilingual teacher shortage. Invest in proven programs, such as Bilingual Teacher Residencies and the Bilingual Teacher Professional Development Program (BTPDP) and remove barriers to a bilingual authorization (Californians Together).

Percentage of school leaders rated as effective, using an evaluation system that includes multiple measures, such as the Administrator Evaluation component of the Tennessee Educator Acceleration Model (TEAM) (Education-to-Workforce Framework).

Staff surveys that can be used to measure effective school leadership include the Effective Leaders subcomponent of the UChicago 5E’s survey instrument, Panorama Teacher and Staff Survey, or The New Teacher Project’s (TNTP) Instructional Culture Insight Survey. However, no research has emerged at this point to show that staff surveys are valid and reliable measures of school leader effectiveness, and survey measures run the risk of offering a biased or potentially politicized rating of a leader, underscoring the importance of examining multiple measures (Education-to-Workforce Framework).

Percentage of school leaders rated as effective, using an evaluation system that includes multiple measures, such as the Administrator Evaluation component of the Tennessee Educator Acceleration Model (TEAM) (Education-to-Workforce Framework).

Staff surveys that can be used to measure effective school leadership include the Effective Leaders subcomponent of the UChicago 5E’s survey instrument, Panorama Teacher and Staff Survey, or The New Teacher Project’s (TNTP) Instructional Culture Insight Survey. However, no research has emerged at this point to show that staff surveys are valid and reliable measures of school leader effectiveness, and survey measures run the risk of offering a biased or potentially politicized rating of a leader, underscoring the importance of examining multiple measures (Education-to-Workforce Framework).

Ensure program directors and school principals have the capacity to provide instructional leadership that supports effective teaching (Alliance for Early Success).

Louisiana’s Content Leaders, who are local educators with the knowledge, skills, and resources to provide high-quality, content-rich, and curriculum specific professional development to teachers in their school (Louisiana Department of Education).

Louisiana’s Mentor Teachers, who are local educators who have the knowledge and skills to effectively coach and support new and resident teachers in their districts (Louisiana Department of Education).

Teacher retention: Percentage of teachers who return to teaching in the same school from year to year. Educator retention can be computed using administrative records from districts’ or states’ staff data management systems linking teachers and principals to schools from one year to the next (Education-to-Workforce Framework).

School leader tenure: Percentage of school leaders who have served in their current positions for less than two years, two to three years, and four or more years. For school leaders, the Education-to-Workforce Framework recommends examining their tenure in the same school. A recommended best practice is to disaggregate retention by measures of educator effectiveness, such as those based on teacher performance ratings or value-added scores, to better assess the impact of staff turnover (Education-to-Workforce Framework).

North Carolina’s Teacher Working Conditions Survey offers a systematic way to capture teachers’ perspectives on the conditions in which they work (NC TWC Survey).

States and/or districts have career progression pathways to support the retention of highly-effective teachers, such as Louisiana’s Content-Leaders and Mentor Teacher roles (Louisiana Department of Education).

States and/or districts have differentiated compensation structures that provide higher rates of pay for teachers demonstrating the most effectiveness, such as Texas’ Teacher Incentive Allotment (TEA Teacher Incentive Allotment).

Percentage of teacher leaders rated effective based on multiple measures of performance (National Education Association).

Percentage of teacher leaders who occupy hybrid roles (National Education Association).

Percentage of teacher leaders with a leadership endorsement/certificate (National Education Association).

Presence of an educator shortage (National Education Association).

State codifies the Teacher Leadership Competencies and/or other standards for teacher leadership (National Education Association).

State includes a state-level endorsement/certificate for teacher leaders (National Education Association).

State provides resources to complete voluntary national certification and endorsements that promote teacher leadership opportunities (National Education Association).

Districts have pathways for teachers who want to remain in their teaching role but make a bigger impact and larger salary. For example, North Carolina’s Advanced Teaching Roles, including the Multi-Classroom Teacher-Leader Role (Department of Public Instruction for the state of North Carolina).

The percentage of teaching positions that remain unfilled at the start of the school year (Tennessee Department of Education).

The number of applicants per open teaching position, a common measure used across districts.

Districts begin cultivation and recruitment a year prior to the present school year (National Education Association).

Districts have plans to recruit and retain accomplished educators (National Education Association).

Districts have plans to recruit educators for shortage areas, such as special education and second language acquisition (National Education Association).

Hiring high quality staff (Results for America).

State tracks educator shortages (National Education Association).

Every student should have opportunities to grapple meaningfully with key ideas and, in doing so, to become a knowledgeable, flexible, and resourceful mathematical thinker and problem solver. Teachers should have opportunities to consider and discuss how each lesson’s activities connect to the concepts, practices, and habits of mind they want students to develop over time. (Teaching for Robust Understanding Observation Guide for Mathematics).

All students work on core mathematical issues in ways that enable them to develop conceptual understandings, develop reasoning and problem solving skills, and use mathematical concepts, tools, methods and representations in relevant contexts. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student engages with grade level mathematics in ways that highlight important concepts, procedures, problem solving strategies, and applications. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student has opportunities to develop productive mathematical habits of mind. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student has opportunities for mathematical reasoning, orally and in writing, using appropriate mathematical language (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student explains their reasoning processes as well as their answers. (Teaching for Robust Understanding Observation Guide for Mathematics).

Students have opportunities to grapple with and make sense of important mathematical ideas and their use. Students learn best when they are challenged in ways that provide room and support for growth, with task difficulty ranging from moderate to demanding. The level of challenge should be conducive to what has been called “productive struggle.” (Teaching for Robust Understanding Observation Guide for Mathematics).

All students have opportunities to make their own sense of important mathematical ideas, developing deeper understandings, connections, and applications by building on what they know. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student engages individually and collaboratively with challenging ideas. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student actively seeks to explore the limits of their current understanding. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student is comfortable sharing partial or incorrect work as part of a larger conversation. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student reasons and tests ideas in ways that connect to and build on what they know. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student explains what they have done so far before asking for help • Continues to wrestle with an idea after the teacher leaves. (Teaching for Robust Understanding Observation Guide for Mathematics).

Classroom activities invite and support the meaningful engagement with core mathematical content and practices by all students. Finding ways to support the diverse range of learners in engaging meaningfully is the key to an equitable classroom. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student contributes to collective sense making in any of a number of different ways (e.g., proposing ideas, asking questions, creating diagrams…). (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student actively listens to other students and builds on their ideas. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student supports other students’ developing understandings. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student explains, interprets, applies and reflects on important mathematical ideas. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student participates meaningfully in the mathematical work of the class. (Teaching for Robust Understanding Observation Guide for Mathematics). 

All students are supported in access to central mathematical content, and participate actively in the work of the class. Diverse strengths and needs are built on through the use of various strategies, resources, and technologies that enable all students to participate meaningfully.. (Teaching for Robust Understanding Observation Guide for Mathematics).

Every student has opportunities to explore, conjecture, reason, explain, and build on emerging ideas, contributing to the development of agency (the willingness to engage academically) and ownership over the content, resulting in positive mathematical identities. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student takes ownership of the learning process in planning, monitoring, and reflecting on individual and/or collective work. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student asks questions and makes suggestions that support analyzing, evaluating, applying and synthesizing mathematical ideas. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student builds on the contributions of others and helps others see or make connections. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student holds classmates and themselves accountable for justifying their positions, through the use of evidence and/or elaborating on their reasoning. (Teaching for Robust Understanding Observation Guide for Mathematics).

All students build productive mathematical identities through taking advantage of opportunities to engage meaningfully with the discipline and share and refine their developing ideas. (Teaching for Robust Understanding Observation Guide for Mathematics).

Classroom activities elicit all students’ thinking and subsequent interactions respond to that thinking, by building on productive beginnings or by addressing emerging misunderstandings. High quality instruction “meets students where they are” and gives them opportunities to develop deeper understandings, both as shaped by the teacher and in student-to-student interactions. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student explains their thinking, even if somewhat preliminary. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student sees errors as opportunities for new learning. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student consistently reflects on their work and the work of peers. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student sees fellow students as resources for their own learning. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student provides specific and accurate feedback to fellow students. (Teaching for Robust Understanding Observation Guide for Mathematics).

Each student makes use of feedback in revising their work. (Teaching for Robust Understanding Observation Guide for Mathematics).

Every student’s learning is continually enhanced by the ongoing strategic and flexible use of techniques and activities that allow students to reveal their emerging understandings, and that provide opportunities both to rethink misunderstandings to build on productive ideas. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers highlight important ideas and provide opportunities for students to engage with them. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers use materials or assignments that center on key ideas, connections, and applications. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers explicitly connect the lesson’s big ideas to what has come before and will be done in the future. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers support the purposeful use of academic language and of representations (e.g., graphs, tables, symbols) central to mathematics. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers support students in seeing mathematics as being coherent, connected, and comprehensible. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers position students as sense makers who can make sense of key conceptual ideas.. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers use or adapt materials and activities to offer challenges that students can use, individually or collectively, to deepen understandings. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers build and maintain classroom norms that support every student’s engagement with those materials and activities. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers monitor student challenge, adjusting tasks, activities, and discussions so that all students are engaged in productive struggle. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers support students without removing the challenge from the work they are engaged in. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers create safe environments. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers use tasks and activities that provide multiple entry points and support multiple approaches to the mathematics. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers provide opportunities for students to see themselves, and their personal and community interests, reflected in the curriculum. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers validate different ways of making contributions. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers build and maintain norms that support every student’s participation in group work and whole class activities. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers support particular needs, such as those of language learners, for full participation. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers expect and support meaningful mathematical engagement from all students, helping them contribute and build on contributions from others. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers create safe climates in which students feel free to express their ideas and understandings. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers use materials that elicit multiple strategies, and have students explain their reasoning, in order to gain information about student’ emerging understandings. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers flexibly adjust content and process, providing students opportunities for re-engagement and revision. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers provide timely and specific feedback to students, as part of classroom routines that prompt students to make active use of feedback to further their learning. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers create opportunities for students’ individual and collaborative reflection on their knowledge and learning. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers provide time for students to develop and express mathematical ideas and reasoning. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers work to make sure all students have opportunities to have their voices heard. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers encourage student-to-student discussions and promote productive exchanges. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers assign tasks and pose questions that call for mathematical justification, and for students to explain their reasoning. (Teaching for Robust Understanding Observation Guide for Mathematics).

Teachers employ a range of techniques that attribute ideas to students, to build student ownership and identity. (Teaching for Robust Understanding Observation Guide for Mathematics).

Schools and instructors use a standards-aligned core course curriculum that meets quality standards (as defined by EdReports) and is culturally relevant, centering the lived experiences and heritage of students’ ethnic or racial backgrounds (Education-to-Workforce Framework).

The Tier 1 curriculum, assessments, and instructional resources in use are closely aligned (Instruction Partners).

When and if appropriate, additional culturally and/or linguistically relevant materials are used alongside curricular materials to support students in making personal connections (Instruction Partners).

Tiered intervention programs in use are structured and systematic; they amplify and accelerate learning from Tier 1 materials (Instruction Partners).

Curriculum-embedded assessments and materials are used seamlessly to design whole- and small-group learning experiences that move every student toward reading proficiency (Instruction Partners).

The school/system uses quality data and assessment resources consistently, cohesively, and strategically to drive instructional decision making for all students (Instruction Partners).

Implement developmentally and culturally appropriate early learning standards that reflect approaches to learning, social/emotional, physical, cognitive, and language development; and build foundational skills in literacy, math, science, social studies, and the arts (Alliance for Early Success).

Schools adopt content-rich, developmentally appropriate curricula linked to standards and assessments (Annie E. Casey Foundation).

State leaders signal quality and incentivize adoption of high-quality instructional materials. Providing students with rigorous, evidence-based, grade-level math instruction through high-quality materials boosts their achievement and prepares them for future success. States can ensure all students, including those with special needs, have access to HQIM for grade-level math by setting clear guidelines and requirements. (CCSSO, A Nation of Problem-Solvers).

States, including Massachusetts, Mississippi, New Mexico and Rhode Island, provide the rubrics used to identify the state-reviewed HQIM for knowledge-building or for districts to use to evaluate the curriculum themselves. Other states, such as Arkansas, incentivize using HQIM through state law, pricing agreements or grants for districts and schools. States should continue to review new product releases for quality and support districts in selecting and using the highest-quality math materials available. (CCSSO, A Nation of Problem-Solvers).

State leaders curate a list of quality materials that signal to districts the materials they should use. (CCSSO, A Nation of Problem-Solvers).

State leaders provide training to districts on selecting materials from the approved list and effectively implementing the selected curriculum. (CCSSO, A Nation of Problem-Solvers).

State leaders provide tools and resources, such as rubrics, to inform district selection and adoption of curricula. (CCSSO, A Nation of Problem-Solvers).

State leaders establish common contracts that ease procurement barriers, making it easy for districts to purchase materials from the state list. (CCSSO, A Nation of Problem-Solvers).

State leaders use available funding to create grants for local curricular purchases for materials from the state list. (CCSSO, A Nation of Problem-Solvers).

State leaders create policies requiring schools needing improvement to purchase and use HQIM from the state’s list as a condition of federal grant funds and use mandated school improvement plans to design an implementation strategy. (CCSSO, A Nation of Problem-Solvers).

Since 2019, Mississippi has prioritized HQIM. The State Board of Education reviewed and adopted five high-quality math curricula for grades K-8. The Mississippi Department of Education and Mississippi teachers partnered with the nonprofit organization EdReports to create the High-Quality Instructional Materials Review Rubric for K-8 and High School. (CCSSO, A Nation of Problem-Solvers).

In addition to creating a list of approved materials, Mississippi incentivized using these materials by providing an exemption for bidding in the purchase of the state-adopted HQIM, making it easier for districts to purchase off the approved list. (CCSSO, A Nation of Problem-Solvers).

As a part of the regional service delivery model, Mississippi provided training on how to use these rubrics and department-provided tools to develop standards-based, differentiated instruction and classroom assessments using HQIM.  (CCSSO, A Nation of Problem-Solvers).

Mississippi also provided training on Mathematics Design Collaborative practices and offered a menu of services for professional learning and technical assistance from which districts select.  (CCSSO, A Nation of Problem-Solvers).

As of 2023, about 40 percent of Mississippi students had access to HQIM in math. Access is even higher among students from low-income families, with more than 75 percent benefiting from these resources. Additionally, Mississippi’s proficiency rates on grades 3-8 state tests suggest students have recovered or exceeded pre-pandemic levels in math. (CCSSO, A Nation of Problem-Solvers).

In 2019, Rhode Island passed a law requiring the commissioner of elementary and secondary education and the Department of Education (RIDE) to develop statewide academic standards and curriculum frameworks, identify at least five examples of high-quality curriculum for each core subject area (math, English language arts and science) and support local education agencies (LEAs) in the selection and implementation of curricular materials. (CCSSO, A Nation of Problem-Solvers).

Under Rhode Island’s legislation, LEAs must adopt HQIM aligned to academic standards, curricular frameworks and statewide standardized tests from an approved list. The Department of Education (RIDE) primarily used EdReports to drive its materials adoption. The department also considered other material reviews, the extent to which materials met the needs of multilingual learners, cultural responsiveness and representation of student identities. (CCSSO, A Nation of Problem-Solvers).

Rhode Island’s law was passed to codify the practices the Department of Education (RIDE) had already begun prior to 2019 to incentivize districts to select and use HQIM. Since this work began, Rhode Island has shown a positive trend in math achievement on state tests. Student proficiency in math rose nearly 2 percentage points from 2022 to 2023 on the Rhode Island Comprehensive Assessment System (RICAS). Since 2021, proficiency has increased by nearly 10 percentage points. Furthermore, the proficiency levels in grades 4-6 in 2023 matched or exceeded pre-pandemic scores, demonstrating significant recovery and improvement. (CCSSO, A Nation of Problem-Solvers).

A high-quality curriculum not only provides a clear framework for teachers, but also ensures coherence across grades and schools. It is essential that legislators promote the selection and periodic review of evidence-based instructional materials and resources in districts. This will help determine if they meet students’ needs or if additional materials and supports are necessary. Don’t remove resources, even flawed ones, without providing educators with effective alternatives first. (Model state: Delaware) (Shanker Institute).

The school/system uses quality data and assessment resources consistently, cohesively, and strategically to drive instructional decision making for all students (Instruction Partners).

Universal screening involves assessing all students to identify those performing at grade level and those who may be struggling. This proactive approach allows educators to detect learning gaps early and implement timely interventions. Research indicates that universal screeners can accurately predict students’ future performance in mathematics, facilitating data-driven instructional planning (Foegen, 2009).

The assessment system in place includes progress monitoring tools to determine how students are progressing toward their individual goals and student growth targets based on nationally-normed benchmarks (Instruction Partners). Regular progress monitoring involves frequent assessments to track students’ advancement toward individual goals and growth targets. This ongoing evaluation enables educators to adjust instruction based on students’ evolving needs. Studies have demonstrated that systematic progress monitoring in mathematics leads to improved student achievement by providing continuous feedback and informing targeted teaching strategies.

The assessment system in place includes a diagnostic assessment that pinpoints the specific skills that students have mastered and/or where they need further instruction and practice (Instruction Partners).

The assessment system in place includes formative assessments (e.g., from the curriculum, anecdotal records) to assess students’ mastery of what is being taught. Note that it is important to consider that additional or alternative assessment data may be necessary to yield a holistic picture of students’ knowledge and skills, particularly for students in priority groups. For instance, a test given in English may not capture the language skills of a Spanish-speaking student; providing them an assessment in Spanish may offer educators a more accurate picture of their skills and knowledge (Instruction Partners).

Assessment and evaluation honor multilingual learners’ (MLs’) primary languages and current English proficiency levels. There is a written policy to ensure that MLs are not held back in the curriculum sequence or small-group work based on primary language influence or current English proficiency level (Instruction Partners).

Each student has clear, individual learning goals and learning targets that teachers, students, and families/caregivers understand (Instruction Partners).

There is a clear and efficient data cycle process in place that supports leaders and teachers in collecting and analyzing student data as well as adjusting instruction based on what is and is not working (Instruction Partners).

When analyzing student data, all educators providing or supporting early literacy instruction are included (e.g., K–2 and language development teachers) (Instruction Partners).

Student data is gathered from multiple forms of assessment (e.g., universal screener, progress monitoring, curriculum assessment, teachers’ observation notes about skills individual students have and have not yet mastered) (Instruction Partners).

Data is analyzed collaboratively from each form of assessment alongside student goals to determine what is working and what may need to be refined to support students in moving toward skill mastery (Instruction Partners).

Data analysis adjusts tier placement for students based on clear entry and exit criteria for intervention with an emphasis on exiting students as flexibly and quickly as possible (Instruction Partners).

Student data is disaggregated and analyzed by demographics; team members use this data to ensure that the needs of students in priority groups are centered when making instructional decisions (Instruction Partners).

Families and caregivers are kept up-to-date on their child’s progress toward goals and play an active role in supporting their child’s journey to becoming a skilled reader (Instruction Partners).

Ensure child assessment tools are developmentally, culturally, and linguistically appropriate (Alliance for Early Success).

Equitable weighted student funding formula (Data sources: Local policy and practice assessments) (StriveTogether 2021).

Equity factor, or the degree of variance between district per-student funding to state average (Data source: U.S. Department of Education) (StriveTogether 2021).

Adequate school funding to ensure access to the resources that afford every child the opportunity to learn. (Annie E. Casey Foundation)

State has an independent body of stakeholders that includes active pre-K through grade 12 educators and administrators who annually assess if state funding is sufficient to provide all students the opportunity to meet rigorous academic standards (National Education Association).

Districts implement measures to broaden their tax base (National Education Association).

Districts use “pupil weights” in their base formula to adjust for diverse student needs (National Education Association).

State funds local efforts to diversify revenue streams (National Education Association).

Passage of voter-approved children’s funds at local levels (Children’s Funding Project).

State implements measures to broaden its tax base (National Education Association).

Access to resources: School finance equity (Birth to Grade 3 Indicator Framework).

The percentage of students, disaggregated by race, ethnicity and income, that have access to fully certified math teachers

The percentage of math teachers in a district who are fully certified to teach math.

The percentage of math teachers who are teaching “out of certification” areas.

The percentage of “emergency certification” teachers who are teaching math

Districts partner with teacher preparation programs on teacher residencies and induction (National Education Association).

Percentage of preparation program graduates surveyed indicating satisfaction with their preparedness to serve as the teacher-of-record (National Education Association).

Preparation programs survey graduates about their preparedness to serve as the teacher-of-record and report their response rates (National Education Association).

Preparation programs use pre-service performance assessments to determine candidate preparedness prior to program completion and/or initial licensure (National Education Association).

Preparation programs work with local school districts to recruit high-achieving high school graduates to pursue careers in education (National Education Association).

Research supports the conclusion that improving the content knowledge of instructors has a significant positive effect on student learning. Moreover, programs which blend discipline content knowledge (i.e. a teacher’s proficiency in traditional undergraduate mathematics), classroom content knowledge (i.e. the instructor’s ability to correctly perform a computation that he or she is presenting in the classroom, a thorough understanding of why the process is correct, and a repository of alternate representations and mathematical methodologies for the problem), and pedagogical content knowledge (i.e. understanding of common student conceptions and misconceptions, proficiency in the design of course and lesson plans, and the use of instructional technology) have shown the most success in aiding student achievement. (A Model for Community Partnerships in Mathematics).

Districts mandate successful completion of a residency program prior to obtaining initial licensure (National Education Association).

Preparation programs require school-based experiences beyond a semester of student teaching (National Education Association).

State provides funding for induction programs (National Education Association).

State provides funding for preparation programs to establish residency programs with local school districts (National Education Association).

State provides resources to grow preparation programs in minority-serving institutions (National Education Association).

Investing in hiring, training and retaining a high-quality and diverse workforce of educators (Urban Institute).

Percentage of novice math teachers in schools and the district.

Qualified, experienced teachers for all students, especially the students who need them most. (Annie E. Casey Foundation)

Same-race student-teacher ratio by race/ethnicity (Data sources: Local school, LEA or SEA human resources, administrative and/or enrollment data) (Education-to-Workforce Framework and StriveTogether 2021).

Educational staff composition by race and ethnicity compared to student composition by race and ethnicity (Education-to-Workforce Framework and StriveTogether 2021).

Percentage of program sites that support a language other than English (STEP Forward with Data Framework).

Percentage of program sites where children from focal populations are exposed to staff in their program who reflect their own identities (STEP Forward with Data Framework).

Percentage of workforce members who are fluent in the language spoken by the children they serve (STEP Forward with Data Framework).

Qualified, experDistricts have plans to recruit educators from underrepresented populations (National Education Association).

Districts have plans to retain educators from underrepresented populations (West Ed).

Re-evaluate “last-in, first-out” practices which are more likely to remove early career teachers who identify as people of color (TNTP).

Build partnerships with organizations that recruit and develop educators of color, such as the Center for Black Educator Development and Men of Color in Educational Leadership.

State policy supports recruitment of promising future educators, including underrepresented populations (National Education Association).

Making educator diversity data visible and actionable to all stakeholders (Education Trust).

Setting clear goals at the state, district and teacher preparation levels to increase educator diversity (Education Trust).

Investing in efforts to retain teachers of color that improve working conditions and provide opportunities for personal and professional growth (Education Trust).

Teachers’ overall ratings on a math specific observation rubric, similar to Instruction Partners’ modified Instructional Practice Guide for Math (Instruction Partners).

Teachers’ overall and subscale scores on an observation rubric associated with an educator observation system (Education-to-Workforce Framework).

Percentage of teachers rated effective based on multiple measures of performance (National Education Association).

Teacher coaching and professional development (Education-to-Workforce Framework).

Percentage of educators surveyed indicating alignment among professional learning, standards, curriculum and assessments (National Education Association).

Percentage of educators surveyed indicating satisfaction with professional learning time and opportunities (National Education Association).

Percentage of educators who participated in job-embedded professional learning opportunities in the previous year (National Education Association).

Districts design, monitor and implement evaluation systems based on state framework in partnership with educators and their associations (National Education Association).

Districts align professional learning with standards, curriculum and assessments (National Education Association).

Districts use evaluations aligned with induction (National Education Association).

Districts use performance evaluations employing multiple measures (National Education Association).

Districts provide “peer assistance” or “peer assistance and review” (PAR) teams (National Education Association).

Districts have professional learning plans, including induction and mentoring, for teachers, education support professionals (ESPs) and specialized instructional support personnel (SISP) (National Education Association).

Districts provide educators with targeted support based on formative and summative evaluation results (National Education Association).

Districts provide extra resources and assistance for those educators in hard-to-staff schools (National Education Association).

Districts provide funding for educators to access professional learning that addresses new education research and technology that will help improve instruction or support for students (National Education Association).

Districts provide ongoing professional learning and support to administrators, including training in equity and racial and social justice to better support Indigenous educators and students as well as educators and students of color (National Education Association).

Districts provide teacher leadership development (National Education Association).

Districts support regular, job-embedded professional learning opportunities (National Education Association).

Districts use a variety of student, educator and systems data to plan, assess and evaluate professional learning (National Education Association).

Providing training and classroom materials (Results for America).

State develops a comprehensive culturally-responsive teaching policy, covering equity and racial and social justice, to increase educators’ cultural and linguistic competence through pre-service education, licensure and ongoing professional learning (National Education Association).

State provides funding and technical assistance to strengthen professional learning in areas with high concentrations of poverty, Indigenous students and students of color, with emphasis on mentoring, implicit bias and cultural competency (National Education Association).

State provides funding for job-embedded professional learning opportunities to help educators improve their instructional repertoire (National Education Association).

State policy mandates multiprofessional collaboration on educator support and evaluation systems staffed by active pre-K through 12 educators (National Education Association).

State policy requires that evaluations be based on multiple measures of performance to determine effectiveness. Measures may include classroom observations, portfolios, leadership roles and professional learning (National Education Association).State provides funding for “peer assistance” and “peer assistance and review” (PAR) teams (National Education Association).

Percentage of teachers surveyed indicating satisfaction with the conditions of employment (National Education Association).

Percentage of teachers surveyed indicating satisfaction with the terms of employment (National Education Association).

Districts have differentiated pay structures for clearly defined roles and responsibilities that account for hybrid/varied educator roles within a school (National Education Association).

Districts offer financial incentives for educators working in hard-to-staff schools (National Education Association).

Districts offer incentives for teachers to take on differentiated or hybrid roles (National Education Association).

Districts offer teachers starting salaries comparable to other professionals with similar skills, knowledge and education. Additionally, education support professionals (ESPs) are paid at least a minimum wage (National Education Association).

State and/or district contributions for health coverage increase at least enough to keep up with health care inflation (National Education Association).

State or district provides access to affordable, quality health insurance for education employees and their families (National Education Association).

Percentage of educators surveyed indicating satisfaction with the number of opportunities to participate in district policy setting (National Education Association).

Percentage of educators surveyed indicating satisfaction with the number of opportunities to participate in school policy setting (National Education Association).

• Districts obtain educator input on instructional minutes (National Education Association).

Districts provide formal opportunities for educators to participate in district policy setting (e.g., accountability systems, hiring and evaluation of administrators) (National Education Association).

Districts dedicate funding to support educator engagement with educator leadership organizations and learning networks (National Education Association).

Districts dedicate resources to design professional learning that supports educator leadership and teacher agency (National Education Association).

Districts dedicate resources toward lifting and amplifying educator voice (e.g., dedicate funds to engagement) (National Education Association).

State has an autonomous standards board, the majority of whom are active pre-K through grade 12 educators and are ethnically and racially representative of the student body (National Education Association).

State requires that all planning and decision-making bodies related to the educator profession include active pre-K through grade 12 educators (National Education Association).

Teacher preparation programs give aspiring teachers opportunities to practice providing instruction, in a simulated or real classroom setting, or opportunities to practice giving an assessment.  In teacher preparation, practice takes many forms, such as one-on-one tutoring with a student, administering a mock assessment to fellow teacher candidates, or conducting a lesson during a field experience (NCTQ Teacher Prep Review).

Teacher preparation programs give aspiring teachers preparation to teach a range of students with diverse needs in learning to read. This includes English language learners (students in the process of acquiring English and who have a first language other than English), struggling readers (students who experience academic difficulties in the area of reading, including students with dyslexia), and students who speak language varieties other than mainstream English (such as speakers of African American English (AAE)) (NCTQ Teacher Prep Review).

State leaders visit classrooms, talk to teachers and staff, and collect qualitative data to help inform approval decisions for teacher preparation programs (NCTQ Teacher Prep Review).

Teacher preparation programs dedicate at least 105 instructional hours to preparing elementary teacher candidates in Elementary Mathematics content knowledge (i.e. Numbers & Operations, Algebraic Thinking, Geometry & Measurement, Data Analysis & Probability) and 45 instructional hours to preparing candidates in Mathematics Pedagogy. Content knowledge references the foundational understanding of mathematics. Programs can instill this knowledge in candidates through coursework that focuses on a conceptual understanding of the mathematics topics that are addressed in the elementary grades. Pedagogical knowledge references the methods of effective instruction that use content knowledge in the classroom. Together, they ensure that teachers know what they need to teach and also know how to teach it. (NCTQ, Preparation for Teaching Elementary Mathematics).

Teacher preparation programs dedicate at least 45 instructional hours (i.e. one full 3-credit course) to preparing elementary teacher candidates in Numbers & Operations content. (NCTQ, Preparation for Teaching Elementary Mathematics).

Teacher preparation programs dedicate at least 20 instructional hours (i.e. just under half of a 3-credit course) to preparing elementary teacher candidates in Algebraic Thinking content. (NCTQ, Preparation for Teaching Elementary Mathematics).

Teacher preparation programs dedicate at least 25 instructional hours (i.e. just over half of a 3-credit course) to preparing elementary teacher candidates in Geometry & Measurement content. (NCTQ, Preparation for Teaching Elementary Mathematics).

Teacher preparation programs dedicate at least 15 instructional hours (i.e. one-third of a 3-credit course) to preparing elementary teacher candidates in Data Analysis & Probability content. (NCTQ, Preparation for Teaching Elementary Mathematics).

Teacher preparation programs dedicate at least 45 instructional hours (i.e. one full 3-credit course) to preparing elementary teacher candidates in Mathematics Pedagogy. (NCTQ, Preparation for Teaching Elementary Mathematics).

Lacking a system of strong diagnostic testing at the point of admissions, teacher preparation programs will need to provide most teacher candidates three content courses and one course in pedagogy. Specifically, elementary teachers need a strong conceptual understanding of four content topics (Numbers and Operations; Algebraic Thinking; Geometry and Measurement; and Data Analysis and Probability), in addition to Math Pedagogy. This knowledge is specialized, so should be aimed only at a teacher audience, not the broader campus population. (NCTQ, Preparation for Teaching Elementary Mathematics).

In the case of graduate programs, teacher preparation programs must make more extensive use of content knowledge tests during admissions, even if only for the purpose of diagnosing where candidates are going to need additional support and coursework rather than rejecting applicants. Regardless, graduate programs also need to add more time to the requisite coursework dedicated to mathematics. (NCTQ, Preparation for Teaching Elementary Mathematics).

Teacher preparation programs build partnerships with nearby districts to create specific feedback loops related to elementary mathematics instruction, reviewing course materials and content expectations for teacher candidates to determine if the program is meeting districts’ needs. Consider the use of focus groups or surveys to understand specifically which key topic areas recent teacher candidates felt well-prepared to teach and which they did not. (NCTQ, Preparation for Teaching Elementary Mathematics).

Teacher preparation programs ensure student teaching placements occur with mentor teachers who have demonstrated knowledge of math content. A large amount of recent research has demonstrated that student teachers who are paired with a more effective cooperating teacher are more effective in their first year of teaching. Programs should also consider how well-versed their program supervisors are in math content.  (NCTQ, Preparation for Teaching Elementary Mathematics).

State policymakers make current standards for elementary mathematics preparation more explicit and assess programs on their alignment to the standards during the program approval process. Currently [as of May 2022], 11 states provide detailed math standards for elementary teacher preparation programs. Arkansas, Massachusetts, and New Mexico stand out for their development of competencies for elementary teachers as a component of teacher preparation program requirements. Another 16 states adopted CAEP standards or require CAEP accreditation that also includes detailed math standards. Further, state education agencies should use these standards for elementary mathematics preparation in their review of programs. (NCTQ, Preparation for Teaching Elementary Mathematics).

State policymakers examine the state licensure tests for elementary licensure candidates to ensure alignment between what is required of elementary teachers and expectations for students. Ensure that the licensure tests require candidates to demonstrate knowledge of the essential math topics found in the standard. (NCTQ, Preparation for Teaching Elementary Mathematics).

State policymakers hold teacher preparation programs accountable for fully preparing any candidate they have admitted by scrutinizing program pass rates on state licensing tests, particularly the first-time pass rates. Only 21 states currently [as of May 2022] use pass rate data in their program approval systems, with none examining the first-time pass rates, the best indicator of program commitment to preparing all of their teacher candidates to meet state standards. To learn more about this issue and how many programs achieve high first-time pass rates regardless of the populations they serve, policymakers can review their state-specific dashboards here. (NCTQ, Preparation for Teaching Elementary Mathematics).

If shortages are a concern, state policymakers could consider creating a certification pathway in mathematics that would qualify a teacher to teach only the early elementary grades (K-2) when much less math knowledge is needed and therefore less preparation coursework would be required. (NCTQ, Preparation for Teaching Elementary Mathematics).

Percentage of children with identified concerns who are connected to services (Education-to-Workforce Framework).

Percentage of educators surveyed indicating feelings of confidence in analyzing and interpreting formative and summative assessment data (National Education Association).

Percentage of educators surveyed indicating satisfaction with the time allotted to analyze assessment results and inform instruction (National Education Association).

Percentage of teachers indicating satisfaction with the sources used to measure student growth (National Education Association).

Percentage of teachers surveyed indicating assessments adhere to the principles of Universal Design for Learning (UDL) (National Education Association).

Percentage of teachers surveyed indicating satisfaction with the quality of student assessments (National Education Association).

Districts provide resources and funding for job-embedded professional learning for teachers to become proficient users of formative and summative assessment data (National Education Association).

Districts release assessment results in time to inform learning (National Education Association).

Districts train school personnel to interpret data system results to inform and improve instruction and identify needed supports (National Education Association).

Districts use both formative and summative student assessments that adhere to the principles of UDL (National Education Association).

Screen all students (i.e. Tier 1) to identify those at risk for potential mathematics difficulties and provide interventions to students identified as at risk. As a district or school sets up a screening system, have a team evaluate potential screening measures. The team should select measures that are efficient and reasonably reliable and that demonstrate predictive validity. Screening should occur in the beginning and middle of the year. Select screening measures based on the content they cover, with an emphasis on critical instructional objectives for each grade. In grades 4 through 8, use screening data in combination with state testing results. Use the same screening tool across a district to enable analyzing results across schools. (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Response to Intervention).

Instructional materials for students receiving interventions (i.e. Tier 2 and 3) should focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5 and on rational numbers in grades 4 through 8. These materials should be selected by committee. For students in kindergarten through grade 5, tier 2 and tier 3 interventions should focus almost exclusively on properties of whole numbers and operations. Some older students struggling with whole numbers and operations would also benefit from in-depth coverage of these topics. For tier 2 and tier 3 students in grades 4 through 8, interventions should focus on in-depth coverage of rational numbers as well as advanced topics in whole number arithmetic (such as long division). Districts should appoint committees, including experts in mathematics instruction and mathematicians with knowledge of elementary and middle school mathematics curricula, to ensure that specific criteria are covered in-depth in the curriculum they adopt. (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Response to Intervention). 

Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review. Ensure that instructional materials are systematic and explicit. In particular, they should include numerous clear models of easy and difficult problems, with accompanying teacher think-alouds. Provide students with opportunities to solve problems in a group and communicate problem-solving strategies. Ensure that instructional materials include cumulative review in each session. (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Response to Intervention).

Interventions should include instruction on solving word problems that is based on common underlying structures. Teach students about the structure of various problem types, how to categorize problems based on structure, and how to determine appropriate solutions for each problem type. Teach students to recognize the common underlying structure between familiar and unfamiliar problems and to transfer known solution methods from familiar to unfamiliar problems. (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Response to Intervention).

Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas. Use visual representations such as number lines, arrays, and strip diagrams. If visuals are not sufficient for developing accurate abstract thought and answers, use concrete manipulatives first. Although this can also be done with students in upper elementary and middle school grades, use of manipulatives with older students should be expeditious because the goal is to move toward understanding of—and facility with—visual representations, and finally, to the abstract. (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Response to Intervention).

Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts. Provide about 10 minutes per session of instruction to build quick retrieval of basic arithmetic facts. Consider using technology, flash cards, and other materials for extensive practice to facilitate automatic retrieval. For students in kindergarten through grade 2, explicitly teach strategies for efficient counting to improve the retrieval of mathematics facts. Teach students in grades 2 through 8 how to use their knowledge of properties, such as commutative, associative, and distributive law, to derive facts in their heads. (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Response to Intervention).

Monitor the progress of students receiving supplemental instruction and other students who are at risk. Monitor the progress of tier 2, tier 3, and borderline tier 1 students at least once a month using grade-appropriate general outcome measures. Use curriculum-embedded assessments in interventions to determine whether students are learning from the intervention. These measures can be used as often as every day or as infrequently as once every other week. Use progress monitoring data to regroup students when necessary. (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Response to Intervention).

Include motivational strategies in tier 2 and tier 3 interventions. Reinforce or praise students for their effort and for attending to and being engaged in the lesson. Consider rewarding student accomplishments. Allow students to chart their progress and to set goals for improvement. (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Response to Intervention).

State accountability system holds schools accountable for multiple measures of school quality and student success (multiple measures may include chronic absenteeism, school climate and access to advanced and rigorous courses) (National Education Association).

State develops a policy that requires the use of both formative and summative student assessments that adhere to the principles of UDL (National Education Association).

State has a comprehensive, aligned and integrated information management system that enables districts and schools to analyze, evaluate and continuously improve student, educator and school performance (National Education Association).

School and district accountability systems advance continuous improvement and a comprehensive vision of student success (Urban Institute).

Research does not support blanket recommendations for instruction to be exclusively “student-centered” or “teacher-directed.” Effective math education incorporates multiple instructional approaches to meet the needs of students. There is a common misconception that special needs students benefit only from explicit instruction. However, this is not true; all students, including those with special needs, benefit from a balanced approach that includes both explicit and conceptual instruction. (CCSSO, A Nation of Problem-Solvers).

Provide systematic instruction during intervention to develop student understanding of mathematical ideas. Effective interventions for improving mathematics achievement for students struggling with mathematics share one key feature: the design of the curricular materials and the instruction provided are systematic. The term systematic indicates that instructional elements intentionally build students’ knowledge over time toward an identified learning outcome(s). Systematic intervention materials are designed to cover topics in an incremental and intentional way. Systematic interventions most often include a “bundle” of practices used to build and support student learning strategically (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades).

Teach clear and concise mathematical language and support students’ use of the language to help students effectively communicate their understanding of mathematical concepts. Mathematical language is academic language that precisely conveys mathematical ideas, including the vocabulary, terminology, and language structures used when thinking about, talking about, and writing about mathematics. Understanding mathematical language is critical to students’ learning because it is used in textbooks, curricular and assessment materials, and teachers’ instruction (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades).

Use a well-chosen set of concrete and semi-concrete representations to support students’ learning of mathematical concepts and procedures. Students who struggle to learn mathematics need additional, focused instruction using representations to model mathematical ideas. Choose representations carefully and connect them explicitly to the abstract representations (mathematical notation). It is also important to provide students with many opportunities to use representations (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades).

Use the number line to facilitate the learning of mathematical concepts and procedures, build understanding of grade-level material, and prepare students for advanced mathematics. The ability to represent different sets of numbers makes the number line a powerful tool for helping students develop a unified understanding of numbers and for supporting their learning of advanced mathematics. Number lines are an important tool for teaching and understanding magnitude and operations for both whole numbers and fractions, graphing coordinates, and displaying and analyzing data (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades).

Provide deliberate instruction on word problems to deepen students’ mathematical understanding and support their capacity to apply mathematical ideas. Learning to solve word problems is an important part of the elementary mathematics curriculum because word problems help students apply the mathematics they are learning, develop critical thinking skills, and begin to connect mathematics to a variety of scenarios or contexts. Becoming successful at solving word problems can deepen students’ understanding of grade-level content and set students up for success in advanced mathematics courses and the workforce (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades).

Regularly include timed activities as one way to build students’ fluency in mathematics. Quickly retrieving basic arithmetic facts is not easy for students who struggle with mathematics. Automatic retrieval gives students more mental energy to understand relatively complex mathematical tasks and execute multistep mathematical procedures. Thus, building automatic fact retrieval in students is one (of many) important goals of intervention. In addition to basic facts, timed activities may address other mathematical subtasks important for solving complex problems. This could include, for example, recalling equivalencies for fraction benchmarks of 1/2 and 1, or quickly evaluating and estimating place value. The goal of these activities is to move students toward accurate and efficient performance of these smaller mathematical tasks so that this knowledge can be easily accessed when necessary for solving problems (What Works Clearinghouse, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades).

State policy should keep a strong focus on progress monitoring through valid and reliable assessments. (Shanker Institute)

Provide guidance and support to districts to align supplemental and intervention learning experiences to core instruction. Student learning accelerates the most when students receive targeted support that reinforces and extends what they are learning in their classroom each day. At some point in their school experience, all students will benefit from additional practice and support in mastering grade-level math concepts. Supplemental and intervention supports — whether through tutoring, summer school, after-school or MTSS/RTI models — should reinforce and extend classroom learning using evidence-based materials aligned with the concepts being taught in core instruction. The ultimate goal of these supports is to ensure students are ready to master future grade-level content, not to remediate all prior unfinished learning. (CCSSO, A Nation of Problem-Solvers).

States can help districts evaluate alignment between supplemental and core curricula by comparing representations and strategies used in the most critical content focus areas. When compared side by side, these curricular resources should be largely similar to create a clear, coherent approach for teachers, students and families. (CCSSO, A Nation of Problem-Solvers).

States can enhance their MTSS and RTI frameworks by shifting from traditional remediation-focused approaches to more effective strategies that emphasize conceptual understanding alongside procedural fluency. By integrating just-in-time supports — often seen in quality tutoring settings — states can accelerate student learning by strategically integrating prior concepts to support mastery of grade-level work in core instruction. (CCSSO, A Nation of Problem-Solvers). 

Learning acceleration approaches, or “just-in-time teaching,” have shown to be more effective than traditional approaches to intervention. In recent years, particularly since the start of the pandemic, there has been a movement to integrate tutoring and other just-in-time instruction for students into states’ traditional intervention structures. States including Arkansas, Colorado, Delaware, Louisiana, Massachusetts, New Jersey and Ohio have invested in initiatives focused on these supports. (CCSSO, A Nation of Problem-Solvers).

State leaders can create or revise state guidance on MTSS and RTI frameworks to ensure these structures are flexible enough to allow for just-in-time instruction for students rather than solely identifying or remediating all of a student’s unfinished learning. (CCSSO, A Nation of Problem-Solvers).

State leaders can provide resources for districts to review materials used in supplemental instruction to ensure alignment with the concepts and strategies taught in core instruction. (CCSSO, A Nation of Problem-Solvers).

State leaders can provide grants for tutoring programs that meet evidence-based standards to accelerate learning. (CCSSO, A Nation of Problem-Solvers).

State leaders can provide training and guidance to district leaders and professional learning providers on incorporating planning for just-in-time instruction during collaborative planning time. (CCSSO, A Nation of Problem-Solvers).

State leaders can create vertical progression documents for the field based on state standards to support just-in-time instruction. (CCSSO, A Nation of Problem-Solvers).

State leaders can train all educators, including paraprofessionals and special educators, in the core curriculum to support supplemental instruction. (CCSSO, A Nation of Problem-Solvers).

State leaders can construct state guidance on school schedules and routines, allowing weekly collaboration between supplemental educators and classroom teachers. (CCSSO, A Nation of Problem-Solvers).

Tennessee districts have been incentivized to provide high-dosage, low-ratio tutoring for eligible students through the state’s TN All Corps tutoring program. Districts chose to participate through a grant-matching program for content focused on reading and math, wherein the district must provide $800 per tutored student per year while the state contributes $700 per student. TN All Corps required districts to serve students in grades 1-5, and they may choose to serve students in grades 6-8, with maximum tutor-to-student ratios of 1:3 and 1:4, respectively. Students receive two to three 30- to 45-minute sessions per week, and data collection and reporting requirements are consistent with what is required in ESSER. (CCSSO, A Nation of Problem-Solvers).

In math, Tennessee partnered with a virtual provider — which aligned tutoring content to the core curricula the state has adopted — to provide high-quality curricular resources that were used flexibly in tutoring sessions to support just-in-time access to grade-level content. Tennessee students are progressing toward pre-pandemic proficiency levels on state test results in math. (CCSSO, A Nation of Problem-Solvers).

Louisiana’s Accelerate Math program is designed to support tutoring implementation to improve student achievement. Accelerate provides guidance and funding for high-impact tutoring and summer learning programs aligned with high-quality curriculum. The acceleration cycle is used as a structure of continuous planning and response to student needs. It includes diagnosing students’ unfinished learning of prerequisite content knowledge and skills, planning for timing and content for acceleration, delivering just-in-time, curriculum-aligned acceleration support through qualified tutors and monitoring progress to adjust supports based on student data. (CCSSO, A Nation of Problem-Solvers).

Tutors delivering instruction in Louisiana’s Accelerate Math program meet with students one-on-one or in small groups with others with common needs. Model materials include mini lessons and activities that scaffold the most immediate needs directly connected to the grade-level content students are learning in class. The resources for each grade level include diagnostic assessments, correlation to in-class lessons, Google slide presentations for each tutoring session and exit tickets for each set of tutoring sessions. Each session consists of one hour of virtual instruction twice a week, with additional practice included. (CCSSO, A Nation of Problem-Solvers).

The provided materials are designed to be adjusted as needed. As a part of Accelerate, Louisiana partnered with Zearn through Louisiana’s Math Refresh. This program is used flexibly to complement core math instruction and intervention, tutoring and summer programs. A two-year study comparing students who used Zearn consistently with those who didn’t showed increased math scale scores, with the most substantial gains observed in students who completed three or more grade-level lessons per week. Louisiana provided free school accounts to all K-8 public schools in the state. Initially, districts could use local funds at the district level from their state-level General Fund, Title I, COVID relief funds, Consolidated Appropriations Act and Direct Student Services allocations to pay for tutoring. However, tutoring is now supported through legislation. (CCSSO, A Nation of Problem-Solvers).

In addition, districts received a Strong Start Tutoring allocation on Feb. 1, 2021, to support the launch of Accelerate. Louisiana students are showing progress toward pre-pandemic proficiency on the state math assessment. (CCSSO, A Nation of Problem-Solvers).

Recent research shows that “just-in-time” support that accelerates student learning by strategically integrating prior concepts to support mastery of grade-level work is more effective than traditional remediation. This type of learning acceleration is most frequently seen in tutoring but can prove valuable in other supplemental learning experiences, such as intervention provided through traditional multi-tiered system of supports (MTSS) or response to intervention (RTI) frameworks. (CCSSO, A Nation of Problem-Solvers).