Evidence-Based Mathematics Instruction

High-quality Tier 1 mathematics instruction provides all students with meaningful access to rigorous, grade-level mathematics while developing conceptual understanding, procedural fluency, mathematical reasoning, problem-solving, and application.

Effective mathematics instruction is explicit and responsive while also providing students opportunities to explore ideas, use and connect representations, engage in mathematical discourse, explain their reasoning, and develop increasingly efficient and flexible strategies.

Within an MTSS framework, educators use multiple sources of data to examine both student response and the strength of Tier 1 instruction before determining whether supplemental intervention is needed.

High-quality mathematics instruction is comprehensive and interconnected. Conceptual understanding, procedural fluency, reasoning, problem-solving, mathematical language, representations, and responsive instructional decision-making develop together—not as separate programs or approaches. The emphasis and support students need may change across grade levels and in response to student need, while all students continue to have meaningful access to rigorous, grade-level mathematics.

Components of High-Quality Tier 1 Mathematics Instruction

Select each component below to explore evidence-based practices, Tier 1 examples, MTSS connections, and considerations for responsive mathematics instruction. 

Responsive Mathematics Instruction  
Using evidence of student thinking to identify needs, adjust instruction, and determine when supplemental support may be warranted. 

Strong Mathematics Instruction Develops…

Understanding
What does it mean?

Fluency
How can I do it accurately, efficiently, and flexibly?

Reasoning
Why does it work? How do I know?

Application & Problem-Solving
When and how can I use it?

Communication & Representation
How can I show, explain, and connect my thinking?

These dimensions develop together through coherent, rigorous, responsive mathematics instruction.

New York State Alignment

This framework is designed to support alignment with the New York State Next Generation Mathematics Learning Standards, NYSED Numeracy Initiative and Numeracy Briefs, NYS PreK–12 Mathematics Curriculum Review Guide, and Culturally Responsive-Sustaining Education Framework.

Within Tier 1, all students should have meaningful access to rigorous, grade-level, standards-aligned mathematics instruction that develops conceptual understanding, procedural fluency, application, reasoning, problem-solving, communication, and mathematical agency.

When Does Tier 1 Support Become Tier 2 Intervention?

The location, group size, or instructional strategy alone does not determine the tier.

Small-group mathematics instruction is not automatically Tier 2. Flexible grouping, re-teaching, additional modeling, representations, scaffolded practice, purposeful questioning, and differentiated instruction can all occur within Tier 1 when they are part of the universal instructional system and responsive to student need.

Tier 2 provides supplemental, targeted instruction matched to a specific, identified mathematical need. It is provided in addition to Tier 1 instruction, delivered with defined frequency, duration, and intensity, implemented with fidelity, and progress monitored to determine student response.

Explore Responsive Mathematics Instruction for additional guidance on data-based decision-making and distinguishing responsive Tier 1 instruction from supplemental intervention. 

Questions for School & District Teams

• Do all students have meaningful access to rigorous, grade-level, evidence-based Tier 1 mathematics instruction?

• Do we have a shared understanding of what high-quality mathematics instruction should look and sound like across classrooms and grade levels?

• Does our mathematics system intentionally develop conceptual understanding, procedural fluency, reasoning, problem-solving, application, and communication rather than emphasizing one at the expense of others?

• How do we know whether our Tier 1 mathematics practices and curricular materials are being implemented as intended?

• How do we use multiple sources of evidence to examine the effectiveness of Tier 1 at the student, classroom, grade, and school level?

• When patterns of difficulty emerge across groups of students, do we examine curriculum, instruction, implementation, opportunity to learn, and access—not only individual student deficits?

• Do our Tier 1, Tier 2, and Tier 3 mathematics supports function as one coherent system rather than separate programs or places?

Instruction ≠ Intervention

Evidence-based practices such as explicit instruction, mathematical modeling, concrete and visual representations, mathematical discourse, purposeful questioning, guided practice, fluency practice, scaffolding, and formative assessment can strengthen mathematics learning for all students within Tier 1.

An intervention is more targeted and intentional. It is selected to address a specific, identified mathematical need, provided in addition to Tier 1 instruction, delivered with defined dosage and intensity, implemented with fidelity, and progress monitored to determine student response.

The strategy itself does not determine the tier—the purpose, intensity, delivery, and use of data do.