MTSS in mathematics
Essential to an effective MTSS framework is the implementation of high-quality evidence-based instruction. The National Council of Teachers of mathematics (NCTM) describes eight key practices that are indicative of strong instructional practice (NCTM, 2014) and discussed in the executive summary.
- Establish mathematical goals to focus learning
- Implement tasks that promose reasoning and problem solving
- Support productive struggle in learning mathematics
- Facilitate meaningful mathematical discourse
- Pose purposeful questions
- Elicit and use evidence of student thinking
- Use and connect mathematical representations
- Build procedural fluency from conceptual understandings
In particular, those practices that have been shown to have the greatest impact on student learning include choosing mathematical tasks that promote reasoning, engaging in purposeful discussion, and building procedural fluency from conceptual understanding. In the links below, you can find more detailed information about each of these practices.
Tier 1 - Quality Core Classroom Instruction
- Choosing mathematical tasks that promote reasoning
- Engaging in purposeful discussion
- Building procedural fluency from conceptual understanding
Students have informal methods for understanding mathematics presented in context. It is from these informal methods that students can build toward procedural fluency as they make use of their own method and try out the methods of others. Teachers support this development by encouraging students to make use of methods or strategies that are being used by others in the class.
Tier 2 - Intervention and Monitoring Progress
Formative assessment in the classroom provides teachers with valuable information to inform instruction. Research recommends that the assessment information and response be aligned to a learning progression (Heritage, 2008 ). In this way, monitoring progress means identifying, at different points in time, where a student's understanding is in respect to the progression.
In mathematics (especially elementary mathematics), many learning progressions have been described and are available in a number of formats. At RESA, we are developing and training teachers to make use of these frameworks, developed through the compilation of a number of bodies of research. We will begin with addition and subtraction in the Fall of 2016 and add other concept areas with time. Watch here for updates. Additionally, some frameworks are available in the right margins of this webpage.
Tier 3 - Intervention and Monitoring Progress
Tier 3 interventions are provided to students who have been a part of tier 2 interventions and show a need for a more targeted approach. This can be done by the classroom teacher, but is often done by an interventionist. Because different educators may be working with the child, it is important that the supports and learning needs are clearly identified and instructional methods are coherent, for the sake of the student's learning needs.
Tier 3 is often informed by the use of a diagnostic assessment. A few examples are suggested to the right, but other methods of monitoring progress exist. Teachers should keep in mind that the tools should be aligned to a progression of learning and have coherence with Tier 1 instruction.
Resources Specific to Mathematical Concepts
Addition and Subtraction
Multiplication and Division
- Multiplication and Division Problem Types
- Multiplication Division Progression_KRESA
- OGAP Multiplication Framework
Book Resources- Instruction and Intervention
- Children's Mathematics - Addition, Subtraction, Multiplication, Division
Teaching Number in the Classroom (4-8 years) - Interventions for Addition, Subtraction, Early Multiplication
Developing Number Knowledge (7-11 years) - Interventions for Addition, Subtraction, Place Value, and Multiplication
- Extending Children's Mathematics - Fractions, Decimals
- Beyond Pizzas and Pies - 10 Strategies for Supporting Fraction Sense
- Beyond Invert and Multiply - Making Sense of Fraction Computation
- Marilyn Burns Reasoning Inventory
- Math Recovery (AVMR - available through training)
Learning Progression Resources
- The Numeracy Continuum
- OGAP Multiplication Framework
- OGAP Fraction Framework
- OGAP Proportionality Framework
- Standards Trajectories Mathematics (Zip File)
Recommended Book Resources for MTSS in Mathematics
- Solving for Why
- Teaching Number in the Classroom (4-8 years)
- Developing Number Knowledge (7-11 years)
- Children's Mathematics (K-4)
Institute for Education Sciences - Practice Guides in Mathematics
- Assisting Students Struggling with Mathematics
- Teaching Young Children Mathematics
- Improving Problem Solving (4-8)
- Effective Fraction Instruction
- Strategies to Improve Algebra Knowledge