Mathematics includes a set of knowledge and skills used to access science, technology, engineering, and mathematics (STEM) applications and careers as well as a tool for improving reasoning and analytic thinking. Effective math instructional strategies include using manipulatives to introduce mathematics concepts and applying systematic strategies for solving word problems.
Overview of Math Principles and Practices
Principle 1: Establish schoolwide practices for enhancing mathematics understanding within relevant content area instruction.
- Practice 1: Encourage students to apply their understanding of mathematics concepts and procedures to draw conclusions and propose solutions about history, science, social studies, economics, and other content areas.
- Practice 2: Ask students to analyze events and phenomena from a quantitative perspective and use their analyses to develop arguments and provide just cations.
Principle 2: Use a universal screener to identify students at risk for mathematics difficulties and to determine interventions to provide these at-risk students. Monitor the development of mathematics knowledge and skills of identified students.
- Practice 1: Identify a system for screening and progress monitoring that prioritizes content and skills necessary for subsequent mathematics development.
- Practice 2: Select a cut score for screening that balances the need to help the most at-risk students with the resources available.
Principle 3: Help students recognize number systems and expand their understanding beyond whole numbers to integers and rational numbers. Use number lines as a central representational tool in teaching this and other rational number concepts.
- Practice 1: Use measurement activities and number lines to help students understand that fractions and decimals are numbers and share number properties.
- Practice 2: Provide opportunities for students to locate and compare fractions and decimals on number lines.
- Practice 3: Use number lines to improve students’ understanding of fraction equivalence, fraction density (the concept that there are an in nite number of fractions between any two fractions), and negative fractions.
- Practice 4: Explain that fractions can be represented as common fractions, decimals, and percentages, and develop students’ ability to translate among these forms.
Principle 4: Develop students’ conceptual understanding of mathematics and provide ample opportunities to improve procedural fluency.
- Practice 1: Use area models, number lines, and other visual representations to improve students’ understanding of formal computational procedures.
- Practice 2: Use meaningful fact practice activities for students lacking a strong foundation in math facts.
- Practice 3: Address common misconceptions regarding computational procedures. Practice 4: Present real-world contexts with plausible numbers for problems.
Principle 5: Provide explicit and systematic instruction during instruction and intervention.
- Practice 1: Include explicit teacher or peer modeling and demonstrate key concepts and skills.
- Practice 2: Include worked examples of key concepts and skills.
- Practice 3: Gradually transition from teacher-modeled problem solving to student- directed problem solving.
- Practice 4: Include opportunities for students to talk aloud about the skills, knowledge, or problem-solving procedures they are learning.
- Practice 5: Provide immediate and corrective feedback with opportunities for students to correct errors.
- Practice 6: Include sufficient, distributed, and cumulative practice and review.
Principle 6: Instruction should include strategies for solving word and algebra problems that are based on common underlying structures.
- Practice 1: Include systematic instruction on the structural connections between known, familiar, and novel word problems.
- Practice 2: Teach common problem types and their structures, as well as how to categorize and select appropriate solution methods for each problem type.
Principle 7: For students who struggle in mathematics, instruction and intervention materials should include opportunities to work with representations of mathematical ideas. Teachers should be proficient in the use of these representations.
- Practice 1: Employ visual representations to model mathematical concepts.
- Practice 2: Explicitly link a visual representation or model with the abstract mathematical symbol or concept.
- Practice 3: Use consistent language across similar representations.
Principle 8: Establish a schoolwide plan to identify and improve teachers’ mathematical and pedagogical content knowledge.
- Practice 1: Assess teachers’ needs in relation to mathematics content knowledge and mathematics pedagogical content knowledge across content areas.
- Practice 2: Select and implement high-quality professional development that acknowledges different teachers’ needs.
- Practice 3: Improve teachers’ knowledge and understanding of making practice decisions based on research evidence and student data.
Principle 9: Discontinue using practices that are NOT associated with improved outcomes for students and teachers.
- Practice 1: Examine the evidentiary bases of practices currently used in teaching mathematics and identify and eliminate practices that are contra- indicated by existing evidence.
- Practice 2: Monitor student learning formally and informally and use trend data to determine whether and how to adjust current practices.