Based on more than 35 years of focusing exclusively on the teaching and learning of math, Math Solutions has identified four key areas of instructional focus to reach math achievement goals: learning environment, reasoning and sensemaking, focus and coherence, and formative assessment. Math Solutions will guide you to recognize what a model classroom that encompasses these key areas looks like with examples for both teachers and students, as shown below:
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Learning Environment 


Teacher Best Practice 
Student Learning Practice 
Provides a respectful, safe learning environment in which mistakes are seen as an opportunity to learn.  Take an academic risk and rely on their own thinking and the thinking of other students. 
Structures the class for independent work, pairs, groups, and whole class in a thoughtful and deliberate way.  Listen and ask questions to each other to clarify information; respectfully challenge ideas; make conjectures. 
Asks questions that both build and reveal new understanding of content and practice. Avoids yes/no questions unless they also ask for justification.  Explain their reasoning; construct viable arguments and critique the reasoning of others. 
Makes appropriate tools available and encourages their use.  Communicate using appropriate mathematical language both orally and in writing. 
Work well in a variety of grouping structures.  
Reasoning & SenseMaking 

Teacher Best Practice 
Student Learning Practice 
Selects rigorous learning experiences.  Persevere in making sense of rigorous problems. 
Makes learning experiences accessible to all students without compromising the rigor in the problem.  Seek out multiple approaches to solving a problem. 
Expects students to justify their reasoning for all answers, whether correct or incorrect.  Use multiple representations when solving problems such as symbols, diagrams, graphs, words, etc. 
Selects learning experiences that represent a balance of conceptual understanding and procedural fluency.  Understand math concepts and use procedures appropriately. 
Use appropriate tools strategically, including mental calculations, that fit the situation.  
Look closely to discern a pattern or structure.  
Focus & Coherence 

Teacher Best Practice 
Student Learning Practice 
Understands the expectation of the standard to be taught and its connection to previous standards; aligns the lesson to grade level content and practice standards.  Connect their current learning to previously learned standards. 
Differentiates instruction based on student needs.  Use math to contextualize and/or decontextualize problems. 
Selects problems that provide opportunities for students to contextualize and/or decontextualize.  Apply the math they know to solve realworld problems. 
Selects problems that provide opportunities for students to apply math to realworld situations.  
Formative Assessment 

Teacher Best Practice 
Student Learning Practice 
Uses data to make instructional decisions based on student need.  Take responsibility for their learning by monitoring their progress toward a learning target. 
Provides feedback to students or structures opportunities for students to provide feedback to each other.  Evaluate the reasonableness of their results using feedback from the teacher or a peer. 
Identifies and communicates the learning target(s) of the lesson.  Articulate what they are learning and why. 
Implements a variety of strategies to monitor student learning. 
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