A strong mathematics program is built on high-quality instructional materials (HQIM) that align with both the Content Standards and the Standards for Mathematical Practice (SMPs).
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Content Standards define what students need to learn at each grade level, ensuring a coherent progression of mathematical understanding.​
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The Standards for Mathematical Practice (SMPs) describe how students engage with mathematical ideas—emphasizing problem-solving, reasoning, modeling, and communication.
HQIM plays a critical role in bridging these elements, providing students with rich tasks, opportunities for discourse, and meaningful connections across concepts. The Coherence Map (Achieve the Core) supports this by helping educators identify how mathematical ideas build over time, ensuring students experience mathematics as a connected and logical progression.
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The Math Pact (Karen S. Karp, Sarah B. Bush, & Barbara J. Dougherty) reinforces the importance of consistent language, notation, and representations across classrooms to prevent student confusion and strengthen coherence.
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Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development (Stein, Smith, Henningsen, & Silver) provides practical strategies for making instructional shifts that center student thinking and align with HQIM.