For students to become genuinely proficient in mathematics, they must build a skillset beyond the ability to solve equations or memorize formulas. They must develop a holistic understanding that combines knowledge, skills and mindset—what we call mathematical proficiency.
This includes solving real-world problems, applying procedures and building confidence in their ability to reason mathematically. ExcelinEd’s FAQ on Math Knowledge and Skills highlights the way in which thoughtfully developed instructional materials can nurture all dimensions of mathematical learning. This ensures that students gain both the understanding and the capability to use mathematics effectively.
From kindergarten through eighth grade, there should be a set of expectations for knowledge and skills. On the knowledge side, students should be able to—beginning in elementary school—engage in number and operation sense, algebra, geometry, and statistics and data to ultimately build up to knowledge sets including:
On the skills side, students should be able to:
In classrooms across the country, students may practice and learn procedures, but oftentimes they miss opportunities to understand why those procedures work, as well as opportunities to connect that knowledge to the world of math around them.
High-quality instructional materials (HQIM) are essential to improving this aspect of math instruction. HQIMs must be aligned to state standards, grounded in coherent learning progressions and intentionally designed to develop the four strands of mathematical proficiency: real-world problem solving, procedural fluency, conceptual understanding and productive disposition.
Adequate instructional time—requiring at least 60 minutes of daily core math instruction—as well as the use of evidence-based intervention for students who need additional support are vital tools for improving math outcomes. Students identified for intervention should receive an individualized math improvement plan within 30 days, along with regular progress monitoring and targeted support delivered by highly effective math teachers. Families should also receive a personalized “math-at-home” plan with strategies and resources that will reinforce math learning away from school.
By combining HQIMs, sufficient instructional time and strong interventions, states can ensure that every student is given an opportunity to build a solid foundation in mathematical knowledge and skills.
To learn more, please reach out to ExcelinEd’s math policy team to see how your state can effectively support mathematical proficiency for all students. Also, we encourage you to explore Math Matters, ExcelinEd’s new digital tool built to help transform math education in your state.
