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To do this, we collected nearly 30,000 in-the-moment student surveys. Using a technology that prompted students in grades six through 12 to answer a few questions at random times during class, we captured a snapshot of their real-time reactions to school. We also surveyed third through fifth graders during the last five minutes of class, and found that elementary students were just as capable as their older schoolmates of providing rich and telling insight into their lives at school.

Across our five partner school systems, we also observed nearly a thousand full-length lessons at all grade levels from K-12, and reviewed almost 5,000 assignments and more than 20,000 individual student work samples. We visited each participating school daily for a week straight at three points in the year, which gave us the chance to see the same teachers and students at the beginning, middle, and end of their time together (and offered a much more comprehensive lens on the learning environment than a single day's lesson could have). These classrooms were not substantially different than the others in their districts, and they represented a wide range: those with new teachers and veterans; those at all age levels; a diverse range of subjects; mixed-ability classes and tracked ones. Four of these school systems were located in states that use standards aligned to the Common Core State Standards; one was not.

To assess the quality of content students worked on, we looked at four elements of every assignment: (1) whether the content in the assignments was aligned to relevant grade-level academic standards; (2) whether the assignments gave students the chance to engage in important content-specific practices, like citing evidence from rigorous texts in literacy, or discussing mathematical ideas using precise mathematical language; (3) whether the assignments gave students a chance to learn relevant content that built their knowledge of the world or helped them see how what they were learning could be applied in the real world; and (4) student performance on both the assignments themselves and against the bar for their grade-level standards.

To study instruction, we observed full-length class periods and assessed (1) whether students were doing what they were asked; (2) whether they were being asked to work on grade-level content; and (3) whether teachers were using instructional practices that gave students the chance to do most of the thinking in the lesson.

We surveyed teachers to capture their knowledge of grade-level standards, their opinions on those standards, and their beliefs about their classroom practices and their students' abilities. We conducted focus groups with nearly 100 teachers and interviewed 24 school leaders at multiple times throughout the year. And we assessed a large set of extant data provided to us by our partner districts on course access, enrollment policies, and district policies on curriculum adoption, among others.

We hypothesized that students' experiences of school were influenced by a confluence of factors-among them, the quality of the work they were doing, the instruction they received, and the expectations of their teachers-and that those factors would interact to have an impact on their academic growth. Taken together with students' in-the-moment survey responses, we were able to triangulate students' perspectives with the classes they were in, the work they were doing and instruction they were receiving, and their academic outcomes.

In addition to amassing this rich data set, we also sat down with a smaller subset of students (more than 50 over two school years), and got to know them. We observed them in class and spoke to them about their experiences, their likes and dislikes, their families, their goals. Just a few of those students are profiled here. While their names and identifying characteristics have been changed throughout this report, their stories help us understand what the data means in the real lives of individual young people.

They also help us understand what real, tangible changes school systems can make-starting tomorrow and over the long haul-to provide more students with school experiences that are meaningful, that honor their aspirations for themselves and their families, and that give them a fighting chance to meet those goals.
For our complete methodology, including further explanation of our analytical approaches and full analysis results, see the Technical Appendix.

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What can 4,000 students teach us about school? Read The Opportunity Myth.

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Discourse with the Desmos Polygraph Tool | BetterLesson Coaching

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Visualizing Math Concepts with the Desmos Graphing Calculator | BetterLesson Coaching

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Try-Measure-Learn (TML): The Heart of Continuous Improvement

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Change teaching and learning one step at a time using the BetterLesson coaching model

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Fostering Mathematical Discourse in Your School

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Fostering Mathematical Discourse in Your School

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Fostering Mathematical Discourse in Your School | BetterLesson Coaching

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The widespread adoption of college- and career-readiness standards, including the Common Core State Standards for Mathematics, presents a historic opportunity to improve mathematics education.

What will it take to turn this opportunity into reality in every classroom, school, and district?

NCTM continues its tradition of mathematics education leadership by defining and describing the principles and actions that are essential to strengthen mathematics learning and teaching for all students.

Principles to Actions: Ensuring Mathematical Success for All offers guidance to teachers, specialists, coaches, administrators, policymakers, and parents:

Builds on the Principles articulated in Principles and Standards for School Mathematics to present six updated Guiding Principles for School Mathematics

Supports the first Guiding Principle, Teaching and Learning, with eight essential, research-based Mathematics Teaching Practices

Details the five remaining Principles-the Essential Elements that support Teaching and Learning as embodied in the Mathematics Teaching Practices

Identifies obstacles and unproductive and productive beliefs that all stakeholders must recognize, as well as the teacher and student actions that characterize effective teaching and learning aligned with the Mathematics Teaching Practices

With Principles to Actions, NCTM takes the next step in shaping the development of high-quality standards throughout the United States, Canada, and worldwide.
Please note: These products can only be purchased via NCTM's Online catalog. Non-web payment methods, such as POs, cannot be used to purchase these items. If you have any questions please call NCTM's Customer Service Department at 800-235-7566.

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Principles to Actions (Download) - National Council of Teachers of Mathematics

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Teaching Perseverance in Math | BetterLesson Coaching

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Building Thinking Classrooms?

Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into a set of 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.

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Building Thinking Classrooms | Teaching Practices for Enhancing Learning Mathematics

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Building Thinking Classrooms in Mathematics helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur.

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Collegial Observation | BetterLesson Coaching

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Accountable and Academic Student Talk Stems | BetterLesson Coaching

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Based on 100+ peer-reviewed research papers

Born out of the Stanford AI lab and in collaboration with leading research institutions, Snorkel AI has published over 100 peer-reviewed research papers on data development and LLMs, with special recognition at events such as NeurIPS, ICML, and ICLR.

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Snorkel AI | Data-centric AI for the enterprise

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The first data-centric artificial intelligence (AI) platform powered by state-of-the-art techniques in programmatic data labeling and weak supervision. Turning data into accurate and adaptive AI applications--fast.