It has been almost a decade since the publication of the Common Core State Standards for Mathematics (CCSSM), which outlined and operationalized what K–12 students need to understand and be able to do in mathematics, emphasizing the importance of conceptual development of ideas and engagement in practices that promote mathematical proficiency (NGA Center & CCSSO, 2010). A few years later, NCTM’s Principles to Actions (2014), provided guidance on how to make that ambitious vision a reality for all students. How have these key efforts influenced the status of mathematics teaching and learning? What progress have we made toward the goal of providing all students with a highquality mathematics education? And what are our persistent challenges? This article takes up these questions.
Since 1977, the National Survey of Science and Mathematics Education (NSSME) has periodically collected data about the status of science and mathematics education in the U.S., providing opportunities to examine the influences of new initiatives such as the CCSSM and Principles to Actions. In 2018, Horizon Research, Inc. conducted the sixth iteration of the study, titled the 2018 NSSME+ (the plus symbol reflects the inclusion of computer science education in the study for the first time).* The study collected an enormous amount of school and teacher data about various aspects of the mathematics education system. In this article, we highlight some key findings about the nature of K–12 mathematics instruction and consider implications for mathematics teacher educators.
Nature of Mathematics Instruction
Study results indicate some promising uptake of instruction envisioned by the CCSSM and Principles to Actions. For example, in 2018, reformoriented instructional objectives, including learning how to do mathematics (e.g., consider how to approach a problem, explain and justify solutions) and understanding mathematical ideas were heavily emphasized in roughly twothirds of K–12 mathematics classes. Conversely, only onethird or fewer of classes focused heavily on traditional objectives such as students learning testtaking skills/strategies and learning mathematics vocabulary.
In terms of instruction, the most common activity was lecture, occurring in nearly all K–12 mathematics classes at least once a week. However, whole class instruction and small group work were also common weekly occurrences. Practicing for standardized tests and reading from a textbook occurred far less frequently. The study also asked how often teachers engaged students in a number of mathematical practices described in the CCSSM. As can be seen in Table 1, in threequarters or more of classes, students were asked to determine whether their answer makes sense, provide mathematics reasoning, develop representations, and work on challenging problems on a weekly basis. Still, given CCSSM’s emphasis on students critiquing different problemsolving approaches, it is somewhat disappointing that only twothirds or fewer of classes had students analyze the mathematical thinking of others or compare and contrast different solution strategies on a weekly basis.
Table 1
Mathematics Classes in Which Teachers Report Students Engaging in Various Aspects of Mathematical Practices at Least Once a Week, by Grade Range

Percent of Classes 

Mathematical Practice 
Elementary 
Middle 
High 

Determine whether their answer makes sense 
85 
(1.5) 
85 
(1.9) 
84 
(1.2) 
Provide mathematical reasoning to explain, justify, or prove their thinking 
85 
(1.5) 
83 
(1.7) 
76 
(1.3) 
Represent aspects of a problem using mathematical symbols, pictures, diagrams, tables, or objects in order to solve it 
88 
(1.1) 
75 
(2.1) 
75 
(1.5) 
Continue working through a mathematics problem when they reach points of difficulty, challenge, or error 
81 
(1.5) 
81 
(1.8) 
79 
(1.3) 
Identify relevant information and relationships that could be used to solve a mathematics problem 
72 
(1.8) 
79 
(2.0) 
73 
(1.7) 
Pose questions to clarify, challenge, or improve the mathematical reasoning of others 
69 
(2.2) 
69 
(1.8) 
63 
(1.5) 
Determine what tools are appropriate for solving a mathematics problem 
71 
(1.8) 
62 
(2.2) 
59 
(1.7) 
Work on challenging problems that require thinking beyond just applying rules, algorithms, or procedures 
74 
(1.6) 
75 
(1.9) 
71 
(1.3) 
Develop a mathematical model to solve a mathematics problem 
75 
(1.8) 
70 
(2.0) 
64 
(1.8) 
Work on generating a rule or formula 
59 
(1.9) 
70 
(1.9) 
61 
(1.5) 
Analyze the mathematical reasoning of others 
65 
(1.9) 
61 
(2.3) 
53 
(1.3) 
Compare and contrast different solution strategies for a mathematics problem in terms of their strengths and limitations 
60 
(1.9) 
55 
(2.2) 
54 
(1.7) 
Overall, these findings on instruction are encouraging and indicate that mathematics teaching and learning is moving in the right direction. But in addition to the promising findings, the NSSME+ results also highlight persistent problems facing the mathematics education system. The remainder of this article highlights two particular areas of concern: the types of instructional materials being used and inequities in student opportunities to learn mathematics.
Instructional Materials
One of NCTM’s guiding principles calls for a robust curriculum that “develops important mathematical ideas along coherent learning progressions” (NCTM, 2014, p. 5). In 2018, teachers reported using a multitude of sources for their lessons, ranging from commercially published textbooks, to units or lessons they developed themselves, to lessons or resources from free or feebased websites (e.g., Teachers Pay Teachers). Further, in 60 percent or more of K–12 classes that used a commercially published textbook or districtcreated material, teachers supplemented with activities from other resources and modified activities from those materials.
The mixing and matching and picking and choosing of these materials raises serious questions and concerns about both the quality and coherence of the mathematics students’ experience. Moreover, it calls for additional guidance to help teachers more critically evaluate their resources and appropriately integrate them into their lessons to meet the needs of their students.
Inequities in Student Opportunities to Learn
Access and equity is another guiding principle where work clearly remains to be done. Although the NSSME+ was not designed primarily as an equity study, results shed light on a number of disturbing disparities that continue to limit some students’ access and opportunities to learn highlevel mathematics. For example, despite making up about half of all students in 2018, students from race/ethnicity groups historically underrepresented in STEM made up 53 percent of students in noncollege prep mathematics classes, but only 22 percent in college level classes (see Figure 1). In order to prepare all students to be college and career ready when they graduate, serious efforts must be made to change this pattern, including increasing student interest and competence in mathematics.
The nature of instruction that particular groups of student experience is another area where disparities are apparent. For example, classes of mostly lowpriorachieving students were significantly less likely than classes of highpriorachieving students to heavily emphasize understanding of mathematical ideas and how to do mathematics. A similar pattern is seen in terms of engagement in aspects of mathematical practices (e.g., providing mathematical reasoning). In addition, classes in highpoverty schools were more likely than their lowpoverty counterparts to have students practice for standardized tests and focus on literacy skills. Not surprisingly, external testing** also occurred more frequently in classes of highpoverty schools, as well as in classes with mostly lowpriorachieving students and students from race/ethnicity groups historically underrepresented in STEM.
Figure 1. Average Percentage of Historically Underrepresented Students in High School Mathematics Courses
Moving Forward
Results from the 2018 NSSME+ provide an opportunity to examine the status of mathematics education and use the findings to catalyze further change in the education system. There is evidence that mathematics instruction reflects aspects of the ambitious vision laid out in the CCSSM and Principles to Actions. AMTE’s (2017) position on standards for teacher preparation programs provides an important mechanism for making additional progress, particularly for reexamining aspects of teacher preparation and professional development programs. When asked about their feelings of pedagogical preparedness, a relatively small proportion of K–12 mathematics teachers reported feeling well prepared to differentiate instruction to meet the needs of diverse learners or incorporate students’ cultural backgrounds into instruction. Teachers also reported that professional development rarely focused on making instructional culturally relevant.
There clearly is more work to be done to provide a highquality mathematics education for all students. More equity findings from the NSSME+ will be presented at the 2020 annual AMTE conference in February. We hope you will join us to discuss these results and take action toward further progress in mathematics education.
References
 Association of Mathematics Teacher Educators. (2017). Standards for preparing teachers of mathematics. Available online at amte.net/standards.
 Banilower, E. R., Smith, P. S., Malzahn, K. A., Plumley, C. L., Gordon, E. M., & Hayes, M. L. (2018). Report of the 2018 NSSME+. Chapel Hill, NC: Horizon Research, Inc.
 National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
 National Governors Association Center for Best Practices and Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Author.
*The 2018 NSSME+ was conducted with support from the National Science Foundation under grant number DGE1642413. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The Report of the 2018 NSSME+ provides more complete results and is available at www.horizonresearch.com/NSSME.
**For the survey, external assessments were defined as assessments that teachers did not develop, such as state or district benchmark assessments.