What is high-quality mathematics instruction and why is it important?
Page 1: High-Quality Mathematics Instruction
Mathematics—one of the core academic subjects in the United States and around the world—is essential to many of our daily activities and routines (e.g., shopping, banking, cooking, home repair). Moreover, in today’s increasingly technology-dependent society, more and more jobs require some level of proficiency in mathematics and science. Students who lack sufficient mathematical knowledge and skills are more likely to experience negative outcomes as adults, including fewer opportunities for meaningful employment and a reduced likelihood of economic independence. Because of these factors, it is critical that students begin developing essential math concepts and skills at an early age. Unfortunately, studies conducted since the 1970s have shown that students in the United States do not perform as well on mathematics assessments as their peers in other countries.
Research Shows
Studies and national and international assessment data, such as those below, have raised concerns about the adequacy of mathematics instruction in the United States.
- In 2022, the Program for International Student Assessment (PISA) compared the mathematical literacy—the ability to express, apply, and interpret mathematics in different contexts—of 15-year-old students in the United States to those in other industrialized countries. Out of 81 countries, the United States ranked 34th.
(Berger, 2023) - In 2023, the Trends in International Mathematics and Science Study (TIMSS) indicated that fourth-grade students in the United States outperformed 28 education systems but performed lower than 21 others. It also indicated that eighth-grade students in the United States outperformed 18 education systems but performed lower than those in 19 others.
(Warner-Griffin et al., 2024) - Every year, the National Assessment of Educational Progress (NAEP) administers mathematics achievement tests to fourth-, eighth-, and 12th-grade students in the United States. Student performance indicates the degree to which they have acquired the knowledge and skills expected at their grade level. The results are categorized into one of four levels: Below Basic (little mastery), Basic (partial mastery), Proficient (mastery), and Advanced (beyond mastery). The 2024 results are illustrated in the table below.
Adapted from https://www.nationsreportcard.gov.
This bar graph illustrates the results of the 2024 National Assessment of Educational Progress (NAEP) mathematics achievement test for fourth, eighth, and 12th grades. The table is divided into three columns—one for fourth-grade results, one for eighth-grade results, and the last for 12th-grade results—and each column is divided into two rows. The top row is labeled Students Proficient & Advanced, while the lower is labeled Students Basic & Below Basic.
The test results are displayed for four categories of test takers: All Students, Students with Disabilities, English Learners (ELs), and Economically Disadvantaged. The All Students bars are colored blue. The Students with Disabilities bars are green. The English Learners bars are brown. Finally, the Economically Disadvantaged bars are purple.
In the fourth-grade column, All Students are 39% in the Proficient & Advanced range and 61% in the Basic & Below Basic range. Students with Disabilities are 16% in Proficient & Advanced and 84% in Basic & Below. Likewise, English Learners are 16% in Proficient & Advanced and 84% in Basic & Below. Finally, Economically Disadvantaged are 25% in Proficient & Advanced and 75% in Basic & Below.
In the eighth-grade column, All Students are 28% in the Proficient & Advanced range and 72% in the Basic & Below Basic range. Students with Disabilities are 16% in Proficient & Advanced and 84% in Basic & Below. English Learners are 5% in Proficient & Advanced and 95% in Basic & Below. Finally, Economically Disadvantaged are 14% in Proficient & Advanced and 86% in Basic & Below.
In the 12th-grade column, All Students are 22% in the Proficient & Advanced range and 78% in the Basic & Below Basic range. Students with Disabilities are 8% in Proficient & Advanced and 92% in Basic & Below. English Learners are 2% in Proficient & Advanced and 98% in Basic & Below. Finally, Economically Disadvantaged are 10% in Proficient & Advanced and 90% in Basic & Below.
What Do These Data Indicate?
The NAEP test is designed so that students who have learned the knowledge and skills deemed important for their grade level should score at the Proficient level at a minimum. However, the NAEP data show that a majority of students perform at the Below Basic and Basic levels, indicating little to partial mastery. And this lack of mastery will likely create new hurdles in subsequent grade levels, where a foundational understanding of mathematical concepts and procedures is required for success. Students who do not master foundational mathematics skills in early grades are likely to fall further behind as they progress through school.
With all of this in mind, take another look at the data in the table above. Note that more than 60% of fourth-grade students have yet to master the expected mathematics knowledge and skills, and this increases to almost 80% of students by the 12th grade. And the results are even worse for students with disabilities, English learners (ELs), and students who are economically disadvantaged.
Something to Consider
College and career readiness standards emphasize that students complete Algebra I, Geometry, and Algebra II. And some states and districts now require four years of math, which might extend beyond Algebra II to include courses such as calculus, trigonometry, or statistics. The rationale for this change is to better prepare students for success in college and future careers.
At the same time, other states have increasingly become more flexible in how students can meet their mathematics graduation requirements. For example, some states have introduced alternative pathways that prioritize subjects like data science, computer science, or financial literacy in place of traditional math sequences that include algebra, geometry, and calculus. These expanded options reflect a broader reevaluation of which mathematical skills are most relevant for students after high school, with an increasing emphasis on practical applications and varied career paths.
Reflect on the NAEP data presented above and consider the number of students who will struggle to meet graduation requirements in their state regardless of the pathway they choose.
Although a large percentage of students across the United States are not proficient in math, the good news is that teachers can take steps to give their students a significantly improved chance to succeed in the classroom. Before we explore those actions on the next page, we will first explore why some students struggle with mathematics.
