What is high-quality mathematics instruction and why is it important?

Page 2: Why Some Students Struggle with Math

The NAEP data on the previous page illustrate that, in general, many students in the United States are not mastering the mathematics knowledge and skills needed to be successful in subsequent grades and later in life. Further, the data indicate that this is especially the case for several groups of students: those with learning disabilities, English learners, and students who are economically disadvantaged. For many of these students, their math difficulties stem from or are exacerbated by reading deficits. These difficulties often occur when students encounter academic language, which is composed of content-specific vocabulary (e.g., fraction, estimate, sum), symbols (e.g., +, -, %), and vocabulary with multiple meanings (e.g., table, factor, line). Read on to learn more about each group.

Students with Learning Disabilities

Compared to the overall population, far fewer students with disabilities demonstrate proficiency in mathematics. Although every learner is different, students with a mathematics learning disability (MLD) often have challenges with mathematical tasks, such as:

• Fluency with basic facts
• Performing multistep computations
• Using and applying strategies accurately
• Solving word problems
• Understanding mathematical notation (e.g., equations, relational symbols [<, =, >, ≠], exponents, multiple ways of representing multiplication [•, x])

Additionally, often students with MLD share certain characteristics that result in these challenges. As illustrated in the table below, these characteristics can be grouped by skills.

Skills	Characteristics
Executive Function, Cognitive Processing, and Attention	Difficulty processing information Difficulty with working memory, which impacts the ability to retain and manipulate information Problem maintaining attention throughout multistep problems Lacks persistence when working through problems, often not completing all steps or verifying that the answer is reasonable Mathematics anxiety Learned helplessness—showing low motivation, passive learning behaviors, and a tendency to attribute success or failure to external, uncontrollable factors (e.g., luck)
Language and Comprehension	Difficulty identifying relevant information within mathematics problems, particularly in word problems Difficulty understanding mathematics language and specialized, academic vocabulary Difficulty translating information into appropriate mathematical expressions or equations
Conceptual Understanding, Procedural Knowledge, and Mathematics Fluency	Difficulty understanding mathematics concepts and recognizing how concepts relate to procedures Weak reasoning and problem-solving skills Difficulty selecting effective problem-solving strategies for different types of problems Difficulty solving multistep problems that require organizing and sequencing information Deficits in math facts and computational skills, which affect accuracy and fluency
Visual-Spatial and Representational	Weak visual and spatial representational skills

English Learners

ELs also have difficulty with mathematics, though their struggles are more likely to result from linguistic issues. While math is often misperceived as a universal language because it involves numbers, it is important for educators to understand that mathematics consists of more than just numbers. As discussed above, even in the early grades, educators typically use academic language (e.g., area, perimeter, quotient) when discussing mathematical procedures and concepts. However, it often takes ELs five to seven years to effectively understand and use this more advanced and complex language. Until they can do so, many ELs find it challenging to fully understand instructions or take part in math discussions. Additionally, word problems are especially challenging for many ELs due to language demands.

To further illustrate how math problems can be confusing to ELs, consider how teachers often use different vocabulary terms to convey the same meaning. As the graphic below illustrates, the math problem 15 – 7 = can be expressed in many ways.

Economically Disadvantaged Students

As a whole, students from economically disadvantaged backgrounds show less proficiency in math and often encounter daily challenges that can impact their learning. The boxes below offer examples of challenges these students might experience and the resulting impact that educators might observe in the classroom.

What Can Teachers Do?

To improve student mathematics performance, more and more schools and districts have implemented high-quality mathematics instruction. This instruction involves the implementation of both:

• A standards-based curriculum—Includes the concepts and skills believed to be important for students to learn; curricula are based on standards
• Evidence-based practices (EBPs)—Strategies or practices shown through research to be effective for teaching mathematical concepts and procedures

We will explore each of these in more detail on subsequent pages.