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

## Page 1: The Importance of High-Quality Mathematics Instruction

One of the core academic subjects in the United States and throughout the world, mathematics is key to many of our most common daily activities and routines, things like shopping, banking, cooking, and home repair. Further, in today’s increasingly technologically reliant 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 to develop 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 do their peers in other countries.

## Research Shows

Studies, such as those below, have raised concerns about the adequacy of mathematics instruction in the United States.

- In 2015, the Program for International Student Assessment (PISA) compared the mathematical literacy—that is, 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 69 countries, the United States ranked 36th.

(Kastberg, Chan, & Murray, 2016) - In 2015, the Trends in International Mathematics and Science Study (TIMSS) indicated that 8th-grade students in the United States were outperformed in math proficiency by students in Singapore, the Republic of Korea, China, Japan, Kazakhstan, the Russian Federation, Canada, and Ireland.

(Provasnik, Malley, Stephens, Landeros, Perkins, & Tang, 2016) - Every year, the National Assessment of Educational Progress (NAEP) administers mathematics achievement tests to 4th-, 8th-, 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 2022 results for 4th and 8th grade are illustrated in the table below. The 12th-grade data are from 2019 because the assessment was not administered to this population in 2022.
(https://www.nationsreportcard.gov)

This bar graph illustrates the results of the 2022 National Assessment of Educational Progress (NAEP) mathematics achievement test for 4th and 8th grades and the 2019 data for 12th grade. The table is divided into three columns—one for 4th-grade results, one for 8th-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 three categories of test takers: “All Students,” “Students with Disabilities,” and “English Learners (ELs).” The “All Students” bars are colored aqua. The “Students with Disabilities” bars are peach. Finally, the “English Learners” bars are yellow.

In the 4th-grade column, “All Students” are 36% in the Proficient & Advanced range and 64% in the Basic & Below Basic range. “Students with Disabilities” are 16% in Proficient & Advanced and 84% in Basic & Below. Likewise, “English Learners” are 14% in Proficient & Advanced and 86% in Basic & Below.

In the 8th-grade column, “All Students” are 26% in the Proficient & Advanced range and 74% in the Basic & Below Basic range. “Students with Disabilities” are 7% in Proficient & Advanced and 93% in Basic & Below. Finally, “English Learners” are 4% in Proficient & Advanced and 96% in Basic & Below.

In the 12th-grade column, “All Students” are 24% in the Proficient & Advanced range and 76% in the Basic & Below Basic range. “Students with Disabilities” are 7% in Proficient & Advanced and 93% in Basic & Below. Finally, “English Learners” are 3% in Proficient & Advanced and 97% 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, of course, 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 many 4th-grade students (60%) have yet to master the expected mathematics knowledge and skills, a percentage that is even greater (75%) for students in the 12th grade. And the results are even worse for students with disabilities as well as for English language learners (ELLs).

The purpose of this module is to explore why some students struggle with mathematics and what steps teachers can take to give their students a significantly improved chance to succeed in the classroom.

## Consider This

In recent years, a greater emphasis on college- and career-readiness has led to higher standards for student mathematics proficiency, as well as to more rigorous graduation requirements. Whereas in the past high school students in most states were required to complete Algebra 1 prior to graduation, those students are now often required to complete Algebra 1, Geometry, and Algebra II. Once more, reflect on the NAEP data presented above and consider the number of students who will struggle to meet these new requirements.

### Why Do Some Students Struggle More with Math?

#### Students with Learning Disabilities

Compared to the overall population, a much smaller percentage of students with disabilities demonstrate proficiency in mathematics. Although every learner is unique, students with a mathematics learning disability (MLD) tend to display any of a number of characteristics that affect their mathematics performance, including:

* mathematics learning disability (MLD)*

Condition characterized by significant difficulty in mathematics calculation and/or problem solving; a specific learning disability (SLD) in the area of mathematics, sometimes referred to as dyscalculia.

- Difficulty processing information
- Difficulty identifying relevant information in mathematics problems, especially in word problems
- Difficulty translating information into a mathematical expression or equation
- Problem maintaining attention
- Difficulty selecting an effective problem-solving strategy
- Poor reasoning and problem-solving skills
- Working through a problem without making sure all steps are completed or that the answer makes sense
- Deficits in the areas of mathematics facts and computational skills
- Memory and vocabulary difficulties
- Difficulty solving multi-step problems
- Weak visual/spatial representational skills
- Difficulty reading about mathematics
- Difficulty understanding the language, or vocabulary, of mathematics
- Difficulty understanding mathematics concepts and how concepts relate to procedures
- Mathematics anxiety
- Learned helplessness—that is, having low motivation, being a passive learner, and attributing both successes and failures to external, uncontrollable factors (e.g., luck)

Diane Bryant, who conducts research on mathematics interventions for students with LD, describes why students with mathematics learning disabilities and those who struggle with mathematics are often grouped together in research in this area (time: 1:00).

Diane Pedrotty Bryant, PhD

Project Director, Mathematics Institute for Learning Disabilities and Difficulties

University of Texas at Austin

**Transcript: Diane Pedrotty Bryant, PhD**

Students who struggle with mathematics and those who have been identified as having mathematics learning disabilities share similar characteristics. For example, both groups of students may have difficulty with what’s called *number sense*, just understanding numbers and the meaning of numbers and certainly calculation. Problem solving is another area. So I think this is one reason that these two groups are often included in studies. Another reason has to do with ensuring that you have a large enough sample size so that you can look at the treatment effects of practices that may become evidence-based practices. Therefore, it’s not uncommon to see both students with mathematics difficulties and students with identified mathematics learning disabilities included in the sample.

#### English Language Learners

ELLs, too, have difficulty with mathematics, though their struggles are more likely to be a result of linguistic issues. It is important for teachers to understand that mathematics consists of more than just numbers; it includes a significant amount of content-specific vocabulary. When teachers discuss mathematical procedures and concepts, they typically use academic language, which is composed of content-specific vocabulary—for example, words like *factor*, *estimate*, and *sum*—vocabulary with multiple meanings—for example, *table*—and complex language structures. Not surprisingly, then, many ELLs struggle to solve mathematical word problems.

* academic language*

The language used in academic settings to communicate information orally and in writing about discipline-specific content.

### What Can Teachers Do?

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

*A standards-based curriculum*— The concepts and skills believed to be important for students to learn*Evidence-based practices (EBP)*— Strategies or practices proven through research to be effective for teaching mathematical concepts and procedures

## Research Shows

- When they provide effective mathematics instruction, teachers can reduce the performance gap between students who are at risk for mathematics difficulty and their average and high-performing peers.

(Clarke, Smollkowski, Baker, Fien, Doabler, & Chard, 2011) - Students with learning disabilities who receive effective mathematics intervention can develop critical skills like problem-solving and abstract reasoning, which are necessary to achieve mathematics proficiency.

(Gersten, Chard, Jayanthi, Baker, Morphy, & Flojo, 2008; Allsopp, Lovin, & van Ingen, 2017)

## Activity

Among the factors that sometimes influence effective high-quality mathematics instruction are teacher and student perceptions and beliefs about mathematics itself.

- Click here to discover your own attitudes and beliefs about mathematics and to reflect on how they might influence your instruction.
**Perceptions and Beliefs Regarding Math**Are the statements about mathematics ability in the boxes below True or False? Read each and click “True” or “False” to find out the answer.

Some students are born with the ability to do math, whereas others are not.feedbackHigh mathematics ability is defined as the ability to perform calculations with accuracy.feedbackMathematics requires logical versus creative thinking.feedbackReading skills are important for success in mathematics.feedbackThe main objective in mathematics is to obtain the correct answer.feedbackIn addition to knowing mathematics facts, students need to understand the underlying concepts of the skill they are learning.feedbackMathematics teachers not only need to have knowledge of the math they are teaching but they should also be able to employ effective teaching practices.feedbackMales are better at mathematics.feedback*(Close this panel)* - If you are completing this activity in class, with a small group, or with a partner, discuss how your attitudes and beliefs about mathematics might influence or have already influenced your instructional practices. Next, brainstorm ideas for improving your mathematics instruction.