More students don’t meet mathematics standards than meet standards in the U.S.—and the percentage not meeting standards goes up at checkpoints in the fourth, eighth, and twelfth grades! This performance greatly impacts the future of these children, limiting their potentials for employment and advanced education.
To improve math performance across the U.S., it is important to tackle this systemic problem by implementing evidence-based instructional practices (EBPs) on key mathematics constructs for all students, particularly those with identified mathematics difficulties. To better understand what instruction is effective, we need to recognize why students struggle with math.
Why Students Struggle with Mathematics
Instruction and learner characteristics play a prominent role in how well a student performs in math and what advanced math courses students take. To help every student succeed, it is important to understand the learning characteristics of those who succeed in mathematics versus those who do not (strategic versus non-strategic learners).
The Arithmetic to Algebra Gap
The “arithmetic to algebra gap” is a term used to describe how students who appear successful in elementary mathematics standards struggle with learning secondary mathematics. This is not a simple issue with elementary mathematics instruction or content or even with how algebra is taught. Rather, it is looking at mathematics learning as a continuous journey where one construct informs the other.
Addressing the arithmetic to algebra gap requires complex understanding of how math proficiency works. This gap has as much to do with what students learn as it does with how they learn it. To fill it, all students deserve empirically validated instruction focused on key math skills.
Explicit and Systematic Instruction
One of the most consistent findings from research is the need for explicit and systematic instruction when teaching mathematics, especially to students with learning difficulties. Explicit instruction is a series of instructional components that are grouped based on the needs of the learner. The more instructional components that are employed, the more intense the instruction. These components are used to guide instruction, preparation, and delivery.
Multiple forms of assessment are also used to drive instruction, including formative assessment. Formative assessment allows a teacher to frequently monitor student performance, which informs instructional decisions. A distinct advantage instructionally is that formative assessment may be easily tied to explicit instruction.
Additional Mathematics Intervention Using Representations
If students are unsuccessful learning through an explicit instructional approach and targeted accommodations, then additional intervention approaches should be considered to improve math performance. One such consideration is the use of representations like concrete manipulatives and the Concrete–Visual–Abstract (CVA) sequence of instruction.
Concrete manipulatives provide a physical interaction with mathematics that aids students’ problem-solving approaches. Research shows that manipulatives are superior to numbers and symbols alone in helping students access both early and complex mathematics.
Concrete–Visual–Abstract Sequence of Instruction
While using concrete materials provides positive gains in mathematics learning, their effectiveness is increased when included as an introductory part of the Concrete–Visual–Abstract sequence of instruction. CVA builds accuracy and conceptual understanding while supporting stepwise mathematics procedures.
Connecting Mathematics Intervention to Core Instruction
Empirically validated math interventions, such as those delivered through explicit instruction and visual representations, are important to improving students’ math performance, but interventions alone are not enough to maximize learning for students who struggle with math. Using the framework of Response to Intervention (RTI), students who receive math interventions concurrently learn core standards.
How Administrators Can Help at Different Levels
While the evidence shared above is effective in many cases, improving students’ math performance is not restricted to teachers and interventionists alone. Administration at multiple levels should work with teachers to tackle challenges at the student, school, and district levels. Schools with better collaborative efforts tend to have higher achievement in math and reading.
Improving Mathematics Performance Has Effects Beyond School
Our white paper details why students struggle with math and how to take an explicit, systematic instructional approach that’s proven to work. Use it to explore ways you can give students the opportunity to not only achieve in math but to build knowledge and acquire skills that enable them to thrive—helping them realize, or even reach beyond, their goals in school and life.