Helping Students With Understanding Mathematics

Helping Students With Understanding Mathematics

The question asked every day by all teachers of mathematics, no matter the grade level or geographic location is, “How can I effectively teach mathematics concepts and skills so that students are able to successfully understand and remember it?” This is a difficult question to answer for many reasons. One reason being that there has not been one singular, proven, systematic method for mathematics instruction that guarantees high levels of student success. This has not happened due largely to the fact that many students struggle with mathematics for entirely different reasons which no one method can address.

What are some of the common issues that contribute to students’ struggle with mathematics? What are some practical classroom instructional strategies that may be implemented to aid students in becoming successful learners of mathematics?

Why do students struggle with mathematics?

When looking at math teacher working with numbers, algorithms, functions, and formulas, math may seem to come easy for them. This makes it very difficult to understand why students do not find it just as easy. You simply learn the algorithm and apply it, right? This is not always the case for every student. When some students look at problems they see things completely different from the way the same problem may appear for someone that is already proficient in mathematics.

Watch the following playful video example of how two different approaches are used to solve a problem.  On the surface, they both appear to be logical to anyone if they weren’t truly knowledgeable of the misconceptions that are underlying the process used.

In this video, one party has one understanding of how to solve the problem, and the other party has a completely different view.

Think about this for a moment, is it possible to have two different views or strategies for how to solve a math problem?

In today’s world when students are being asked to work with mathematics at a deeper level of understanding than their parents or grandparents were asked.

Students of today are being asked to solve mathematical problems that fall outside of the typical drill and practice scenarios which their parent’s faced just one generation ago. In many cases, students must be able to create their own solutions to these unique situations and be able to explain their process to be correct.

With that being said, in order for students to be able to do this successfully, unlike “ma” and “pa” in this video, students must have a much deeper understanding of the mathematics behind their strategies.

How do we get a struggling student to the point of understanding mathematics?

Let’s first look at some of the common causes, as identified by Sherman, Richardson, and Yard (2009), of that they call unproductive student struggle.

There are two main categories into which these identified causes can be grouped: environmental causes, and personal or individualized causes.

Environmental Causes

  1. Instruction: Instruction that does not allow time for problem-solving, productive student struggle, work with cognitively demanding tasks, and a focus on building conceptual connections and relies too heavily on rote memorization of standard algorithms will not produce students that have a deep conceptual understanding of mathematics that can be applied in a variety of unique problem situations, thus leaving them ill-equipped and struggling when attempting to find an appropriate solution.
  2. Curricular Materials: Teaching the same content year after year in the same fashion each time is a common occurrence in many schools. Unfortunately, it is a mistake that many make because a student that is not successful with the curriculum the first time is very unlikely to be successful in repeated attempts without changes in the materials themselves and changes in the way the material is delivered. Another point to be made about students who have previously been unsuccessful in mathematics are typically given lower-level, repetitive materials, and assignments that are meant to assist them in gaining basic skills. This type of work significantly limits students’ chances to reason with the mathematics, thus creating meaning for themselves. It also sets low expectations for future work with mathematics and inadvertently places limits on a student’s depth of mathematical knowledge.
  3. Learner-Subject Matter Gap: Students’ real life communication with others about numbers outside of the school setting have a significant impact on their success with academic mathematics. When students are limited in these interactions, mathematics becomes irrelevant causing a learning gap that is left to the teacher to fulfill. Gaps of this type also exist due to excessive absenteeism, frequent movement from school to school where materials and/or pacing differ. Without immediate intervention strategies being implemented the student will fall further and further behind.

Personal or Individualized Causes

  1. Locus of Control: For some students something happens in their school career that leads them to the false beliefs that any success they may have or have had is due solely to easy content or luck, while any failure that they may have or had can be attributed to their own lack of ability or lack of intelligence. With beliefs such as these students limit their capacity to study mathematics and as a result, limit their own chances of deeply understanding what they are studying.
  2. Memory Ability: For many, the innate ability to memorize facts and algorithms comes easy, while for others this is a skill that may not be fully developed. Having poor memorization and recall skills cause students to have difficulty with organizing their thinking and using it to develop successful solution strategies.
  3. Attention Span: Students who are easily distracted may have difficulty with multi-step problems. For these students, working with problems that incorporate a large quantity of variables or other pieces of information, especially in the developmental stage of the understanding, may impede achievement.

The Language of Mathematics: Mathematics is unique from some other subjects in that it has its own specialized language, grammatical patterns, and rules. Several of the keywords within this specialized language have dual meanings in and out of the classroom. For example, the words table, foot, power, yard, and volume have one meaning in typical everyday use and another meaning in the academic world of mathematics.

This can be very confusing to students, especially those in the beginning stages of English language acquisition. Also, students lack understanding of the meaning of specific content-related words, i.e. addend, divisor, or exponent may interfere with students conceptual understanding. Note: when we talk about understanding the meaning of specific vocabulary words, we do not mean students being able to write the definition of the word. We are referring to the skill of being able to attach a formal label or word to specific actions or components of a mathematics problem.

When considering the challenges that face both teachers and students in gaining a deep understanding of mathematics, several strategies are available to be implemented based on the student and the root cause of the challenges they face.

Before looking at strategies related to specific challenges, it must first be noted that for teachers to successfully implement any intervention strategy they must first understand each student’s individual challenges. That is to say, they must be able to pinpoint specific challenges in relationship to specific students in order to choose the appropriate strategy for implementation.

With that being said, below are few accredited online self-paced courses that, when implemented, may help to clear the roadblocks and make the path to mathematical understandings less difficult to travel for your students.

  1. Developing Mathematical Expertise in a Problem-Centered Classroom
  2. Teaching Mathematics with Rigor and Results, Grades 3-10
  3. Preparing Students For The More Rigorous Math Assessments, Grades 3 – 10
  4. Academic Discourse for All Students (Grades 6-12)
  5. Creating a Learning Classroom for Today’s Students (Grades K-12)
  6. Building Academic Vocabulary and Deep Comprehension, Grades K – 5
  7. Building Academic Vocabulary and Deep Comprehension, Grades 6 – 12

For more information please contact us at or toll-free 1-855-498-4400.