How to Teach Multiplication & Division to Students Struggling with Math
Voyager Sopris Learning
Math is characteristically difficult for many students. After basic addition, division and multiplication are the first skills students will have to learn. Therefore, it is incredibly important for teachers to use techniques that address the challenges of math while incorporating assessments that gauge students’ understanding of the concepts.
Having an understanding of why students struggle with math can then lead to better teaching of the basics, but the basics can also be strategic and fun. According to research, collaborative action plans revealed some of the best ways to teach the fundamental concepts of math are through using a variety of learning resources, teaching strategies, student activities, and individual interventions. Here, we’ll talk through why students often struggle with math and then address different ways to strategically teach multiplication and division to those students.
Why Do Students Struggle with Math?
There are a number of reasons why children often struggle with math. Learning difficulties, anxiety, or a negative view of the subject can make learning math hard, especially when it comes to multiplication and division. For example, dyscalculia is a learning difficulty that involves a child’s ability to perform number-related concepts. It is sometimes referred to as “math dyslexia” or “number dyslexia.” Difficulties like this interfere with a child’s number sense.
Number sense relates to someone’s ability to understand—or make sense of—numbers. Without a strong sense of numbers, it is hard to relate and connect them because students cannot think about them fluently. Number fluency, just like language fluency, allows students to take numbers apart and put them back together in different ways, just like how children learn to break down words and put them back together.
Another reason some students may struggle with math is because they view it as a hard and boring subject. This is a problem because it can then lead to more students struggling if their general view or approach to the task is negative. Consequently, it is important to approach the teaching and instructing of math in a way that is fun and engaging as well as productive and informational.
The Institute of Education Sciences (IES) offers several recommendations for assisting students who are struggling with mathematics. Some of these include screening students in the beginning to identify anyone at risk, providing explicit and systematic instruction during intervention, and monitoring progress throughout. Another recommendation involves using motivational strategies.
Multiplication and Division: Teaching Basics
Once students have a solid foundation of addition and subtraction, they can move on to learning the next two basic arithmetic operations: multiplication and division. While these are separate mathematical concepts, they are also related. Kids usually begin learning multiplication in second grade and division in third grade. Through using programs and strategies that build proficiency in these subjects, students can then be on a successful path for future subjects, like algebra.
Multiplication is the process or skill of multiplying, or increasing groups of equal sizes. In second grade, teachers often use repetition and multiplication tables to help lay the foundation for a deep understanding of the concept. Some students may even memorize multiplication facts, but memorization may be too difficult for some.
Division, on the other hand, is the opposite of multiplication. When students learn to divide, they are trying to see how many times they can split a specific number into equal parts. Short division and long division are the two primary algorithms, and there are a number of different ways to teach students how to divide numbers.
Because math concepts usually build on each other, the student has to have a full understanding of addition before they move on to multiplication. Salisbury University designed an instructional sequence to “help a group of children entering fourth grade develop both conceptual understanding and procedural fluency for multiplication and division.” A conceptual understanding of mathematical concepts is perhaps more important than just a procedural understanding because the procedure alone is not strong enough to allow students to grasp more complex problems. The consequences of not having a good understanding of the basics can cause disadvantages in day-to-day activities and in the workforce once students leave high school.
Strategies for Teaching Multiplication to Struggling Students
Because there are so many facets to multiplication, there are different strategies that can target specific areas of weakness students are experiencing. Multiplication can range from simple multiplication problems to multidigit multiplication, and there are many strategies that can address these ideas. Some of the basic strategies include multiplication facts and multiplication tables. These, however, often involve memorization, and many students struggle with this ability. Instead, strategies like using a manipulative or an array can help visually address some of the more complex issues of math.
The goal of all these is to have students be able to automatically retrieve the basic facts of math from their long-term memory. When students lack the basic facts and functions of multiplication, then the rest of their performance is subsequently hindered. Eastern Illinois University conducted a study in which they compared traditional strategies like flash cards and board games to newer online tools. They found both methods of practice improved the automaticity of multiplication facts for the students in the study.
Along with this, students should be able to apply some of their own strategies to their learning to make it more fun and engaging. According to a research paper published by International Education Studies, “Mathematics lessons that involve multiplication activities should start with learners working individually using their own prior mathematical knowledge; after that, the teacher and learners discuss as a whole class to compare different individual approaches and solutions to the activities. This whole class activity discussion provides learners with vast opportunities in conceptual understanding of multiplication facts and application of different approaches.”
When it comes to students with a poor performance in mathematics, specifically in recalling multiplication facts, studies have found it highly meaningful to incorporate “systematic review and corrective feedback.” Therefore, the strategies listed below are all great places to start, but a routine system of review and correction is also crucial in solidifying the concepts.
Manipulatives are physical tools or objects students can physically move or manipulate to better grasp a concept. Using tiles or blocks—or sometimes even candy—teachers can visually show students how a number may increase. Students will line the manipulatives in equal groups to represent the problem and more clearly see the numbers or groups they are counting.
Skip counting is when students will use intervals—or skip counts—by adding a number each time to the previous number. For example, skip counting by 3 is 3, 6, 9, 12, and so on. Skip counting is helpful when it comes to multiplication facts and tables, which can help them memorize the facts.
The commutative property of multiplication simply means that the order in which numbers are multiplied does not change the end product. For example, 2 x 6 = 12 and 6 x 2 = 12. This is an important skill for students to learn because it will reduce the number of multiplication facts that have to be memorized, thus leaving more room in their long-term memory for additional skills.
Arrays are visual ways to show multiplication patterns using rows and columns. This arrangement of rows and columns will match a multiplication equation. These arrays can be used with pictures, numbers, or even physical items to display a clear visual of a numerical concept.
Multiplication Rules and Patterns
Multiplication—as with all of math—ultimately breaks down into rules that follow patterns. Once students understand the rules and begin to notice the patterns, they can then move on to the next skill with more confidence and more opportunity for success. Putting these rules and patterns onto anchor charts for the classroom can give students those visual cues to help them remember what they have learned as they practice problems.
Strategies for Teaching Division to Struggling Students
Students struggle with multiplication and division alike. After all, they are related concepts, and because of this, teachers can use students’ prior learning of multiplication to help them activate that knowledge for division. In addition to this, some of the strategies for teaching division to students who may be struggling to understand division are similar to those of multiplication. Division also has math facts and times tables that can be memorized. And for those who struggle with memorization, there are strategies to help with that, too. Dividing physical items into groups that visually represent a division equation can help make numbers more engaging and approachable for students.
As stated above, manipulatives are physical tools or objects students can physically move or manipulate to better grasp a concept. This time, instead of having a bunch of small items that can be sectioned into equal groups, students will start with the whole group of manipulatives and are asked to divide them among a given number.
Division facts are number sentences as they relate to times tables. There are an infinite number of division facts, but the ones most often taught are 0 to 12. These are usually taught using charts or tables and are necessary before students move on to learning long division.
Using partial quotients is helpful when it comes to solving larger division problems. A partial quotient is when students focus on a part, or a chunk, or the number. This can help a student view the larger number as more approachable and less abstract. If students are having a hard time with the numbers alone, they can use a box model or an area model to help even further.
Area models, also referred to as box models, use a rectangular diagram that breaks down larger numbers into smaller numbers and then use boxes to make the calculation simpler. By using the rows and columns to devise smaller calculations, they can then use the numbers outside of the box to find the correct answer.
5 Fun Ways to Teach Multiplication and Division
One of the best strategies for teaching math is to make it engaging. Finding ways to incorporate both fun and function into a lesson is the perfect combination for teaching foundational skills like multiplication and division. Because the concepts themselves can be complex, teachers must be creative and strategic when they teach them. Amy E. Lieberman, in her article “Creating a Multiplication Pedagogical Toolkit for Upper Elementary Mathematics Educators,” stated, “It is a teacher’s responsibility to be able to creatively teach complex mathematical topics, such as multiplication, to their students, in order to promote high levels of understanding among all students.”
Any time you can incorporate games into your activities, it can transform your lesson. Students love to play games, so combining learning with gaming can be highly beneficial. This is also a great opportunity to make learning math collaborative by incorporating some teamwork and competition. Games can range from board games that involve math, to a classic deck of cards, to online game-style activities.
Incorporating technology into the classroom is common today as technology continues to be so prominent in the world around us. Finding some online programs that help teach students multiplication and division can not only make learning fun, but it can also help differentiate learning and allow students to move at their own pace and understanding.
Using some consumable manipulatives is always a popular strategy with students. Try giving students candy or snack manipulatives they can eat after they successfully practice their equations. If food items aren’t allowed or encouraged in your room, you can always offer incentives like stickers or other small prizes.
Activate the Arts
Math is often associated with the left side of the brain, so incorporating some art into a math lesson can help activate the right side of the brain. This then encourages students to use their whole brain when learning. Whether you choose to sing songs when skip counting or draw flower petals when multiplying, incorporating art into a math lesson can help make learning more fun and meaningful.
Use What You Have
Having fun with lesson planning doesn’t have to mean going out and getting a bunch of new materials or supplies. Sometimes having fun in class means getting more creative with what you already have.
While math might have its challenges, it doesn’t have to be a hard or boring subject for students. There are a multitude of easy and fun ways to approach some of the more difficult concepts of math, and there are many resources to help. Voyager Sopris Learning® is here to offer additional resources for teaching multiplication and division for elementary and middle school students. Our VmathLive® program empowers students in grades K–8 to master math content at their own pace in a motivating and engaging online environment.