Mastering Math with Manipulatives

Civilizations across the globe including ancient Chinese villages, marketplaces in early Greece, and theaters in Roman cities all used manipulatives to solve everyday math problems. Whether they were clay beads, wooden trays, or the original abacus counters, these items served as the first manipulatives to help people understand the sometimes complex concepts of math. Today manipulatives have come to be considered essential in teaching mathematics at all grade levels. The manipulatives may have changed and evolved to include fraction strips, geoboards, spinners, coins, place value mats, and pattern blocks to name a few, but the goal is the same: to help students use a hands-on concrete object to introduce, understand, practice, or remediate math concepts.

The educational foundation for using math manipulatives is supported by the learning theory research completed by Jean Piaget. According to Piaget, children are active learners who master concepts by progressing through three levels of knowledge–concrete, pictorial or representative, and abstract. By using manipulatives, students can explore a math concept in a concrete way that will help them not only internalize the concept but also allow them to understand “why” a math procedure makes sense. For example, students using fraction strips can visibly see that 4/8 is equal to 3/6 by looking at each strip and seeing that the same amount is there, just broken up into different fraction amounts. We have seen it first hand in our classrooms here at North Shore Christian School, that children are allowed to explore and deeply understand complex math ideas by first using the concrete manipulatives. Let’s take a look at the benefits of using math manipulatives in our classrooms.

Concrete Representations – Students who work with a physical object will better understand what they are learning. By actively engaging with the manipulatives, the students can see how a math concept can be broken down into smaller parts representing actual items.
Engagement – Educators have known for decades that “paper and pencil” work reaches only a certain percentage of their students. By engaging senses of sight and touch, manipulatives reach a wider range of learners, such as those who don’t perform well on paper-and-pencil tasks.
Problem Solving Skills – Students who solve math problems only on paper must wait for a teacher to tell them whether their answer is correct, while students who use manipulatives can see a real life representation of the problem right in front of them and s/he has the tools to figure out the answer with the manipulatives.
Enjoyment and Confidence – Studies have shown that students have a higher confidence level in their math skills and their ability to solve a problem on their own than students only using paper and pencil tasks. And let’s face it, there is no contest when it comes to enjoyment level of working with colorful blocks, spinners, or dice rather than a math worksheet.

North Shore Christian School uses many math manipulatives at different grade levels to help students advance from concrete learners to those who understand more complex abstract math ideas. If you are looking for more resources on math manipulatives or the research behind it, we have provided several links below.

Teacher Vision – Using Math Manipulatives

Hand2Mind Resources Understanding the Research Behind Manipulatives