“Manipulatives can be important tools in helping students to think and reason in more meaningful ways. By giving students concrete ways to compare and operate on quantities, such manipulatives as pattern blocks, tiles, and cubes can contribute to the development of well-grounded, interconnected understandings of mathematical ideas.” – Stein and Bovalino (2001)
The use of manipulatives have often been recommended in the teaching of subjects like Mathematics because they enhance and deepen student understanding. It has been said that a picture is worth a thousand words. In the teaching of abstract concepts, manipulatives provide students that picture. Manipulatives allow students to move from concrete experiences to abstract reasoning.
For example, students learning about fractions may find it difficult to grasp that 1/2 is larger than 1/8 because, in their understanding of numerical values, 2 is smaller than 8. By observing a physical representation of 1/2 compared to 1/8, they can visualise why 1/2 is larger than 1/8.
Studies demonstrate that students using manipulatives make gains in the following areas (Heddens; Picciotto, 1998; Sebesta and Martin, 2004):
- verbalizing mathematical thinking
- discussing mathematical ideas and concepts
- relating real-world situations to mathematical symbolism
- working collaboratively
- thinking divergently to find a variety of ways to solve problems
- expressing problems and solutions using a variety of mathematical symbols
- making presentations
- taking ownership of their learning experiences
- gaining confidence in their abilities to find solutions to mathematical problems using methods that they come up with themselves without relying on directions from the teacher
Students using manipulatives in specific mathematical subjects are also more likely to achieve success than students who do not:
- Some children need to use manipulatives to learn to count – Clements, 1999.
- Using manipulatives increases students’ understanding of place value – Phillips, 1989.
- Students learning computational skills tend to master and retain these skills more fully when manipulatives are used as part of their instruction – Carroll and Porter, 1997.
- Using manipulatives has been shown to help students reduce errors and increase their scores on tests that require them to solve problems – Carroll and Porter, 1997; Clements, 1999; Krach, 1998.
- Students who have appropriate manipulatives to help them learn fractions outperform students who rely only on textbooks when tested on these concepts – Jordan, Miller, and Mercer, 1998; Sebesta and Martin, 2004.
- Students who have appropriate manipulatives to help them learn fractions also have significantly improved achievement when tested on ratios when compared to students who do not have exposure to these manipulatives – Jordan, Miller, and Mercer, 1998.
- Research indicates that students who used manipulatives in their mathematics classes have higher algebraic abilities than those who did not use manipulatives – Chappell and Strutchens, 2001.
The use of manipulatives deepens the understanding of concepts and relationships, makes skills practice meaningful, and leads to retention and application of information in new problem-solving situations.
Every pre-service, beginning, and veteran teacher will benefit from these how-to resources for using manipulatives (both concrete and virtual) to unleash the power of multi-modal, conceptually based, hands-on instruction. These manipulatives allow any teacher to explore the hands-on materials in their own learning as well as in the process of lesson preparation. Kits come with resource/activity guides, online lesson plans, and easy storage.
Manipulatives included: cuisenaire rods, fraction tower equivalency cubes, fraction circles, fraction number lines, geobord, snap cubes, base ten blocks, color tiles, two-color counters, pattern blocks, tangrams, dot dice, and virtual manipulatives.
Manipulatives included are: algebra tiles, XY coordinate pegboard, GeoReflector mirror, AngLegs, relational geosolids and nets, cuisenaire rods, tangrams, fraction circles, fraction number lines, two-color counters, fraction tower equivalency cubes, polyhedral dice, and virtual manipulatives.
Manipulatives can also be used for other subjects, like science. The Connecting Color Tiles Periodic Table Set provides students a hands-on experience with the elements of the periodic table, and is designed for grade 4 and up (age 8+). The 1” x 1″ color-coded tiles snap together and are printed with the atomic symbol, atomic number, atomic weight, and electron configuration of each of the 115 elements. The set also includes 45 additional tiles of common elements for constructing equations and compounds, and an activity guide. Everything is packaged in a storage container.
Science education products incorporate applied math and science principles into classroom projects. Teachers in pre-K, elementary, and secondary classrooms use science education kits and products alongside science, technology, engineering, and math (STEM) curriculum to demonstrate STEM concepts and real-world applications through hands-on activities. Science education projects include a broad range of activities, such as practical experiments in engineering, aeronautics, robotics, energy, chemistry, physics, biology, and geology.
- Brilliant Minds Montessori Math Kit
- Cool Science: The Periodic Table and Mad Science
- Games that Teach Children about the Periodic Table Elements
- Home Lesson Plans: Periodic Table and Other Subjects
- Educational Apps from Touch Press
- Apps: DragonBox Elements – master geometry through play