Integrating Concrete and Virtual Manipulatives in Early Childhood Mathematics

Fundamental Questions (1): What are manipulatives in mathematics?

1. Concrete Manipulatives

Concrete manipulatives are physical objects students can manipulate when working through mathematical problems. These manipulatives offer students a “hands-on” (Rosen, D., & Hoffman, J, 2009, p. 26) experience to promote students to obtain a deeper understanding of mathematical concepts and make real-world connections to their learning. Students can manipulate concrete manipulatives by using their hands to “slide, flip, rotate and turn” (Rosen, D., & et al, 2009, p. 26) a physical object.

1. Virtual Manipulatives

Virtual manipulatives are digital learning tools which can be incorporated into mathematics to deepen and expand student learning. These manipulatives “are interactive, Web-based [and] computer-generated images of objects” (Rosen, D., & et al, 2009, p. 26) that students can manipulate using technology (computer, iPad, phone, etc). Virtual objects can be manipulated by students in similar ways they would manipulate concrete objects, but in this case, digitally. The use of virtual manipulatives is a more engaging way to approach mathematics content as they are “gamelike” (Rosen, D., et al, 2009, p. 32) tools that are more intriguing to students’ interests, thus ultimately motivating and providing students with more opportunities to become further involved in their learning processes. Virtual manipulatives can be found on various apps, websites and digital platforms that are accessible to anyone with a technology device and internet connection.

Part-Whole Questions (1): Why is digital literacy important for students early on in their life?

The digital world is expanding and will continue to become more involved in our daily lives as technology advances. Many schools currently have multiple laptops or other technology devices that students can access for their learning. In fact, about “91 percent of students are using computers” (Rosen, D., & et al, 2009, p. 32) for their learning by first grade. Furthermore, many students have “access to high-speed internet, and children as young as 4 years are online several times a week” (Rosen, D., & et al, 2009, p. 32), ultimately indicating the dire need for students to obtain digital literacy skills early on in life. When the internet is used in positive ways, it can be resourceful and fun, however, the internet can be a dangerous place. If students are going to use technology and the digital world, inside and outside of the classroom, they must first know how to safely use it. Educating students about how to use digital platforms and technology will provide students with skills to “become better equipped to successfully navigate our digital world” (Rosen, D., & et al, 2009, p. 33) in a more positive, safe and rewarding way.

Part-Whole Questions (2): How can educators effectively integrate virtual manipulations in early childhood mathematics?

To integrate virtual manipulatives into mathematics, educators must first discover useful and safe platforms for students to utilize. Educators, and anyone else, can find virtual manipulatives for “free on the internet” (Rosen, D., & et al, 2009, p. 32), however, it is important to master the learning experiences before incorporating them into the classroom. Furthermore, educators must ensure virtual manipulators are being “used in combination with concrete manipulatives and other real-world exploration” (Rosen, D., & et al, 2009, p. 32) to enhance the full potential of all student learning. Students must understand the expectations of technology use and be shown how to effectively navigate various digital platforms. Lastly, educators must provide students with “time and access to develop comfort, knowledge, and skills” (Rosen, D., & et al, 2009, p. 29) using digital learning platforms to ensure the effectiveness of student learning.

Hypothesis Questions (1): If technology is used in the classroom, will it deteriorate student learning in mathematics?

Integrating technology into a classroom will not deteriorate student learning in mathematics. In fact, using virtual manipulatives and technology in mathematics “can play an important complementary role” (Rosen, D., & et al, 2009, p. 32) for the learning of all students. Integrating virtual manipulatives into mathematical content will assist educators in discovering “new ways to meet the challenging needs” (Rosen, D., & et al, 2009, p. 32) of each student in the classroom, thus promoting the learning of all students. Since students require “a variety of methods to convey representations and build new understanding of mathematical ideas” (Rosen, D., & et al, 2009, p. 32), using a variety of strategies and learning experiences, involving virtual and concrete manipulatives, will ensure each student’s needs are being met. Furthermore, virtual manipulatives embedded within mathematical content will “encourage discussion and critical thinking” (Rosen, D., & et al, 2009, p. 32) about mathematical processes and concepts among students, ultimately promoting students to obtain a deeper understanding of the content material.

Critical Questions (1): What are examples of virtual and concrete manipulatives and platforms that can be used to enhance student learning?

1. Virtual Manipulatives:

• Google Slides – Using Google Slides students can create and manipulate various shapes, lines and graphs. This platform can be accessed on all technology devices.
• Utah State University National Library of Virtual Manipulatives (NLVM) – NLVM is a computer application that offers grade specific virtual manipulatives. Some manipulatives included are algebra tiles, graphs, pattern blocks, scales, counter chips, coins and base blocks.
• Shapegrams – This website offers educators with lesson plans to connect shapes to our everyday life. Students can use a variety of shapes to construct images of real-world things such as a house, animals, food, etc. Shapegrams also offers students engaging tutorial videos to follow along with.
• The Math Learning Center – This website offers a variety of math applications that can be accessed on most technology devices. Some manipulatives included are money pieces, clocks, number lines, number frames, number rack, geoboards, pattern shapes and base blocks.
• Toy Theater – This website offers a variety of digital games for various subjects that students can participate in. It also provides educators with learning and assessment tools. Some manipulatives included are geoboards, clocks, fraction strips, ten frames, place value charts, number lines, pattern blocks and money pieces.
• Didax – This website offers educators with a variety of lesson plans and tutorial videos for each virtual manipulative offered. Some manipulatives included unifix cubes, coloured counters, pattern blocks, place value disks, geoboards, dice, balance scales and rekenrek counting frames.
• Cool Maths 4 Kids – This website offers a variety of grade and concept specific digital math games, lessons, quizzes, manipulatives, brain teasers and flashcards. Some manipulatives included are ten frames, base blocks, number lines and pattern blocks.
• Mathigon – This website offers a variety of lesson plans, tutorials and concept specific manipulatives. Some manipulatives included are shapes, rulers, protractors, number lines, base blocks, balance scales, clocks and polyominoes.

2. Concrete Manipulatives:

• Base Blocks – Can be used as blocks to identify and represent numbers by place values.
• Geoboards – Using rubber bands, students can “identify, manipulate and create” (Rosen, D., & et al, 2009, p. 29) geometric shapes.
• Unifix Cubes – Cubes can be connected to one another to represent basic number operations, sequence of patterns and counting.
• Money Pieces – enables students to make real-world connections through counting, fractions and decimals.
• Clocks – Can be used to identify and tell the time.
• Counter Chips – Can be used to represent and count numbers.
• Pattern Blocks – Can be used as blocks to identify and discuss various “shapes, colours, sizes” and “sorting” (Rosen, D., & et al, 2009, p. 29) arrangements.
• Balance Scales – Can be used to determine the mass of something.

Critical Questions (2): What is my opinion about using virtual manipulatives and technology in the classroom?

I believe using virtual manipulatives, alongside concrete manipulatives, will promote a deeper understanding of mathematics, and other subjects, for students. Combining concrete and virtual manipulatives into content, specifically mathematics, will make learning more “motivating, exciting” (Rosen, D., & et al, 2009, p. 32) and fun for students to participate in. Using virtual manipulatives and technology within the classroom will assist students in discovering ways that best fit their individual needs to effectively convey their understanding of content. Furthermore, technology is becoming more popular among young children, therefore it is clear that students must be taught how to effectively and safely partake in the digital world to benefit themselves. Generally, virtual manipulatives are “accessible” (Rosen, D., & et al, 2009, p. 32) wherever you are as long as you have a network connection and access to a technology device. Ensuring students know how to use virtual manipulatives and digital platforms in ways to promote their learning will be especially beneficial if schools have to switch to remote learning a gain in the future.

Using technology and digital platforms to enhance student learning is something that I was introduced to in an Educational Technologies course I took a few semesters ago. I wrote a blog post called “Frame Your Digital Identity” for that class, which goes more into depth about why it is important to integrate technology into the curriculum and teach students how to safely and effectively navigate the digital world.

References

Rosen, D., & Hoffman, J. (2009). Integrating concrete and virtual manipulatives in early childhood mathematics. YC Young Children, 64(3), 26.