By Joshua L Davis III

Math is a subject most students detest. They solve sums just by substituting numbers into a memorized formula to get an idea. Not understanding the formulas, they usually end up applying the wrong formula to sums.

In fact, students who apply math formulas by rote never do understand the formulas they use and its logic. To make things worse, there are so many formulas to memorize. And teachers just go on teaching new formulas without giving students time to develop a strong foundation to understand mathematics.

There is help for such students by conceptually presenting math problems using manipulatives. Physical manipulatives like blocks, chips and geoboards are common in mathematics classrooms. However now with schools having 3D printers and CAD software, teachers can use digital fabrication to create computer-aided 3D virtual manipulatives to use while teaching.

Make math concrete with digital fabrication

Digital fabrication is the process of creating physical objects based on digital designs developed on a computer. Classroom computers become personal fabrication systems by installing CAD software and connecting them to a 3D printer, a die cutter and a standard inkjet or laser printer.

Digital fabrication helps students look at 3D solid models and identify its key attributes like shapes and number of faces. Students can design, rotate, measure and transform 3D solids using CAD software. They create onscreen virtual manipulatives, print the shape’s net on cardstock, vinyl or some other material and use a die cutter to cut the net’s outer edges and perforate fold lines to easily construct the 3D solid.

Students use the software to design their own one-inch cardstock cubes and solids and measure its various attributes, look at its different views and print physical models based on its virtual manipulatives.

Digital fabrication helps students define surface area based on the relationship between faces and surfaces, the key attributes of identified 3D solids and their prior area knowledge.

Then using the software, they explore the connection between the printed, folded cubes and cubes’ nets by rotating and exploring all six faces. Accordingly, they hypothesize calculating the surface area.

Then students use the software to rotate and color the cube’s different faces and explore the relationship between the cube and the net’s colored faces. After learning how to calculate the cube’s surface area, students can construct other rectangular prisms and calculate its surface area. Thus students learn the definition of surface area and its calculations.

Helps develop skills

2D representations of rectangular prisms give kids only its top, front and side face view. They have to understand each visible face with an invisible corresponding face. However digital fabrication helps students develops strategies to learn surface area by recognizing 3D figure qualities they can’t see in 2D representations.

Digital fabrication lets them rotate 2D representations of prisms to see the invisible faces. Students thus see both the solid’s 2D representation and its corresponding net with all of its faces. Students also explore physical models of the solids.

They also use the software to learn how to keep track of their work by listing the areas of faces by labeling each face with letters and marking faces with calculated areas. Students learn how to keep track of the calculated face areas by coloring each face and exploring the relationship between opposite faces. Using their fingers as calipers, they count the physical prism faces in pairs and also label faces with a mark, letter or its area.

Digital fabrication and ISTE standards

The ISTE Standard for students state that students should use their knowledge to generate new products or processes and use model and simulations to explore complex issues and systems, both implemented through digital fabrication.

The ISTE Standard for teachers states that teachers need to design, develop and evaluate the students’ learning experiences and assessments using contemporary tools and resources to maximize their content learning which digital fabrication achieves.

Digital fabrication also follows the ISTE Standards for Administrators encouraging school and district leaders to promote the frequent and effective use of technology for learning and providing learner-centered environments with technology and learning resources meeting the learners’ individual and diverse needs.

Digital fabrication also supports the Principles and Standards for School Mathematics Technology Principle which states technology can help students engage with and own abstract mathematical ideas. Technology improves the quality and range of investigations by viewing mathematical ideas using multiple perspectives.

It’s thus proven that its possible to make math concrete with digital fabrication and help students understand surface area. Students develop conceptual understandings of surface areas using physical and virtual manipulative and thus develop two problem-solving strategies to apply to other content areas.