Use a 3D model as a tool for reasoning, not just as an object to name. Have students build or inspect a solid, describe its parts, turn it to examine different views, and connect what they see to a 2D drawing. Ask them to explain how they know what is hidden and what stays the same as the object moves.
Why teach geometry with 3D models?
Recognizing a cube or sphere is only a starting point. Students also need to reason about faces, edges, vertices, how parts fit together, and how a solid is represented from different viewpoints. Some students struggle to mentally manipulate a 3D shape shown in a representation, so making and handling the object can give them something concrete to inspect while they develop that reasoning.
A framework developed by Fujita and colleagues identifies manipulating representations of 3D shapes and reasoning about their properties as important capabilities in 3D geometric thinking. The authors reported that some students did not manipulate representations effectively when solving challenging problems. Read the study in the Journal of Mathematical Behavior.
A classroom sequence that links solids to drawings
The sequence below is a practical lesson structure, not a single intervention tested as a package in the cited studies. Adapt the object and questions to students’ age and current geometry work.
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Build or inspect a solid
Give students cubes, a solid model, or other simple construction material. Ask pairs to reproduce a target shape or build one that matches a verbal description. For example: “Make a solid with a square base and one cube centered on top.” Ask students to check whether their construction matches the description before moving on.
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Describe and justify its properties
Ask students to identify faces, edges, and vertices, and to explain how they know. Have them describe relationships between parts: which faces meet, how many cubes form a layer, or how the upper part is supported. Encourage precise explanations rather than relying on a shape’s name alone.
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Turn the object and compare views
Invite students to rotate the solid or walk around it. Ask what becomes visible, what is hidden, and which properties remain unchanged. They might draw or describe the solid from the front, side, and above, then compare those views. The goal is to make spatial thinking visible rather than assume students can mentally turn the object without support.
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Bridge the 3D object and a 2D representation
Show a drawing or other 2D representation and ask students to build the solid it could represent. Then reverse the task: have them draw or sketch a solid they built. Discuss what the drawing shows clearly and what it leaves out, such as hidden faces or depth.
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A teaching experiment with first graders used cubes to reproduce two 3D shapes, first from a 3D model and then from a 2D representation. The authors described different levels of local and global structuring, including progress toward understanding more complex relationships between components and composites. Read the study in Sisyphus — Journal of Education.
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Explain and compare constructions
Ask each pair to explain why its model fits the target and how it interpreted the drawing or description. Let students compare two constructions or sketches: what is the same, what differs, and could both represent the same solid? A peer’s different viewpoint can reveal an assumption that a student did not notice while working alone.
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Choose a physical or digital model for the task
Physical and digital representations offer different ways to work with a solid. Choose based on the specific reasoning you want students to practice rather than assuming one format is always more effective.
| Representation | What students can do | Useful teaching focus | Evidence and limits |
|---|---|---|---|
| Physical solids or cubes | Handle, assemble, inspect, and turn a model directly. | Building component relationships and checking a 2D representation against a tangible solid. | A first-grade experiment used cubes to reproduce shapes from 3D models and 2D representations. It does not establish that physical materials outperform digital tools. Study details. |
| Digital or ICT representations | Work with a digitally presented model; the exact capabilities depend on the tool. | Use when the activity benefits from changing or viewing a representation in ways available in the chosen software. | A study compared ICT-supported learning with physical manipulatives among 74 fourth graders aged 10–11 in a month-long program. Its abstract does not establish a universal winner. Study details. |
The cited studies involve different ages, tasks, and research designs, so their findings should not be treated as a single head-to-head ranking of classroom materials. For either format, make students’ construction, comparison, and explanation part of the task; a model alone does not show what a student understands.
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What the evidence says—and what it does not
The studies address related but distinct questions. Together they support attention to representation and spatial reasoning, but they do not validate one universal lesson sequence or prove that one type of model works best for every student.
- Grades 7–9: Fujita and colleagues proposed a six-category framework for 3D geometric thinking based on work with Japanese students aged 12–15. Their findings highlight difficulty manipulating representations in some challenging problems. Study.
- First grade: Conceição and Rodrigues examined how pupils used cubes to reproduce shapes from 3D models and 2D representations, documenting different strategies for structuring parts and wholes. Study.
- Grades 4–9: A survey of 1,357 students in Japan, alongside a classroom-based study, examined spatial reasoning about 2D representations of 3D shapes. The sample is not a national estimate of all students. Study.
- Grades 6–9: An ERIC-indexed record describes a study of 196 pupils comparing SketchUp-based 3D-modeling training with a control group and reports improved spatial reasoning after training. The indexed abstract does not provide an effect size. ERIC record.
What to look for in student explanations
When assessing an activity, look beyond whether students produce a correctly named solid. Listen for whether they can explain how its parts fit together, connect a drawing to a possible solid, and justify what should be visible from a given viewpoint. Ask follow-up questions when a model is correct but the reasoning is unclear.
Quick Recap
- “Which faces meet here, and how can you tell?”
- “What would you see if you looked from above?”
- “Which part of the drawing helped you decide how many cubes to use?”
- “What changes when we turn the solid, and what does not?”
- “Could another construction match this drawing? Explain why or why not.”
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