Autism & Developmental

Virtual and concrete manipulatives: a comparison of approaches for solving mathematics problems for students with autism spectrum disorder.

Bouck et al. (2014) · Journal of autism and developmental disorders 2014
★ The Verdict

Virtual 3-D blocks beat real ones for teaching subtraction to elementary students with autism.

✓ Read this if BCBAs teaching math to elementary students with autism in clinic or classroom settings.
✗ Skip if Preschool or adult programs, or staff without tablet access.

01Research in Context

01

What this study did

Three elementary students with autism learned subtraction with two kinds of blocks. One kind was real plastic blocks they could hold. The other kind was the same blocks shown on a computer screen in 3-D.

The teacher switched between the two tools every day. She counted how fast and how accurately each child solved the problems.

02

What they found

Every child was faster and more accurate with the virtual blocks. The gains carried over when the teacher later gave real-world word problems.

03

How this fits with other research

Trimmer et al. (2017) extends this idea. They used real coins first, then pictures, then numbers. Their middle-schoolers with intellectual disability mastered money skills. The sequence matters: start concrete, then fade to symbols.

Lee et al. (2025) looked at 5 studies that added pictures to reading lessons for students with autism. Paper pictures beat computer ones. That seems to clash with our target study, but the tasks differ. The reading studies used flat 2-D clip-art. The math study used movable 3-D blocks on screen. Kids could drag, rotate, and snap them. The extra action may be why virtual won here.

Kellems et al. (2016) used short math videos with adults. Like the target study, they alternated treatments and saw tech win. Together these papers show that when the digital tool is interactive, learners with disabilities often do better than with static objects.

04

Why it matters

You can swap out plastic blocks for a free virtual set tomorrow. Pick apps that let kids move, stack, and break apart the pieces. Start with one-step subtraction, then mix in word problems. Watch speed and accuracy for a week. If you see the same jump, keep the virtual set and save shelf space.

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→ Action — try this Monday

Download a free base-ten block app and run five subtraction problems; time and score versus your usual plastic set.

02At a glance

Intervention
other
Design
alternating treatments
Sample size
3
Population
autism spectrum disorder
Finding
positive
Magnitude
small

03Original abstract

Students with autism spectrum disorder (ASD) are included in general education classes and expected to participate in general education content, such as mathematics. Yet, little research explores academically-based mathematics instruction for this population. This single subject alternating treatment design study explored the effectiveness of concrete (physical objects that can be manipulated) and virtual (3-D objects from the Internet that can be manipulated) manipulatives to teach single- and double-digit subtraction skills. Participants in this study included three elementary-aged students (ages ranging from 6 to 10) diagnosed with ASD. Students were selected from a clinic-based setting, where all participants received medically necessary intensive services provided via one-to-one, trained therapists. Both forms of manipulatives successfully assisted students in accurately and independently solving subtraction problem. However, all three students demonstrated greater accuracy and faster independence with the virtual manipulatives as compared to the concrete manipulatives. Beyond correctly solving the subtraction problems, students were also able to generalize their learning of subtraction through concrete and virtual manipulatives to more real-world applications.

Journal of autism and developmental disorders, 2014 · doi:10.1007/s10803-013-1863-2