Jimenez, B. A., & Besaw, J. (2020). Building early numeracy through virtual manipulatives for students with intellectual disability and autism . Education and Training in Autism and Developmental Disabilities , 55 (1), 28–44. http://www.daddcec.com/etadd.html

Journal Article

Jimenez, B. A., & Besaw, J. (2020). Building early numeracy through virtual manipulatives for students with intellectual disability and autism. Education and Training in Autism and Developmental Disabilities, 55(1), 28–44. http://www.daddcec.com/etadd.html


no doi reported


Autism; Educator survey; Elementary; Intellectual disabilities; Manipulatives; Math; No age; No disability; U.S. context





Virtual manipulatives were presented using a digital tablet application within a multi-component story-based virtual manipulative package, with embedded research-based and evidence-based practices (prompting, modeling, positive reinforcement, and manipulatives). As part of the baseline data collection of student performance on three early numeracy skills, students received the concrete / tangible form of the manipulatives, for comparison of the conditions.


Two students in a self-contained setting attending an elementary school in a rural district in the Southeast (U.S.) participated. Their teacher provided social validity data on her beliefs and perceptions about virtual manipulative accommodations; therefore, she was included as a study participant. The students' demographics and pre-study academic skills based on extended content standards were described. Both students were identified with autism and comorbid intellectual disabilities; the students were pre-screened with the Differential Ability Scales®-II (DAS-II; Elliott, 2007) and the Test of Early Mathematics Ability, third edition (TEMA-3; Ginsburg & Baroody, 2003). The first student was an 8-year-old Hispanic/Latino male; his IQ score was reported to be in the extremely low range, and he received English-as-a-second-language (ESL) services. The second student was a 9-year-old White (non-Latino) male; his IQ score was reported to be unattainable, and his adaptive behavior score was reported to be in the low range.

Dependent Variable

Early numeracy skill acquisition and student engagement were assessed "in-vivo" during one-on-one math lessons taught by the classroom. The students were assessed on their responses and engagement across baseline data, intervention, and generalization phases. The first dependent variable, accuracy on early numeracy skills, was embedded within a story-based math lesson, which focused on set making, non-standard measurement, and patterning. Students used 3D manipulatives for the baseline portion and virtual manipulatives for the intervention portion (presented through an iPad application). For the set-making task students were provided with extra manipulatives and asked to make a set of ≤ 5. In the non-standard measurement task, students were provided objects from the story and required to measure the length with manipulatives. In the pattern task, students were asked to continue an ABA pattern with materials associated with the story. The students completed five test-like tasks on each of the three skill areas during each lesson. Engagement was observed and measured based on whether the student displayed a threshold number of off-task behaviors within test sessions; researcher observations indicated whether the student appropriately used the manipulatives (tangible or virtual) during each trial. The teacher survey presented a rating scale on value, impact, and likelihood of implementing accommodation, yielding social validity data.


Participating students' performance data demonstrated a prompt response and increasing trend upon implementation of virtual manipulatives for the early math skills of set making, non-standard measurement, and patterns. Students also increased in engagement toward task completion when using virtual manipulatives. Students were able to generalize math skills across other math contexts. The educator survey yielded that virtual manipulatives have been effective in addressing academic, attention, and sensory needs; further, the accommodation was deemed cost- and time-effective and easy to implement. Limitations of the study were reported, and future research directions were suggested.