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Abstract: Manipulatives support students with and without disabilities in mathematics. However, as students age, concrete manipulatives can be limiting and potentially not age appropriate (Satsangi, 2015). An alternative is virtual manipulatives, including app-based manipulatives. This study compared the use of app-based manipulatives to concrete manipulatives in supporting students with disabilities in solving subtraction problems with regrouping Using an adapted alternating treatment design with three middle school students with disabilities, the researcher found app base 10 blocks were more effective in terms of solving subtraction with regrouping for two of the students. They also found that all three students were more independent with the app-based manipulatives, although only two of the three students preferred the app-based manipulatives to the concrete manipulatives.

Students with disabilities struggle with mathematics, and generally more so than students without disabilities (The Nation's Report Card, 2016). The average score for fourth-grade students with disabilities on the 2015 National Education Assessment Program (NAEP) was 218, as compared to the average score of 244 for fourth-grade students without disabilities. Similarly, for eighth-grade students with disabilities, the 2015 NAEP data suggested an average score of 247 for students with disabilities as compared to 287 for students without disabilities (The Nation's Report Card, 2016).

Given the struggle students with disabilities face in mathematics, researchers and practitioners have sought effective practices. In mathematics, manipulatives are considered an effective strategy for teaching students with and without disabilities (Marley & Carbonneau, 2014). Mathematics manipulatives - generally assumed to be concrete manipulatives - are physical objects students can manipulate with their hands. Over the past few decades, an alternative form of mathematics manipulatives was developed and used to support students: virtual manipulatives. Virtual manipulatives are digital manipulatives that serve similar functions as concrete manipulatives - and are often similar to concrete manipulatives - but exist in a digital form (Bouck & Flanagan, 2010). Previously, virtual manipulatives were online (or Internet-based) manipulatives, such as ones available from the National Library of Virtual Manipulatives (NLVM). However, more recently, with the increase in attention to mobile devices, a newer form of virtual manipulatives exists: app-based manipulatives.

Although the use of concrete manipulatives is supported in research and practice for students with disabilities (Lai & Berkeley, 2012; Maccini & Gagnon, 2000), concrete manipulatives posses...

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