Schema-Based Instruction With Concrete and Virtual Manipulatives to Teach Problem Solving to Students With Autism

Abstract

ArticleMost mathematics educators would identify problem solving as the cornerstone of mathematical learning (National Council of Teachers of Mathematics [NCTM], 2000). Teaching problem solving allows students to learn when and why, not just how, to apply these skills. Students typically learn problem solving through the use of word problems. Fuchs et al. (2008) note that word problems can be a source of difficulty for many students because these problems require not only calculation, but also comprehension of linguistic information.According to Mayer's (1985) model of problem solving, there are four sequential phases to solving a mathematical word problem, including problem translation, problem integration, solution planning, and solution execution. Each phase requires different cognitive skills for successful completion. At the problem translation phase, semantic language skills construct meaning from the problem for which a student must be able to determine "what is happening" to identify known and unknown information. The problem integration phase requires selection of integral parts of the problem (e.g., known and unknown amounts) and translating them to a mathematical structure (e.g., number sentence in equation format). Once the student has a mathematical understanding of the problem, he or she needs to devise a plan for finding the solution. The solution planning and execution phases involve choosing the correct operations and carrying out those computations to arrive at a correct answer. Because problem solving is innately a chained task of discrete behaviors, each phase of problem solving is dependent upon successful completion of the previous phase in order to yield correct execution and ultimate arrival at a correct answer (Jitendra, Griffin, Deatline-Buchman, & Sczesniak, 2007).The challenge of teaching word problem solving to students with developmental disabilities like autism spectrum disorders (ASD) and intellectual disability (ID) is twofold. First, there is a lack of research on instructional strategies for teaching word problem solving to individuals with ASD and ID. Browder, Spooner, Ahlgrim-Delzell, Harris, and Wakeman (2008) conducted a meta-analysis to determine effective practices for teaching mathematical standards to students with moderate or severe developmental disabilities 643592R ASXXX10.1177/0741932516643592Remedial and Special EducationRoot et al. research-article2016 AbstractThe current study evaluated the effects of modified schema-based instruction on the mathematical word problem solving skills of three elementary students with autism spectrum disorders and moderate intellectual disability. Participants learned to solve compare problem type with themes that related to their interests and daily experiences. In addition, researchers compared the effects of concrete and virtual manipulatives within the treatment package. Results of the multiple probes across participants with an embedded alternating treatments design showed a functional relation between modified schemabased instr...

Estudio Exploratorio sobre Estrategias y Errores de un Estudiante con Trastorno del Espectro Autista al Resolver Problemas de División Partitiva

“…The work by Yakubova, Hughes and Shinaberry (2016) has shown the effectiveness of a video modeling intervention with CRA instructional sequence when teaching mathematics concepts to students with ASD. Some other intervention studies have successfully used virtual and concrete manipulatives to teach students with ASD arithmetic facts (Bouck, Satsangi, Doughty, & Courtney, 2014) and problem solving (Root, Browder, Saunders, & Lo, 2016).…”

Bilimsel-Dayanaklı Uygulamaları Belirlemede “Tek-Denekli Deneysel Araştırmaların Niteliksel Göstergeleri” Yönergesi’nin Matematik Becerileri Öğretimi Örneğinde Ele Alınışı

“…Independent Variable. Root, Browder, Saunders and Lo (2017) met all three quality indicators under the independent variable category, while Tiger et al (2007) met two of the three quality indicators under this category. Table 7 shows information presented in each article that was used when evaluating whether the study met the respective quality indicators.…”

Visual representations and verbal schemas: a case study of one student with high‐functioning autism

“…Root, Browder, Saunders, et al. () used a modified SBI to teach three elementary students with ASD and moderate ID to solve compare type word problems. However, research is still needed to investigate how SBI can be applied to the specific needs of students with HFA.…”

“…Saunders, Lo and Browder (2016) utilised a modified SBI to teach students with ASD and moderate intellectual disability how to make change, making specific modifications such as task analyses, colour-coded graphic organisers, and systematic prompting. Root, Browder, Saunders, et al (2017) used a modified SBI to teach three elementary students with ASD and moderate ID to solve compare type word problems. However, research is still needed to investigate how SBI can be applied to the specific needs of students with HFA.…”

“…For example, gestures may be essential for supporting working memory as students with HFA are engaging in difficult and unfamiliar mathematics situations that require students with HFA to think critically (Barrouillet, Bernardin, Portrat, et al, 2007;Goldin-Meadow and Alibali, 2013;Landa and Goldberg, 2005). Strategic use of manipulatives or math notation on paper to support productive mathematical conversations may be essential for some students with HFA who struggle with auditory processing and benefit from teaching that incorporates manipulatives into instruction as a support for spoken language (DePape, Hall, Tillmann, et al, 2012;Root, Browder, Saunders, et al, 2017).…”