Autism Society records most keynote and concurrent sessions at their annual conferences. You can see and hear those recordings by purchasing full online access, or individual recordings.

Friday, July 8, 2011: 1:15 PM-2:30 PM

Captiva 1&2 (Gaylord Palms Resort and Convention Center)

In this interactive session, participants will learn about the findings from a study that reviewed the literature in the area of instructional interventions in mathematics for students with ASD. A teaching-mathematics-for-understanding lens was used to analyze the studies that met the criteria for this review. Participants will be involved in a demonstration involving a mini-lesson in mathematics that highlights the differences in the two teaching strategies. Implications for classroom practice will also be discussed.
Increasing prevalence rate for autism coupled with the National Research Council’s (2001) recommendation and legislative requirements means that more students with autism spectrum disorders (ASD) will be placed in general education classrooms where teachers will be charged with supporting these students to learn mathematics. Characteristics of ASD may help or hinder academic performance. For example, although students with ASD that may have deficits in social communication (Baron-Cohen, 2008), they may also possess substantial visual-spatial abilities (Schuler & Baldwin, 1981) and preference towards detail-oriented thinking (Happe, 1999). In addition, contrary to a common perception that a majority of individuals with ASD are cognitively impaired, recent literature suggests that these individuals are increasingly recognized as having normal to above normal levels of intelligence (e.g. Croen, Grether, Hoostrate, & Selvin, 2002). As equity for students with ASD is sought and secured, teachers must prepare to face the challenges and opportunities created in the form of access to high-quality mathematics instruction.

The question of how to best teach mathematics to students with ASD is raised. The first step in understanding “best practice” is to turn to the literature exploring existing practices. Reviews relating to the instructional interventions in mathematics for students with ASD are very limited. The purpose of this presentation session is to share the findings from the literature review I conducted which, through a teaching-mathematics-for-understanding lens, examined the instructional strategies and tasks used to teach mathematics to students with ASD. Below is: 1) a discussion of the teaching-mathematics-for-understanding theoretical framework as it may apply to students with ASD; 2) a description of the search method used in the study; 3) a summary of the findings; and 4) an overview of the planned interactive presentation and the learning objectives.

**Teaching Mathematics for Understanding**

The National Council of Teachers of Mathematics recommends that all students have opportunities to engage in meaningful instruction in mathematics for developing understanding of mathematical content and procedures (NCTM, 2000). However, for students with special needs, Bottge (2001) argues that their natural intuitions in mathematics are often stymied due to instructions that focus on rote memorizations and procedural knowledge. These types of surface-level knowledge often have limited connections to the underlying mathematical concepts. That is, special education students taught in this manner often fail to build the foundational understanding of mathematical structures and concepts (Allsopp et al., 2008). Bottge (2001) recommends that teachers create learning environments that are meaningful and rich to allow students to apply the learned content to other environments. For students with ASD, this type of learning environment may provide them the opportunity to engage in thinking and reasoning in order to advance their conceptual understanding of mathematical content and procedures so that they may develop mathematical proficiency. Taken together, the aim of teaching mathematics for understanding requires an emphasis on scaffolding and building upon students’ natural intuitions and inclinations through the active engagement of thinking and reasoning of mathematical concepts and ideas.

Given the importance of providing appropriate instruction in mathematics, the literature review utilized a teaching-mathematics-for-understanding lens to examine: 1) the assessment procedures used to guide and evaluate interventions to improve mathematics performance in students with ASD; 2) the intervention methods used to improve mathematics performance in students with ASD; 3) the outcomes of the interventions used to improve mathematics performance in students with ASD.

**Method**

The method for identifying articles for the current review was conducted through a process involving electronic and hand-searches. The first step was an electronic search of the Educational Resources Information Center (ERIC) and the PsychoINFO databases. The keywords used in the first search were *mathematics *or *math* or *arithmetic* and *autism or Asperger’s *and *intervention* or *instruction. * This search resulted in 41 articles.* *Only articles from peer-reviewed journals were considered. The citation abstracts from the databases were reviewed and articles that examined interventions in mathematics for students with ASD were selected. Seven articles met the criteria. The second step involved a hand search of the reference sections of these seven articles. Four additional articles met the inclusion criteria from the hand-searches. Thus, a total of 11 articles published between 1989 and 2010 were included in this review. Literature reviews in the area of mathematics intervention for students with ASD were not found in the search.

**Summary of Findings**

The literature in the instructional interventions in mathematics for students with ASD is very limited. Thus, caution needs to be taken when interpreting these outcomes. The current literature seems to suggest that students with ASD show positive gains in mathematical skills when taught using procedures that ensure success and/or when reinforcers are present during the instructional process. On the other hand, the literature also seems to indicate that these students do not have access to mathematical tasks and instruction that target conceptual understanding. That is, students with ASD are often subject to mathematics that lack meaning or substance. In addition, the assessment procedures used in these studies to evaluate students with ASD’s current level of knowledge and thinking were often inadequate. Most studies utilized only one basic measure such as the correctness of the answers to determine whether the student understood the concept. Comprehensive systems of assessments, which are often considered to be best practices in gauging a student’s level of understanding (in particular those with ASD), were not implemented in the studies reviewed. These results are consistent with other studies that found that mathematical tasks such as counting, calculation, or number matching, and basic forms of assessments are commonly used in the instructional process of students with disabilities (e.g. Browder, Spooner, Ahlgrim-Delzell, & Wakeman, 2008).

**Interactive Presentation**

The presentation will be formatted so that participants will be involved in a comparative demonstration of a lesson involving the teaching-mathematics-for-understanding framework and one involving rote-memorization procedures. Through this demonstration, participants will play the role of students and experience the differences of the two approaches. In the role as students, participants will be asked to answer questions and be engaged during a short lesson in mathematics. Following the demonstration, participants will have a chance to discuss their thoughts of the experience, and the findings from the study will be presented. Towards the end of the presentation, time will be allotted for a discussion on the recommendations for teaching students with ASD mathematics for understanding, and the agenda for future research in mathematics interventions for students with ASD

**Learning Objectives**

By the end of the presentation, participants will:

1) Be able to distinguish between a lesson involving a teaching-mathematics-for-understanding framework and one involving rote-memorization procedures.

2) Understand the importance of using high-quality instruction to teach mathematics to students with ASD.

3) Learn about the findings from the literature review in the domain of instructional interventions and assessments in mathematics for students with ASD.

4) Be able to identify four or five recommendations for best practices in mathematics instructions for students with ASD.

**Conclusion**

The reviewed studies point to low expectations in the area of mathematics for students with ASD and provides evidence that supports NCTM’s argument that students with disabilities are often taught mathematical lessons that lacks substance (NCTM, 2000). For students with ASD the vision of high-quality mathematics education is seemingly distant. These students do not have access to instruction that is designed to support cognitive development. As the call for equity for all students is heard, who is working to see that NCTM’s vision is enacted with and for students with ASD? In the quest to improve the lives of students with ASD, *we* must ensure that quality mathematics instruction is delivered.

**References**

Allsopp, D. H., Kyger, M. M., Lovin, L., Gerretson, H., Carson, K. L., & Ray, S. (2008). Mathematics dynamic assessment:Informal assessment that responds to the needs of struggling learners in mathematics. *Teaching Exceptional Children, 40*(3), 6-16.

** **

Baron-Cohen, S. (2008). *Autism and Asperger syndrome*. New York: Oxford University Press.

Bottge, B. A. (2001). Reconceptualizing mathematics problem solving for low-achieving students. *Remedial and Special Education, 22*(2), 102-112.

Browder, D. M., Spooner, F., Ahlgrim-Delzell, L., & Wakeman, S. (2008). A meta-analysis on teaching mathematics to students with significant cognitive disabilities. *Exceptional Children, 74*(4), 407-432.

Croen, L. A., Grether, J. K., Hoogstrate, J., & Selvin, S. (2002). The changing prevalence of autism in California. *Journal of Autism and Developmental Disorders, 32*(3), 207-215. * *

Happe, F. (1999). Autism: cognitive deficit or cognitive style? *Trends in Cognitive Sciences, 3*(6), 216-222.

National Council for Teachers of Mathematics (2000). *Principle and standards for school mathematics.* Reston, VA.

National Research Council*, *Division of Behavioral and Social Sciences and Education, Committee on Educational Interventions for Children with Autism (2001). *Educating children with autism*. Washington, D.C.: National Academy Press

Schuler, A. L., & Baldwin, M. (1981). Nonspeech communication and childhood autism. *Language, Speech, and Hearing **Services in Schools, 12*, 246-257.

**Learning Objectives**:

- By the end of the presentation, participants will be able to distinguish between a lesson involving a teaching-mathematics-for-understanding framework and one involving rote-memorization procedures.
- Understand the importance of using high-quality instruction to teach mathematics to students with ASD.
- Learn about the findings from the literature review in the domain of instructional interventions and assessments in mathematics for students with ASD.
- Be able to identify four or five recommendations for best practices in mathematics instructions for students with ASD.

**Content Area:** Applied Research

Presenter:

Paulo Tan, M.S., Ed.

Doctoral student

Indiana University

Dr. Tan is currently a second-year doctoral student in special education at the University of Indiana. His area of specialization is autism spectrum disorders and his minor is mathematics education. Prior to pursuing his doctoral degree, he taught math at the secondary level for 10 years.