etadd_47(3) - Division on Autism and Developmental Disabilities

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lesson with the entire class (8–10 students). Teacher trainings occurred in a university conference room. Materials Figure 1. Sample math story and graphic organizer for Geometry. Instructional materials. Middle school mathematics standards were selected using the state’s mathematics standards. These standards were simplified for instruction with the target population and reviewed by a university level mathematics content expert to ensure that each target skill was aligned with the target standard. The research staff then created sets of word problems for each standard using the same problem solving method (e.g., solving an equation; comparing graphed data) but with different applications (e.g., shop- 376 / Education and Training in Autism and Developmental Disabilities-September 2012
ping, dining out, voting) and differing numbers. Because of the students limited numeracy skills, the problems used numbers from 1–10. Each word problem was typed with key vocabulary (e.g., character in the word problem story) paired with pictures using a picture symbol software program (i.e., Writing with Symbols©). Eight problems per math standard (i.e., algebra, data analysis, geometry, and measurement) were given to the teacher, with a total of 32 math stories provided. These adapted word problem stories were printed in color and placed in page protectors for durability. The teacher was provided a binder divided by each standard which was called a unit (e.g., Geometry Unit). Within each divided section of the binder, the teacher was provided the graphic organizer for that unit (standard) and the adapted stories that corresponded to the unit. The graphic organizers were printed in color and laminated for durability. Velcro was used to manipulate numbers on the graphic organizer if the student was not able to use a visa-vi marker to write numbers. Additional manipulatives were provided as necessary to complete the math lessons (e.g., paper money for measurement, green and red chips for the algebra prompt, nonpermanent markers for geometry). Teachers were also provided a poster size graphic organizer for each of the units to use for group instruction. Figure 1 shows a sample adapted story and graphic organizer from the geometry unit for which the standard focused on finding points, line segments, and points on a plane. Dependent Variable The dependent variable was the number correct math responses made by the student during the unit (e.g., algebra) assessment probe. To investigate changes in student behavior in response to teacher’s use of the story-based math problems, four assessments of student responses were used (see Figure 2). The graduate assistant conducted one to two assessment probes with each student per week. A task analysis was created for the steps for each math standard (see Table 2). For each of the four math tasks, task analytic assessments were developed (Browder, Spooner, & Jimenez, 2011). During each of the assessments, the researcher displayed the needed materials and posed a question for the student to solve (e.g., “Show me how to ___ (find point A).” The student was given five seconds to begin each step of the task analysis. If the student did not complete a step, the researcher completed the step and said, “Keep going.” Students received praise for paying attention and working on the tasks. No task specific prompts or feedback were given. Each step of the task analysis was scored as correct () or incorrect (). For generalization, students were probed on math problem stories that had not been used during instruction, but required the same mathematical problem solving skill (e.g., steps to solve an equation.) Experimental Design and Analysis A single subject design was used to demonstrate a functional relationship between the mathematics intervention and the dependent variable which was acquisition of math responses. Specifically, the design was a multiple probe across four math units (standards) with concurrent between participant replications for the four target participants who received instruction as a group (Gast, 2010; Horner & Baer, 1978). During baseline, the math responses were probed for each student at minimum of three sessions or until data was consistent for three sessions. Following baseline, instruction began on Unit 1 (i.e., Geometry standard) for all four students. Students received task-analytic math lessons by the special education teacher. Prior to the students moving from Unit 1 to Unit 2 (i.e., Algebra), all individual students’ data had to show a change or trend after receiving instruction for a minimum of 5 weeks instruction on that unit. Once the students were ready to move to Unit 2, the students were each probed on Unit 2, Unit 3, and Unit 4 responses. After students’ data for Unit 2 showed a change in level or trend after receiving a minimum of five weeks instruction, Unit 3 (i.e., Data-Analysis) and Unit 4 (i.e., Measurement) were probed. Unit 3 was then taught following the same guidelines for Units 1 and 2, before Unit 4 was introduced. Prior to Unit 4 being taught, Unit 4 was probed. Instruction contin- Grade-Aligned Secondary Math / 377
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Education and Training in Autism an
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ities. Scholars have argued that do
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discussions were held with 12 addit
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TABLE 1 A Sample of Community Funds
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et al., 2007). At the school, stude
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students opportunities to work and
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Browder, D. M., & Cooper-Duffy, K.
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of words, and in the short term wer
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TABLE 3 Word Lists List No. Trainin
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TABLE 6 Pairwise Comparisons on Pos
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Word Identification or Word Attack
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erate to severe disabilities. Excep
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ess in a variety of subjects includ
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TABLE 1 Target Vocabulary Words by
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Figure 1. Example of PowerPoint Sli
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TABLE 3 Mean Percentage of Correct
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Figure 4. Jake’s percentages corr
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man-Martin et al. (2005) by demonst
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used in the study that did not foll
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lected. Stories were read in a quie
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y determining the number of interva
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with the removal of the interventio
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Accordingly, recent research has in
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Method Participants Four male child
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TABLE 2 Play Scale - Developmental
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elated utterances, which were used
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Figure 1. Ian’s Progress in Play
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Figure 3. Ryan’s Progress in Play
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Figure 5. Social Validity: Average
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(2000). A comparison of video model
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Method Participants Four high schoo
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TABLE 1 Task Analyses for all Tasks
Page 75 and 76: Figure 1. Holly multiple baseline g
Page 77 and 78: Figure 3. Norman multiple baseline
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Page 85 and 86: TABLE 2 Task Analyses Including Vid
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Page 89 and 90: Figure 2. Percent of steps with err
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Page 93 and 94: our students, it may have been diff
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Page 97 and 98: TABLE 2 Participants Demographic Da
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Page 101 and 102: TABLE 4 Total Number of Items Answe
Page 103 and 104: Figure 2. Total number of procedura
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Page 111 and 112: & Cobb, 2002). Generalization, the
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Page 115 and 116: Procedure Baseline. In this multipl
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Page 119 and 120: was repeated across all participant
Page 121 and 122: Boning, R. A. (1997). SRA Specific
Page 125: TABLE 1 Student demographic informa
Page 129 and 130: TABLE 2 Content Standards, Alternat
Page 131 and 132: Student Achievement Figures 3-6 pro
Page 133 and 134: Figure 4. Student data across math
Page 135 and 136: Figure 6. Student data across math
Page 137 and 138: A second limitation of the current
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Page 143 and 144: TABLE 1 Studies of Mathematics Inte
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Page 147 and 148: Neef and colleagues (2003) demonstr
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