**ERIC Number:**ED559601

**Record Type:**Non-Journal

**Publication Date:**2013

**Pages:**289

**Abstractor:**As Provided

**Reference Count:**N/A

**ISBN:**978-1-3033-1436-0

**ISSN:**N/A

Proportional Reasoning Word Problem Performance for Middle School Students with High-Incidence Disabilities (HID)

Brawand, Anne Eichorn

ProQuest LLC, Ph.D. Dissertation, George Mason University

Schema-based instruction (SBI) was used to examine the solving of proportional reasoning word problems for middle school students with high-incidence disabilities (HID). Seventh- and eighth-grade students with HID participated in the study. Students were randomly assigned to one of three groups. A multiple-baseline-across-groups design was utilized, which included baseline and staggered treatment phases. The SBI process consisted of nine lessons for all groups, lasting 35 minutes each, for 2-3 days per week. The SBI process consisted of three phases. Phase I was baseline when data were gathered about students' current level of performance solving proportional reasoning word problems. After Phase I, students in the three groups were provided with an overview on schema instruction using proportional reasoning problems that were already solved (worked problems). During the overview, schema instruction was introduced using already worked problems to identify and represent information in story problems on a diagram. In Phase II (SBI Process), students needed to enter information from the word problem into a diagram. Students also had to determine missing numbers needed to calculate an answer, write a number sentence, and solve word problems in this phase. In Phase II the students received explicit instruction on how to use the SBI process to solve proportional reasoning word problems. Teaching of the SBI process also incorporated FOPS, a four-step problem-solving strategy. A FOPS checklist was referred to as the following steps were introduced and explained: F- Find out if it is a proportional problem, O-Organize the information in the problem using the diagram, P-Plan to solve the problem, and S- Solve the problem. Finally, Phase III measured whether the students maintained the number of categories completed correctly in the SBI process 4 weeks after the SBI intervention. The three proportional reasoning types (unit rates, proportions, and scale drawings) were taught separately and had different difficulty levels of computation (novice, intermediate, and advanced). Data were analyzed separately for all groups, both with and without a calculator. The levels of analysis included overall improvement with the SBI process to solve proportional reasoning word problems, as well as across groups. Performance was measured using a five-category rubric for the Proportional Reasoning Word Problem Probes. The five categories were drawing shapes for the diagram, labeling, knowing the type of problem, writing a number sentence, and having the correct answer. Probes had three problems on the front, which students solved without a calculator, and three problems on the back, for which students could use a calculator. On the probes without a calculator, all groups increased to an overall level of 64.2%, SD = 16.0 (from 3.8% in baseline); with a calculator, the increase for all groups was to a level of 53.9%, SD = 19.6, (from 1.6% in baseline). All groups (both with and without a calculator) had a flat trend in baseline and demonstrated an increasing trend at different times per group within Phase II. The overall variability in baseline was low as compared to the levels, and students' performance in Phase II also demonstrated low variability as compared to the accelerating trends. All groups had a slow immediacy of change when the SBI process was introduced and minimal overlap of data points. In Phase II, the data points were consistently higher than in baseline. Results indicated that all groups of students learned the first three categories of the SBI process but did not learn the last two categories for writing a number sentence and having the correct answer. In Phase III, students also maintained learning for the first three categories with increases for two categories (shapes and labeling) four weeks after instruction. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Descriptors: Middle School Students, Disabilities, Logical Thinking, Word Problems (Mathematics), Problem Solving, Grade 7, Grade 8, Mathematics Instruction, Direct Instruction, Instructional Effectiveness

ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site: http://www.proquest.com/en-US/products/dissertations/individuals.shtml

**Publication Type:**Dissertations/Theses - Doctoral Dissertations

**Education Level:**Middle Schools; Secondary Education; Junior High Schools; Grade 7; Elementary Education; Grade 8

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A