Doing the Math: How Prepared are College-Bound Students With Disabilities?

Posted on December 12, 2013

math

In the process of moving through secondary grades towards high school graduation, treat many students with mild disabilities (e.g., more about specific learning disabilities, attention deficit disorder, emotional disturbance) fall behind their peers without disabilities in math achievement (Powell, Fuchs, & Fuchs, 2013; Wagner, Newman, Cameto, & Levine, 2006). This gap in math achievement places students with mild disabilities at a disadvantage when it comes to entering postsecondary education. Over half of all students with specific learning disabilities enter higher education (e.g., applied technology colleges, community colleges, universities), but only about one-fourth of them are awarded diplomas (compared to 54% of peers without disabilities).

The gap in math achievement is likely caused by several factors. First, many students are well behind grade level expectations when they are evaluated for special education eligibility. Second, special education teachers themselves are often not specialists in math assessment and instruction. Third, special instruction is often delivered in resource rooms which may reduce opportunities of both teachers and students from interacting in the general education classroom and understanding the high math expectations. Fourth, limitations in funding have eliminated qualified teacher and paraprofessional positions critical to provision of intensive, individualized instruction (Strawser & Miller, 2001).

We wanted to determine the extent to which students with mild disabilities were ready for college math, but by investigating teacher perception rather than test scores. Teacher perceptions are important because they have a powerful influence over what is taught in the classroom and how. We conducted a survey to find out the extent to which resource classroom special education teachers in high schools perceived students with mild disabilities (those who had postsecondary education goals) to be prepared for math at the college level. “College” was defined as either two or four-year post-secondary institutions. We also wanted to find out what resource teachers perceived as barriers to math preparedness and what they suggested as possible solutions.

Participants

Participants were 47 resource special education math teachers from Utah high schools (53% response rate). We targeted these teachers because they provided the perspective of educators responsible for preparing students with mild disabilities for college mathematics. We did not ask general education teachers to participate in this study.

Questionnaire

We developed a web-based survey questionnaire containing items requiring teachers to rate student readiness on four math constructs: (a) subject knowledge (subdivided into algebra; geometry; and calculus, trigonometry, and probability), (b) measurement and data representation, (c) number sense, and (d) mathematical reasoning and generalization (Corbishley & Truxaw, 2010). For example, the algebra item stated: “Students possess subject knowledge of algebra (i.e., students are able to solve one-step equations, word problems, and two variable equations; combine expressions; graph functions; find inverses).” We also asked about calculator and study skill abilities. Using a Likert-type scale (1=very poor, 2=poor, 3=adequate, 4=proficient, 5=excellent), teachers rated student abilities as well as the importance of the skill to college success (1= not at all important, 2=somewhat important, 3=important, 4=very important, 5=absolutely critical). Additionally, two questions asked teachers to rate how successful students with mild disabilities could be in college (1=not at all successful, 2=rarely successful, 3=somewhat successful, 4=successful, 5=highly successful) and how important it was for such students to attend college (1= not at all important, 2=somewhat important, 3=important, 4=very important, 5=absolutely critical). Finally, teachers answered open-ended questions about math preparedness, barriers and solutions.

Results

Mathematical readiness. Figure 1 presents average ratings on mathematical content. To assess the size of the gap between ratings of importance and ability, the average ratings of ability were subtracted from average ratings of importance for each item to determine a rating difference score. The larger the rating “gap” between importance and student ability, the larger the rating difference score. As shown in Figure 1, ability was rated lower than importance, on average, for all items.  In general, average ratings on all but one of the ability items were between 2 (poor) and 3 (adequate). Calculator use and number sense ranked highest, with subject knowledge of calculus, trigonometry, and probability ranked lowest of the other seven items. Average ratings of importance were more varied, with all but one falling between 3 (important) and 5 (absolutely critical), and study skills, calculator use, and reasoning and generalization rated the highest.  Interestingly, two of the top three items ranked most important, study skills and reasoning and generalization, demonstrated the largest difference between ratings of importance and ability.  This mismatch in critical math skills indicates a need to provide a stronger focus during math instruction on foundational skills that will help students with mild disabilities be more successful in math.

figure1 

Perceived barriers. We coded teacher responses to create categories of perceived barriers. All barriers fell into categories that we labeled system, student, family, or teacher. Within each category, the highest frequency responses are shown in Figure 2.

figure2

 

Perceived solutions. After coding, solutions suggested by respondents fell into the same categories as barriers. Figure 3 shows responses with the highest frequency solutions within each category.

figure3

Comparison of ratings of student preparedness to college success. Teachers rated the importance of college attendance and math between important and very important, 3.3 and 3.9, respectively on a 5-point scale.  They rated how successful students could be in college between somewhat successful and successful, or 3.7 on a 5-point scale.  However, teachers’ mean rating of student math ability was below the mid-point (between poor and adequate, or 2.4 on a 5-point scale).

Discussion

This survey study investigated the perceptions of a sample of high school special education teachers regarding the mathematical preparedness of high school students with mild disabilities. Results showed that teachers perceived students to have low ability on most mathematical knowledge or skills, and that the knowledge and skills were rated very important or critical to success in college. The largest differences in perceived ability and math importance were found to be in study skills, reasoning and generalization, and subject knowledge of calculus, trigonometry, and probability. Although all areas were rated as important, the findings suggest that these three are critical for students with mild disabilities who want to participate in college math classes.

Calculator use was rated as the second highest in math importance (4.2) with the smallest difference between importance and ability (1.1). However, many teachers commented that their students are “dependent” on calculators, even to do basic calculations. Two participants stated frustration that calculators could not be used in developmental college classes.  Taken together, these comments suggest a need for greater clarification of how and when a calculator should be used.

Respondents rated study skills by far the highest in importance, but near the middle in student ability, giving it the largest rating difference score (2.0). Ironically, when asked how they spend instructional time during math, none of the respondents stated that they spent time teaching study skills, and none stated that they wished they had more time to teach study skills. It seems that these teachers believe students should have the necessary study skills by the time they reach high school, and that it is not the teacher’s responsibility to teach study skills. However, given the reported discrepancies between the importance of study skills, lack of time spend teaching them, and lack of students’ ability with study skills, study skills seem to represent a significant gap that teachers need to address.  Explicitly teaching students study skills at all grade levels would not only benefit students in college, but throughout elementary and secondary school, potentially reducing some of the barriers teachers reported that were related to students.

Perhaps the finding of this study that raises the most concern was what teachers perceived about accountability for student math preparedness. Teachers definitely recognized the importance of students with disabilities enrolling in college and that they were not prepared mathematically; yet they seemed to be saying “someone else is/was responsible; there’s nothing I can do.” While teaching is certainly not the only variable affecting student math achievement, teachers must take responsibility for implementing solutions, particularly when many of the other perceived solutions are not within their control.

Our findings also suggest the need for greater communication between IEP teams and post-secondary personnel (such as college disability services office professionals and college advisors) about what math skills are required, so that teams can determine priorities and plans for individual students. Because more students with mild disabilities are attending college (whether they were expected to or not), special educators and administrators need to improve programs and services to increase student preparation, particularly in math—which is one of the greatest barriers to college success.

Authors: Adam D. King, Robert L. Morgan, Department of Special Education and Rehabilitation, Utah State University, and Catherine A. Callow-Heusser, Department of Mathematics and Statistics, Utah State University

References available upon request of the first author.