The importance of strong self-efficacy, value for mathematics, and low anxiety toward mathematics for supporting learning is well documented (Marsh & Yeung, 1997; Meece, Wigfield, & Eccles, 1990; Pajares & Graham, 1999). Unfortunately, as students progress through school, they tend to value mathematics less and their ability beliefs tend to steadily decline (Jacobs, Lanza, Osgood, Eccles, & Wigfield, 2002). Students with learning disabilities have significantly lower academic self-beliefs than their non-disabled peers; this discrepancy is apparent as early as third grade and persists into high school (Chapman, 1988; Tabassam & Grainger, 2002). Thus, there is a need to understand which instructional practices can be motivating for mathematics learners, particularly those with learning disabilities.

Conceptual Perspective

In a mastery-oriented classroom, there is an emphasis on learning, effort, and improvement, whereas a performance-oriented classroom emphasizes grades, ability, and comparison (Ames, 1992). Students who perceive their teacher to have mastery goals are more likely to be mastery-oriented and to feel efficacious about mathematics (Friedel, Cortina, Turner, & Midgley, 2007). However, students with learning disabilities are more likely than their peers to adopt performance goals (Baird, Scott, Dearing, & Hamill, 2009).

It is unclear how recommendations for motivating students in mathematics align with recommendations for instructing learning disabled students. Although explicit instruction is more effective for struggling learners than supporting students to build their own understandings (Kroesbergen, Luit, Maas, 2004), a focus on conceptual understanding has motivational benefits (Stipek et al., 1998). Explicit instruction and teaching of heuristics have the strongest effect sizes in supporting achievement of students with learning disabilities, but there is evidence that other practices, such as having students verbalize their thinking, may enhance these effects (Gersten et al, 2009). It is possible that effective instruction for students with special needs could be both conceptually oriented and explicit; research is needed to explore if such a blend could be motivating.

Two research questions guided this study: (1) What are learning disabled students’ motivations toward fractions in this classroom, and how did they change over time? (2) Which instructional practices were influential in altering students’ motivations toward fractions?

Methods

Participants and Setting

All students were enrolled a private school for students with language-based learning differences; mathematics ability varied, ranging from at- to below-grade level. Eleven out of twelve students in the class participated. Of these, ten were sixth grade students and one was in fifth grade. Seven of the students were girls. The students in this class received approximately 40 minutes of daily mathematics instruction.

The teacher, Ms. Jordan (a pseudonym), had taught in the elementary grades for over 17 years. Due to weak prior knowledge, Ms. Jordan included fraction skills from the prior two years in her fraction unit. Consequently, the unit spanned three months.

Data Collection and Analysis

Motivation surveys were administered at the beginning and end of the fraction unit. Interviews explored students’ motivations qualitatively (triangulated with survey data) and captured students’ perspectives about what motivated them. 28 video-recorded observations were used to describe teachers’ instructional practices (triangulated with students’ self-reports in interviews).

Motivation questionnaire. The 15-item survey investigated students' motivations toward fractions using a 7-point scale. Three scales were included in the survey: anxiety (e.g., When someone asks you some questions to find out how much you know about fractions, how much do you worry that you will do poorly?), ability perceptions (e.g., How good at fractions are you?), and value of fractions (e.g., In general, how useful is what you have learned about fractions?). The survey was adapted from prior work (Eccles et al., 1993; Wigfield & Eccles, 2000; Wigfield & Meece, 1988) by changing math to fractions. Means and standard deviations were found for each scale.

Interviews. Immediately after solving some fraction problems, students were asked about anxiety, ability perceptions, and valuing of fractions using questions consistent with the survey. Students were also asked how their current feelings about fractions compared to their feelings prior to the instruction. Finally, students were asked to explain whether anything in their classroom experience led them to feel differently about fractions. Two analysts double-coded interviews to identify (a) descriptions of changes in students’ motivation and (b) factors observed in the teacher's classroom practices that supported changes in motivation.

Videos. Two analysts double-coded a sample of nine videos of classroom instruction distributed across time to identify instructional practices the teacher implemented during the fraction unit.

Results

Students’ Motivation

Students’ motivation improved along all three survey scales, as evidenced by significantly higher scale means, despite documented trends that would predict decreased or perhaps stable levels among this student population (Jacobs et al., 2002; Lapointe et al., 2005; Wigfield & Meece, 1988). Qualitative data confirmed these improvements.

Instructional Practices

Collectively, students described four factors that contributed to changes in their feelings toward fractions: a focus on strategies, a deepened understanding, extra support from the teacher (often after school), and the extended amount of time spent on fractions.

Video analyses aligned with students’ self-reports. Ms. Jordan's classroom was noticeably mastery-oriented. Her focus was on understanding, as illustrated by her "why" questions, emphasis on student thinking, and use of activities, manipulatives, and real-world connections to foster learning. Grades were de-emphasized and students were encouraged to take risks. Ms. Jordan explicitly restated concepts when students arrived at a significant idea, but students were first encouraged to reason, make connections, and then verbalize their thinking. Multiple strategies for solving problems were emphasized, but instruction did not focus heavily on general heuristics.

Conclusions

Although this teacher did make concepts explicit for students, it was typically after students had an opportunity to reason and verbalize their thinking. This finding underscores a need to describe the nature of effective direct instruction in greater detail (Gersten et al., 2009). If teachers want to both motivate and support achievement of students with learning disabilities, then instruction that includes a focus on making concepts explicit and that connects instruction to students’ thinking appears to be promising. This study represents an existence proof of mathematics instruction that motivates middle school students with learning disabilities.

References

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