Practitioner Perceptions of Algebra Strategy and Intervention Use to Support Students With Mathematics Difficulty or Disability in Rural Texas

Survey Development

The authors reviewed meta-analyses and syntheses (see Durlak et al., 2011; Gersten et al., 2009; Rakes et al., 2010; Zheng et al., 2013), research reports (e.g., NMAP, 2008; Star et al., 2015), and online resources (e.g., IRIS Center, National Council of Teachers of Mathematics [NCTM], What Works Clearinghouse) to identify mathematics practices. Next, we established an expert panel that included (a) professors of mathematics, special education, and curriculum and instruction; (b) algebra teachers; (c) special education teachers; (d) curriculum specialists; and (e) a high school principal certified in mathematics. In addition to being content specialists, each panel member had relevant experience working with students with mild disabilities including relevant disability-specific knowledge. Delphi procedures were used to increase the likelihood that we captured both empirically validated and often-used strategies. Delphi procedures involve asking a confidential panel of experts to address a series of questions, followed by a review process, to reach consensus (Moore, 1987). The method was originally used in industry and has more recently been applied to education decision making (see Clayton, 1997). Each of the 18-member expert panel was contacted individually by email and asked to review a list of practices for students with mathematics difficulties and disabilities, indicate any missing strategies and interventions, or remove strategies or interventions that did not fit. Although strategy and intervention are often used interchangeably, strategies are generally instructional and behavioral practices. Interventions include prescribed procedures that are systematically implemented (Vaughn & Bos, 2015). After the initial review, a follow-up email was sent to panelists that summarized group responses and inclusion criteria on a scale ranging from −2 (strongly disagree) to 2 (strongly agree; Clayton, 1997). Finally, the Delphi process resulted in unanimous strategy and intervention agreement among panelists.

Considering expert panel recommendations, the first author drafted a cross-sectional survey comprised of five sections. The first section included demographic questions followed by three sections of Likert-type items to address each of the research questions. The last section included two open-ended questions to allow participants the opportunity to provide additional information related to their practice. Next, the expert panel reviewed the survey individually and then collectively by email. The panel made several recommendations, including adding demographic questions (e.g., teacher’s native language, number of preparations) and adding open-ended questions related to professional development.

The authors reviewed and incorporated suggested updates, compiled a list of suggestions from the panel, and emailed a second version of the survey link for further comment. Two panelists recommended rewording of a question related to professional development experiences. After questions were modified, all members of the panel unanimously agreed that the survey aligned with research questions, was an appropriate length, and items were clearly defined. To further support validation, 23 graduate-level education students reviewed and completed the electronic survey. Further adjustments were made to open-ended questions to assist with item order and clarity. The revised electronic survey included demographic questions, 51 Likert-type items to address research questions, and three open-ended questions.

Questionnaire Implementation

Phase 2 involved conducting individual, semistructured interviews to glean additional insight into teacher knowledge and use of evidence-based practices to meet the needs of students with MD or MLD. In addition, the researcher hoped to develop a greater understanding of teacher professional development needs to support students with MD or MLD. Interviewees were asked to answer the following questions: (a) What are the most challenging aspects of meeting the needs of rural Texas students with MD or MLD? (b) How do teachers select interventions and strategies to support students with MD or MLD? (c) What barriers are present that affect strategy selection and implementation? (d) What professional development has been helpful? and (e) What professional development opportunities have not been helpful? The final two questions of the survey were intended to be general questions to see whether students with MD or MLD would emerge in responses without prompting. Follow-up questions specific to students with MD or MLD were asked whether participants did not initially mention this population.

Teacher Interview Procedures

After completing the survey, participants had the opportunity to volunteer to complete a brief follow-up interview. Sixty-three respondents volunteered for follow-up interviews. The researcher selected a purposeful sample of 22 volunteers who represented the survey population with regard to teaching experience, region, and professional licenses. Semistructured phone interviews were completed by trained graduate research assistants. The interview protocol included five questions related to instructional strategy use, access to resources, barriers to implementing evidence-based strategies, and professional development practices and needs. Interviews ranged from 26 to 48 min. After each interview was completed, a graduate research assistant transcribed the interview. First-level member checks were used to assist with credibility (Brantlinger, Jimenez, Klingner, Pugach, & Richardson, 2005). After transcriptions were completed, interviewees were emailed a copy of their responses to check for agreement with the transcription.

Data Analysis

After reading transcriptions in their entirety, a graduate research assistant and the first author independently completed open coding of a series of interviews. This initial open coding resulted in 18 initial themes. Next, five primary categories and 12 subcategories were identified, agreed upon, and defined through an iterative axial coding (Patton, 2005). To assist with maintaining consistency and trustworthiness of the analysis, a third coder served as a peer debriefer (Brantlinger et al., 2005).

Participants

Full-time, in-service teachers responsible for providing algebra instruction in rural Texas public schools were targeted. Respondents included 258 teachers from 176 rural districts. The sample included teachers from each of Texas’ regions employed within 17 out of 20 regional service center areas.

Most respondents reported working in high schools (86%), followed by middle schools (13%) and elementary schools (1%). More than 67% of respondents reported 1 to 3 years of teaching experience with the second highest years of experience group ranging from 7 to 15 years of experience (23%). The remaining respondents reported 4 to 6 years of experience (3%) and 16 or more years of experience (7%). Most respondents were Caucasian, native English speakers (90%). Approximately 75% of respondents identified as female with about half of those respondents having earned a master or educational specialist degree. Participants reported a variety of certifications with the most common including elementary mathematics, middle grades mathematics, or secondary mathematics. Approximately 8% of respondents reported having special education, counseling, and/or administration and supervision endorsements. Most respondents reported teaching ninth-, 10th-, and 11th-grade algebra courses (84%). Less than 10% of respondents reported teaching algebra courses in Grades 6 to 8. Respondents were responsible for teaching one to eight sections of algebra with the majority teaching two to three sections (58%). Preparations ranged from one to seven with a majority of respondents reporting three or more preparations (67%). Course responsibilities varied and included teaching engineering, precalculus, geometry, physics, and statistics courses in addition to algebra.

Participants indicated that their classrooms included English language learners, students with disabilities, students who receive free and reduced lunch, and students from minority backgrounds. More than 90% of respondents indicated that they taught students with learning disabilities. A majority of respondents indicated that their classrooms include more than 50% of students who are eligible for free and reduced lunch. In addition, many participants reported that 51% to 75% of the students in their classes experience difficulty passing classroom assessments, district benchmarks, and/or state tests, thus, suggesting that their classrooms include students with MD. As the grade level increased, the percentage of students experiencing difficulty also increased as did the percentage of students from minority backgrounds, English language learners, students eligible for free and reduced lunch, and students with disabilities. For example, most teachers (82%) who worked with 11th-grade students reported a majority of their students struggled to complete grade-level assessments and reported many of their students were included in one of the previously mentioned groups (88%).

Summary of Phase 1 Findings

Results suggest that rural Texas teachers are comfortable with the mathematics domains associated with the algebra curriculum; however, results indicate that teachers are uncomfortable teaching students with MD or MLD. Furthermore, teachers’ knowledge and perceptions of evidence-based practices appear limited.

Knowledge and use of strategies

The most frequently reported strategies and interventions included learning styles, lecture, providing a range of examples to illustrate key concepts, and use of different algebraic representations. Approximately 16% of respondents indicated that they implemented learning styles at some point during the year and an additional 50% of respondents indicated routine use of learning styles. Teacher-delivered lectures were used routinely by approximately 70% of respondents and implemented at some point during the year by an additional 21% of respondents. Respondents indicated routinely using a variety of examples to illustrate key concepts (42%). Approximately 90% of teachers reported incorporating solved problems into classroom instruction and activities at some point during the year (48%) or routine use of the strategy (42%). Respondents also reported teaching students that different algebraic representations can convey different information about a problem with more than 95% reporting using the strategy in their classrooms. PBL was another familiar strategy. Yet, only 41% of respondents reported routine use of PBL strategies.

Although teachers indicated a variety of practices that they use in their classrooms, they also shared that they are familiar with several strategies but did not implement those strategies in their classrooms. For example, 28% of teachers reported being familiar with learning styles but not using the strategy; 10% were familiar with mind-sets but elected not to use the strategy.

Table 1 provides a summary of reported strategy use.

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Table 1.

Reported Use of Instructional Strategies.

Strategy	Unfamiliar with the strategy	Know about the strategy but do not use the strategy	Implemented the strategy at some point during the year	Routinely use the strategy
Embodied cognitive processing	45% (n = 116)	5% (n = 13)	42% (n = 108)	8% (n = 21)
Use of solved problems into classroom instruction and activities	0% (n = 0)	10% (n = 26)	48% (n = 123)	42% (n = 109)
Lecture	5% (n = 13)	5% (n = 13)	21% (n = 55)	69% (n = 177)
Learning styles	6% (n = 16)	28% (n = 72)	16% (n = 41)	50% (n = 129)
Mind-sets	0% (n = 0)	10% (n = 26)	48% (n = 123)	42% (n = 109)
Problem-based learning	0% (n = 0)	24% (n = 62)	35% (n = 90)	41% (n = 106)
Reflective questioning	10% (n = 26)	5% (n = 13)	63% (n = 164)	21% (n = 55)
Teach algebraic representations can convey different meanings	0% (n = 0)	5% (n = 13)	53% (n = 136)	42% (n = 109)

Knowledge and use of interventions

The most routinely used interventions to support students with MD or MLD included explicit instruction, providing a range of examples, teacher feedback, and visual representations. Conversely, fewer teachers reported use of empirically validated interventions including CRA sequence, instructional sequencing, schema-based instruction, or student feedback with goal setting. Approximately 64% of respondents indicated that they were unfamiliar with schema-based instruction or familiar with, but do not use, schema-based instruction. More than 50% of respondents were unfamiliar with or do not use the CRA sequence. See Table 2 for a summary of teacher knowledge and use of interventions.

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Table 2.

Reported Use of Interventions to Support Learners With MD or Disability.

Intervention	Unfamiliar with the intervention	Know about the intervention but do not use the intervention	Implemented the intervention at some point during the year	Routinely use the intervention
Concrete–representation–abstract sequence	37% (n = 95)	16% (n = 40)	37% (n = 95)	11% (n = 28)
Explicit instruction	0% (n = 0)	0% (n = 0)	47% (n = 121)	53% (n = 137)
Heuristics	42% (n = 108)	11% (n = 28)	31% (n = 81)	16% (n = 41)
Instructional sequencing	26% (n = 67)	11% (n = 28)	42% (n = 109)	21% (n = 54)
Peer tutoring	0% (n = 0)	5% (n = 13)	61% (n = 160)	33% (n = 85)
Schema-based instruction	32% (n = 83)	32% (n = 83)	31% (n = 80)	5% (n = 12)
Sequencing/range of examples	0% (n = 0)	0% (n = 0)	39% (n = 101)	61% (n = 157)
Student feedback	0% (n = 0)	5% (n = 13)	64% (n = 164)	31% (n = 81)
Student feedback with goal setting	0% (n = 0)	26% (n = 67)	42% (n = 108)	32% (n = 83)
Student verbalizations/think alouds	5% (n = 13)	21% (n = 54)	47% (n = 124)	26% (n = 67)
Teacher feedback	0% (n = 0)	11% (n = 28)	31% (n = 81)	58% (n = 149)
Visual representations	0% (n = 0)	0% (n = 0)	53% (n = 137)	47% (n = 121)

Note. MD = mathematics difficulty.

Knowledge and use of resources

The majority of respondents indicated knowledge and routine use of popular social media and outlets including Facebook (52%), Pinterest (72%), and blogs (58%) for locating interventions to support students with MD or MLD. Reliance on conversations with other teachers (94%) and Teachers-Pay-Teachers (68%), as well as conversations with district specialists (27%), were other popular resources that were reported as routinely used. More than 40% of teachers indicated familiarity with several mathematics education practitioner journals but noted they do not use them as a resource. In addition, some teachers reported knowledge of professional organizations. For example, 30% of teachers indicated that they were familiar with the Council for Exceptional Children (CEC) but less than 5% reported use of CEC resources. Teachers were more familiar with the NCTM resources, with 60% indicating knowledge of NCTM and approximately 21% of teachers reporting routine use of NCTM resources. Respondents were generally unfamiliar with RtI Network (21%), Intervention Central (56%), and PBIS.org (82%). See Figure 1 for teacher use and routine use of interventions.

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Figure 1.

Teacher use of resources.

Summary of Phase 2 Findings

The interview participants painted a similar picture of current practices, professional development offerings, the definition of high-quality professional development, and current barriers to implementing evidence-based practices. Most teachers reported using a mixture of both evidence-based and non–evidence-based instructional strategies, including those learned during their undergraduate coursework or those learned informally through other teachers. Teachers agreed on many of the characteristics of high-quality professional development, but reported limited access to this type of ongoing learning beyond expensive and logistically unfeasible university coursework. Participants also reported similar perceived obstacles to implementing professional development in their districts or schools. General themes and representative quotes are summarized below.

Interview participants cited two main sources for credible instructional strategies—strategies they were taught during their undergraduate coursework or those they learned from other teachers. A middle school algebra teacher shared the following:

. . . I learned about PBL [problem-based learning] during a course at Stephen F. Austin. We designed labs and students completed activities. I like PBL and believe it helps my students. If all teachers had the opportunity to use PBL, STAAR scores [state test] would go up.

Another participant reported the following:

. . . I talk to the elementary math teacher. At least we both teach math. We have a lot of student needs and I am not exactly sure how to meet them all. I teach the standards. Some kids get it and they routine [sic] share that they are bored. Others, no matter what I do, don’t get it. We talk [elementary teacher] afterschool and try to come up with ways to make Algebra interesting. Often, we try to create hands-on activities that allow students to explore real world applications.

Approximately 77% (17/22) of the participants shared that many of the strategies they use were taught during undergraduate course work. The 17 respondents varied in age, experience, and degrees obtained. The five interviewees who did not mention undergraduate coursework also varied in age and experience levels.

The strategies that participants shared as credible and effective included both evidence- and non–evidence-based practices, which were given equal credence. The evidence-based strategies shared included peer tutoring, cooperative learning, teacher modeling, and questioning strategies. Approximately 64% (14/22) of participants mentioned an empirically validated strategy included in recent meta-analyses or research reports reviewed for the study. Several strategies that lack empirical support, including learning styles and mind-sets, also were shared. A 10th-grade teacher reported,

You have to understand how kids learn. I have students that learn through visuals and others who are auditory learners. You have to figure out how a kid learns and then teach to his style.

Participants reported the need for ongoing, high-quality, formal professional development beyond their informal shared network of teacher strategies, but many (73%, 17/22) felt current professional development could benefit from improvements in format and content. In addition, participants (64%, 14/22) shared that the available professional development is often a “one shot” day that does not include necessary follow through to ensure effective implementation or sustainability. A respondent from West Texas shared, “We often do not get to do the math. We are just told to implement a strategy. One-day seminars don’t really work.” Another participant reported,

There are limited professional development offerings. Many of them are not helpful and do not help us with students from poverty or the growing number of students who need special education. All of the professional developments lack follow up by management and administration. Administration has to buy-in for stuff to truly be implemented/work . . . There has to be follow up and the chance to integrate new strategies provided.

Limited access to high-quality professional development was reported as the primary obstacle to implementing new evidence-based practices in participants’ classrooms. Participants also reported limited, or no, access to professional development beyond taking college courses that are expensive and too far away (e.g., cannot drive from school and get to campus by 4:30 p.m.). In addition, 36% (8/22) participants mentioned class size as a barrier to meeting the needs of students with MD or MLD.

Limitations

Like all studies, this study had several limitations. First, the results of the study relied on self-reporting of practice. Participants may have over- or underreported their understanding, their use of strategies or interventions, and/or their professional development participation. Second, as with all survey research, there were difficulties ensuring that a representative sample was obtained. The qualitative analysis in this study was intended to clarify and support the survey results; this methodological triangulation lends credibility to the findings. Although there was representation from all regions and more than half of districts, it is plausible that responses may not be indicative of true population norms. The majority of respondents were in their first years of teaching. This could be because the survey was distributed electronically, a format veteran teachers may be less comfortable with, causing fewer veteran teachers to respond, or could be due to changing demographics of rural special education. For example, Sullivan and colleagues (2017) found upward of 40% of Texas teachers exit the special education field within their first 3 years of service; thus, we may be seeing a decline in the number of midcareer teachers as well as losing teachers to retirement. To address the potential limitation of novice teachers, we oversampled veteran teachers in the qualitative interviews.

Future Research Directions

To better understand the performance of rural students, additional research in the areas of performance on state measures of accountability by locality would be beneficial. Additional research is needed also to understand special education teacher mobility in Texas. As researchers continue to focus on developing effective interventions to support practitioners, it is also important to assess both the social validity of interventions and ensure that dissemination efforts are effective. There are many areas of future work that have the potential to improve outcomes for rural students with MD or MLD. Implementation and evaluation of professional development to support secondary mathematics instruction, particularly in algebra 1 is desperately needed. These professional development offerings need to take into account the unique needs of rural educators. Assessments should include both teacher and student data to track effectiveness. Additional studies may examine follow-up professional activities using technology such as Twitter chats, blogs, and social media. Finally, and perhaps most important, strategies to ensure that teachers remain in the field and have the supports necessary to meet the demands of students are imperative.