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Project DREAM: Perceptions of Algebra Strategy and Intervention Use in Rural East Texas



Algebra I is a gateway course correlated with success in upper-level high school mathematics courses, college admission, entry into STEM majors, and high-earning careers. To provide the foundation necessary for students to access, persist, and complete math-oriented majors, algebra teachers must have access to high-quality, empirically validated professional development. Project DREAM (Developing Rural Educators’ Algebra Methods) explores the feasibility of disseminating evidence-based practices through a comprehensive, online professional development model. Specifically, Project DREAM targets East Texas teachers working with students from diverse backgrounds (non-native English speakers, students from low socioeconomic backgrounds, students with math difficulty or disability). Results of the needs assessment completed during Year 1 suggest that East Texas algebra teachers do not have access to professional development to equip them to support diverse learners and are unfamiliar with, or do not regularly implement, evidence-based strategies. Further, East Texas algebra teachers report regular use of practices with an insufficient evidence base. Findings, a summary of Year 2 goals, and implications for practice are described
Supported by:
The opinions expressed in
this report are those of the
author(s) and do not necessarily
reflect the views of
Greater Texas Foundation.
Project DREAM: Perceptions of Algebra Strategy and Intervention
Use in Rural East Texas
Brittany L. Hott
Texas A&M University-Commerce
Algebra I is a gateway course correlated with success in upper-level high school mathematics
courses, college admission, entry into STEM majors, and high-earning careers. To provide the
foundation necessary for students to access, persist, and complete math-oriented majors, algebra
teachers must have access to high-quality, empirically validated professional development.
Project DREAM (Developing Rural Educators’ Algebra Methods) explores the feasibility of
disseminating evidence-based practices through a comprehensive, online professional
development model. Specifically, Project DREAM targets East Texas teachers working with
students from diverse backgrounds (non-native English speakers, students from low
socioeconomic backgrounds, students with math difficulty or disability). Results of the needs
assessment completed during Year 1 suggest that East Texas algebra teachers do not have access
to professional development to equip them to support diverse learners and are unfamiliar with, or
do not regularly implement, evidence-based strategies. Further, East Texas algebra teachers
report regular use of practices with an insufficient evidence base. Findings, a summary of Year 2
goals, and implications for practice are described.
Algebra I is a gateway course for success in upper-level high school mathematics
courses, eventual entry into STEM majors, and high-earning careers. Although Texas continues
to focus on improving mathematics achievement, college readiness, and college completion,
there are widespread discrepancies in algebra performance, particularly for students who are
non-native English speakers, students from low socioeconomic backgrounds, and students with
disabilities. This is evidenced by performance measures. For example, Spring 2017 State of
Texas Assessments of Academic Readiness (STAAR) Algebra 1 results indicate that 18% of
students (n = 77,102) did not meet state standards and most likely require intensive intervention
(Texas Education Agency [TEA], 2017). An additional 32% (n = 137,574) are approaching
mastery of algebra content; however, significant gaps in their knowledge of essential skills are
evident. Students scoring in this category may need remediation to master critical concepts
(TEA, 2017). A greater percentage of students from economically disadvantaged backgrounds (n
= 248,341; 23% Did Not Meet standards, 37% Approaches standards) and students who are at-
risk (n = 235,210; 29% Did Not Meet standards, 33% Approaches standards) earned Did Not
Meet and Approaches standards scores than the state average. Students with disabilities (n =
39,849; 58% Does Not Meet standards, 29% Approaches standards) performed significantly
lower than any other group in the state, with over 87% of students not meeting standards.
Although important advances in what we know constitutes quality mathematics
instruction and intervention have occurred, research-based practices are not always successfully
incorporated into classroom instruction (Cook, Cook, & Landrum, 2013). Rural districts often
lack access to specialists, have few discretionary resources, and are geographically isolated
(Feinberg, Nujens, & Canter, 2005). There is a critical need to understand and remove the
barriers that impede mathematics performance (Chen et al., 2014). In Texas, as well as across the
United States, it is important that greater attention be placed on successful completion of Algebra
courses. Algebra I is a gateway course that supports higher-level mathematics skills (NMAP
Report, 2008) and failure to provide access to a rigorous algebra course minimizes the likelihood
that students will be able to pursue advanced mathematics courses, access higher education,
and/or be successful in STEM careers (Gojak, 2013). Approximately 36% (n = 445) of Texas
districts are classified as rural districts (TEA, 2015). These districts have an enrollment of less
than 300 students or an enrollment between 300 and the median enrollment for the state, with an
enrollment growth rate of less than 20% (TEA, 2015). To begin addressing the unique needs of
rural Texas algebra teachers serving diverse students, an assessment of intervention and strategy
use was completed. The data reported for rural East Texas districts is part of larger statewide
project. The following research questions guided this study:
(1) What are rural East Texas algebra teachers’ knowledge and comfort with teaching
mathematics standards?
(2) What strategies do rural East Texas teachers use to teach students from diverse
backgrounds (non-native English speakers, students from low socioeconomic
backgrounds, and students with disabilities)?
(3) What interventions do rural East Texas teachers use to teach students from diverse
backgrounds (non-native English speakers, students from low socioeconomic
backgrounds, and students with disabilities)?
(4) What resources do rural East Texas teachers use to meet the needs of students with from
diverse backgrounds (non-native English speakers, students from low socioeconomic
backgrounds, and students with disabilities)?
(5) What are rural East Texas teachers’ perceptions of barriers to implementing evidence-
based algebra practices to support students with mathematics difficulty or disability?
Mixed methods (Creswell, 2013) were used to develop an understanding of teacher
knowledge and perceptions of algebra strategies and interventions to support students with
mathematics difficulty or disability. Quantitative results from a cross-sectional survey provided
an overview of the research problem, and qualitative results from open-ended questions and
follow-up interviews assisted with explaining the thoughts and perceptions of rural Texas algebra
teachers (Creswell & Plano-Clark, 2011). Data were collected in two phases: (1) an electronic
survey of teachers responsible for algebra instruction, and (2) follow-up interviews, including a
sample of educators, to expand on findings from the survey and to contextualize participants’
Survey Development
Meta-analyses and syntheses (see Durlack et al., 2011; Gersten et al., 2009; Rakes,
Valentine, McGatha, & Ronau, 2010; Zheng, Flynn, & Swanson, 2013), research reports (e.g.,
NMAP, 2008, Star et al., 2015), and online resources (e.g., IRIS Center; National Council of
Teachers of Mathematics, What Works Clearinghouse) were used to identify mathematics
practices. Next, an expert panel was established that included the following: (1) professors of
mathematics, special education, and curriculum and instruction, (2) algebra teachers, (3) special
education teachers, (4) curriculum specialists, and (5) a high school principal certified in
mathematics. In addition to being content specialists, each had relevant experience working with
students from diverse backgrounds in rural settings. 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, pp.1517). The method was
originally used in industry and has more recently been applied to education decision-making (see
Clayton, 1997). Each expert was contacted individually by email and asked to review the list of
strategies and a list of interventions, to indicate any missing strategies and interventions, or to
remove strategies or interventions that did not fit. Next, a follow-up email was sent to panelists
that summarized the 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.
A cross-sectional survey comprising five sections was created, which incorporated expert
panel recommendations. 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.
Several recommendations were suggested, including adding demographic questions (e.g.,
teacher’s native language, number of preparations), adding open-ended questions related to
professional development, and adding open-ended questions related to ineffective professional
development. After the questions were modified, all members of the panel unanimously agreed
that the survey aligned with research questions and was an appropriate length, and that the items
were clearly defined. To further support validation, 23 graduate-level education students
reviewed and completed the survey. Further adjustments were made to open-ended questions to
assist with item order and clarity. The revised survey included demographic questions, 51 Likert-
type items to address research questions, and three open-ended questions.
Quantitative items. The first section included 11 demographic questions related to
teacher characteristics, teaching experience, degrees earned, certifications, school location, and
classroom makeup. Items included a drop-down menu with forced choices and an “other” choice
that allowed for an open-ended response.
The second section included 15 Likert-type items related to teacher perceived knowledge
and comfort levels with Texas algebra curriculum domains (i.e., Seeing Structure in Expressions,
Arithmetic with Polynomials and Rational Functions, Creating Equations, Reasoning with
Equations and Inequalities, and Mathematical Practices). The first five items asked teachers to
rate their content knowledge, the second five items asked them to rate their comfort with
teaching content areas, and the third asked them to rate their comfort with supporting students
who experienced mathematics difficulty or disability in meeting content standards. Analysis of
items using Cronbach’s α suggested that internal consistency for perceived knowledge (.92) and
comfort (.96) were in the excellent range.
The third section included 20 questions that assessed teachers’ perceived knowledge and
use of strategies and interventions to address the needs of students with mathematics difficulty or
disability. The items included a randomized list of practices and operationalized definitions
validated using the aforementioned Delphi procedures. Item ratings were the following:
Unfamiliar with the Strategy, Know about the Strategy but Do Not Use the Strategy, Know and
Implemented the Strategy this Year, and Routinely Use the Strategy. Analysis of items using
Cronbach’s α showed internal consistency in the good range for knowledge (.89) and excellent
range (.94) for strategy and intervention use.
The fourth series of the items included 16 questions focused on knowledge and use of
evidence-based resources, also established using Delphi procedures. Similar to the previous
section, items were rated using a Likert scale from 1 to 4, with Unfamiliar with Resource, Know
about Resource But Do Not Use Resource, Know and Use Resource, Know and Use Resource
Regularly. Analysis of items using Cronbach’s α showed internal consistency in the excellent
range for knowledge (.94) and use of evidence-based resources (.92).
Qualitative items. Three open-ended questions related to use of evidence-based practices
and instructional barriers were included. These questions were designed to provide participants
an opportunity to share details and perspectives related to their current practice, access to
resources, and barriers to implementing strategies and interventions. At the conclusion of the
open-ended questions section, space was provided to include an email address for participants
interested in scheduling follow-up interviews.
Survey Distribution
Following approval from the university’s institutional review board, an anonymous
electronic survey link was distributed though regional service centers, university faculty, district
superintendents, and social media groups. Full-time, in-service teachers responsible for
providing algebra instruction in rural Texas public schools were targeted. To assist with ensuring
a representative sample of East Texas teachers was obtained, respondents were asked to identify
their region and district from a dropdown list. Three $50 gift cards were provided to randomly
selected respondents to encourage participation. The survey remained open for eight weeks, with
two follow-up emails to targeted districts sent after two weeks and six weeks. Respondents
included 458 teachers from 176 rural districts. Of those, 129 identified as working in East Texas
Interview Protocol Development
Phase 2 involved conducting individual, semi-structured interviews to glean additional
insight into teacher knowledge and use of evidence-based practices to meet the needs of diverse
learners. Additionally, the researcher hoped to develop a greater understanding of teacher
professional development needs to support diverse learners. The following questions were
addressed: (1) What are the most challenging aspects of meeting the needs of diverse students?
(2) How do teachers select interventions and strategies to support diverse learners? (3) What
barriers are present that impact strategy selection and implementation? (4) What professional
development has been helpful? and (5) What professional development opportunities have not
been helpful?
Teacher Interview Procedures
After the 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 that represented the survey population
in regard to teaching experience, region, and professional licenses. Of those, seven were East
Texas teachers. Semi-structured 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 29 to 46 minutes. After each interview
was completed, a graduate research assistant transcribed the interview. First-level member
checks were used to assist with credibility (Bratlinger et al., 2005). After transcriptions were
completed, interviewees were emailed a copy of their responses to check for agreement with the
Data Analysis
After reading the transcriptions in their entirety, a graduate research assistant and the first
author independently completed open coding of a series of interviews. Next, 5 primary
categories and 12 subcategories were identified, agreed upon, and defined. To assist with
maintaining consistency and trustworthiness of the analysis, a third coder served as a peer de-
briefer (Bratlinger et al., 2005).
Phase 1 Results
Most East Texas respondents reported working in high schools (91%), followed by
middle schools (8%) and elementary schools (<1%). Over 79% 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 (13%). The remaining respondents reported 4!to!6 years of experience
(3%) and 16 or more years of experience (5%). Most respondents were Caucasian, native English
speakers (94%). Approximately 82% of respondents identified as female, with about 33% of
those respondents having earned a Master’s or Educational Specialist degree. Participants
reported a variety of certifications, with the most common including elementary mathematics,
middle grades mathematics, or secondary mathematics. Approximately 6% of respondents
reported having special education, counseling, and/or administration and supervision
endorsements. Most respondents reported teaching 9th, 10th, and 11th grade algebra courses
(88%). Less than 5% of respondents reported teaching algebra courses in grades six to eight.
Respondents were responsible for teaching one to eight sections of algebra with the majority
teaching two to three sections. Preparations ranged from one to seven, with a majority of
respondents reporting three or more preparations (74%). Course responsibilities varied and
included teaching engineering, pre-calculus, 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. A majority of respondents indicated that their classrooms include over 50% of
students who are eligible for free and reduced lunch. Additionally, the majority of participants
reported that 51% to 75% of their classes experience difficulty passing classroom assessments,
district benchmarks, and/or state tests. 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 who worked with 11th grade students
reported that most of their students struggled to complete grade level assessments (91%) and that
many of their students were included in one of the previously mentioned groups (87%).
Summary of Phase 1 Findings
Results suggest that rural East Texas teachers are comfortable with the mathematics
domains associated with the algebra curriculum; however, results indicate that teachers are
uncomfortable teaching students who experience mathematics difficulty or have disability.
Further, teachers’ knowledge and perceptions of evidence-based practices appear limited.
Content knowledge and comfort. Responses suggest that teachers perceive their content
knowledge of the Texas Algebra standards, including Seeing Structure in Expressions,
Arithmetic with Polynomials and Rational Functions, Creating Equations, Reasoning with
Equations and Inequalities, and Mathematical Practices as exceptional, as evidenced by over
98% of teachers rating their skills as exceptional mastery of related concepts. Less than 2% of
teachers rated their content knowledge for any of the domains as knowledgeable, but could learn
more. None of the respondents indicated that they needed additional content training in any of
the content areas.
Although participants indicated that they are knowledgeable regarding content, results
indicate that participants are uncomfortable teaching some of the algebra content. For example,
over 70% of respondents indicated that Mathematical Practices and Arithmetic with Polynomials
and Rational Functions are difficult or extremely difficult to teach, with less than 8% indicating
extremely comfortable teaching any of the five content areas. Over 70% of respondents indicated
that each of the five areas was difficult to extremely difficult to teach students from diverse
backgrounds in all five domains. Less than 4% of respondents indicated comfort in teaching
Mathematical Practices to students from diverse backgrounds.
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 26% of respondents
indicated that they implemented learning styles at some point during the year, and an additional
55% 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 88% of teachers reported
incorporating solved problems into classroom instruction and activities at some point during the
year or routine use of the strategy. Respondents also reported teaching students that different
algebraic representations can covey different information about a problem, with over 90%
reporting using the strategy in their classrooms. Problem-based learning (PBL) was another
familiar strategy, yet only 36% 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, 14% of teachers reported being familiar with learning styles but
not using the strategy; 8% were familiar with mindsets, but elected not to use the strategy.
Table 1 provides a summary of reported strategy use.
Knowledge and use of interventions. The most routinely used interventions to support
students from diverse backgrounds included explicit instruction, providing a range of examples,
teacher feedback, and visual representations. Conversely, fewer teachers reported use of
empirically validated interventions, including Concrete-Representation-Abstract (CRA)
sequence, instructional sequencing, schema-based instruction, or student feedback with goal
setting. Approximately 77% of respondents indicated that they were unfamiliar with schema-
based instruction or were familiar with, but do not use, schema-based instruction. Over 60% 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.
Knowledge and use of resources. The majority of respondents indicated knowledge of,
and routine use of, popular social media and outlets including Facebook (26%), Pinterest (37%),
and blogs (26%). Reliance on conversations with other teachers (74%) and Teachers-Pay-
Teachers (27%); as well as conversations with district specialists (21%), were other popular
resources that were routinely used. Over 40% of teachers indicated familiarity with several
mathematics education practitioner journals, but noted that they do not use them as a resource.
Additionally, some teachers reported knowledge of professional organizations (26% to 44%), but
also indicated that they do not use this resource. Respondents were generally unfamiliar with
evidenced-based resources. See Figure 1.
Professional development activities. The majority of participants answered at least one
of the open-ended questions related to use of evidence-based practices. The most common
response to professional development activities attended within the last year included variations
of not able to attend professional development or no professional development was provided.
The majority of teachers who listed professional development activities indicated that the
activities focused on “using required technology” or “dealing with technology in the classroom.”
One teacher indicated attending a workshop on robotics. The most common response to areas of
need included activities to help students learn study skills, note taking, accountability, and goal
setting. Barriers to implementing research-based strategies included time, funding, “district buy
in,” principal support, access to quality substitute teachers, and funding to enable attendance at
professional development activities.
Phase 2 Results
The interview participants painted a similar picture of their current practices, professional
development offerings, definition of high-quality professional development, and current barriers
to evidence-based practices. Most of the teachers reported using instructional strategies taught in
undergraduate coursework or learned informally through other teachers; these strategies were a
mix of both evidence-based and strategies that lack empirical support. Although teachers
reported limited access to sustained professional development beyond expensive and logistically
unfeasible university coursework, participants agreed on what constituted high-quality
professional development. However, participants also reported similar perceived obstacles to
implementing such professional development in their districts/school. General themes and
representative quotes are summarized below.
There were two main sources of credible strategies for interview participants. When
considering knowledge and comfort with implementing evidence-based practices, teachers
reported that they primarily used the strategies they were taught during their undergraduate
coursework or learned from other teachers. A high 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:
My neighbor down the road teaches. We talk a lot about how to best teach our
students. We use games. We try to create problems that are interesting and relevant.
We share materials. We share ideas.
Approximately 85% (6/7) of the participants shared that they learned many of the
strategies they use during undergraduate course work. The respondents varied in age, experience,
and degrees obtained. !
The strategies that participants shared as credible and effective included both evidence-
based and non-evidence-based practices, which were given equal credence. The evidence-based
strategies shared included providing real-world examples and active questioning techniques.
Approximately 57% (4/7) of participants mentioned at least one empirically validated strategy
included in the recent meta-analyses or research reports reviewed for the study.
However, several strategies that lack empirical support were also shared including
learning styles and mindsets. 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 were aware of the need for ongoing, high-quality, formal professional
development beyond their informal shared network of teacher strategies. Each of the participants
(100%, 7/7), however, felt that their current professional development could benefit from
improvements in format and content. Additionally, participants (85%, 6/7) shared that what
professional development is available is often “one-shot” days and does not include the
necessary follow through to ensure effective implementation or sustainability. A respondent
shared, “We are forced to attend district trainings. Often the presenters do not understand our
students and there is no additional training beyond the one day.” Another participant reported the
I attend the before-school required meetings. Beyond that, nothing. Nothing in over five
years. I would like to be able to attend conferences, but they are too expensive and there
is no money.
Limited access to high-quality professional development was 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., teachers cannot leave their school and get to campus by 4:30
p.m.). Additionally, 75% (6/8) participants mentioned class size as a barrier to meeting the needs
of students experiencing mathematics difficulty or with a disability. A teacher from deep East
Texas shared the following:
In rural Texas, there is always enough room to add a portable. In rural schools, you have
men that just go out and build them. We then have to figure out how to teach in these
portables without resources or space. You can’t turn away kids. We have to take them all
regardless of space to put them. Ninth graders are big and need their space.
Summary and Discussion of Findings
The process of ensuring that research-based practices are implemented is multifaceted
and complex. First, high-quality, relevant research must be conducted (Cook & Odem, 2013).
Second, dissemination approaches must be purposeful and relevant to practitioner needs (Cook,
Cook, & Landrum, 2013). Third, there must be an understanding that educators have varying
levels of access and knowledge of quality instructional practices. Some are in the beginning
stages of understanding and need exposure to evidence-based practices. Others understand the
need for empirically validated practices but need assistance with determining which practices are
appropriate, while others need assistance with fidelity of implementation. Factors such as access
to professional development, time, and resources also impact teachers’ ability to implement
quality interventions (Klingner, Boardman, & McMaster, 2013). These issues are compounded in
rural school settings, where professionals with significant expertise have limitations such as
multiple duties and limited time to support initiatives (Steed, Jakubiec, & Kooyman, 2013).
Findings suggest that there are several areas that would be helpful in supporting rural
East Texas teachers with implementing evidence-based practices to meet the needs of students
experiencing mathematics difficulty or with a disability. These areas include assistance with
identifying evidence-based practices and easy ways to implement practices within the context of
East Texas schools. Although participants reported that they are comfortable to extremely
comfortable with algebra content, they indicated that they needed support to meet the needs of
students with diverse learning needs, particularly in the areas of Mathematical Practices and
Arithmetic with Polynomials and Rational Functions. Furthermore, training to support
implementation of effective strategies and interventions is warranted. Although it is promising
that participants identified explicit instruction and modeling as routinely used strategies, it is
concerning that participants are unfamiliar with, and report that they do not use, empirically
validated interventions such as the CRA sequence (see Strickland & Maccini, 2010) or schema-
based instruction (see Jitendra et al., 2017). Also concerning is that two of the most commonly
reported strategies were learning styles and mindsets, both of which lack a clear evidence base
for effectiveness (see Landrum & McDuffie, 2014). Participants shared that learning styles are
occasionally taught in the region’s institutions as part of the undergraduate courses, or presented
as part of professional development, which may account for some of the weight given to this
particular strategy.
Teachers reported using internet sites such as Facebook, Pinterest, and Teachers-Pay-
Teachers to locate teaching resources, but not using websites that offer evidence-based teaching
strategies and interventions, such as RtI Network, Intervention Central, and Many
teachers appeared unfamiliar with these websites. Allowing opportunities for teachers to explore
the sites and dialog about strategy use and implementation would be beneficial. Teachers also
stated that although they are familiar with practitioner journals and professional organization
websites, they do not use them. Information from these sources could be disseminated through
blogs or interactive environments, which are cost-effective and have the potential to lead to
instructional changes.
Several concerns related to professional development were reported, including not being
able to attend because of scheduling conflicts or lack of qualified substitute teachers,
professional development focused on technology integration instead of on evidence-based
teaching practices, and professional development not being offered at all. Providing no-cost or
low-cost resources that do not require enrollment in a university course may be a viable option to
support teachers. These resources would be available in a format accessible to teachers at any
time and from any location, such as a website or document sharing site. Including opportunities
for follow up and discussion may also prove beneficial as teachers reported “one shot”
professional development was not sufficient. Finally, teachers reported difficulties in teaching
algebra concepts not only to students with disabilities, but also to students learning English and
students from low socioeconomic backgrounds. Professional development should include
strategies and interventions shown to be effective for each of these populations, such as feedback
with goal setting and instructional sequencing.
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 to ensure
that dissemination efforts are effective. There are many areas of future work that have the
potential to improve outcomes for students with mathematics difficulty or disability.
Implementation and evaluation of professional development to support secondary mathematics
instruction, particularly in Algebra 1, seems critical. These 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.
Algebra I is a gateway course that is correlated with advanced mathematics study, college
admission, and STEM degree obtainment (Chen et al., 2014; Hott & Carlson, in press).
Therefore, teachers need to implement quality strategies and interventions to meet the needs of
students who experience mathematics difficulties or have disabilities. Findings from this study
suggest that East Texas algebra teachers do not have access to, or have not implemented,
empirically validated interventions such as CRA and schema-based strategies that could be
beneficial in meeting the needs of students experiencing mathematics difficulty or with a
disability. Furthermore, East Texas algebra teachers need additional, targeted professional
development and relevant follow-up activities to meet the needs of students from diverse
Brantlinger, E., Jimenez, R., Klingner, J., Pugach, M., & Richardson, V. (2005). Qualitative
studies in special education. Exceptional Children, 71(2), 195207.
Chen, S., Hall, T. R., Jackson, C. A., Liu, X., Morin, Z., & Sargent, O. T., & Steere, V. S.
(2014). Postsecondary Completion in Rural Texas: A Statewide Overview. Bush School
of Government and Public Service: College Station, TX.
Clayton, M. J., (1997). Delphi: A technique to harness expert opinion for critical decision-
making tasks in education. Educational Psychology, 17, 373386.
Cook, B. G., Cook, L., & Landrum, T. J. (2013). Moving research into practice: Can we make
dissemination stick? Exceptional Children, 79, 163–180.
Cook, B. G., & Odem, S. L. (2013). Evidenced-based practices and implementation science in
special education. Exceptional Children, 79, 135–144.
Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods
approaches. Thousand Oaks, CA: Sage.
Creswell, J. W., & Plano-Clark, V. L. (2011). Designing and conducting mixed methods
research (2nd ed.). Thousand Oaks, CA: Sage.
Durlak, J. A., Weissberg, R. P., Dymnicki, A. B., Taylor, R. D., & Schellinger, K. B. (2011). The
impact of enhancing students’ social and emotional learning: A meta-analysis of school-
based universal interventions. Child Development, 82, 405432.
Feinberg, T., Nuijens, K., & Canter, A. (2005). Workload vs. caseload: There’s more to school
psychology than numbers. NASP Communique, 33.
Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009).
Mathematics instruction for students with learning disabilities: A meta-analysis of
instructional components. Review of Educational Research,79(3), 12021242.
Gojak, L. (2013). Algebra: Not “If” but “When”, National Council of Teachers of Mathematics:
Reston, VA. Retrieved from:
Hott, B. L., Carlson, M. A. (in press). The influence of student and school characteristics on the
college entry and STEM degree obtainment. White paper. Texas OnCourse Research
Network, Austin, TX.
Jitendra, A. K., Lein, A. E., Im, S. H., Alghamdi, A. A., Hefte, S. B., & Mouanoutoua, J. (2017).
Mathematical interventions for secondary students with learning disabilities and
mathematics difficulties: A meta-analysis. Exceptional Children, 64, 2143. doi:
Klingner, J. K., Boardman, A. G., & McMaster, K. L. (2013). What does it take to scale-up and
sustain evidence-based practices? Exceptional Children, 79, 195211.
Landrum, T. L., & Landrum, M. K. (2014). DLD Current Practice Alerts: Learning styles.
Retrieved from:
Moore, C. M. (1987). Group techniques for idea building. California: Sage.
National Mathematics Advisory Panel. (2008). Foundations for Success: The Final Report of the
National Mathematics Advisory Panel, U.S. Department of Education: Washington, DC.
Rakes, C. R., Valentine, J. C., McGatha, M. B., & Ronau, R. N. (2010). Methods of instructional
improvement in algebra: A systematic review and meta-analysis. Review of Educational
Research, 80(3), 372400.
Star, J. R., Caronongan, P., Foegen, A., Furgeson, J., Keating, B., Larson, M. R., Lyskawa, J.,
McCallum, W. G., Porath, J., & Zbiek, R. M. (2015). Teaching strategies for improving
algebra knowledge in middle and high school students (NCEE 2014-4333). Washington,
DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute
of Education Sciences, U.S. Department of Education. Retrieved from the NCEE
Steed, E., Pomerleau, T., & Muscott, H. (2013). Program-wide positive behavioral interventions
and supports in rural schools. Rural Special Education Quarterly, 32, 7885.
Strickland, T. K., & Maccini, P. (2010). Strategies for teaching algebra to students with learning
disabilities: Making research to practice connections. Intervention in School and
Clinic, 46(1), 3845.
Texas Education Agency. (2017). State of Texas Assessments of Academic Readiness: Summary
Report Algebra 1. Retrieved from: file:///Users/brittanyhott/Downloads/staar-eoc-
Texas Education Agency (2015). District Type Glossary of Terms. Retrieved from:
Zheng, X., Flynn, L. J., & Swanson, H. L. (2013). Experimental intervention studies on word
problem solving and math disabilities: A selective analysis of the literature. Learning
Disability Quarterly, 36, 97-111.
Table 1
Reported Use of Instructional Strategies
Unfamiliar with
the Strategy
Know About the
Strategy But Do
Not Use the
Implemented the
Strategy at Some
Point During the
Routinely Use the
Embodied Cognitive Processing
43% (n = 116)
4% (n = 13)
41% (n = 108)
8% (n = 21)
Incorporating Solved Problems into
Classroom Instruction and Activities
0% (n = 0)
12% (n = 15)
41% (n = 53)
47% (n = 61)
3% (n = 4)
4% (n = 5)
18% (n = 23)
75% (n = 97)
Learning Styles
5% (n = 6)
14% (n = 18)
26% (n = 34)
55% (n = 71)
2% (n = 3)
8% (n = 10)
36% (n = 46)
54% (n = 70)
Problem Based Learning
5% (n = 6)
24% (n = 31)
35% (n = 45)
36% (n = 47)
Reflective Questioning
10% (n = 13)
6% (n = 8)
63% (n = 81)
21% (n = 27)
Teach Algebraic Representations Can
Convey Different Meanings
1% (n = 1)
5% (n = 6)
51% (n = 66)
43% (n = 56)
Table 2
Reported Use of Interventions to Support Learners with Mathematics Difficulty or Disability
Unfamiliar with
the Intervention
Know About the
Intervention But
Do Not Use the
Implemented the
Intervention at
Some Point
During the Year
Routinely Use
the Intervention
Concrete-Representation-Abstract Sequence
62% (n = 80)
14% (n = 18)
13% (n = 17)
11% (n = 14)
Explicit Instruction
0% (n = 0)
6% (n = 8)
40% (n = 51)
54% (n = 70)
40% (n = 52)
15% (n = 19)
22% (n = 28)
23% (n = 30)
Instructional Sequencing
26% (n = 34)
11% (n = 14)
38% (n = 49)
25% (n = 32)
Peer Tutoring
9% (n = 12)
5% (n = 6)
53% (n = 68)
33% (n = 43)
Schema-based Instruction
77% (n = 99)
4% (n = 5)
14% (n = 19)
5% (n = 6)
Sequencing/Range of Examples
0% (n = 0)
8% (n = 10)
32% (n = 41)
60% (n = 78)
Student Feedback
1% (n = 1)
5% (n = 6)
63% (n = 81)
31% (n = 41)
Student Feedback with Goal Setting
4% (n = 5)
28% (n = 36)
36% (n = 46)
32% (n = 42)
Student Verbalizations/Think Alouds
5% (n = 6)
22% (n = 28)
47% (n = 61)
26% (n = 34)
Teacher Feedback
0% (n = 0)
14% (n = 18)
33% (n = 43)
53% (n = 68)
Visual Representations
0% (n = 0)
5% (n = 6)
46% (n = 61)
47% (n = 62)
Figure 1. Teacher Knowledge and Use of Resources
Teaching Exceptional Children Journal
Intervention in School and Clinic Journal
Council for Exceptional Children
Intervention Central
RTI Network
National Council for Teachers of Mathematics
Teachers Pay Teachers
Conversations with Specialists
Conversations with Colleagues
... Some rural districts can offer only a small number of upper-level math and science courses because they don't have enough teachers and students to form the classes. And regardless of subject area, opportunities for professional development and collaboration are often lacking for teachers in isolated areas (Hott, 2018). ...
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The Institute of Education Sciences (IES) publishes practice guides in education to provide educators with the best available evidence and expertise on current challenges in education. The What Works Clearinghouse (WWC) develops practice guides in conjunction with an expert panel, combining the panel's expertise with the findings of existing rigorous research to produce specific recommendations for addressing these challenges. The WWC and the panel rate the strength of the research evidence supporting each of their recommendations. See Appendix A for a full description of practice guides. The goal of this practice guide is to offer educators specific, evidence-based recommendations that address the challenges of teaching algebra to students in grades 6 through 12. This guide synthesizes the best available research and shares practices that are supported by evidence. It is intended to be practical and easy for teachers to use. The guide includes many examples in each recommendation to demonstrate the concepts discussed. Practice guides published by IES are available on the What Works Clearinghouse website at
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This article describes the quantitative findings from an evaluation of program-wide positive behavioral interventions and supports (PBIS) in three rural preschool programs. Each rural preschool program included children 3 through 5 years of age with and without disabilities. Following 3 years of on-site training, technical assistance, and coaching support in universal tier PBIS, participating preschool programs increased their use of strategies and supports to prevent young children's challenging behavior. Specific improvements in universal PBIS practices are presented across each year of the initiative. The successes and challenges involved in implementing program-wide PBIS in rural preschools are discussed.
This article discusses the strategic scaling up of evidence-based practices. The authors draw from the scholarly work of fellow special education researchers and from the field of learning sciences. The article defines scaling up as the process by which researchers or educators initially implement interventions on a small scale, validate them, and then implement them more widely in real-world conditions. Examples of scale-up research are included. The authors discuss challenges to scaling up and sustaining evidence-based practices, followed by factors that can potentially support scaling up, including professional development and district leadership. A case example describes how these issues can play out by highlighting experiences with a Collaborative Strategic Reading (CSR) scale-up research project in a large urban school district. The article concludes by offering recommendations for research, policy, and practice.
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