Supporting Statement for Paperwork Reduction Act Submission

Description of Statistical Methods (Part B)

1. Sampling Design

The primary sampling frame for the profiles of practice are schools and districts that have received grants 

through the High School Graduation Initiative (HSGI) (see www2.ed.gov/programs/dropout/awards.html). 

Many of these sites are engaged in activities to support student success in Algebra I, given the role of 

Algebra I as a gateway to more advanced coursework and the well-established relationship between poor 

performance in Algebra I and dropping out of high school. As described in the introduction to this request, 

the work products of this project will enable high schools—including HSGI grantees—to enhance their 

efforts to foster success in Algebra I, particularly among struggling students.

To generate the sample, the project team proposes to generate a purposive sample of 10 sites, two from 

each topical area. Based on the practice being examined there will be greater emphasis placed on data 

collection at the district or school levels (see Exhibit B.1). For example, for the topical area of curricular 

alignment much of the data will be collected at the district because the alignment of mathematics 

curricula across grade levels and schools is under the purview of the central office. For other topics, such 

as instructional practices, the project team will focus on the school-level. (Exhibits B.1 through B.5 specify 

the level at which the project team will collect data for each topic.)

Site selection criteria:

In selecting sites for the practice profiles, the primary objective will be to identify HSGI grantees that have 

implemented activities associated with the five topical areas that are the focus of this project. In addition, 

for the practice profiles to be of greatest utility to practitioners and policymakers, they should describe 

sites that have some track record of success in Algebra I. To enhance the probability that practitioners will 

identify with the school and district sites, we will seek variation with regard to urbanicity, school size, and 

student demographics. Thus, to the extent possible, the full set of 10 sites will reflect the following 

criteria:

 Criterion 1: Sites will represent exemplars of the particular topical area for which they are 

identified. That is, their practices in each topical area will reflect those that are consistent with the 

literature review for each topic as described below: 

o Instructional Practices: Selected sites will be schools with an established track record (at 

least three years) of teaching algebra for conceptual understanding and procedural 

fluency. Schools that systematically promote this type of teaching for all algebra teachers 

are those in which we would expect to see lessons, tasks and assessments in which 

concepts and procedures are mutually reinforced. Finally, the project team will seek 

schools that have some evidence of improved student outcomes (e.g., algebra end-ofcourse exam scores increased since the school implemented this type of instruction). 

o Professional Development: Selected sites will be districts or schools with professional 

development programs targeted at improving the teaching and learning of Algebra I or 

courses that promote algebraic thinking (e.g., programs that develop algebraic thinking in 

Grades 6–8). The professional development activities may include workshops or seminars 

that are developed and delivered by district staff and professional learning communities 
that form within or across schools in the district. The focus of the professional 

development activities may include specific content (e.g., understanding the big ideas of 

algebra, linear relationships), pedagogical techniques (e.g., questioning strategies, use of 

multiple representations of algebraic concepts), instructional materials (e.g., how to 

implement adopted materials or other lessons and tasks focused on algebraic concepts), 

and assessments (e.g., how to implement formative assessment lessons). The district 

should have a systematic approach to implementing and supporting these types of 

professional development activities.

o Instructional Coaching: Selected sites will be schools that are implementing a 

mathematics coaching program focused on improving teachers’ mathematics instruction.

Although mathematics coaches within these schools may be responsible for a number of 

activities, the majority of their time should be spent working directly with teachers to plan, 

deliver, and evaluate mathematics instruction. Ideally, the school will have established a 

policy for hiring/training mathematics coaches to ensure that individuals in these roles are 

leaders with knowledge of mathematics content, mathematics teaching and learning, and 

teacher leadership. In addition, the school should have a support structure in place to 

provide coaches with the time and resources they need to work with teachers in this 

capacity.

o Curricular Alignment: Selected sites will be districts with an established curricular 

framework that is vertically aligned to prepare students for Algebra I. More specifically, 

this curricular framework should specify a series of standards that are vertically aligned to 

support students in the development of skills and understandings needed for Algebra I.

These include, but are not limited to, an understanding of whole number and fraction 

operations and the ability to reason algebraically. The standards within the curricular 

framework should be clearly stated and organized to support a connected progression of 

skills and understandings that will ultimately prepare students for Algebra I.

o Supplementary Learning Opportunities: Selected sites will be schools that (1) have 

potentially promising outcomes for students, in the short and or longer term, and (2) 

provide professional development and curricular frameworks for double-dose algebra 

teachers. Specifically, promising outcomes can be demonstrated by improvements in 

Algebra I course failure rates or grades, standardized test scores in math and reading (in 

any grade in high school), on-time graduation, or college matriculation rates. Recent 

evidence demonstrates that double-dose algebra may have delayed effects on 

standardized test scores and that improvements may extend beyond math achievement to 

reading if double-dose algebra courses emphasize written and oral communication of 

mathematic concepts. In addition, high-quality double-dose algebra programs must go 

beyond extending students’ learning time for algebra and provide specific guidance and 

curricular materials for enriching and supporting learning for struggling students in 

double-dose algebra courses. These materials should be accompanied with appropriate 

professional development opportunities for teachers.

 Criterion 2: Each site should provide some evidence of improved outcomes. Although the team 

cannot set a specific achievement threshold or percentage point gain (in none of the topics is the 

literature consistent enough to warrant this), each nominated site should provide documentation 

that shows improvement, whether in student performance on standardized tests, student pass 
rates in Algebra I, student grades in Algebra I, student engagement, or other measures as 

appropriate for each topical area.

 Criterion 2: Sites will reflect geographic diversity, with regard to both regional location within the 

United States and urbanicity. For each topical area, the team will identify two sites representative 

of the primary unit (districts or schools) that are in different regions of the United States. In 

addition, the project team will seek to ensure that the set of ten sites includes at least one rural 

site.

 Criterion 3: Sites will reflect the diversity of enrolled students. The team will structure the 

profiled sites so that they reflect students of diverse ethnic, racial, and socioeconomic 

backgrounds—recognizing that students who struggle in Algebra I are disproportionately students 

of color or English learners. Thus, for each site selected, at least one-third the students will be 

ethnically or racially diverse or are English learners.

Identification Procedures:

To identify prospective sites, AIR will first pinpoint programs or initiatives related to each topical area 

among HSGI grantees. After reviewing grant applications, program descriptions, and web-based resources 

on the HSGI sites, AIR will conduct informal conversations with prospective sites to determine the level of 

implementation of each targeted practice. AIR will enter all information about each site into a Microsoft 

Access database that will track each program/site, its characteristics, and its progression through the 

selection process. With full information on each possible site, the project team will identify sites based on 

each criterion in succession. The project team also will identify a set of five replacement sites in the event 

that sites decline to participate.

2. Procedures for Data Collection

The data collection procedures of each of the main components of the project (interviews and focus 

groups, classroom observations, and document collection) are discussed in detail below.

Data Collection Activities by Topical Area

Because each topic for which the contractors are to collect data reflects different purposes, practices, and 

implementation, the data collection activities will vary for each. The common elements are that each will 

involve interviews or focus groups at the district and school level, and each will involve some form of 

document collection. All focus groups and interviews are expected to require one hour, while classroom 

observations could range from 60 to 90 minutes, depending on the organization of the school day. The 

specific numbers and roles of interviewees and focus group participants are detailed below.

Instructional Practices. The purpose of the instructional practices topic is to understand strategies, 

processes, and policies in schools that have made an effort to blend procedural and conceptual foci in 

their Algebra I instruction. Hence, the school is the unit of analysis for this topic, and the project team will 

visit two such schools. However, the contractors intend to collect data from the district level to better 

understand the context in which each school is situated. Because the contractors intend to conduct 

classroom observations, each site visit for this topical area will last two or three days, including one site 

visit lead and one site visit associate.
Exhibit B.1: Data Collection Activities for Instructional Practices

Instructional Practices. Sites: 2 Schools

Level Respondent Total n of 

respondents

District (n = 2) Interview with district official with primary responsibility for mathematics 2

School (n = 2) Observations of up to 5 teachers 10

Interviews with each teacher who is observed 10

Principal interview 2

Interview with math department chair or algebra team lead 2

Interview with instructional coach, if applicable 2

Documents Teacher assignments 10

Lesson plans 12

Schoolwide planning documents with regard to the instruction of Algebra I Variable

Curricular Alignment. The purpose of the curricular alignment topic is to describe districts that have 

developed and implemented a curricular framework that promotes the skills and understanding needed 

to be successful in Algebra I prior to enrollment in an Algebra I course. The site level for this topic is the 

school district because this is the level at which the curricular framework and pacing guides are 

established, as well as the vision with regard to Algebra I instruction. The team will visit two districts in 

two different states. Each site visit for this topic will last two days, with two site visitors: one site visit lead 

and one site visit associate.

Exhibit B.2: Data Collection Activities for Curricular Alignment

Curricular Alignment. Sites: 2 Districts

Level Respondent Total n of 

respondents

District (n = 2) Interview with math leaders at the district level 2–4

School Focus group of teachers who teach classes prior to Algebra I (elementary, across 

schools)

5 or 6

Focus group of teachers who teach classes prior to Algebra I (middle, across schools) 6–8

Focus group of teachers of Algebra I (cross-schools) 6–8

Focus group of math coordinators (or department chairs, depending on school 

organizational structure) from different schools

4 or 5

Documents Curricular framework

variable

Pacing guides

Additional instructional resources that support these ideas and concepts in the early 

grades

Professional Development. The purpose of the professional development topic is to explore innovative 

practices in terms of professional learning opportunities designed to deepen teachers’ content 

knowledge, conceptual understanding, and instructional capacity with regard to Algebra I. Because 

professional development policies are often mapped out at the district level, the school district may be 

the most appropriate site for this topic. However, there are often situations in which schools take on 

innovative professional learning practices that are not replicated elsewhere in the district. At this point, 

the project team proposes to identify the level of the practice profile after learning more about such 
practices in the HSGI sample. At present, the assumptions in Exhibit B.3 reflect a situation in which 

professional development was planned and enacted by the district; note, however, that such a plan 

includes data collection from school staff as well, as it is critical to understand how professional 

development opportunities are perceived.

The team will visit two districts or schools in two states. Each site visit for this topic will last two days, with 

two site visitors: one site visit lead and one site visit associate.

Exhibit B.3: Data Collection Activities for Professional Development

Professional Development. Sites: 2 Districts or Schools

Level Respondent Total n of 

respondents

District (n = 2) District math coordinator 2

Schools Focus group of teachers from secondary schools* (across up to 5 schools in the district) 10

Focus group of principals from secondary schools (across up to 5 schools in the district) 10

Focus group of school math coordinators (elementary across up to 5 schools in the 

district)

10

Focus group of high school math department chairs (across up to 5 schools in the 

district) 

10

Documents

Professional development documents (handouts, outline/agenda, PowerPoint 

presentations, district professional development plan, template for teacher/school 

professional development plans) variable

Observations Observe a professional development session (if possible)

*This may include either middle or high schools, depending on the way in which Algebra I instruction is organized in the 

district.

Instructional Coaching. The purpose of this topic is to understand how districts and schools use 

mathematics coaches to support teachers as they continue to improve their mathematics teaching. In 

addition to learning more about the role of mathematics coaches as they interact with teachers, the 

project seeks to learn more about the policies and structures that support the training, development, and 

activities of those coaches. The team is interested in how the coaching program was developed, the 

supports that contributed to its success, and the challenges that were overcome. The team will conduct 

site visits to two districts and will include data collection activities in two schools in each district. The site 

visits will last three days and will be conducted by one site visit lead and one site visit associate.
Exhibit B.4: Data Collection Activities for Instructional Coaching

Instructional Coaching. Sites: 2 schools

Level Respondent Total n of 

respondents

District (n = 2) Interview with district mathematics coordinator 2

Interview with district official responsible for math coaching 2

School (n = 2) Interviews with math coaches (in each school) 2-4

Interviews with principals (in each school) 2

Interviews with math department chair or teacher leader (in each school) 2

Focus groups with math teachers in each school (up to 5 teachers) 10

Documents Coach training manuals

Coach job description/guidelines variable

Coaching materials (e.g., rubrics, forms used to provide feedback, forms to monitor 

teacher progress, schedules)

Supplementary Algebra. The purpose of this topic is to explore the structures and implementation 

processes associated with instructional programs in which students receive additional Algebra I 

instruction. For example, students may participate in a traditional Algebra I class but then attend a second 

Algebra I class that reinforces what they have learned. The team will conduct site visits and collect data 

from two schools in two districts. Each site visit for this topic will last two days, with two site visitors: one 

site visit lead and one site visit associate.

Exhibit B.5: Data Collection Activities for Supplementary Algebra

Double-Dose Algebra. Sites: 2 School

Level Respondent Total n of 

respondents

District (n = 2) District math coordinator 2

School (n = 2) Principal interview (high school) 2

Math department chair/teacher leader interview 2

Supplementary algebra teacher focus groups (up to 5 teachers in each school) 10

Observations of supplementary algebra classrooms and their associated standard 

Algebra I classroom/session (1 observation of supplementary algebra and associated 

algebra class session for each of four schools) 

2

Documents Example lesson plans from each supplementary algebra teacher in each school (2 

lesson plans and a “syllabus” for up to 5 teachers in each school)

District and school guidance on course placement policies for supplementary variable

algebra

District and school curricular guides for supplementary algebra class sessions
Site Visits

Protocol Development

Interview and Focus Group Protocols. Two contractors, AIR and Windwalker, have developed protocols to 

guide the interviews and focus groups. These protocols include both open-ended questions and 

closed-ended questions. The open-ended questions will encourage in-depth responses and incorporate 

flexibility so that the project team can follow threads of conversation to their logical conclusion. The 

closed-ended questions will ensure that similar types of data are collected across the sites participating in 

the fieldwork. The team recognizes the utility of including broad questions to initiate discussion, followed 

by focused probes to ascertain insights in important areas. In developing protocol questions, the team has 

sought to avoid language that may be loaded, leading, or likely to yield socially desirable responses.

Interview and focus group protocols have been designed to explore the guiding questions without placing 

undue burden on the respondents. 

The contractors anticipate that site visitors will adapt the protocols for the context in the site visit schools. 

To facilitate this process, the protocols include suggested probes, topics that that the interview should 

“listen for,” and notes to indicate where the interviewer should adapt the protocol to the particular 

respondent’s circumstances. Although each question contains many possible probes, the interviewer is 

not required (or expected) to ask each of these. Rather, the probes are intended to ensure that the 

interviewer is attuned to the full range of possible topics and variables to be addressed in the responses 

and—in rare cases—to prompt a less communicative interviewee.

Following publication of this OMB submission for public comment, the project team conducted piloting 

interviews with fewer than 10 district officials, principals, and teachers in three locations. Team members 

asked these educators and administrators to react to (1) the overall organization, flow, and length of the 

interview; (2) the clarity of the interview wording and language; (3) specific questions that were unclear 

or difficult to answer; and (4) any recommended changes. The project team then used the responses from 

these pilots to modify the protocols to make them as suitable as possible for the actual site visits. 

Classroom Observation Protocol. As part of the data collection on instructional practices, the team will 

conduct a small set of classroom observations using instruments that AIR has developed and successfully 

implemented in other projects focused on math teaching and learning. For example, AIR has a lowinference instrument that captures the frequency with which teachers focus on concepts, procedures, or 

both. 

Request for Documents. The plans for each topical area include some collection of documents, as relevant 

for the specific topic. Because each topic requires a different set of documents, the team has prepared a 

separate request for documents for each of the five areas. In general terms, there are two types of 

requests: 

(1) A general request. The project team requests a straightforward set of documents that are 

generally readily accessible, such as a district’s curriculum framework, pacing guides, or a training 

manual.

(2) A request with detailed guidelines. For example, the request for teacher assignments includes 

specific guidelines on how many assignments are to be submitted by each teacher, the focus of 

the assignment, and the intended level of cognitive demand for the student.
Prior to conducting site visits, AIR will ensure that all data collection procedures (including informed 

consent forms, in Appendices A - E of this document) are approved by its Institutional Review Board.

Training and Preparation

Training for Site Visitors. The team will train the site visit team so that each member brings to his or her 

on-site work a consistent understanding of the relevant policies, the project, and the data collection 

needs. Prior to the first wave of data collection, all site visit staff from AIR and Windwalker will convene in 

Washington, DC, for a one-day training session. The site visit team leads from AIR and Windwalker will 

jointly develop and conduct the training so that consistent messages and training content are delivered 

across organizations. The one-day training will cover many topics, including the major concepts and big 

ideas of algebra, site visit approach and activities, data collection on-site (including brief review of 

interview protocols), and coordination of site visit work.

For the training, the site visit task leaders will develop a site visit checklist that will outline all tasks the site 

visitors need to perform before, during, and after each visit. All site visit team members will adhere to this 

checklist to ensure that visits are conducted efficiently, professionally, and consistently. There will be 

regular meetings of the site visit task leaders from AIR and Windwalker as well as weekly email updates 

and periodic larger meetings of the site visit staff. 

Preparation for Site Visits. Prior to each site visit, the project team will compile and review all extant 

background information on the school. Although some document data must be collected on-site, 

Web-based resources (primarily state, district, and school websites) include important contextual 

information on the history, priorities, performance, community support, and staffing of each school. Staff 

will review these closely before each visit and will enter preliminary information in a data capture 

template.

Administration of the Site Visits

Each site visit team will consist of two project team members from either AIR or Windwalker. Having the 

members work as a team during the site visits will enhance the consistency and reliability of data 

gathered. The same team will be responsible for scheduling and conducting the visits, and both site 

visitors will attend all interviews if possible. However, site visitors may conduct interviews separately if 

this is necessary to collect information from all respondents. Because of this, each interview and focus 

group will be audio recorded. In preparation for each visit, site visitors will review notes from interviews 

with state officials, review extant data on each site, consider the reasons each jurisdiction was selected 

for inclusion in the sample, review other relevant documentation, and annotate each section of the 

individual interview protocols accordingly. Further, these notes will be used to guide the wording of each 

question. The use of experienced interviewers, coupled with careful preparation, will ensure that 

interviews are not “canned” or overly formal. The lead site visitor for each site will have ultimate 

responsibility for completing and submitting the specified set of standard deliverables on the checklist for 

each site visit or follow-up.

Two-person site visit teams will be instructed to be flexible in determining how to organize each school 

visit, being mindful of district and school context and the need to collect data that answer specific 

evaluation questions. However, the site visits will have a standard set of features, including interviews and 

focus groups with district-, and school-level respondents; all topics will include the collection of document 

data as well.
Three of the topical areas include cross-school focus groups that will include five or six respondents across 

schools of a given level (elementary or secondary). To convene these focus groups, AIR and Windwalker 

will work with a district administrator to facilitate communications with school-level respondents and to 

identify a central location with convenient access for required respondents. In addition, the contractors 

will be as flexible as possible with regard to the timing of interviews and focus groups, so as not to disrupt 

school schedules.

Throughout the process of data collection and reporting, the contractors will make all efforts to protect 

the privacy of respondents participating in the site visits. The team will not identify by name any of the 

interviewees and will not attribute quotations. Although the team will identify the names of states in the 

final reporting of profiles of practice, districts and schools will be identified by pseudonyms. 

Collection of Documents and Files

All the topics include the collection of some document data, including schoolwide planning documents, 

professional development training guides, curricular framework, and pacing guides, among others. Two 

documents in particular—lesson plans and teacher assignments—will require more specific guidelines for 

the data collection team.

First, the team plans to collect two sets of lesson plans from each teacher whose class is observed: (1) 

plans for the classes in which teachers are introducing a new topic and (2) plans for the days during which 

students are preparing for a test. In addition to the plans themselves, the project team will collect 

associated slide presentations, handouts, and other supporting materials. 

Second, the team will collect two sets of teacher assignments from each teacher whose class is observed. 

One assignment will be what the teacher considers to be a “typical” assignment, whereas the second 

should be a more challenging assignment. The teacher should also submit the answer key and details 

regarding how he or she would grade the assignments—that is, the number of points possible for each 

part as well as the way in which points would be allocated or reduced on the basis of student work. The 

purpose of these data will be to provide examples of practice in the technical assistance tools that the 

contractors will develop.

3. Methods to Maximize Response Rate

Data collection is a complicated process that requires careful planning. The team has developed interview

and focus group protocols that are appropriately tailored to the respondent group and are designed to 

place as little burden on respondents as possible. The team has also piloted core data collection 

instruments to ensure that they are user-friendly and easily understandable, all of which increases 

participants’ willingness to participate in the data collection activities and thus increases response rates.

In addition to careful instrument design, a high response rate among the sites may be ensured through 

careful recruitment materials. These recruitment materials will emphasize the social incentive to 

respondents by stressing the importance of the data collections to provide much-needed technical 

assistance and practical information to districts and schools. AIR’s experience in past data collection 

efforts has demonstrated the importance and value of building a consensus of support with participating 

districts. Investing in site development at the front end reduces problems in the back end, helping to 

ensure smooth implementation of the evaluation. Based on prior experience collecting data through site 

visits, the project team anticipates a nearly 100 percent response rate – not less than 90 percent.
4. Expert Review and Piloting Procedures

Following publication of this OMB submission for public comment, the project team conducted piloting 

interviews with district officials, principals, and teachers in three states (not more than three respondents 

per topic). Project team members asked these educators and administrators to react to (1) the overall 

organization, flow, and length of the interview; (2) the clarity of the interview wording and language; (3) 

specific questions that were unclear or difficult to answer; and (4) any recommended changes. The 

project team then used the responses from these pilots to modify the protocols to make them as suitable 

as possible for the actual site visits. For example, earlier drafts of the protocols included more questions 

about the interviewee’s background, but these yielded unfocused and lengthy responses at the expense 

of topics more central to Algebra I. In addition, the project team identified questions that were difficult 

for teachers to address (specifically questions that would require some involvement in instructional 

decision making), so these questions were moved to the principal protocols. Importantly, the piloting 

procedures enabled the project team to determine the likely duration of the interviews and focus groups 

and to shorten the protocols accordingly.

5. Individuals and Organizations Involved in Project

AIR is the contractor for Promoting Student Success in Algebra I. The project director is Dr. Kirk Walters, 

who is supported by an experienced team of educators leading the major tasks of the project (see Exhibit 

B.9 for a list of key staff and responsibilities). 

During data collection and particularly during the initial phase of analysis, the contractors will draw on the 

cross-staffing of some key members of the project, including the project director, deputy project director, 

and team leaders. Contact information for the individuals and organizations involved in the project is 

presented in Exhibit B.9.

Exhibit B.9. Organizations, Individuals Involved in Project

Responsibility Organization Contact Name Telephone 

Number

Project Director AIR Dr. Kirk Walters (202) 403-5838

Deputy Director AIR Dr. Nicholas Sorensen (312) 283-2318

Task Lead: TWG Meeting and 

Senior Math Consultant

AIR Dr. Toni Smith (202) 403-5926

Senior Math Content Advisor AIR Steven Leinwand (202) 403-6926

Task Lead: Profiles of Practice AIR Dr. Kerstin Carlson Le Floch (202) 403-5649

Task Lead: Qualitative 

Analysis

AIR Andrea Boyle (650) 843-8294

Windwalker Jennifer Grossman (703) 970-3518

Windwalker Meschelle Linjean (703) 970-3554

Windwalker Lauren Malone (703) 970-3542

Windwalker Alison McNeil (703) 970-3528

Windwalker Samantha Schwartz (703) 970-3519
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