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Regional Educational Laboratory Midwest
Teaching Fractions Toolkit Evaluation
OMB# 1850‐0986NEW
Supporting Justification
for OMB Clearance
Section A
Submitted by:
National Center for Education Evaluation (NCEE)
Institute of Education Sciences (IES)
U.S. Department of Education
Washington, DC
May 2023
Attachments
Appendix A. Teaching Fractions Toolkit Evaluation Recruitment Materials
Appendix B: Teaching Fractions Toolkit Evaluation Teacher Survey Questionnaire
Appendix C: Teaching Fractions Toolkit Evaluation Teacher Survey Communication Materials
Appendix D: Teaching Fractions Toolkit Evaluation Teacher Interview Protocol
Appendix E: Teaching Fractions Toolkit Evaluation Administrator Implementation Checklist
Tracking and OMB Number: 1850‐0986NEW
Revised: XX06/XX11/XXXX2024
Contents
Overview ....................................................................................................................................... 1
Description of the Teaching Fractions Toolkit ............................................................................... 2
A1. Circumstances Necessitating the Data Collection ................................................................... 4
A2. Purpose and Use of the Data .................................................................................................. 5
Data Collection Activities for Which Clearance Is Requested as Part of This Package ............... 8
Evaluation Activities for Which Clearance Is Not Requested as Part of This Package
(provided for context) ............................................................................................................. 11
A3. Use of Technology to Reduce Burden ................................................................................... 12
A4. Efforts to Avoid Duplication of Effort .................................................................................... 13
A5. Methods to Minimizing Burden on Small Entities ................................................................. 14
A6. Consequences of Not Collecting Data ................................................................................... 14
A7. Special Circumstances ........................................................................................................... 14
A8. Federal Register Announcement and Consultations Outside the Agency ............................. 15
A9. Payments or Gifts .................................................................................................................. 15
A10. Assurances of Confidentiality .............................................................................................. 16
A11. Justification for Sensitive Questions ................................................................................... 17
A12. Estimates of Hours Burden ................................................................................................. 18
A13. Estimates of Cost Burden to Respondents .......................................................................... 20
A14. Annualized Cost to the Federal Government ...................................................................... 20
A15. Reasons for Program Changes and Adjustments ................................................................ 20
A16. Plans for Tabulation and Publication of Results .................................................................. 20
A17. Approval not to Display the Expiration Date for OMB Approval ......................................... 22
A18. Exception to the Certification Statement ............................................................................ 22
References .................................................................................................................................. 24
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
Overview
The U.S. Department of Education (ED), through its Institute of Education Sciences (IES),
requests clearance for the recruitment materials and data collection protocols under the Office
of Management and Budget (OMB) clearance agreement (OMB Number 1850‐NEW0986) for
activities related to the Regional Educational Laboratory (REL) Midwest Program under contract
91990022C0011.
Computational skills with fractions underpin advanced mathematics (Booth & Newton, 2012),
are essential for success in high school mathematics, and are a prerequisite for college‐level
mathematics courses (Siegler & Lortie‐Forgues, 2015). Unfortunately, student difficulty with
fractions is well documented (Barbieri et al., 2020; Liu, 2018; Siegler & Lortie‐Forgues, 2015).
Even after studying fractions and related topics for several years, U.S. students often lack a
conceptual understanding of fractions (Siegler et al., 2010). These fraction difficulties are
widespread and critical to address because “early fraction knowledge strongly predicts later
mathematics knowledge even after children’s IQ, reading comprehension, working memory,
whole‐number arithmetic knowledge, race, ethnicity, and parental education and income are
statistically controlled” (Fazio et al., 2016, p. 1).
Difficulties with fractions‐related content are not confined to students; teachers often have
difficulties as well. Teachers often struggle with fraction computation (Harvey, 2012), and many
practicing and preservice teachers have considerable difficulty with fraction operations, including
multiplication and division (Tekin‐Sitrava, 2020; Whitehead & Walkowiak, 2017). In a recent
study, only 42 percent of prospective teachers who attempted to solve equations with fractions
solved the equations correctly (Jones et al., 2020). Although teachers’ work with students is at the
heart of student learning, administrators also are essential in building systemic approaches to
improving teaching and learning and in providing the appropriate supports for teacher success
(Park et al., 2019). Therefore, administrators need to be prepared to set standards, identify
needs, and provide the appropriate supports if teachers are to be effective.
To address these needs, REL Midwest is developing a toolkit (the Teaching Fractions Toolkit)
that supports teachers to enact evidence‐based practices summarized in Developing Effective
Fractions Instruction for Kindergarten Through 8th Grade (Siegler et al., 2010). Drawing on the
recommendations and implementation steps outlined in the practice guide, the toolkit will
address teacher understanding of fraction computation, rates, and ratios, as well as
implications for classroom practices related to fractions content for grade 6 teachers. REL
Midwest is developing the toolkit in collaboration with district partners in Illinois.
ED, in consultation with the American Institutes for Research® (AIR®), which is ED’s contractor
for REL Midwest, is planning a two‐part evaluation of the toolkit in 40 Illinois public schools
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
across 6–10 school districts. The evaluation will consist of an impact study and an
implementation study. OMB approval is being requested for recruitment and a multimode data
collection and analysis of a group of schools, students, and staff members in these Illinois public
schools.
Description of the Teaching Fractions Toolkit
The Teaching Fractions Toolkit is based on and
supports implementation of five evidence‐based
recommendations in the What Works
Clearinghouse practice guide Developing
Effective Fractions Instruction for Kindergarten
Through 8th Grade (Siegler et al., 2010). The
practice guide recommendations (see Box 1) are
based on rigorous research for improving K–8
students’ understanding of fractions, with the
expectation that general education teachers,
mathematics specialists and coaches, special
educators, and administrators will use these
resources to improve their teaching of fractions.
This toolkit includes two types of supports:
teacher supports and institutionalizing supports
for administrators and mathematics leaders who
support mathematics teachers.
Box 1: Recommendations in the Developing
Effective Fractions Instruction for
Kindergarten Through 8th Grade practice
guide
1. Build on students’ informal understanding
of sharing and proportionality to develop
initial fraction concepts.
2. Help students recognize that fractions are
numbers and that they expand the number
system beyond whole numbers.
3. Help students understand why procedures
for computations with fractions make sense.
4. Develop students’ conceptual
understanding of strategies for solving ratio,
rate, and proportion problems before
exposing them to cross‐multiplication as a
procedure to use to solve such problems.
5. Professional development programs
should place a high priority on improving
teachers’ understanding of fractions and of
how to teach them.
The primary audience for the teacher supports is
grade 6 mathematics teachers in general
education classrooms. Teacher supports include six teacher professional development (PD)
modules. Each professional development module consists of two synchronous sessions led by a
PD facilitator, separated by approximately three hours of asynchronous assignments in the
interim between sessions. In each module, teachers engage in individual and collaborative PD
activities, including exploration of mathematics tasks, student work analysis, lesson planning,
the use of formative assessment items, and reflection on classroom practice, all of which will
support teachers’ understanding related to the implementation steps for practice guide
Recommendations 2–4 as well as how to mitigate possible roadblocks identified for
Recommendations 2–4. The toolkit also includes associated resources to support engagement
in PD in each module, including mathematics tasks, interactive applets, protocols for student
work analysis and planning, videos, student artifacts, readings, and reflection prompts. The
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
toolkit includes a teacher reflection tool to assess initial and developing classroom practices
aligned with the practice guide recommendations and questions to inform lesson planning and
reflection. The teacher PD is designed so that it can be used with in‐person meetings or fully
online for all activities (synchronous and asynchronous). The modules and materials will be
designed with flexibility so that local facilitators and teachers will be able to implement all or
part of the PD in an in‐person environment if they choose to do that. The guidance for
facilitators will make suggestions about how to lead teacher discussions either in person, if
feasible, or via videoconference using whatever videoconference platform the district employs.
The primary audience for the institutionalizing supports is administrators and mathematics
leaders (principals, assistant superintendents, curriculum directors, mathematics coaches, and
teacher leaders) who support teachers of mathematics. Institutionalizing supports include:
Three videos—one to introduce the toolkit and two to introduce what the practice guide
recommendations look like in practice
Two leader handouts—one summarizing the practice guide recommendations and one
outlining the progression of fraction content represented in the practice guide
A tool for administrators and leaders to assess district conditions to support fractions
instruction
Facilitation guides for school leaders to lead professional development for grade 6
teachers
The institutionalizing supports will bolster the understanding of administrators and
mathematics leaders of the importance of the mathematics content embodied in the practice
guide recommendations; inform them about the research basis for teacher practices included
in the recommendations; guide decisions about supporting teachers to enact the
recommendations; and support leaders such as mathematics coaches or other PD providers to
lead the PD that is part of the teacher supports.
All materials that users need in order to implement the teacher PD and other toolkit activities
and supports are included in the toolkit and will be accessible in one central online location
(https://ies.ed.gov/ncee/rel/Midwest/Toolkit) with a clear and user‐friendly linked menu on the
landing page. The toolkit development team will work with the IES website contractor to get
the online platform ready prior to the start of the evaluation so that participating educators will
be able to access all toolkit materials online. The landing page will have a brief overview of the
toolkit resources, environment, and overarching goals plus sections for institutionalizing
supports and teacher supports. The teacher supports section includes the six PD modules. Each
module will include a participant workbook, a facilitator guide, and two slides decks (one for
each synchronous meeting). Modules will be linked for easy cross‐movement and include a
navigation menu to the module overview, learning objectives, individual learning activities, a
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
link to resources and tools for that module, the teacher practice monitoring tool, support tips, a
glossary of terms and acronyms, and references. All resources will be navigable with a screen
reader. When clicked, links will appear in a new tab or window so that the user remains
connected to the module. Videos and animations will be captioned with audio available in
transcripts to ensure accessibility and Section 508 compliance. Templates, checklists, and tools
will be provided in HTML, PDF, and editable document formats. The modules will include links
to some interactive GeoGebra applets for use by teachers and their students when working on
mathematics tasks. These applets will be developed in the open‐source GeoGebra website and
made available to teachers through links from the Teaching Fractions Toolkit website and
modules.
A1. Circumstances Necessitating the Data Collection
As part of the REL solicitation request (Solicitation #91990020R0032), IES required each applicant
to develop at least one research‐based toolkit to support educators’ use of evidence‐based
practices and to conduct an independent efficacy and implementation evaluation of the toolkit.
Per the solicitation:
IES is invested in developing practitioner‐friendly toolkits to help educators use
evidence‐based practices in classrooms – from preschool through postsecondary
settings. Some of the best evidence available is consolidated in the WWC Practice
Guides, in which researchers and practitioners review the evidence from the most
rigorous studies available, develop recommendations for practice, and create action
steps for how to use the recommended practices. To help get this evidence into the
hands of stakeholders, RELs shall partner with educators and postsecondary instructors
(if relevant) to develop one toolkit based on an assigned WWC Practice Guide, which
shall include all materials necessary for effective implementation.
The toolkit contains the following two components: (1) institutionalizing supports for
administrators and mathematics leaders who support mathematics teachers and (2) teacher
professional development modules and associated resources that build teachers’ knowledge
and practices, including diagnostic and monitoring tools—formative assessment probes for use
with students and a teacher practice monitoring tool for reflecting on practice. The solicitation
also states that RELs must evaluate the efficacy and implementation of the professional
development resources in the finished toolkit. According to the solicitation, “(t)he evaluation
shall examine changes in teacher practice and may also include measures of teacher knowledge
and/or teacher self‐efficacy.”
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
The purpose of this data collection will be to measure the efficacy and implementation of the
REL Midwest‐developed toolkit designed to improve teacher self‐efficacy and practices for
fraction computation and rate and ratio instruction, as well as student learning outcomes in
grade 6 mathematics. The study will address the following research questions (RQs):
1. What is the impact of the toolkit on grade 6 teachers’ self‐efficacy and teaching
practices for fraction computation and rate and ratio instruction compared to the
business‐as‐usual condition?
2. What is the impact of the toolkit on grade 6 students’ performance in solving fraction
computation and rate and ratio problems compared to the business‐as‐usual condition?
3. How did the professional development supports and resources available to grade 6
math teachers differ in treatment and control schools?
4. To what extent is the toolkit implemented with fidelity within each participating school
and overall across all participating schools?
5. To what extent is the fidelity of implementation associated with teachers’ self‐efficacy
and practices and students’ performance on solving fraction computation and rate and
ratio problems?
6. What contextual factors support or hinder the adoption and implementation of the
toolkit?
7. To what extent do the participating teachers and school leaders perceive the toolkit as
usable, useful, and feasible to implement? What aspects of the toolkit do they perceive
could be improved?
The toolkit evaluation will produce a report for district and school leaders who are considering
strategies to improve fraction teaching and learning in grade 6. The report will be designed to
help them decide whether and how to use the toolkit to help them implement the practice
guide recommendations. The findings from the evaluation also will inform further refinement
of the toolkit.
A2. Purpose and Use of the Data
Data collected for this evaluation will be used to examine the implementation of the toolkit in
participating schools and the toolkit’s efficacy in improving teacher self‐efficacy and practices
for fraction computation and rate and ratio instruction, as well as student learning outcomes in
grade 6 mathematics.
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
REL Midwest will conduct the evaluation during the 2024/25 school year. This study will not be
replicated under this contract, as it ends in 2027; in other words, this is not a recurring data
collection. The evaluation team aims to recruit 40 schools in Illinois so that the study will be
powered to detect effects of the toolkit on student learning and teacher practice outcomes that
are of statistical and practical significance and are comparable in magnitude to those effects
reported in previous studies of similar interventions. The evaluation will employ an
experimental design in which schools that have expressed interest in using the toolkit and have
agreed to participate in the evaluation will be randomly assigned within blocks to treatment
condition (toolkit) or business as usual (control) in summer 2024. Each district with multiple
schools participating in the study will serve as its own randomization block. Schools from
districts in which only one school is participating in the study will be grouped into blocks based
on school locale and prior‐year school performance. In schools assigned to the toolkit group,
grade 6 teachers and their administrators will be invited to use the toolkit materials with the
guidance of a local facilitator. In control schools, grade 6 teachers and administrators will not
have access to the toolkit until after the study. Both groups will be asked to participate in study
data collection, which will include teacher surveys, teacher classroom observations, teacher
interviews, school and district leader and facilitator interviews, and an assessment of students’
abilities to solve fraction computation and rate and ratio problems. The study will also collect
administrative data, including background information about students and teachers and
student scores from state math assessment in prior year (when students were in grade 5).
Table 1 provides an overview of the data that REL Midwest will use for this study, including the
data source, key measures, type of data collection (primary or secondary), respondent,
condition (treatment or control group), time of data collection, and RQs addressed.
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
Table 1. Overview of data sources, measures, and RQs
Data collection
type
Condition
Dates for
acquiring data
RQ
120 teachers
Treatment and
control
September 2024;
May 2025
RQ1, RQ3, RQ5,
RQ6, RQ7
Primary
120 teachers
Treatment and
control
January–May
2025
RQ1, RQ5
Student ability to solve fraction
computation and rate and ratio
problems
Primary
2,400 students
Treatment and
control
May 2025
RQ2, RQ5
PD
implementation
checklist
Implementation fidelity
Secondary
(implementation
team)
8 facilitators
Treatment
May 2025
RQ4, RQ5
Administrator
implementation
checklist
Implementation fidelity
Primary
20 school
administrators
(principals or
designees)
Treatment
May 2025
RQ4, RQ5
PD records and
artifacts
Implementation fidelity
Secondary
(implementation
team)
60 teachers; 8
facilitators
Treatment
May 2025
RQ4, RQ5
Teacher
interviews
Teacher experience with
implementation
Primary
12 teachers
Treatment
April–May 2025
RQ6, RQ7
School leader
and facilitator
interviews
School leader and facilitator
experience with implementation
Primary
6 leaders
(facilitator or
principal)
Treatment
April–May 2025
RQ6, RQ7
District
administrative
data
Student characteristics, student state Secondary
assessment scores from prior year
(district)
(2023/24), teacher characteristics,
and student–teacher links (rosters)
10 districts
Treatment and
control
Fall 2024
RQ1, RQ2, RQ5
School
characteristics
School characteristics
40 schools
Treatment and
control
January 2024
RQ1, RQ2, RQ5
Data source
Measure
Teacher surveys
Teacher self‐efficacy; teacher
experience with implementation
Primary
Classroom
observations
Teacher practice
Student
assessment
Secondary
(publicly available)
Target sample
Note: PD = professional development.
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
REL Midwest will safeguard all data collected for this evaluation through protocols approved by
the contractor’s federally approved Institutional Review Board, including adherence to Family
Educational Rights and Privacy Act (FERPA) regulations. REL Midwest will analyze the data
collected through this evaluation using statistical models that are preapproved by IES via an
independent peer review process. The contractor (AIR) will then summarize the impact and
implementation findings in a report, and that report will undergo review for quality and
relevance by IES’s external review contractor. Once the report has undergone IES review,
findings will be published through IES for educators and education researchers alike.
Finally, once data are analyzed and summarized, REL Midwest will sanitize the data files of any
information that can be linked to students, teachers, schools, or districts. Data files will then be
submitted to IES and made available to other researchers as restricted‐use files.
Data Collection Activities for Which Clearance Is Requested as Part of This
Package
We describe below the purposes for each recruitment and data collection activity for which
OMB approval is being sought. These activities involve burden on respondents and are
therefore the basis for seeking clearance.
District and school recruitment. The evaluation team will first identify Illinois districts with at
least one school serving grade 6 students and will collect publicly available data on relevant
district and school characteristics (e.g., school locale, enrollment, student demographic, pupil–
teacher ratio, financial information such as expenditure per student) from the Illinois State
Board of Education (ISBE) website and from the Common Core of Data from the National Center
for Education Statistics (NCES). The evaluation team will then work with partners at ISBE and
leverage existing relationships with Illinois districts to help widely distribute information about
the study to districts across the state (see appendix A1). Districts that are interested in
participating in the study will be asked to complete an online form to indicate their interest and
provide information to the evaluation team to help determine their eligibility for the study (see
appendix A2). Districts will be eligible to participate if they serve students in grade 6, are willing
to participate in a randomized controlled trial with delayed implementation for control schools
and are not already providing professional development in grade 6 math instruction that is of
the same type and level of intensity as that being provided by the toolkit. The evaluation team
will schedule initial virtual informational meetings with districts that have expressed interest to
confirm their interest and eligibility and to answer any questions district leaders may have. At
this meeting, the evaluation team will inform district leaders about the roles, responsibilities,
and benefits of the study. If district leaders are interested in participating, the evaluation team
will ask for their help contacting schools and their ideas for how the study might be a fit for
their schools. The team will follow up with one‐on‐one meetings with school leaders, if
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
requested, to answer questions and confirm their interest. Researchers on the team will ask
school districts to sign a memorandum of understanding, indicating that they understand the
intervention and the study and that schools will participate in the study regardless of the
condition to which they are assigned. The evaluation team will obtain approval from the
Institutional Review Board at AIR and research approvals or data agreements from participating
districts for the evaluation activities.
Teacher recruitment. Upon district agreement, the team will reach out to school principals and
offer to schedule a school‐specific information meeting to provide information directly to
teachers and to hear their thoughts. Teachers who teach at least one regular grade 6 math class
will be eligible to participate in the study. For the proposed evaluation, a regular grade 6 math
class refers to a class that is designated by the school as a general education class and that
teaches the district’s middle‐track grade 6 math curriculum. This definition excludes advanced
classes, such as gifted and talented programs and accelerated classes, as well as remedial
classes and self‐contained special education classes. The evaluation team will prepare a study
information sheet for teachers and distribute it to teachers before the meeting (see appendix
A3). The team will remain flexible and adaptive in the face of emerging recruitment experiences
(e.g., by extending the information session to address any immediate concerns of teachers).
The evaluation team will collect consent forms from all eligible teachers in participating schools
in late summer 2024, after randomization of schools and prior to the start of the 2024/25
school year (see appendix A4 for a copy of the consent form). Only those teachers who have
consented will participate in data collection for the evaluation.
Teacher surveys. To assess the impact of the toolkit on teachers’ self‐efficacy for fractions
instruction, the evaluation team will administer an online survey to participating teachers in
treatment and control schools in fall of 2024 (baseline survey) and spring 2025 (post survey).
The team will use measures with established reliability and validity, including a measure of self‐
efficacy related to using and teaching with visual representations in math (DePiper et al., 2019),
a measure of self‐efficacy for pedagogy in math (McGee & Wang, 2014), and a measure of self‐
efficacy for teaching math content (McGee & Wang, 2014). The visual representations self‐
efficacy measure (α = 0.96), developed and validated by researchers at Education Development
Center (DePiper et al., 2019), includes 10 items that ask teachers to indicate how confident they
are in using visual representations in math and in teaching with visual representations in math.
The self‐efficacy for pedagogy in math measure (α = 0.86), developed and validated by McGee
and Wang (2014), contains 7 items that ask teachers to rate their level of self‐efficacy for key
pedagogical strategies and practices (for example, motivating students, using a variety of
assessments, implementing alternative teaching strategies). The self‐efficacy for teaching math
content measure (α = 0.86), also developed and validated by McGee and Wang (2014), contains
15 items that ask teachers to rate their level of self‐efficacy for teaching math content specific
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
to elementary school. With input from math content experts, the evaluation team made
changes to the wording of 6 items and replaced another 2 items to make the measure align
better with grade 6 math content. In addition to the teacher self‐efficacy measures, the teacher
survey will include items to collect information about professional development trainings that
teachers attend during the 2023/24 and 2024/25 school years, implementation of the toolkit
(for treatment teachers only), and teacher background characteristics. The survey draws items
from the PD characteristics scales used in the analysis of service contrast in the Middle School
Mathematics Professional Development Study by Garet et al. (2010; α = 0.69–0.90) and the
2015 Grade 8 NAEP Mathematics Teacher Questionnaire. We expect that each teacher survey
will take 20 to 30 minutes to complete (see appendix B for a copy of the teacher survey
questionnaire and appendix C for sample email invitation and follow‐up emails).
Interviews with teachers. The evaluation team also will conduct virtual interviews with a
purposeful sample of 12 teachers in spring 2025. The evaluation team will first identify six
schools in which to conduct interviews. Schools will be selected based on project staff initial
rating of teacher uptake and engagement—ratings will include three levels: low, average, and
high teacher uptake and engagement. Interview schools will be selected randomly by these
rating levels. In each school, two teachers, randomly selected from a list of willing teachers, will
be interviewed. Interviews will be recorded and transcribed with permission. Each interview
will take about 45 minutes to complete (see appendix D for a copy of the teacher interview
protocol).
Administrator implementation checklist. To assess implementation fidelity, the evaluation
team will ask administrators in treatment schools to complete a short online checklist in spring
2025 that asks about their use of institutionalizing supports. The checklist should take no more
than 30 minutes to complete (a copy of the checklist is provided in appendix E).
District administrative data. The evaluation team will collect district administrative records
regarding teacher and student background characteristics to describe the study sample, to test
baseline equivalence, and to include as covariates in the impact analysis. Teacher background
characteristics will include teacher total years of teaching experience, highest degree, and
certification status. The evaluation team will also request teacher email addresses in order to
email teachers the invitation to complete the surveys and to schedule interviews and classroom
observations. Student background characteristics will include student characteristics
(race/ethnicity, gender, multilingual learner student status, special education status, and
eligibility for the National School Lunch Program) and student scores on the state math
assessment from spring 2024 (when students were in grade 5). Masked student identifiers will
be requested to allow the evaluation team to link administrative data over time and across
multiple district sources. Student–teacher links (classroom rosters) will be requested. District
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
staff will submit information electronically using secure file transfer procedures. We expect it
will take each district a total of 20 hours of staff time to prepare and submit the data.
Evaluation Activities for Which Clearance Is Not Requested as Part of This
Package (provided for context)
The following activities will not involve burden on respondents or are not subject to Paperwork
Reduction Act per OMB guidance (5 C.F.R. 1320.3(h)). They are listed here to provide a
complete picture of the study.
Classroom observations. To examine the toolkit’s impact on classroom instruction, the
evaluation team will conduct in‐person classroom observations in treatment and control
schools in winter/spring 2025, using a protocol adapted from the classroom observation
protocol used in the Middle School Mathematics Professional Development Impact Study
sponsored by IES (Garet et al., 2010). The observation will focus on three validated classroom
practice measures from the Garet et al. protocol that are related to the goals of the toolkit and
that align with recommendations in the WWC fraction practice guide, including: Teacher
focuses on mathematical reasoning (α = 0.62), teacher elicits student thinking (α = 0.70), and
teacher uses representations (α = 0.81). Observations will be conducted by the evaluation team
members from AIR, ED’s contractor for REL Midwest, who are trained on the observation
instrument. Each teacher will be observed for a single class period. OMB approval is not
required for in‐person classroom observations because facts or opinions obtained through
direct observation by an employee or agent of a federal agency is not to subject to the
Paperwork Reduction Act per OMB guidance (5 C.F.R. 1320.3(h)(3)).
Student assessment. The evaluation team will administer a 30‐minute assessment to examine
the impact of the toolkit on students’ abilities to solve fraction computation and rate and ratio
problems in spring 2025. The evaluation team has constructed a customized test by drawing on
items from existing state standardized tests (released items or practice test) that correspond to
the standards of focus in the toolkit and that measure students’ uses of problem‐solving
strategies emphasized in the WWC practice guide. State assessment items have undergone
analysis for validity and reliability, as well as review to remove bias, ensuring item functioning.
The assessment will be administered online, but the evaluation team will support paper‐and‐
pencil administration if a participating school is not able to administer the online assessment.
The evaluation team will work with schools to offer appropriate accommodations that students
typically use during classroom instruction and classroom assessments. OMB approval is not
sought for the student assessment because examinations designed to test aptitude, abilities, or
knowledge is not to subject to the Paperwork Reduction Act per OMB guidance (5 C.F.R.
1320.3(h)(7)).
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
Professional development records and artifacts. The evaluation team will collect training
records (e.g., teacher professional development session attendance records) and artifacts (e.g.,
teacher reflection plans) from facilitators and teachers in treatment schools. These data
provide evidence that toolkit activities were completed as intended and complement the
toolkit platform statistics. OMB approval is not sought for collection of professional
development records and artifacts because teachers and facilitators will be completing and
submitting these materials to the implementation team during the implementation of the
professional development. The implementation team will transfer these records to the
evaluation team for analysis.
Facilitator implementation checklist. To assess implementation fidelity, the implementation
team will create an implementation checklist that identifies key activities for each synchronous
session and will ask the facilitator to complete the checklist for each session, as well as identify
toolkit resources used for planning and implementing the professional development. OMB
approval is not sought for this data collection activity because facilitators will be completing
and submitting the checklist to the implementation team during and as part of the
implementation of the professional development. The implementation team will transfer the
completed checklists to the evaluation team for analysis.
Interviews with school leader and facilitator. The evaluation team will conduct interviews with
a purposeful sample of six school leaders, including facilitators, to gather data on their
experiences with the implementation of the toolkit. Interviews will be recorded and transcribed
with permission. Because interviews will be conducted with fewer than 10 individuals, OMB
approval is not sought for this data collection activity.
Data on school characteristics. The evaluation team will collect data on school characteristics—
including school size, locale, student racial and ethnic composition, school financial data, and
prior school performance—from the ISBE website and the Common Core of Data. OMB
clearance is not requested for this data collection activity because the evaluation team will
collect these data from publicly available sources.
A3. Use of Technology to Reduce Burden
The data collection plan was designed to obtain reliable information in an efficient way that
minimizes respondent burden, and technology will be used to reduce burden for all the data
collections for which we are seeking clearance.
Teacher surveys will be administered online using an online platform that will allow
respondents to complete the survey at a time and place that are convenient for each
respondent. The evaluation team will email to study participants a link to the online surveys. To
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reduce the burden on respondents, the software is flexible and allows survey respondents to
participate using a multitude of devices, such as computers and Smart phones, and to switch
between devices while completing the survey.
Administrators also will complete the implementation checklist through a secure online
platform that allows them to complete the checklist at a time and place that are convenient for
each administrator.
The teacher survey, administrator implementation checklist, and student assessment will be
created and administered using Jotform integrated with an Airtable base. Forms created with
Jotform are Level A and Level AA compliant with Web Content Accessibility Guidelines (WCAG)
2.1 standards. The Form Accessibility setting of the Jotform allows users to create Section 508
compliant forms. Documentation of Jotform’ accessibility can be found at this link:
https://cdn.jotfor.ms/assets/pdf/JotForm_VPAT_v.1.0.pdf. REL Midwest will use no question
types that are not 508 compliant. IES will confirm that all electronic data collection materials
being used in the study are 508 compliant before they are administered to participants.
Teacher interviews will be conducted virtually (via phone or an online platform such as
Microsoft Teams meetings) to reduce the writing burden for teachers. This mode of data
collection is appropriate for the conversational exchange necessary to obtain answers to the
open‐ended questions and allows probing for more detail than a self‐administered survey can
provide.
For the district administrative data, we will reduce burden by gathering the data electronically
rather than in hard copy. We will provide clear instructions regarding the data requested and
methods of transmitting the data securely.
The evaluation team will record participant interviews (with permission) so that participants’
responses can be accurately transcribed and analyzed with a focus on efficiency (recording to
be destroyed after transcription).
A telephone number to a staffed help desk and an e‐mail address will be available during the
data collection process to permit respondents to contact REL Midwest with questions or
requests for assistance. These procedures are designed to minimize the survey burden on
respondents.
A4. Efforts to Avoid Duplication of Effort
Throughout the evaluation, efforts will be made to minimize and reduce the burden on
respondents. Wherever possible, the evaluation team will rely on secondary data sources to reduce
burden on district and school personnel. By collecting administrative records on teachers, the
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
evaluation team will eliminate the need for several items on the teacher survey and thereby avoid
redundancy. The evaluation team will collect school‐level characteristics, such as size, locale, and
student composition, from publicly available sources and thereby reduce the burden on district and
school personnel. The evaluation team will use data that are collected by the implementation team
during the professional development to measure fidelity of implementation, thus reducing the
burden on teachers and facilitators. The primary data collection that is part of this study includes
only information that is not available from other sources.
A5. Methods to Minimizing Burden on Small Entities
The evaluation team will aim to recruit districts from diverse settings in terms of geographic
locale and district size. We expect one or more of the school districts that decide to participate
in the evaluation will be small (i.e., have a population of fewer than 50,000 students). The
evaluation team has developed the data collection plan based on this assumption.
The use of administrative records will reduce the burden on school educators by ensuring that
only the minimum amount of original data is requested from districts to meet the objectives of
this study. To avoid placing extra burden associated with travel on small entities, the
implementation events are conducted separately in each district. The evaluation team will work
closely with districts to ensure the most efficient processes are established for data collection
to minimize burden on the part of district and school personnel. Further, whenever possible,
data will be collected through electronic means—online—to reduce the length of time it takes
respondents to respond.
A6. Consequences of Not Collecting Data
The Education Sciences Reform Act of 2002 (ESRA) states that the central mission and primary
function of the RELs is to support applied research and provide technical assistance to state and
local education agencies within their region (ESRA, Part D, section 174[f]). If the proposed data
were not collected, REL Midwest would not be fulfilling its central mission to serve the states in
the region and provide support for evidence‐based research. The systematic collection and
analysis of the data described above is required to accomplish the goals of the research project
approved by IES. Participation in all data collection activities is voluntary. Information for site
recruitment will be collected using the process described in response to question A2. This is a
one‐time study (i.e., not recurring); therefore, periodicity is not addressed.
A7. Special Circumstances
There are no special circumstances involved with this data collection. Data collected will be
conducted in a manner consistent with the guidelines in 5 CFR 1320.5.
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
A8. Federal Register Announcement and Consultations Outside the
Agency
A 60‐day Federal Register Notice was published on [DATE TO BE COMPLETED BY IES]. A 30‐day
notice was published on [DATE TO BE COMPLETED BY IES].
ED has consulted with the following groups regarding the availability of data, the soundness of
the evaluation design for addressing evaluation questions, and the clarity of measures:
The REL Midwest contractor that proposed this evaluation based on the needs identified
within the Midwest region.
A subject matter expert Dr. Joshua Polanin, who is a principal researcher at AIR and an
expert in research design and evaluation, has provided feedback on the evaluation
methodology and outcome measures.
The REL Midwest contractor has consulted with former educators within its organization
about teacher surveys and interviews. These former educators reviewed the survey and
interview questions for clarity of wording, for “loadedness” of questions (i.e., whether
questions are written to elicit only one type of response), and appropriateness of
response options.
ED also has contracted with another organization to review technical aspects of project
plans and reports submitted by REL contractors. This external peer review contractor
examines the rigor of the evaluation design, the analytic approach for determining
impact and fidelity of implementation, and the degree to which findings address the
evaluation questions and conclusions are supported by the data. The evaluation plan
has been reviewed by the external review contractor and was approved by IES in March
2023.
The REL Midwest contractor has submitted the study for review by AIR’s Institutional
Review Board (IRB) and the study is anticipated to be approved by IRB in June 2023.
A9. Payments or Gifts
The study team has proposed incentives for the surveys and interviews to partially offset
respondent time and effort in completing the survey or interview. Incentives are proposed
because high response rates are needed to make the survey findings reliable, and we are aware
that teachers are the targets of numerous requests to complete surveys on a wide variety of
topics from state and district offices, independent researchers, and ED.
The evaluation team proposes to provide teachers a $30 50 gift certificate and administrators a
$50 gift certificate upon completion of the interview. These amounts were determined based
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
on average hourly wages for teachers and administrators, which were calculated based on the
most current estimates of yearly salaries (currently from 2021) in the Bureau of Labor Statistics
(BLS) Occupational Outlook Handbook. Per IES guidance, “the minimum incentive, no matter
how much time the research activity requires, is one full hour of wages”. Teachers completing
the survey will receive a gift card of $30 50 for completing each of two 30‐minute surveys
(baseline survey before the intervention and follow‐up survey after the intervention) for a total
of $60 per person. Incentives will be distributed electronically (i.e., a link to a gift card) after
respondents complete the data collection instruments.
No incentives will be given to principals for completing the administrator implementation
checklist or to district staff for completing the collection of district administrative records.
A10. Assurances of Confidentiality
AIR, ED’s contractor for REL Midwest, will be following the policies and procedures required by
ESRA, Title I, Part E, Section 183, which requires “All collection, maintenance, use, and wide
dissemination of data by the Institute” to “conform with the requirements of section 552 of
title 5, United States Code, the confidentiality standards of subsection (c) of this section, and
sections 444 and 445 of the General Education Provision Act (20 U.S.C. 1232g, 1232h).” These
citations refer to the Privacy Act, FERPA, and the Protection of Pupil Rights Amendment.
In addition, for student information, ESRA states “The Director shall ensure that all individually
identifiable information about students, their academic achievements, their families, and
information with respect to individual schools, shall remain confidential in accordance with
section 552a of title 5, United States Code, the confidentiality standards of subsection (c) of this
section, and sections 444 and 445 of the General Education Provision Act.”
Subsection (c) of section 183 referenced above requires the Director of IES to “develop and
enforce standards designed to protect the confidentiality of persons in the collection, reporting,
and publication of data.”
Subsection (d) of section 183 prohibits disclosure of individually identifiable information as well
as making the publishing or communicating of individually identifiable information by
employees or staff a felony.
AIR, ED’s contractor for REL Midwest, will protect the confidentiality of all information collected
for the study and will use it for research purposes only. No information that identifies any study
participant will be released. Information from participating institutions and respondents will be
presented at aggregate levels in reports. Information about respondents will be linked to their
institution but not to any individually identifiable information. No individually identifiable
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
information will be maintained by the study team. All members of the study team have obtained
their certification on the use of human subjects in research; REL Midwest staff have also obtained
federal security clearances. All institution‐level identifiable information will be kept in secured
locations, and identifiers will be destroyed as soon as they are no longer required.
REL Midwest will request unique identifiers (IDs) for each student, as well IDs for the
mathematics teacher(s) associated with each student. To minimize access to personally
identifiable information, REL Midwest will request that districts send a separate crosswalk file
that links teacher names to IDs. Both the implementation and the evaluation teams will
maintain data security by allowing access to shared folders only to team members who need it.
REL Midwest also will create a process whereby the project director must approve all requests
for access to these folders (and maintain a list of individuals who have access).
In addition to these safeguards, AIR, ED’s contractor for REL Midwest, routinely employs the
following to carry out privacy assurances with respect to study data:
All AIR employees sign a privacy pledge emphasizing its importance and describing their
obligation.
Identifying information is maintained on separate forms and files, which are linked only
by sample identification number.
Access to hard‐copy documents is strictly limited. Documents are stored in locked files
and cabinets. Discarded materials are shredded.
Computer data files are protected with passwords, and access is limited to specific
users.
Especially sensitive data are maintained on removable storage devices that are kept
physically secure when not in use.
A11. Justification for Sensitive Questions
There are no personally sensitive questions in this data collection. Teachers completing the
survey will be asked questions to measure their self‐efficacy in teaching math to students in
grade 6, about the type of professional development activities they are enrolled in, their
opinions about the quality of the professional learnings offered by the toolkit, and information
about their academic and teaching background characteristics (years of experience,
certification, undergraduate and graduate major). REL Midwest will not collect data on teacher
gender, race, or ethnicity, either through survey or in collection of administrative data.
Teachers completing the interview will be asked about their experiences with implementing the
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
toolkit and their opinions about the toolkit. School administrators completing the checklist will
be asked about their use of institutionalizing supports during implementation of the toolkit.
A12. Estimates of Hours Burden
For this clearance package, the evaluation team has calculated hours of burden for three
components: recruitment activities, primary data collected from study participants, and extant
data provided by the districts. The evaluation team has calculated hours of burden for two
recruitment activities: districts filling in an interest and eligibility form and teachers reviewing
and completing a teacher consent form. The evaluation team has calculated hours of burden
for six primary data collection activities: a teacher survey, classroom observations, a student
assessment, an administrator implementation checklist, interviews with teachers, and
interviews with school leaders. Table 2 shows the hourly burden overall and for each activity.
The total burden associated with activities included in this clearance package is 374 hours, with
an annualized burden of 187 hours over two years. Based on average hourly wages for
participants, the total burden amounts to an estimated total monetary cost of $11,485 and an
annualized cost of $5,743. The annualized number of responses is 206, for a total of 412
response across two years.
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
Table 2. Estimated annual burden and respondent costs
Target
sample
Size
Recruitment and data
collection activity
Recruitment
Estimated
response
Rate
Number of
respondents
Number of
administrations
Total
number of
responses
Average
burden
hours per
response
Total
burden
hours
Estimated Estimated
respondent monetary
average
cost of
hourly wage
burden
District recruitment
(completing the eligibility
form)
50
20%
10
1
10
0.5
5
$50
$250
Teacher recruitment
(completing the consent
form)
158
85%
134
1
134
0.25
33.5
$30
$1,005
Primary data collection
Teacher survey
134
85%
114
2
228
0.5
14
$30
$3,420
Classroom observations*
134
85%
114
1
114
0
0
$0
$0
2,400
85%
2,040
1
2,040
0
0
$0
$0
Administrator
implementation checklist
20
90%
18
1
18
0.5
9
$50
$450
Interviews–teachers
12
100%
12
1
12
1
12
$30
$360
Interviews–school
leaders*
6
100%
6
1
6
1
6
$50
$300
District administrative
data collection
Administrative data on
teachers and students
10
100%
10
1
10
20
200
$30
$6,000
Student assessment*
Totals
Annualized totals
298
149
412
206
374
187
$11,485
$5,743
* Indicates activities for which OMB clearance is not being sought and that are not included in the estimated total burden hours or estimated monetary cost.
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A13. Estimates of Cost Burden to Respondents
There are no additional respondent costs associated with the data collection for this study
other than the hour burden accounted for in item 12. The collection of qualitative and
quantitative data proposed in this package is a one‐time series of data collection activities.
There are no plans for follow‐up studies or other recurring data collections outside of what is
being proposed in this package.
A14. Annualized Cost to the Federal Government
The total cost to the federal government for developing, fielding, and analyzing the evaluation
over all five years is approximately $1,185,000, and the estimated annualized cost to the
federal government for each year of the study is approximately $237,000 (over five years).
Funding includes staff time for REL Midwest staff to recruit participants and collect, clean, and
analyze data from the study. Also included are costs incurred by REL Midwest staff related to
study preparation and submission of the study information to IES (from proposed research
design through reporting of results).
A15. Reasons for Program Changes and Adjustments
This is a new study.
A16. Plans for Tabulation and Publication of Results
All results for REL rigorous studies will be made available to the public through peer‐reviewed
evaluation reports that are published by IES.
The analyses will be carried out using hierarchical linear modeling, where appropriate, to take into
account nesting (e.g., the nesting of students and teachers within schools) and will incorporate
covariates measured at baseline to maximize precision. To avoid potential selection bias, the impact
analyses will employ an intent‐to‐treat approach, in which all students and teachers in all randomly
assigned schools during the 2024/25 school year are included in the analyses, whether or not the
teachers actually participated in the toolkit professional development or participated to the full
extent expected. This approach is explained further in Part B.
Findings that are answers to the research questions will be presented regardless of whether
they are statistically significant. The main report will focus on findings about the student
achievement measure and the domain averages for teacher self‐efficacy and teacher practice
and on findings about service contrast. Findings from the exploratory analyses (analyses by
individual characteristics, analysis of individual measures within the teacher self‐efficacy and
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
teacher practice domains) will be presented in appendixes. The main report will describe key
findings with text and a simple table or a graph (e.g., a bar chart). The full detailed findings will
appear as tables in an appendix.
No responses or data will be reported for individual staff members, students, or schools.
Reported data will contain no fewer than four cases per reported table cell to protect
confidentiality and mask individually identifiable data.
After the study report is finalized, the evaluation team will prepare restricted‐use data files in
accordance with NCES standards. These files will contain all the primary survey data collected
for the study with all personal identifiers removed. Thorough documentation will be provided
for each data file, including a detailed codebook and explanations of the unit of observation,
weights, and methods for handling missing data. All restricted use files are required to be
reviewed by IES’ Disclosure Review Board. The Disclosure Review Board (DRB) comprised of
members from each NCES Division, representatives from IES’ Statistical Standards Program, and
a member from each of the Institute of Education Sciences (IES) Centers. The DRB will review
disclosure risk analyses conducted by the REL contractor to ensure that data released do not
disclose the identity of any individual respondent. The DRB approves the procedures used to
remove direct identifiers from restricted‐use data files. IES restricted‐use data sets require a
user’s license that is applied for through the same process as NCES restricted‐use data sets.
Even the evaluation team would be required to obtain a restricted‐use license to conduct any
work with the data beyond the original evaluation.
District administrative data collected in this evaluation, however, will not be included in a
restricted‐use data file. Instead, the study team will prepare an alternate file, with the relevant
documentation needed to replicate the analysis or answer additional research questions in the
event that our district partners were to make administrative data available for such an analysis.
In a .txt format, the alternate file will describe the data requested from participating districts
and instructions on how to obtain those data, as well as the steps the study team took to merge
and clean the data, create variables, and run the analyses.
The timeline for the activities in this project, including data collection, analyses, and reporting
are in Table 3.
Table 3. Project Timeline
Activity/milestone
01
02
03
04
05
06
07
08
09
10
11
12
2022
Submit evaluation proposal.
Submit data management plan.
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
Activity/milestone
Develop and refine evaluation
instruments.
01
02
03
04
05
06
07
08
09
10
11
12
2023
Develop and refine evaluation
instruments (continued).
Receive notice of institutional review
board approval or exemption.
Submit Office of Management and
Budget clearance package (after first
round of REL peer review of the
evaluation proposal is complete).
Recruit districts, schools, and teachers.
2024
Recruit districts, schools, and teachers
(continued).
Establish data‐sharing agreement.
Implement intervention.
Collect data.
2025
Implement intervention (continued).
Collect data (continued).
Analyze data.
Draft report.
Submit summative report.
Implement intervention (delayed
treatment).
2026
Implement intervention (delayed
treatment; continued).
A17. Approval not to Display the Expiration Date for OMB Approval
The Institute of Education Sciences is not requesting a waiver for the display of the OMB
approval number and expiration date.
A18. Exception to the Certification Statement
This submission does not require an exception to the Certificate for Paperwork Reduction Act
(5 CFR 1320.9).
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Regional Educational Laboratory Midwest Teaching Fractions Toolkit Evaluation
References
Barbieri, C. A., Rodrigues, J., Dyson, N., & Jordan, N. C. (2020). Improving fraction understanding
in sixth graders with mathematics difficulties: Effects of a number line approach
combined with cognitive learning strategies. Journal of Educational Psychology, 112(3),
628–648. http://eric.ed.gov/?ID=EJ1247111
Booth, J. L., & Newton, K. J. (2012). Fractions: Could they really be the gatekeeper’s doorman?
Contemporary Educational Psychology, 37(4), 247–253. http://eric.ed.gov/?ID=EJ977998
DePiper, J. N., Nikula, J., & Louie, J. (2019). Shifts in self‐efficacy for teaching English learners:
Emergent findings from mathematics teacher professional development. In S. Otten, A.
G. Candela, Z. de Araujo, C. Haines, & C. Munter (Eds.), Proceedings of the forty‐first
annual meeting of the North American Chapter of the International Group for the
Psychology of Mathematics Education (pp. 547–551). University of Missouri.Fazio, L. K.,
Kennedy, C. A., & Siegler, R. S. (2016). Improving children’s knowledge of fraction
magnitudes. PLoS ONE, 11(10), Article e0165243.
https://doi.org/10.1371/journal.pone.0165243
Garet, M. S., Wayne, A., Stancavage, F., Taylor, J., Walters, K., Song, M., Brown, S., Hurlburt, S.,
Zhu, P., Sepanik, S., & Doolittle, F. (2010). Middle school mathematics professional
development impact study: Findings after the first year of implementation (NCEE 2010‐
4009). U.S. Department of Education, Institute of Education Sciences, National Center
for Education Evaluation and Regional Assistance. https://eric.ed.gov/?id=ED509306
Harvey, R. (2012). Stretching student teachers’ understanding of fractions. Mathematics
Education Research Journal, 24, 493–511. https://eric.ed.gov/?id=EJ984997
Jones, D. L., Zientek, L. R., Sharon, V. V., & Swarthout, M. B. (2020). Solving equations with
fractions: An analysis of prospective teachers’ solution pathways and errors. School
Science & Mathematics, 120(4), 232–243. https://doi.org/10.1111/ssm.12402Liu, Y.
(2018). Fraction magnitude understanding and its unique role in predicting general
mathematics achievement at two early stages of fraction instruction. British Journal of
Educational Psychology, 88(3), 345–362. https://doi.org/10.1111/bjep.12182
McGee, J. R., & Wang, C. (2014). Validity‐supporting evidence of the Self‐efficacy for Teaching
Mathematics Instrument. Journal of Psychoeducational Assessment, 32(5), 390–403.
https://eric.ed.gov/?ID=EJ1030705 Park, J. H., Lee, I. H., & Cooc, N. (2019). The role of
school‐level mechanisms: How principal support, professional learning communities,
collective responsibility, and group‐level teacher expectations affect student
achievement. Educational Administration Quarterly, 55(5), 742–780.
https://eric.ed.gov/?id=EJ1232698
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National Assessment of Educational Progress. (2015). Mathematics Teacher Questionnaire:
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https://nces.ed.gov/nationsreportcard/subject/about/pdf/bgq/teacher/2015_bq_teach
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Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray, J.
(2010). Developing effective fractions instruction for kindergarten through 8th grade: A
practice guide (NCEE 2010‐4039). U.S. Department of Education, Institute of Education
Sciences, National Center for Education Evaluation and Regional Assistance.
https://eric.ed.gov/?id=ED512043
Siegler, S. F., & Lortie‐Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal
of Educational Psychology, 107(3), 909–918. https://doi.org/10.1037/edu0000025
Tekin‐Sitrava, R. (2020). Middle school mathematics teachers’ reasoning about students’
nonstandard strategies: Division of fractions. International Journal for Mathematics
Teaching and Learning, 21(1), 77–96.
Whitehead, A. N., & Walkowiak, T. A. (2017). Preservice elementary teachers’ understanding of
operations for fraction multiplication and division. International Journal for
Mathematics Teaching & Learning, 18(3), 293–317. https://eric.ed.gov/?id=EJ1164169
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| File Type | application/pdf |
| File Title | Microsoft Word - RELMidwest_5.1.7_TFTEfficacyStudy_Supporting Statement Part A_revised61124_TRACKED |
| Author | Juliana.Pearson |
| File Modified | 2024-06-14 |
| File Created | 2024-06-14 |