A Data-Driven
Review of
Instructional
Materials
California County
CCSESA Superintendents
Educational Services
Association
Mathematics Adoption Toolkit
Curriculum & Instruction
Steering Committee
1
Mathematics Adoption Toolkit
Foreword
On behalf of the County Superintendents of the State of California, we are pleased to introduce
the Mathematics Adoption Toolkit developed by the Mathematics Subcommittee of the Curriculum and
Instruction Steering Committee with support from the California Mathematics Council. Standards-based
materials that meet the needs of students are essential for their achievement in mathematics. The
Mathematics Adoption Toolkit offers a clear, data-driven process for reviewing mathematics
instructional materials to help district personnel make informed, objective recommendations to local
Boards of Education to best meet local needs.
The California County Superintendent Educational Services Association (CCSESA) is an
organization consisting of the County Superintendents of Schools from the 58 counties in California
working in partnership with the California Department of Education. The Curriculum and Instruction
Steering Committee (CISC) is a subcommittee of CCSESA, consisting of county office associate
superintendents, focusing on curriculum, instruction, and professional development.
The County
Superintendents of California are pleased to provide support to California schools for the mathematics
instructional materials selection process.
Dr. David Long
County Superintendent, Riverside County
Office of Education
Past President, CCSESA, California
County Superintendents
Educational Services Association
Larry Champion
Associate Superintendent
Tehama County Office of Education
Past Chair, Curriculum and Instruction
Steering Committee
Mary Jane Burke
County Superintendent,
Marin County Office of Education
President, CCSESA, California
County Superintendents
Joyce Wright
Assistant Superintendent,
Sacramento County Office of Education
Chair, Curriculum and Instruction
Steering Committee
Mathematics Adoption Toolkit
1
Contributing Authors
Doreen Heath Lance, Chair
Sonoma County Office of Education
April Cherrington
San Mateo County Office of Education
Joanie Commons
UCSD, Cajon Valley Union School District, CMC
Babette DeCou
Paso Robles Public Schools, CMC Representative
Linda Dilger
Monterey County Office of Education
Luke Dilger
Monterey County Office of Education
Joan Easterday
Sonoma County Office of Education
Tim Gill
Lake County Office of Education
Satinder Singh
San Joaquin County Office of Education
Frances Basich Whitney
Santa Cruz County Office of Education
Debbie Williams
San Joaquin County Office of Education
Kathy Woods
Madera County Office of Education, CMC
Special Thanks
Linda Menvielle
Chair, CISC Mathematics Subcommittee
Assistant Superintendent for Instructional Services,
Imperial County Office of Education
Harold Asturias
President, California Mathematics Council
Dean Gilbert
Chair, Science Adoption Toolkit,
CISC Science Subcommittee
Members of the CISC Mathematics Subcommittee
County Superintendents of Public Instruction
Paul Giganti
Cover design
Department of Education California
Phil La Fontaine
CDE Division Director
Professional Development and Curriculum Support
Developed by the Mathematics Subcommittee,
Curriculum and Instruction Steering Committee
California County Superintendents Education Services Association
 2007 All rights reserved
Mathematics Adoption Toolkit
2
Mathematics Adoption Toolkit
Table of Contents
Table of Contents
Foreword
---------------------
1
Introduction and Overview
---------------------
4
Facilitator’s Guide
---------------------
10
District Lens
---------
17
Standard(s) Sampling
---------
19
Program Components Review
---------
22
Additional Options
---------
24
Making A Decision
---------
26
Planning Forward
---------
30
Templates
Section #1
Developing the District Lens
------
32
Section #2
Standards Sampling
------
49
Section #3
Reviewing Program Components
------
58
Glossary
---------------------
78
Williams Settlement
---------------------
81
Mathematics Adoption Toolkit
3
Mathematics Adoption Toolkit
Introduction
As a State, Are We Ready for 2014?
With the advent of No Child Left Behind, education has been held accountable for its work more
closely than any other time in history. This mathematics adoption will be the adoption that sees us –
students and educators – through to the year 2014! While all adoptions are serious business in
education, the adoption of instructional materials for mathematics may be a key factor for schools and
districts challenged to meet required levels of proficiency for all students by 2014.
Participation on a district adoption committee can be an exciting process, enabling educators to
impact a district’s choice of instructional materials. Our goal is to support your efforts by helping you
establish a focus toward best meeting the needs of students and teachers in your district. The task
you are about to undertake will demand effort and availability of resources – time and staff to review
programs. These resources vary from district to district. For this reason, the Toolkit can be
implemented in a variety of ways, ensuring the facilitation of a successful adoption process, one
focused on meeting the needs of students and teachers in your district.
The members of the
Curriculum and Instruction Steering Committee (CISC) urge schools and districts to craft a careful
plan to analyze the myriad of State Board of Education (SBE) adopted programs for mathematics.
An Overview of the Mathematics Adoption Toolkit
The Mathematics Adoption Toolkit is designed to support the selection of grades K-8
instructional materials for core programs, Algebra Readiness, and Intervention, but can also support a
grades 9 – 12 adoption process
The Toolkit is organized around accountability questions guiding the work in California
schools:
What do you want your students to know? (Mathematics Content)
How will you know your students “know it”? (Assessment)
How will you make sure your students “know it”? (Instructional Strategies)
How will you make sure ALL students “know it”? (Universal Access)
The Toolkit is divided into three worksheet sections (Developing the District Lens, Standard
Sampling, and Program Component Review) each section is subdivided into four topics: Mathematics
Content, Instructional Program, Assessment, and Universal Access. Section #4 offers options for
further review. These sections and topics will help you thoroughly analyze the selected mathematics
programs. Section #5, presents a process for coming to consensus on the choice for adoption. The
Mathematics Adoption Toolkit
4
review and ultimate selection of a mathematics program are your first steps in preparing your district
for the year 2014.
Chart: Mathematics Adoption Toolkit: A Complete Adoption Process.
Mathematics
Content
Yes
Instructional
Program
Yes
Assessment
Yes
Universal
Access
Yes
- Task #1 – CA Expectations for Math Students
- Task #2 – District’s Expectations for Math Students
- Task #3 – District’s Needs for Student Population
- Task #4 – Assessment Data for Math
- Task #5 – District’s Learning Configurations
- Task #6 – District’s Needs for Teacher Population
- Task #7 – District’s Current Instructional Resources
- Task #8 - Resources Supporting Mathematics
Section #2: Standard Sampling
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Section 1: Developing the District Lens
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Section #3: Program Components
Yes
Yes
Yes
Yes
Section #4: Further Options for Review
Yes
Yes
Yes
Yes
Section #5: Coming to Consensus
Yes
Yes
Yes
Yes
The
Yes
Mathematics Adoption Toolkit is based on the premise that a district’s adoption should
reflect its unique and specific needs. The most appropriate adoption for one district might not be the
most appropriate for another.
Therefore, creating the district lens for analyzing the materials
(completing Section #1) is critical to making the best selection for your students and teachers.
However, if a district recently reviewed its needs and resources in the science materials adoption
process, your adoption committee could update information relevant to mathematics needs and
proceed to Section #2.
 Section #1: Developing the District Lens
The school or district adoption committee develops a lens through which to view and
evaluate the various program materials.
Establishing a profile of the district’s needs and
resources creates this lens. The Toolkit provides a series of eight tasks analyzing state
expectations in mathematics instruction, district expectations for mathematics instruction,
student performance data, and the needs of your teacher population. The data needed for this
section is, for most schools and districts, readily available and should be provided as
informational packets to the committee. For schools and districts without ready access to
data, an avenue for compiling the documentation can be accessed via an internet link to
DataQuest http://dq.cde.ca.gov/dataquest/ Completing the District Lens will enable the
school/district to determine the type of instructional program it needs and Toolkit sections #2Mathematics Adoption Toolkit
5
#4 will help focus the evaluation of these programs based on district needs for students and
teachers.
Developing the District Lens is a very important part of the process. It is not only an
important initial step, it is powerful professional development for the committee members to
“ground” themselves in the framework and specific needs of their district. While publishers
may develop their own “toolkits” these have limited value in the sense that they are “lens free”
and do not take into consideration the very specific and often challenging needs of a district. It
is in a school’s/district’s best interest to thoroughly investigate their unique needs to determine
the program that has the greatest likelihood of addressing those challenges. (See: pp.17-19,
32-48)
An important tip for this stage - Start now!! It is not necessary to wait to see what the State
Board of Education (SBE) adopts in order to clarify what critical components need to be in the
program that best meet the needs of your students and staff. Once the SBE adopts a list of
instructional materials, you are in a position to begin the work of investigating programs.
Once the committee has established school/district priorities for a mathematics program via the
lens, it is ready to begin the work of reviewing the programs that the SBE has adopted. All programs
adopted by the SBE are considered to meet the state requirements for instructional materials outlined
in the framework. This was the work of the Instructional Materials Advisory Panel (IMAP) composed
of teachers, educators, and a member of the Content Review Panel (CRP) during the summer of
2007. The panels have determined if the programs meet or do not meet the criteria including
mathematical accuracy. The SBE votes after reviewing the recommendations of the Curriculum
Commission who is advised by the IMAP and the CRP. Your committee work is to determine the
quality of the program in best meeting your district needs. The Toolkit suggests different options for
the analysis of instructional materials.
To start this stage, the committee evaluates the grade level configurations (K-5, K-6, K-8, 6-8,
etc.) of the recommended instructional materials. It may be that some programs are eliminated at this
point, without further investigation, due to the fact that the grade level configurations of the program
do not meet the needs of the district.
 Section #2 - Standards Sampling: Taking a Deeper Look at Mathematics
Of great concern in the selection of a mathematics program is the ability of that program to
support the instruction required to prepare all students for grade level proficiency and Algebra
I. In an attempt to judge the quality of mathematics instruction, the committee will want to
perform a deeper analysis of the instruction in key mathematical concepts and standards that
Mathematics Adoption Toolkit
6
prepare students for further mathematics. (See: pp.19-22, 49-57). This is an opportunity to
review programs through the lens of the standards that are challenging to teach in your district.
The Standard Sampling analysis will inform the committee of the strength of the
mathematics critical in the selection of instructional materials that will take our schools to the
year 2014. Information gleaned from the Standards Sampling indicating a strong balance of
mathematics - procedural fluency, conceptual understanding, problem solving, and
mathematical reasoning - will serve as a means for identifying programs you want to
investigate further as the committee works to identify the best program for your school/district.
 Section #3 - Analyzing Program Components: Matching District Needs to Instructional
Materials.
Following the Standards Sampling, the committee will begin a formal review of the
program components that make up the instructional program – a series of questions are
provided to guide the program component review as committee members investigate and
evaluate the four topics:
Mathematics Content, Instructional Strategies, Assessment, and
Universal Access.
Each time committee members investigate the programs, they will start by reviewing
the district lens so that district priorities guide the analyses of the program components. An
exciting feature of this Toolkit is that the feedback by reviewers for the program components
can be done online. This allows the person facilitating the process to compile data on the
programs, monitor committee member progress, prompt if needed, and develop a report
based on the rubric scores assigned by the committee members for each component of each
instructional material investigated. (See: pp. 17-19, 58-77)
 Section #4 - Additional Review Options: Piloting, Blind Review, Student Surveys and
Executive Committee.
Some school districts, after determining the top scoring programs for their students and
staff, will choose to undergo a pilot phase of the programs before making a recommendation
to its local school board.
Another option is to conduct a blind review. Teachers compare the same lesson from all
programs under consideration. The name of the program is masked. Teachers compare the
lessons looking for strengths and weaknesses.
Student surveys are used to develop a picture of how students make sense of
mathematics while using the textbook.
Mathematics Adoption Toolkit
7
After identifying areas of top priority in the district lens, some committees may choose to
convene a subcommittee of experts in an area(s) of high priority. For example, if English
Language Learners are a top priority, instructors of second language learners may be
convened to evaluate materials from that perspective. (See: pp. 24-26)
Certainly the prior steps are crucial in making an informed decision for program selection geared
to meet the proficiency needs of our students by 2014. However, we are aware that not all districts
have the resources needed to complete this ideal process. For that reason, we have suggested
alternate pathways for determining the program that will best meet the needs of the students and
teachers in your district.
For example, your district may choose to use Section #2, Standards
Sampling to gather evidence and then proceed to Section #5, Making a Decision. The graphic shows
different options for using the Toolkit.
Section #1: Develop District Lens
Section #2: Standards Sampling
Section #5: Make a Decision
Section #3: Program Components
Section #5: Make a Decision
Section #4: Further Comparison
Section #5: Make a Decision
Section #6: Implementation
 Section 5: Making a Decision – Coming to Consensus
The committee members tally and summarize comments about the four topics analyzed
through the templates that guide this process. They review the results from a grade level and
school wide perspective looking for program strengths and weaknesses.
The committee
comes to consensus about a program that all committee members will support throughout its
implementation. (See: Facilitator’s Guide, pp. 26-30).
The qualitative and quantitative results from this work will be documented on a report to
help arrive at the recommendation for adoption by your district. A helpful component of the
Toolkit is the report that is generated electronically. This report neatly summarizes the
Mathematics Adoption Toolkit
8
information and the scores of the programs and is an ideal document to submit to the local
board in the recommendation packet.
 Section 6: Next Steps, Implementation
The next phase takes us to effective implementation of the selected program. With the
critical role that this mathematics adoption is going to play as we prepare all students for
proficiency in mathematics, we must update our instructional practices with this new program’s
implementation.
A
complete
mathematics
program
will
include
staff
development,
implementation of instructional materials, and evaluation and analysis of student progress. No
mathematics adoption will be a perfect match for your district needs, so you will need to be
cognizant of gaps between what your students are expected to know and what they actually
learn. Additional professional development will be needed to close these gaps.
While your committee is convened, take the time to brainstorm ways the district can
support the serious and expedient implementation of its new adoption. This may include
aligning current systems with the new program, e.g., benchmark assessments. The success
of the adoptions is measured in its strategic and purposeful execution.
Mathematics Adoption Toolkit
9
Mathematics Adoption Toolkit
FACILITATOR’S GUIDE
Mathematics Adoption Toolkit
10
Mathematics Adoption Toolkit
Facilitator’s Guide
Facilitator’s Guide to the Mathematics Adoption Toolkit
As a facilitator you will guide the process of identifying district needs and matching them to
state-adopted instructional materials. The purpose of this Toolkit is to support schools and districts in
conducting a data driven adoption process that identifies a balanced instructional program for
students. Balanced instruction is the use of universal access strategies to provide students with
experiences in conceptual understanding, procedural fluency, and problem solving while using
mathematical reasoning (Mathematics Framework for California Schools, pp. 4-5).
Data is used to analyze and identify district needs and determine priorities in choosing a new
mathematics program (See: pp.17-19, 32-48). Your school/district most likely has collected and
organized this data for other purposes that will facilitate an easy transfer of information. Identifying
district priorities for adoption should be completed before reviewers begin examining the mathematics
programs.
The Mathematics Adoption Toolkit will guide your adoption committee as it gathers
evidence, and will provide a structure for informed decision making. The size and resources available
to a school or district may impact the degree of use of the Toolkit. Regardless of such constraints,
any utilized portion of the Toolkit will provide valuable resources to a school or district seeking an
instructional program that best meets the needs of its students and teachers.
OVERVIEW OF TOOLKIT SECTIONS
This Toolkit has six sections: Developing The District Lens, Standards Sampling, Program
Components, Additional Review Options, Making a Decision, and Next Steps: Implementation. All
sections are organized around four topics: Mathematics Content (What do you want your students to
know? – color coded red); Instructional Program (How will you make sure your students “know it”? –
color coded green); Assessment (How will you know if your students “know it”? – color coded blue);
and Universal Access (How will you make sure ALL students “know it”? – color coded orange).
The first section of the Toolkit involves developing a clear picture of district needs: in effect,
creating a “District Lens”. To accomplish these first steps, you will need a thorough understanding of
Section #1: Developing A District Lens.
Mathematics Adoption Toolkit
11
The second part of the process outlined in Section #2 is focused on Standards Sampling (See
pp. 19-22, 49-57) to determine the depth and range of the mathematics content of the programs under
consideration. The choice of standards to be sampled will reflect those most challenging to teach for
your district teachers. The work in Section #3 is used after potential programs are narrowed down to a
select few.
At this stage, all materials within each selected program are scrutinized to find the
instructional program that best matches the districts identified needs (See: pp.22-24, 58-77). Section
#4 provides an outline of further filter processes: piloting, blind testing, and/or student surveys (See:
pp.24-26). Section #5 outlines a process for compiling and reporting evidence of strengths and
weaknesses for each considered program. Section #5 guides building committee consensus for the
final decision and recommendation (See: pp. 26-30). The Toolkit concludes with Section #6 Next
Steps: Implementation.
To provide each school/district with flexible options for conducting the process, California
County Superintendents Educational Services Association (CCSESA) is providing you a choice of:
print documents, CD version of materials, - as well as, the option of web based recording and
tabulation. All materials are available at http://www.ccsesa.org or www.cmc-math.org. The CD version
has Word documents to enable your reviewers to expand the cells as needed.
Additionally, it
contains a PowerPoint presentation providing an overview of the Toolkit process, and a folder of
completed Standards Sampling for sixth grade division of fractions.
Electronic Report requires a computer with both the Internet and browser. You may want to
assemble the committee in a computer lab that is Internet accessible. As facilitator, you will first need
to register your district and receive an online code. This code will provide confidentiality for your
district data. Once your district is registered, you can provide the URL site and district code to
committee members, instructing them to register and then proceed with data entry for each publisher.
An advantage of the website is the opportunity for teachers to independently and thoroughly review
materials before committee discussions. The website also offers opportunities to turn questions on or
off to reflect the district priorities, as well as, enable you to quickly tabulate and collect the reviewers
data.
The following tables provide an outline of the steps in the process and the materials and
resources to support your work.
Mathematics Adoption Toolkit
12
Mathematics Adoption Toolkit
Adoption Process Options
Section #1 (3 hours):
Developing the District Lens
Section #2 (3 - 6 hours):
Standards Sampling – Partial or Full
Eliminate Programs
Section #5 (3 hours)
Making a Decision
Section #3 (6 hours):
Review Program Components
Eliminate Programs
Section #5 (3 hours)
Making a Decision
Section #4:
Additional Review Options
Pilot Programs
Blind Test of Lessons
Survey Students
Executive Committee
Eliminate Programs
Mathematics Adoption Toolkit
Section #5 (3 hours)
Making a Decision
13
Mathematics Adoption Toolkit
Facilitator’s Guide
Advance Preparation
The 2007 Mathematics Adoption Toolkit is organized to help you, the adoption process facilitator, and your team identify the
Basic grade level, Intervention, and Algebra Readiness programs best suited to the needs of your students and teachers. The
Facilitator’s Guide illustrates how working through the sections in the Toolkit can produce customized program selections tailored to
meeting the needs of all students as well as providing support and instructional clarity to teachers. The intent of these tools is to create a
process by which decisions can be made objectively, based on collected data and program findings.
The facilitator needs to coordinate the logistics, as well as, the process for the adoption process. The following section provides
an outline of work that will help the process to run smoothly.
TASK
1.
Establish a timeline.
ACTIVITIES
MATERIALS
Consider:
 When the district board needs the recommendation.
 Amount of time the process will require.
 Configuration of time for work – release, after-school, etc.
 Scheduling meeting rooms.
 For information on the CA Department of
Education’s timeline for adoption, refer to:
www.cde.ca.gov/ci/cr/cf/timeline05to08adoptions.asp
2.
Identify and gather state
adopted publisher
materials.
Consider:
 Which programs has the state approved?
 How will you acquire and store the materials?
 How will the committee members access the materials?
 Materials submitted for state adoption are
available at the regional Learning Resource
Display Centers (LRDC):
www.cde.ca.gov/ci/cr/cf/lrdc.asp
 Information of state processes and publisher:
www.cde.ca.gov/ci/cr/cf/imagen.asp
 Publisher materials and contact information:
http://www.cde.ca.gov/ci/ma/im/
3.
Identify, recruit, and
convene the committee.
Collaborate with district leadership to consider:
 Variety of stakeholders who will actively participate:
- Classroom teachers (elementary and secondary).
- EL, Special Ed. Advanced Learner teachers.
- Teachers with AB466 or SB472 training in math.
- Administrators
- Parents and other community members.
 Lists and contact information for perspective
members including teachers, administrators,
parents, community members, higher
education faculty.
 Letter of invitation explaining the process and
time commitment.
Mathematics Adoption Toolkit
14
4.
Collect district data to
ensure match of
materials to district
needs.
- Members of local school board
- Representatives from higher education faculty.
 Grade level or course groupings.
Data sources that should be considered and organized for
Section #1, District Lens are:
 Student assessment data including CELDT report.
 Student demographic data.
 Teacher data (expertise, credential type, years in present
assignment).
 School configuration data.
 Resources, technology, equipment, and tools in district.
 Curriculum guidelines, pacing guides, or curriculum maps.
Suggestion:
 Provide hardcopies of relevant data reports to create
packets for participants.
 Hardcopy could be inserted with the individual tasks in
Section #1 as relevant.
 Or, consider entering the data ahead of time into the
website.
Mathematics Adoption Toolkit
15
 Data previously collected for other purposes
e.g., for the science adoption
 Collect data and enter onto web ahead of
time or collect and print
Gender:
http://dq.cde.ca.gov/dataquest/ (Enrollment)
http://www.jftk-ca.org
http://star.cde.ca.gov/star2006/Viewreport.asp
Ethnicity:
http://dq.cde.ca.gov/dataquest/ (Enrollment)
http://www.jftk-ca.org
http://star.cde.ca.gov/star2006/Viewreport.asp
Socio-Economically Disadvantaged:
http://dq.cde.ca.gov/dataquest/ APIBase
http://www.jftk-ca.org
English Learners:
http://dq.cde.ca.gov/dataquest/ CELDT
http://dq.cde.ca.gov/dataquest Language Census
http://www.jftk-ca.org
http://star.cde.ca.gov/star2006/Viewreport.asp
Students with Disabilities:
http://dq.cde.ca.gov/dataquest/ SpecEd
http://www.jftk-ca.org
http://star.cde.ca.gov/star2006/Viewreport.asp
Gifted and Talented:
http://dq.cde.ca.gov/dataquest/ Enrollment
http://star.cde.ca.gov/star2006/Viewreport.asp
Mobility:
http://dq.cde.ca.gov/dataquest/ APIBase2006
Prevalent Languages:
http://dq.cde.ca.gov/dataquest Language Census
CST:
http://star.cde.ca.gov/star2006/Viewreport.asp
http://dq.cde.ca.gov/dataquest/APIBase
http://www.jftk-ca.org
CELDT:
http://dq.cde.ca.gov/dataquest/CELDT
District Technology:
http://www1.edtechprofile.org
Mathematics Adoption Toolkit
16
5.
Publish resources for
committee members.
Prepare materials for committee members
1. Overview of Adoption Process
a. Timeline for adoption
b. List of adopted publishers
c. Graphic of process
2. District data
3. How to access website
4. CA Mathematics Framework
5. CA Blueprint for STAR
6. Mathematics Released Items
7. Toolkit worksheets: print or Electronic copies
8. Contact information for committee members
9. District pacing guide, benchmark
assessments and results.
A Closer Look - Section by Section
The primary intent of the Toolkit is to identify District needs for both students and teachers, and provide process steps to match
these needs to a mathematics program best situated to support them. Each Toolkit section represents a different phase in the decisionmaking process, comparable to how you might work through a major purchase. The process steps in the Facilitator’s Guide have been
worked around the scenario of buying a car. Section #1 (District Lens) identifies needs by creating a District “lens” – a filter that articulates
student needs, as well as needs of teachers. Section #2 (Standards Sampling), #3 (Program Component Review), and #4 (Additional
Review Options) provide several options for analyzing and comparing programs against the priorities for adoption. Section #5 (Coming to
Consensus) outlines a consensus process whereby the accumulated data from Sections #1 through #4 are used to make final decisions
and a customized selection.
Section #1: Creating the District Lens
Warm-Up Activity: Creating a Mindset for Process
You are getting ready to purchase a new car. Before walking onto a car lot and being influenced by a creative salesperson, and
well before forking over a down payment, you do your homework and create a “shopping list”. You are determined to find the
“best” car for your money; a car that will meet your needs and stand the test of time and use. In doing your homework, you
establish what it is you have to have in a car. Some choices are essential (e.g., 4-wheel drive if you live where it snows; or air
Mathematics Adoption Toolkit
17
conditioning if you live in the desert) and other choices are optional (e.g., a moon roof, or burl wood dash accents). Yet one
person’s essential choice is another’s options. It is important to know your bottom line before you encounter the pressure of the
car salesperson.

Have team members generate a list of essential car features. In a quick popcorn share-out, discuss which features
are essential, which are optional, and why. Is there agreement? Any differences of options?

Relate responses to the Toolkit process step, Creating the District Lens. As with the lists just generated,
essential features versus those that are optional are not uniformly agreed upon.
Consider the magnitude of the textbook purchases your District is about to make. Unlike a car that decreases in value as soon as it’s
driven off the lot, the textbook program you purchase must help increase the mathematical knowledge and understanding of all students!!
While all adoptions are serious business in education, the adoption of instructional materials for mathematics may be a key factor for
schools and districts challenged to meet required levels of proficiency for all students by 2014.
Summary / Outcome: Establish district needs for all students and for teachers. It is crucial time be given at the onset to create the
District Lens, as all subsequent decisions should reflect a true accounting of your learner populations and teacher needs. The data
should guide the work done in all process steps as well as help prioritize essential program features in the “shopping list”. These
priorities become your adoption itinerary!!!
SECTION
Section #1:
Developing the District
Lens.
Pages: 32-48
Mathematics Adoption Toolkit
ACTIVITIES
MATERIALS
Task #1:
 Become familiar with Mathematics CA. Framework (balanced
program and reasoning standards)
 The rating bar is for individual use and not recorded on website.
Task #2:
 Identify district’s progress toward meeting state expectations for
mathematics instruction.
Task #3 - 7:
 Use district-generated data to identify student and staff needs.
Task #8:
 Identify the availability of local mathematics resources.
18

Mathematics framework, hard copy or
electronic.
http://www.cde.ca.gov/ci/ma/cf/index.asp





Worksheets – pages 32-48
For electronic templates see:
http://www.ccsesa.org
District data compiled and/or entered in
Advance Preparation #4 (above),
Local benchmark assessment and
results
Meeting supplies: chart paper,
Summary
 Key findings – compile summary statements (ah ha’s) from
committee members into a district summary chart
 Use a chart to prioritize district needs for students and teachers.
District Summary Chart:
Content
Assessment
Instructional
Program
overheads, pens, etc.
Universal
Access
Student Needs
Teacher Needs


Identify the nonnegotiable priorities. These describe the elements
any adopted program must have.
This chart should be referred to before the beginning of each
meeting and be the basis of all decision-making.
As facilitator with your district leaders:
 Examine the other sections of the Toolkit and determine which
questions best address your district needs. And which questions do
not need to be addressed.
 Using the website or using a Word document, you may turn off any
questions that do not pertain to your district (See: Technology
Support Document).
Note: At this point you may choose to move to Section #2, #3 or #4.
Section #2: Standards Sampling
District strengths and areas of needs have been identified in Section #1. The team is now ready to begin narrowing the field of
program choices. The process shifts toward hands-on experiences with the Teacher’s Edition (TE) to determine which programs
demonstrate the most robust mathematics course of instruction to meet the needs of students and teachers. Standards Sampling will
allow you to evaluate program quality, depth, and integrity as you trace a standard’s introduction, development, and assessment as it is
presented in the TE. The TE is the only portion of the program to be examined at this time: the TE is often the only universally
Mathematics Adoption Toolkit
19
purchased program component. More often than not, the TE is the only part of the program readily available to teachers several years
into an adoption.
The Instructional Materials Advisory Panels (IMAP) and the Content Review Panels (CRP) established that all adopted programs meet
the minimal criteria for 1) mathematical content/alignment with standards; 2) program organization; 3) assessment; 4) universal access;
and, 5) instructional planning and support. Standards Sampling creates an opportunity to evaluate a program’s TE and its treatment of
2 or 3 “big ticket” standards you deem critical to student understanding. Help the team understand that an adopted program at worse
meets minimal requirements; the team’s work should focus on identifying the extent of content development. The goal here is to create a
side-by-side comparison of each program’s TE materials to narrow the field to those programs that best match the needs of students and
teachers. In the words of one mathematics educator, “…if the math isn’t ‘good’, then nothing else matters!’”
Comparing Specs & Data Sheets: Establishing Program Depth and Complexity
Armed with your list of priorities, you continue doing homework to find the car that best matches your needs. You are ready to
begin narrowing the list of possible choices by comparing vehicle specifications. You can do a side-by-side comparison of vehicle
Specs & Data sheets to assess performance and efficiency features, handling and braking features, exterior and aerodynamics
features, as well as interior features. How well each vehicle does against this comparison will help to narrow the field of choices
before you step on to a sales lot and into a car for a test drive.
Standards Sampling Process

Select 2 to 3 standards to sample. Be strategic in choosing which standards:
-
Select a standard(s) that the data that shows students struggle with, or
-
Select a standard(s) teachers have identified as difficult to teach, or
-
Select a standard(s) that threads through several grade levels. This type of sampling allows for tracking the development of
concept(s) across grades.

A sampling of three standards is optimum, but if this is not possible, 1 or 2 comprehensive samples will inform your process.
Mathematics Adoption Toolkit
20

Using only a program’s TE, analyze how the standard is introduced, developed, reviewed, enhanced, and assessed. The needs
identified by the District Lens should be used as the guiding criteria throughout every part of the analysis.
Summary/Outcome: Identify programs that show the strongest development of critical standards with the Teacher’s Edition (TE). This
sampling will highlight the likelihood of a program meeting student and teacher needs. The goal is to narrow the adoption list of
prospective programs that will be taken to the next level of examination. Sampling is limited to the TE as this may be the only universally
purchased program component: it is often the only tool a teacher has access to several years into an adoption.
Section #2:
Standards Sampling:
Taking a Deeper Look at
the Mathematics.
Pages: 49-57
Mathematics Adoption Toolkit
Step 1:
 Identify 3 challenging standards per grade level to use in sampling.
In choosing what to sample, you will most likely choose one part of a
standard. For example, choosing “division of positive fractions’ from
the sixth grade standard: 2.1 “Solve problems involving addition,
subtraction, multiplication, and division of positive fractions and
explain why a particular operation was used for a given situation”.
 Brainstorm what the ideal instruction for this partial standard would
be.
 Review with committee the questions in Section #2 to develop
common understanding of intent and meaning.
 May use the folder with completed standards sampling to show how
to complete forms.
 Point out that there may be relevant information before and after the
target lesson(s).
Step 2:
 Decide which members will review which programs at which grade
level.
 Teachers may do this work independently, or a grade level group
may work together, individually gathering evidence on their
program(s) while simultaneously comparing programs with other
group members. It takes about 2 hours to complete one publisher
per standard.
Step 3:
 Complete one set of worksheets pp. 49-57 (per standard) for each
publisher
 Identify where in the program this partial standard is taught. Fill in
the worksheet noting where the materials the standard is addressed.
This will be important to use during discussions.
21
 Chart of District Priorities
 Teacher’s edition for each program to
be considered.
 Standards Sampling worksheets or
electronic version, word or website –
each reviewer will need a separate
worksheet for each standard and each
program reviewed. Worksheet p. 48-56
 For electronic Word templates see:
http://www.ccsesa.org
 Chart of worksheet, District Summary
Chart to compile results of individual
worksheets.
 Chart paper, pens
 Reference: folder of completed
standards sampling for sixth grade
division of fractions.
 Framework, Chapter 2 Content
Standards and Chapter 3, Grade Level
Considerations



Add comments in text, + for area of strength, ? for question or
concern, and then score each question: 1 = does NOT meet district
need, 2 = MEETS district needs, or 3 = EXEMPLARY.
A synthesis of findings for each question may add important
elaborations not specifically identified in question
Find the mode – the score that occurs most frequently - for each
section
Step 4:
 Compile modes for four topics from each reviewer on District
Summary Chart for Standards Sampling p.49-57
Step 5:
 Review results of compilation and consider each program in terms of
the district priorities. Committee members will explain where they
found evidence or why they rated the question the way they did.
 Use the District Summary Chart to notice if mode is consistently
strong or weak across grade levels.
 Decide which programs will continue to be reviewed and which
programs will be eliminated from review.
Note: At this point you may choose to move to Section #5: Making a
Decision or to continue on to Section #3: Reviewing Program
Components or Section #4: Options for Further Review.
Section #3: Program Components Review
The list of prospective programs has been pared down to the most promising candidates. Now comes the time to conduct a deeper,
more thorough investigation of each program. Section #2 Standards Sampling provided team members time to deconstruct the Teacher’s
Edition (TE). The Program Components Review enables the team to conduct a deeper analysis by deconstructing all of the other
remaining program components. The analysis should answer the question: “Do the materials meet the needs of our students and
teachers?”
Base Model vs. Options Packages
You’ve reviewed the Specs & Data Sheets. It’s time to begin exploring the available options packages. You know what the base
models possess – the safety features, seating configurations, performance expectations, handling and braking standards. Now
Mathematics Adoption Toolkit
22
it’s time to consider the options packages. When buying a car, the options packages can make a huge difference with features
such as comfort and maneuverability.
-
Section #2 Standards Sampling explored a program’s TE: you know what the “base model” has to offer in comparison to
the other programs.
-
Now it’s time to investigate the different “options packages” available in the ancillary materials that accompany the TE.
You can liken the five general program categories to different aspects of the options packages:
General Program Categories
Car Analogy: Options Packages
Mathematics Content / Alignment with Standards What is the base model as listed on the Specs & Data
(Standards Sampling) Sheets.
Program Organization What are the seating configurations? Does it have 2doors or 4 doors? Moveable seats? What is its cargo
capacity?
Universal Access Does the program offer advice for alternative forms of
transportation (walking paths, bike, bus, train,
airplane, boat)?
Instructional Planning and Support Does the options package offer different fuel choices
(gas, diesel, ethanol, electric, hybrid)?
Summary/Outcomes: The Program Components Review will give team members a chance to review all of the ancillary materials that
accompany the TE. Each of these components must be thoroughly examined for content and usage. The goal here is to refine the list of
programs to 2 or 3 very strong candidates to be considered for piloting during the next phase of the process.
Mathematics Adoption Toolkit
23
Section #3: Program
Component Review:
Matching District Needs
with Instructional
Materials.
Pages: 58-77
Step 1:
 Decide whether each committee member will review independently
or in a group setting.
 Options of: each member will review ONE program for all
components, or EACH program reviewed for one component.
 Direct on how committee members can access all materials for
review. (check out, central location in district, LRDC, at meeting
location)
Step 2:
 Each member keeps notes taken during process which will be used
in Section #5 – Making a Decision
 Complete either a print or electronic worksheet for each program
scoring: 1 = does NOT meet district needs, 2 = MEETS district
needs, or 3 = EXEMPLARY.
 Write summary statements for each of four topics
Step 3:
 Facilitator collect data from committee
 Scores need to be compiled
 Summary statements need to be collected for District Summary
Chart for Review of Program Components
 Duplicate results, or if web based, tabulation is automatic, but
reports will also need to be printed out for committee review.
Summary:
 Committee needs to review and discuss results.
 Maintain the focus on meeting the needs of students and teachers
identified in the District Priorities Chart while deciding which
programs need further review. Try to eliminate all but 2 or 3.




District Priorities Chart
Complete sets of programs for teacher
review
Mathematics Framework
CST blueprints

www.cde.ca.gov/scrpts/texis.exe/webinator/
search?query=Blueprints&submit=GO
CST released items



www.cde.ca.gov/ta/tg/sr/css05rtq.asp
Worksheets for Section #3
For electronic templates see:
http://www.ccsesa.org
District Summary Chart for Review of
Program Components.
Note: At this point you may choose to move to Section #5: Making a
Decision or to continue on to Section #4: Options for Further Review.
Section #4: Additional Review Options
Congratulations! You have successfully narrowed the list to 2 or 3 very strong programs that best match the needs of your students and
teachers. The team is ready to begin piloting programs. The pilot will allow teachers to “kick the tires” and get a feel for how the program
handles.
Mathematics Adoption Toolkit
24
Taking a Test Drive
Now it’s time to take the car around the block for a test drive. Does it make it up a steep hill? How does it handle on the open
road? In traffic? What does the stereo system sound like at full blast (okay, maybe our students would do this)! What’s the gas
mileage really like? Do all the bells and whistles work? Which bells and whistles did you use? Were they useful?
-
Find the “test drivers” for each grade level. Who will pilot? Are there additional personnel who should be included for pilot
purposes (English Learner specialists, BTSA teachers and leaders, CAHSEE prep teachers, etc.)?
-
Determine the length of pilot
-
Will the test drive be a pilot or blind test? Will students be surveyed?
Summary/Outcome: Field tests of the 2 or 3 strongest programs will provide real-time information regarding implementation in the
classroom. Piloting will allow teachers to reconcile the research with real-time investigations. It may be determined that additional
analysis is needed with more pilots, blind testing, etc. Once recommendations are made, plans for short- and long-term professional
development can be drafted.
Section #4:
Additional Review
Options: Piloting, Blind
Test, Student Survey,
Executive Committee.
Options:
 Blind Test
- Duplicate a similar lesson from each program and mask the
name of the program.
- Teachers analyze each lesson for strengths and
weaknesses

Blind Test: Copies of same lesson
from each program with identification
of program masked.


Pilot Programs
- See CA Department of Education guidelines
- Committee teachers teach lessons from Brand A for 4
weeks and then teach lessons from Brand B for 4 weeks.
Student Survey
 Students in small groups review two lessons and respond to
survey questions.
Teachers:
1. Lay out publisher’s materials, one set at a time.
2. Have students work individually or in small groups of 3
or 4.
Mathematics Adoption Toolkit
25
 Piloting: CDE guidelines for piloting
http://www.cde.ca.gov/ci/cr/cf/imagen.asp

Student materials from program(s)
under consideration.

Survey questions.:
Directions: Look through the student
mathematics book. Review two entire
lessons.
1. Were there pictures, graphs,
diagrams, or examples?
2. If there were pictures, graphs,
diagrams, examples, were they
helpful?
3. Was the book too easy, just right, or
too difficult?
4. Rate the lesson from 1 – 5. 1 = not
very good, 2 = just okay, 3 = good,
4 = really good, 5 = excellent.
5. Retell three important facts from the
lesson. Was this easy to do?
6. Describe what you like from the
lessons.
7. Describe what you didn’t like from
the lessons.
3. Go over directions and survey questions with students.
4. Demonstrate how to browse through materials with an
objective in mind.
5. Demonstrate the group discussion, or Grand
Conversation, method of discussion where students
take turns discussing the book, and answering the
questions about the book.
6. When students are comfortable, they may work on their
own. Allow 20 –45 minutes.

Source - Dos Palos-Oro Loma Unified School District


(Science Adoption Toolkit p. 63)
http://www.ccsesa.org.
Committee of those who reflect district’s highest priority, e.g.,
English Learners, or Support for New Teachers, or high school exit
exam, conducts a more thorough search of possible programs for
best match.
Section #5: Making a Decision
At this point you have eliminated all the programs that do not meet your district criteria and you have “test driven” the two programs that
come closest to meeting your district’s needs. Now it is time to identify the program that everyone on the committee can fully support.
Coming to Consensus
Honor everyone’s time, effort, and energy. It’s time to get the “family” to agree on which car to purchase. Remind everyone that
it’s time for the entire family (teenagers, mom, dad, grandparents) to come to agreement on which model will best meet
everyone’s needs. It’s time for some negotiations between each other, as well as with the dealership.
-
Team member negotiations – review the strengths and areas of need within the district as prioritized by the District Lens.
Review the non-negotiable needs. A consensus process decision means each team member agrees they can support
EITHER program A or program B, as both programs met district prioritized needs and both showed well during the pilot.
Team members must understand they have a responsibility in supporting the adoption as it is implemented throughout the
district.
Mathematics Adoption Toolkit
26
-
Textbook Company negotiations – can the “dealership” offer any incentives? Price might be a defining aspect to consider,
as well as any deals that can be negotiated into the contract.
Summary/Outcomes: The Adoption Team comes to consensus on one program that is recommended for adoption by the district. This
program has been selected based on district data and analysis and has been found to best meet the needs of students and teachers.
Section #5:
Making a Decision:
Coming to Consensus
1 Establish Group
Norms
2 Review History of
Process
3 Individual
Prioritization of
Programs
Mathematics Adoption Toolkit
Source: Miguel Carrillo, Ed.D, Poway School District
Goal: The group will come to consensus on the most appropriate choice of
program after all points of view have been heard. Everyone in the group will
support the choice of the group, even if it was not their first choice.
Committee sitting in grade level groups will generate group norms
such as:
 Let everyone be heard
 Assume best intentions
 Be present and prepared
 Base decisions on evidence collected from multiple perspectives
 Select a program to meet the needs of the district’s students and
teachers.
 Do not comment on another’s perspective—this is what they did
or did not see in light of their own personal experience
Briefly discuss the process of:
 Developing the district lens: Identifying needs and priorities of our
students and teachers.
 Identifying the priorities and criteria for investigating mathematics
programs
 Standards Sampling
 Investigating program components
 Piloting programs
Each committee member reviews their notes on the evidence
personally collected regarding the positives and the concerns for
each program. From an individual perspective, each committee
member indicates his or her current level of support for EACH
program.
27
 Chart of District Priorities
 Data from reviews of Section 2, 3 and 4
is summarized in a report and shared
with committee members.
Chart paper to list agreed upon norms



Teacher’s editions of each program
for reference.
Notes
Straw Poll Wall Chart (below)
Straw Poll (record results on the wall chart).
5 I can support this program fully. I will champion it.
4 I strongly agree with this program
3 This material is OK with me. I am willing to go along with this
choice
2 I have reservations and I am not yet ready to support this
material
1 I am opposed to this set of materials
Fist I veto this proposal regardless of the will of the group
A reviewer could indicate 5 for both programs. Or a member
could indicate a level 5 support for Brand A and level 3 for Brand
B. (Some may be confused thinking they need to split the 5
between the two publishers)
Target a level of support between 3 and 5. If there are fists, 1s, or
2s, concerns have not been heard well enough.
Straw Poll Chart
Note: You will need one chart for each program.
Straw Poll Program A
5
4
3
2
Individual Support
Grade Level Consensus
Across Grade Consensus - 1
Across Grade Consensus - 2
Mathematics Adoption Toolkit
28
1
Fist
Grade Level
Consensus
Each grade level group appoints a recorder. Then, the groups
discuss the positives and concerns. When every member of the
group agrees on a positive or a concern, the recorder writes:



Light green and red or pink post-its and
a dark ink pen for each group.
Positive aspects of each program on a green post-it
Concerns for each program on a pink post-it
Grade level and publisher on each post-it.
Take a Straw Poll to see if level of support has shifted after this larger
sample. Record on wall chart.
Four positive/concerns charts for each
program being considered:
 Mathematics Content
 Instructional Program
 Assessment
 Universal Access.
See examples below.
Positives / Concerns Charts
Prepare 4 charts (Mathematics Content, Instructional Program, Assessment, Universal Access) for each program considered:
Math Content
Program A
Instructional
Program A
Assessment
Program A
Universal Access
Program A
Math Content
Program B
Instructional
Program B
Assessment
Program B
Universal Access
Program B
Mathematics Adoption Toolkit
29
Large Group
Consensus
Synthesize chart information across grades moving from a grade
level perspective to a K-5 or 6-8 perspective.
 If any post-it comments are duplicates, put them on top of
each other, so it is one comment but you can still see that this
was observed by multiple grades.
 Go over each chart with the whole group. Ask for additional
strengths or concerns. If the group agrees that this comment
goes across all grade levels, add post-its on the appropriate
charts.
 Discuss proportion of pink to green post-its
 Take a third straw poll for each publisher now from a whole
program perspective. Record on chart.
 If there are any fists, 1s, or 2s for either publisher, give those
members a chance to express their concerns.
 Fourth and final straw poll. Record on chart.
 Make a decision. It may be very clear just from the number of
each color of post-its that one program has more strengths
than the other, or they may have similar strengths, but one
has more concerns. If both programs are equal at this point,
now is the time to consider any differences, or extra items
“free” with the program, or the level of professional support
provided by the publisher.
If the decision is not
yet clear
Options:
 Prioritize the criteria on all the charts.
 Which criteria is a deal breaker? How does each program
rate?
 What are the second most important criteria? How does each
program rate?
 Evaluate each program in terms of the most immediate needs
of district (e.g., number of new teachers needing support).
Reconfirm
commitment to
program
Even though this might not have been the first choice of each
individual committee member, there is consensus that this is the best
program for the district.
Mathematics Adoption Toolkit
30
Straw poll and Positive/Concerns
charts.
Section #6: Planning forward
Congratulations!! The district made a decision and your Board of Education has approved the adoption.
As you have seen, no program is complete or perfect, but because of your thorough analysis, you have selected the best program. You
now need to address the needs of students and teachers beyond just selecting a textbook. It’s time to begin the planning process for
successful implementation.
Now it’s time to put teachers in the driver’s seat as we develop a successful implementation plan.
Closure/summary:
You’re in the driver’s seat. The journey begins.
Section #6:
Next Steps:
Implementation
Mathematics Adoption Toolkit
Staff Development
 Committee input on staff development needs for:
- Effective implementation
- Assessment to notice student trends and gaps
 Input on what district structures e.g., benchmark assessments,
pacing guides, will need to be upgraded to be coherent with new
adoption
 Input from Executive Committee on how to use the program to meet
high priority district needs.
31
Mathematics Adoption Toolkit
Templates for Section #1
Developing
the District Lens
Mathematics Adoption Toolkit
32
SECTION 1 - DEVELOPING THE DISTRICT LENS
TASK #1: California’s Mathematics Expectations for Students
Section 1 of the Mathematics Adoption Toolkit involves eight tasks. Each task is keyed to the four
topics: Mathematics Content, Assessment, Instructional Program, and Universal Access. Task #1 is
the preliminary work needed to establish the district’s strengths and area of need. The goal of Task
#1 is to assess your district’s progress toward accomplishing the goals identified in the California
Department of Education Mathematics Framework.
District Lens, Task #1 - MATHEMATICS CONTENT
Questions to Consider
1. What is the depth of
knowledge that is expected
for students?
CA Mathematics Framework 2006
Students should:
 develop fluency in basic computational and procedural skills, an
understanding of mathematics concepts, and the ability to use
mathematical reasoning to solve problems.
 communicate precisely.
 develop logical thinking.
 make connections.
 apply mathematics.
 develop an appreciation for the beauty and power of mathematics.
Framework Ch. 1, pp. 2-3
District progress toward achieving student depth of mathematical knowledge:
1
Limited
2
2. What mathematical
reasoning skills are
students expected to
know and to be able to
do?
3
4
Developing
5
6
7
Successful
8
9
10
Exemplary
Students must:
 Develop the habits of logical thinking.
 Recognize and critically question all assumptions.
Mathematical reasoning involves:
 Explaining arithmetic facts.
 Solving problems and puzzles at all levels.
 Understanding algorithms and formulas.
 Justifying basic results in all areas of mathematics.
Framework, Ch. 3, p. 110
District progress on student’s application of mathematical reasoning skills:
1
Limited
2
Mathematics Adoption Toolkit
3
4
Developing
5
6
7
Successful
8
9
10
Exemplary
33
District Lens, Task #1 – INSTRUCTIONAL PROGRAM
Questions to Consider
CA Mathematics Framework 2006
3. What are the key
components of an effective
mathematics program?
a. Assessment
b.
See Assessment Strand, page 36
Quality Instruction
In an effective mathematics program, teachers:
 possess in-depth understanding of the content standards and the
mathematics.
 are able to select research-based instructional strategies.
 effectively organize instruction.
 use the results of assessment to guide instruction.
 use instructional grouping options and strategies
Framework Ch. 1, p. 9
District progress on quality instruction:
1
Limited
2
3
4
Developing
5
6
7
8
Successful
9
10
Exemplary
c. Maximized
Instructional
Time
In an effective mathematics program:
 Adequate time is allocated (50 – 60 minutes).
 Additional instructional time is allocated for students who are
performing substantially below grade level.
 Instructional time is maximized and protected from interruption.
 Learning time is extended through homework.
Framework, Ch. 1, p.10
District progress on maximizing instructional time:
1
Limited
2
3
4
Developing
5
6
7
8
Successful
9
10
Exemplary
d. Instructional Resources
In an effective mathematics program, instructional resources should:
 emphasize depth of coverage.
 balance basic computational and procedural skills, conceptual
understanding, and problem solving and stress the interdependency of
all three.
 provide ample opportunities for students to explain their thinking,
verbally and in writing, formally and informally.
 supply ideas or tools for accommodating diverse students
performance within any given classroom. They offer suggestions for
re-teaching a concept, providing additional practice for struggling
students, or condensing instruction so that advanced students can
concentrate on new material.
Framework, Ch. 1, pp. 9-11
Also: p.207, 211 and 217
District progress on instructional resources:
1
Limited
2
Mathematics Adoption Toolkit
3
4
Developing
5
6
7
8
Successful
9
10
Exemplary
34
e. Professional
Development
In an effective mathematics program:
 teachers receive excellent preservice training.
 staff development is a long-term, planned investment.
 professional development should be ongoing and focused on:
- maximizing instructional time.
- raising teacher proficiency in mathematics.
- balancing the curriculum.
- expanding the understanding of student differences.
- knowing which standards provide the core mathematics
foundation for all students at each grade level.
- developing strategies to help parent involvement.
Framework, Ch. 1, pp. 12-13; Ch. 8, pp. 247-251
District progress on professional development:
1
Limited
2
3
4
Developing
5
6
7
8
Successful
9
10
Exemplary
f. Administrative practices
In an effective mathematics program:
 mathematics achievement is among the highest priorities.
 long-term and short-term goals for the school, each grade level, and
individuals are outlined clearly and reviewed frequently.
 mathematics specialists are considered for teaching most or all of the
mathematics classes or to coach other teachers.
 instructional groups can be realigned frequently (master schedule).
Framework, Ch. 1, p. 13
District progress on administrative practices:
1
Limited
2
3
4
Developing
5
6
7
8
Successful
9
10
Exemplary
g. Community Involvement
In an effective mathematics program:
 parent input is used for program planning.
 materials are organized so that parents, siblings, and community
members can provide extended learning experiences.
 community connections are used to provide examples of how and why
mathematics is important.
Framework, Ch. 1, p. 13
District progress on community involvement:
1
Limited
2
Mathematics Adoption Toolkit
3
4
Developing
5
6
7
8
Successful
9
10
Exemplary
35
The students’ use of technology builds on the skills and understandings
needed to master basic mathematics skills. The uses of technology promote
students’ understanding of mathematical concepts, quantitative reasoning,
and achievement through the solving of problems, by testing conjectures,
accessing data, and verifying solutions.
4. What are the expectations
for the types and uses of
technology?
Types of technology include:
 electronic tools
 databases
 programming language
 simulations.
Framework, Ch. 9, pp.253-259
District progress toward making technology available for students and teachers to use:
1
Limited
2
3
4
Developing
5
6
7
8
Successful
9
10
Exemplary
District Lens, Task #1 - ASSESSMENT
Questions to Consider
CA Mathematics Framework 2006
5. What are the key
components of an effective
assessment program?
In an effective mathematics program, assessment:
 aligns with and guides instruction
 measures the specific content it was designed to measure (validity)
 provides information that is used to inform instruction
Framework, Ch. 1, pp. 8-9
District progress toward components of an effective assessment program:
1
Limited
2
6. What are the types and
uses of assessment that the
district is expected to
implement?
3
4
Developing
5
6
7
8
Successful
9
10
Exemplary
Regular and accurate assessment of student progress is essential. The
types of assessments that are the most crucial to student achievement are:
 Entry-level assessment.
 Progress monitoring.
 Summative evaluation.
Framework, Ch. 5, pp. 221-4
District progress toward using all types of assessments:
1
Limited
2
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4
Developing
5
6
7
8
Successful
9
10
Exemplary
36
District Lens, Task #1 – UNIVERSAL ACCESS
Questions to Consider
7.
CA Mathematics Framework 2006
What are the expectations
for supporting all students
mastering the standards?
Procedures and processes are in place to:
 assess student understanding at the start of instruction, frequently
during instruction, and use results for placement and program
planning
 Determine skills and understandings a students already possesses,
and those the student needs to learn next

Alignment of
Instruction

Diagnostic Teaching,
Differentiation,
Grouping, Accelerating
for At-Risk Students




diagnose the nature and severity of student difficulties
differentiate curriculum or instruction or both for all learners
use flexible grouping strategies
implement intervention strategies

Planning for Special
Needs Students

Plan for adapting to individual needs through careful organization of
resources and instruction

English Learners

Address English fluency

Advanced Learners

provide a combination of acceleration and enrichment
Framework, Ch. 6, pp. 229-239
District systems in place to support all students becoming proficient in mathematics:
1
Limited
2
3
4
Developing
5
6
7
Successful
8
9
10
Exemplary
Individual Summary Statements Task #1, California Expectations for students of mathematics:
Implications for Adopting Mathematics Instructional Materials
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SECTION 1 - DEVELOPING THE DISTRICT LENS
TASK #2: District’s Mathematics Expectations for Students
This task examines how the District uses data to establish expectations for students, monitors
achievement of students, and develops district curriculum guides to support those expectations. The
goals of this task are to examine the district’s strengths and areas of need.
District Lens, Task #2 - MATHEMATICS CONTENT
Questions to Consider
Current District Conditions
1. Does the District have a current
curriculum guide and/or map aligned
with the state’s mathematics content
standards? What changes, if any, will
be made to this document? If no
guides/maps, what processes are being
implemented to generate them?
2. What is the district philosophy for the
use of curriculum guides and/or maps?
3. What are the district’s expectations for
preparing students for Algebra 1 and
high school graduation?
District Lens, Task #2 – INSTRUCTIONAL PROGRAM
Questions to Consider
Current District Conditions
4. How much instructional time is allotted
to implement district expectations in
mathematics?
5. How are teachers and/or grade level
teams implementing the guide and/or
map?
Individual Summary Statements Task #2, District Expectations for Students:
Implications for Adopting Mathematics Instructional Materials
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SECTION 1 - DEVELOPING THE DISTRICT LENS
TASK #3: District Needs for Student Population
This task examines how the District uses data to establish particular needs of specific student
populations. The goals of this task are to examine the district’s strengths and areas of need.
District Lens, Task #3 – MATHEMATICS CONTENT
Questions to Consider
1.
Current District Conditions
Analyze the unique mathematics
needs of the following populations?
How will you match their needs with
the newly adopted materials?
a. Gender
b. Ethnicity
c. Socio-economically
Disadvantaged
d. English Learner
e. Students with Disabilities
f. Gifted and Talented
g. Other
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District Lens, Task #3 – UNIVERSAL ACCESS
Questions to Consider
Current District Conditions
2. What is the student mobility rate
and how might it impact student
achievement in mathematics?
3. What are the most prevalent
languages represented? Will your
math textbook adoption consider
primary language support as an
essential component?
Individual Summary Statements Task #3, District Needs for Students:
Implications for Adopting Mathematics Instructional Materials
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SECTION 1 - DEVELOPING THE DISTRICT LENS
TASK #4: State and District Data Related to Mathematics
This task examines how the District uses state data and district assessment programs to identify
achievement of particular student populations.
District Lens, Task #4 – ASSESSMENT
Questions to Consider
Current District Conditions
1. CST: What pattern of strengths and
weaknesses does the CST assessment
data reveal? Is this trend consistent
over the course of a single year and/or
multiple years?
2. Do district benchmark assessments
validate these findings?
3. Looking are the numbers and
percentages of students who are
advanced and proficient, how do we
meet their needs? What should we do
to support their learning?
4. Looking at the numbers and
percentages of students in strategic
(Basic to Below Basic) or intensive
(Below Basic to Far Below Basic)
programs, how do we meet their needs?
What should we do to support their
learning?
5. Does the data indicate student
deficiency in reading skills that might
impact mathematics instruction and
overall student achievement?
6. CELDT: English Learners
a. Looking at numbers and percentage
of students are at each level of the
California English Language
Development Test (CELDT), how do
we meet their needs? What should
we do to support their learning?
b. In what strands do EL students
excel? Struggle?
Mathematics Adoption Toolkit
Areas of strength:
Areas of struggle:
41
7. Does the district use progress
monitoring to guide teacher instruction
and summative assessments to
validate student mastery of
mathematics concepts and skills? Are
these assessments teacher generated
or does the district rely on publisher
resources? Will they be updated or
replaced by this adoption process?
8. What types of assessments are
commonly used in the classroom? Are
these assessments teacher-generated
or does the teacher rely on publisher
resources?
9. What other district programs address
student needs for remediation or
acceleration?
Individual Summary Statements Task #4, State and District Data:
Implications for Adopting Mathematics Instructional Materials
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SECTION 1 - DEVELOPING THE DISTRICT LENS
TASK #5: District Learning Configuration
The goal of this section is to examine the district’s strengths and areas of need. This task is to look at
your district’s structures that impact mathematics instruction.
District Lens, Task #5 – INSTRUCTIONAL PROGRAM
Questions to Consider
Current District Conditions
Task #
1. What special needs must be
considered for the different school
configurations in the district (e.g.,
K-8, K-5 or K-6, 6-8 or 7-8, selfcontained, combination classes,
departmentalized, houses, etc.)?
2. What are the implications for
textbook selection for schools within
the district that are being monitored
by state and/or federal school
improvement initiatives?
District Lens, Task #5 – UNIVERSAL ACCESS
Questions to Consider
3. How will you plan for differentiation
of instruction with the newly
adopted materials for schools
within the district with a high
concentration of special education
students, English learners, or
advanced learners?
Current District Conditions
Special education students:
English learners:
Advanced learners:
Individual Summary Statements for Task #5, Instructional Program:
Implications for Adopting Mathematics Instructional Materials
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SECTION 1 - DEVELOPING THE DISTRICT LENS
TASK #6: District Needs for Teachers
The goal of this section is to examine the district’s strengths and areas of need. This task is to
consider the long-range professional development needs of district teachers.
District Lens, Task #6 – MATHEMATICS CONTENT
Questions to Consider
Current District Conditions
1. How will you provide mathematics
content training for teachers to
become more knowledgeable of the
mathematics they teach and the
ways to teach?
2. What mathematics guidance do
new teachers receive from the
district or from a BTSA support
provider?
District Lens, Task #6 – INSTRUCTIONAL PROGRAM
Questions to Consider
Current District Conditions
3. How will your long term professional
development plans accommodate
teachers who move from one grade
level to another?
4. Does the district/site have math
coaches? If not, what actions and
resources are needed to institute
coaching for the newly adopted
math textbooks?
5. What types of on-going
mathematics professional
development (e.g., SB 472,
coaching, differentiation, lesson
study) does the district provide? If
none, what actions and resources
are needed to implement ongoing
staff development?
6. What non-district professional
development opportunities are
available for teachers?
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District Lens, Task #6 – UNIVERSAL ACCESS
Questions to Consider
Current District Conditions
7. How will you support new teachers
with professional development after
your math textbook adoption? Will
the support of veteran teachers look
much different than that of new
teachers?
8. How will your long term professional
development plans accommodate
teachers who move from one grade
level to another?
9. Does the district/site have math
coaches? If not, what actions and
resources are needed to institute
coaching for the newly adopted
math textbooks?
10. What types of on-going
mathematics professional
development (e.g., SB 472,
coaching, differentiation, lesson
study) does the district provide? If
none, what actions and resources
are needed to implement ongoing
staff development?
11. What non-district professional
development opportunities are
available for teachers?
Individual Summary Statements Task #6, District Needs for Teachers:
Implications for Adopting Mathematics Instructional Materials
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SECTION 1 - DEVELOPING THE DISTRICT LENS
TASK #7: District Current Instructional Resources
This task examines the instructional resources available to support the implementation of the
mathematics program. The goal of this section is to examine the district’s strengths and areas of
need.
District Lens, Task #7 – INSTRUCTIONAL PROGRAM
Questions to Consider
Current District Conditions
1. What is the district philosophy on
the use of instructional resources
(ancillary materials, manipulatives,
tools, and technology) to support
mathematics? Will this be an
important consideration in the
adoption process?
2. To what extent are ancillary
materials, manipulatives, and tools
being used to develop conceptual
understanding?
3. What professional development is
available on the effective use of
these materials? Will this be an
important consideration in the
adoption process?
4. What kinds of technology hardware
and software are in place to support
the mathematics program? What is
the compatibility with the computer
platforms in the district?
Individual Summary Statements Task #7, District Instructional Resources:
Implications for Adopting Mathematics Instructional Materials
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SECTION 1: DEVELOPING THE DISTRICT LENS
TASK #8: Resources to Support Mathematics
This task examines community resources available to support the mathematics program. The goal of
this section is to examine the district’s strengths and areas of need.
District Lens, Task #8 – UNIVERSAL ACCESS
Questions to Consider
Current District Conditions
1. What local informal mathematics
learning opportunities can
supplement the instructional
materials?
2. Will supplemental service providers
utilize the instructional materials?
3. Are district mathematics volunteers
using the instructional materials
along with the teachers?
4. What student events, programs, or
parent education opportunities does
the district provide to extend
mathematics learning?
5. What organizations in the
community sponsor student events
promoting mathematics?
Individual Summary Statements for Task #8, Resources:
Implications for Adopting Mathematics Instructional Materials
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DISTRICT SUMMARY CHART
District Lens: Needs of Students and Teachers
Task #1
Task #2
Task #3
Task #4
Task #5
Task #6
Task #7
Task #8
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Mathematics Adoption Toolkit
Templates for Section #2
Standards Sampling
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49
SECTION 2: STANDARDS SAMPLING
California Content Standards for Mathematics
In an effective and well-designed mathematics program, students move steadily from what
they already know to a mastery of skills, knowledge, and understanding. Students progress
from an ability to explain, and then justify their thinking to being able to derive formal proofs.
Framework, Ch. 1, pp. 8-13
This activity is to do a side-by-side comparison of standards development to determine which materials best meet the learning
needs of your students. The sampling of three standards provides a good indicator of match. In conducting the sampling, refer
to the District Chart of Needs for Students and Teachers.
1. Choose three standards important to the success of student mathematical achievement. Since most standards include multiple
concepts, choose just one concept as you focus for sampling. In elementary grades, sample standards might include a standard from
Number Sense critical to subsequent mathematics understandings, another standard from Measurement and Geometry showing a
high number of items on the CST blueprint, and a third standard from Algebra and Functions.
2. For each selected standard, complete the Sampling survey for each textbook program reviewed. You will need one survey form per
standard, per program for each committee/group conducting the review.
3. Use the table of contents, index, pacing guide, and/or standards map to find all places in the program where the identified standard is
presented. Note the location and page reference (e.g., Teacher Edition p. 210; Student Edition p. 210; Language Supplement p. 48).
4. As you gather evidence take notes and mark whether it is evidence of strength “+” or concern “?”.
Answer each questions outlined below. Assign points to each element using the following rubric:
1 = Does not meet district needs
2 = Meets district needs
3 = Exemplary
5. Compare the results of this analysis to determine which programs meet the district needs well enough to merit further review and
which materials no not merit further review.
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STANDARD SAMPLING of California Mathematics Content Standards
Program Title and Publisher:
Program Type:
CORE
INTERVENTION
ALGEBRA READINESS
Content Standard(s):
Grade
Strand
Number
Standard
Program Component(s):
Page number and component where standard instruction and support are found (e.g., ELD p. 278).
Teacher Edition:
Student Edition:
Supplement(s):
Technology:
Other:
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Evidence:
1. Is the math content superficial or does it deepen
conceptual understanding, procedural fluency,
problem solving, and mathematical reasoning?
2. How well does “Teacher Background” prepare a new
teacher or a teacher new to the grade level to:
 Present the concept?
 Build procedural fluency?
 Build mathematical reasoning?
 Make connections between conceptual
understanding, procedural fluency, problem
solving, and mathematical reasoning?
3. What suggestions are provided to prevent or correct
the development of misconceptions as students
learn?
4. How does the program support the teacher in
facilitating mathematical discourse about this
concept?
Mode:
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Score
MATHEMATICS CONTENT
+ Strength
? Concern
Score:
1 = Does NOT meet district needs
2 = Meets district needs
3 = Exemplary
Section 2 – Standard Sampling
1 = Does NOT meet district needs
2 = Meets district needs
3 = Exemplary
INSTRUCTIONAL PROGRAM
Evidence:
1. When the concept is first introduced, what connections
are made to students’ lives and prior knowledge?
2. What materials are available to help with the learning
of vocabulary essential to understanding this standard:
 Definitions with visuals and examples?
 Pronunciations?
 Words used in context and in sentences?
 Suggestions for teaching and practicing both
academic language (prove, analyze) and content
vocabulary (denominator, divide)?
3. How well do the different types of student work
support:
 Developing conceptual understanding? Is there
evidence of a progression from concrete to pictorial
to more abstract means of learning concepts?
 Learning and practicing the necessary skills and
procedures? Is there evidence of developing skills
in the context of problem solving and
investigations?
 Developing mathematical reasoning?
 Applying their understanding to solve problems?
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Score
Score:
+ Strength
? Concern
Section 2 – Standard Sampling
4. What kinds of practice of the standard are there for
students to:

Immediately practice the skill or concept?

Revisit and apply what has been learned later in
the program?

Revisit and apply what has been learned in a
different context (e.g., area model to practice
multiplication, metric measurement to practice
computation with decimals)?
Evidence:
5. How does technology support a balanced curriculum
of this standard for:
 Conceptual understanding?
 Skills and procedures?
 Mathematical reasoning?
 Applying their understanding to solve problems?
6. Are the technology-based activities engaging for
students?
Mode:
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Score:
1 = Does NOT meet district needs
2 = Meets district needs
3 = Exemplary
ASSESSMENT
Evidence:
1.
What support is available to help teachers check for
student misconceptions?
2.
How well do the progress monitoring assessments
inform instruction of this concept (e.g., distracters in
the multiple choice items provide information on
student understanding and/or misconceptions)?
3.
How well do the assessments adequately assess
student procedural knowledge, conceptual
understanding, and mathematical reasoning?
Mode:
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Score
+ Strength
? Concern
Section 2 – Standard Sampling
1 = Does NOT meet district needs
2 = Meets district needs
3 = Exemplary
UNIVERSAL ACCESS
Evidence:
1. What support is provided for English Language
Learners (e.g., visual aides, advanced or graphic
organizers such as word webs or concept maps,
manipulatives, reference charts, word walls, etc.)?
2. What support is provided for Special Education
students (e.g., modified or alternative tasks, advanced
graphic organizers, tactile or auditory support, etc.)?
3. What opportunities are provided for advanced learners
to deepen or extend their understanding of the standard
(e.g., complex tasks, extension of learned skills, links to
other content areas, special challenges, etc.)?
4. How well do the Universal Access strategies present
the concept in an alternative form (e.g., hands-on,
different context, etc.)?
Mode:
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Score
Score:
+ Strength
? Concern
Section 2 – Standard Sampling
Program Title and Publisher:
DISTRICT SUMMARY CHART
Standards Sampling
Summary for Section #2
1 = Does not meet district needs
2 = Meets district needs
3 = Exemplary

Kindergarten Content Standard(s):

First Grade Content Standard(s):

Second Grade Content Standard(s):

Third Grade Content Standard(s):

Fourth Grade Content Standard(s):

Fifth Grade Content Standard(s):

Sixth Grade Content Standard(s):

Seventh Grade Content Standard(s):

Eighth Grade Content Standard(s):
Mathematics Instructional
Content
Program
Assessment
Universal
Access
Mode:
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Mathematics Adoption Toolkit
Templates for Section #3
Reviewing
Program Components
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Section 3 - Program Component Review
MATHEMATICS CONTENT
MATHEMATICS CONTENT
Based on school / district needs:
1. In this unit, are the standards addressed comprehensively leading students to mastery?
 The standards are clearly identified in each lesson/unit of study.
 The lesson/unit identifies the skills, the concepts, and opportunity to problem solve.
 The outcomes and standards-based objectives are identified and logically sequenced
with key standards revisited over time.
 The standards are addressed in a manner that will support students in becoming adept
at problem solving.

Summary statements:
Score:
2. Is the key mathematics vocabulary adequately identified and addressed?
 The essential vocabulary in the instructional material is clearly aligned with the
vocabulary in the standards and framework.
 Instructional strategies are provided to create opportunities for students to use
mathematical vocabulary with a focus on precision.
 The definitions are easy for students to understand. Materials use cognates, real life
examples, realia, posters, etc. to support student use of vocabulary.
 The vocabulary words are referenced within the text: glossary with a pronunciation
guide, within the index, used in a sentence, and includes a visual representation.

Summary statements:
Score:
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3=
EXEMPLARY
1 = Does NOT
meet needs
Section 3, Program Component Review:
2 =MEETS
needs
Where the Standards Sample examined the materials from a very sharp focus, The Program Component
Review examines the materials from a chapter or unit focus. The Program Component Review examines a
publisher’s presentation of mathematics content and the standards in light of identified district needs. The
goal is to determine if the program will adequately support the learning of procedural skills, conceptual
understanding, and problem solving in becoming proficient in mathematics. Refer to the District Summary
Chart of Needs of Students & Teachers.
Based on school / district needs:
3=
EXEMPLARY
MATHEMATICS CONTENT
2 =MEETS
needs
1 = Does NOT
meet needs
Section 3, Program Component Review:
3. Are the mathematics reasoning standards addressed so that students can both master them as
individual strategies and apply them to their mathematics content standards?
 The mathematical reasoning standards needed in this lesson/unit are directly
addressed in a variety of problem situations.
 Students make decisions about how to approach problems.
 Students use strategies, concepts, and skills in finding solutions.
 Students determine if a solution is complete and move beyond a particular
problem by generalizing to other situations.

Summary statements:
Score:
4. Do the charts, graphs, diagrams, pictures and so forth appropriately and adequately support
the teaching of the identified standards?
 The lesson/unit asks students to read, interpret, and create diagrams, charts,
and graphs.
 The charts, graphs, diagrams, and so forth adequately support student
understanding of content standards.

Summary statements:
Score:
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Based on school / district needs:
5. Are connections delineated between grade-level mathematical strands?
 Connections are made to prior learning in the development of the
standard(s).
 Content is structured to provide opportunities to apply mathematics in
authentic contexts.

Summary statements:
Score:
6. Does the teacher’s edition provide adequate, adult-level background information (concepts
and examples) to equip the teacher to teach the standard?
 Clear and complete adult-level explanations of the concepts, principles, and
theories are provided to refresh or enhance knowledge of the topic.
 Instructional material provides additional resources for further background
information.
 Alternative algorithms from other cultures and why they work are included.

Summary statements:
Score:
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3=
EXEMPLARY
MATHEMATICS CONTENT
2 =MEETS
needs
1 = Does NOT
meet needs
Section 3, Program Component Review:
Program Title & Publisher:
Program Component Review:
Total Score:
MATHEMATICS CONTENT
INDIVIDUAL SUMMARY STATEMENTS FOR MATHEMATICS CONTENT:
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Section 3 - Program Component Review
INSTRUCTIONAL PROGRAM
INSTRUCTIONAL PROGRAM
3=
EXEMPLARY
1 = Does NOT
meet needs
Section 3, Program Component Review:
2 = MEETS
needs
This section examines the publisher’s presentation of mathematics content in light of identified district
needs. The goal is to determine if the program will adequately support the learning of procedural skills,
conceptual understanding, and problem solving in becoming proficient in mathematics.
Based on district/school needs:
1. Does the material present the content in multiple ways to promote student understanding of
the standards?
 Instructional material includes opportunities for students to receive direct
instruction and guided practice.
 Instructional material provides multiple opportunities for students to engage
in mathematical reasoning.
 Instructional material includes activities/tools for the development of precise
mathematical language.

Comments/Commendations:
Score:
2. Do the activities and problems promote student understanding of the standards and all their
components?
 Activities and problems are directly aligned to standards.
 Activities and problems build on prior learning.
 Activities and problems form a basis for subsequent learning.
 Activities and problems promote mathematical reasoning.
 Activities and problems include progress monitoring and summative
assessments requiring students to demonstrate mastery of the standards.

Comments/Commendations:
Score:
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3=
EXEMPLARY
INSTRUCTIONAL PROGRAM
2 = MEETS
needs
1 = Does NOT
meet needs
Section 3, Program Component Review:
Based on district/school needs:
3. Does your school have adequate materials, tools, and manipulatives to support the activities
and strategies presented?
 Materials are easily accessible and support the activities and instructional
strategies presented.
 Materials needed are appropriate to reinforce conceptual understanding,
procedures, and problem solving.

Comments/Commendations:
Score:
4. Are there sufficient instructional strategies and resources to meet the identified needs of all of
students (e.g., diverse learners, struggling students, and advanced learners)?
 Instructional strategies and resources address the needs of English
Learners.
 Instructional strategies and resources provide multiple entry points for
students with limited reading or comprehension skills.
 Instructional strategies and resources include accommodations for students
with an Individualized Education Program (IEP).
 Instructional strategies and resources include “extended activities” to
reinforce/enrich the learning for all students (e.g., writing activities, structured
cooperative grouping, class discussion, inquiry activities, materials for
independent study, practice, and review).
 Instructional strategies and resources include activities that connect content
to real-life application.
 Curriculum guides delineate how content can be organized to deliver a
balanced mathematics program.

Comments/Commendations:
Score:
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INSTRUCTIONAL PROGRAM
Based on district/school needs:
5.
3=
EXEMPLARY
1 = Does
NOT
meet needs
2 = MEETS
needs
Section 3, Program Component Review:
Are there opportunities for students to make connections in the unit of study?
 Connections are made between mathematical strands.
 Connections are made to prior learning during instruction, including
suggestions for reaching students who are functioning below grade level.
 Application of the mathematics is made within authentic contexts.

Comments/Commendations:
Score:
6. Is there support to help teachers identify unit design and instructional strategies for content
development and student mastery of concepts?
Within the lesson and/or unit:
 Standards are designated.
 Specific outcomes and standards based objectives are stated.
 Appropriate progress monitoring & summative assessments are included.
 A sufficient number of activities that support student mastery of the learning
objectives are included.
 Clear, concise daily lesson plans, with appropriate pacing, are included.
 Wide ranges of differentiated instructional strategies are included.
 A wide range of recommended instructional strategies for instructional
intervention are included i.e., alternative algorithms, structured cooperative
groupings, writing, mathematical discussions, etc.
 Research-based instructional strategies for the development of academic
language specific to the needs of mathematics (e.g., Frayer Model, Direct
Vocabulary Instruction, Graphic Organizers, Concept Wheel, etc.).

Comments/Commendations:
Score:
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Based on district/school needs:
7. Does the material provide time options and pacing guides for instruction with focus on key
standards (see CST Blueprints)?
3=
EXEMPLARY
INSTRUCTIONAL PROGRAM
2 = MEETS
needs
1 = Does NOT
meet needs
Section 3, Program Component Review:
 Materials included in each instructional lesson/unit contain an appropriate
pacing guide that allows for student mastery of the standards.
 Ancillary teaching materials contain appropriate, alternative pacing guides
that accommodate limited instructional time.
 Materials offer suggestions for prioritizing standards when time to teach
mathematics is limited.
 Materials offer several suggestions for pacing to accommodate a variety of
student needs as well as school / district schedules.

Comments/Commendations:
Score:
8. Does the teacher’s edition offer sufficient suggestions for presenting the material effectively to
all learners?
 Ancillary teaching materials contain numerous research-based instructional
strategies to accommodate a diverse student population (e.g., English
Learners, Advanced Learners/Gifted and Talented Students, Students with
Disabilities, and so forth).
 Ancillary teaching materials contain suggestions for integrating other content
disciplines (e.g., English/Language Arts, Science, Art, Music) into instructional
units.

Comments/Commendations:
Score:
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Program Title & Publisher:
Program Component Review:
Total Score:
INSTRUCTIONAL PROGRAM
INDIVIDUAL SUMMARY STATEMENTS FOR INSTRUCTIONAL PROGRAM:
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Section 3 - Program Component Review
ASSESSMENT
ASSESSMENT
Based on district/school needs:
1. Do the materials offer multiple measures to assess student mastery of the content
mathematical reasoning standards?
 High quality multiple-choice items, formatted like state assessment items, are
provided.
 Various types of assessments, such as multiple-choice, short-answer, essay,
project options, portfolio use, and open-ended types, are provided and mirror
instructional strategies in the program.
 Assessments measure mathematical reasoning.
 Performance assessments with scoring guides are provided to assess
mathematical reasoning.
 Comments/Commendations:
Score:
2. Do the materials provide assessments that diagnostically measure the extent of students’
existing knowledge and skills (entry-level or pre-instructional assessment)?
 Specific and various types of entry-level assessments are included in the
materials and reflect balance as defined by the mathematics framework.
 Entry-level assessments provide useful information for planning instruction.
- Pre-assessing prerequisite skills
- Pre-assessing upcoming chapter content
 Entry-level assessments include mathematical reasoning as well as content.

Comments/Commendations:
Score:
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3=
EXEMPLARY
1 = Does NOT
meet needs
Section 3, Program Component Review:
2 = MEETS
needs
The goal of this section is to examine the publisher’s presentation of student assessment for entrylevel assessment, progress monitoring, and summative evaluation in light of identified district needs in
order to differentiate instruction to more adequately support the teachers and students in the district.
Based on district/school needs:
3=
EXEMPLARY
ASSESSMENT
2 = MEETS
needs
1 = Does NOT
meet needs
Section 3, Program Component Review:
3. Do the materials provide assessments that measure the progress of students toward mastery of
the content standards and mathematical reasoning standards?
 There are a variety of progress-monitoring assessments that measure student
progress and reflect a balanced mathematics program.
 Varied progress monitoring assessments are available to support daily
instruction.
 The assessments include opportunities for students to monitor their own
progress.

Comments/Commendations:
Score:
4.
Do the materials provide assessments that accurately measure student mastery of the
standards after the completion of a unit of instruction (summative assessments)?
 The summative assessments are correlated to specific mathematics content
and content standards and reflect a balanced mathematics program.
 Varied summative assessments are available to measure student mastery of
mathematical content and content standards.
 The assessments measure mastery of mathematical reasoning standards.
 Comments/Commendations:
Score:
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Based on district/school needs:
5. Do the assessments provide the information teachers need to make instructional decisions?


The assessments provide sufficient information to ascertain student
misconceptions.

The assessments provide sufficient information to determine appropriate
interventions and/or remediation to meet students’ needs.

A variety of assessments, including those that are not language dependent,
provide specific information regarding the progress and needs of English
Learners.

The varieties of assessments provide specific information regarding the
progress and needs of students with disabilities.

The variety of assessments provides specific information regarding the
progress and needs of students who are advanced learners.
3=
EXEMPLAR
Y
ASSESSMENT
2 = MEETS
needs
1 = Does NO
meet needs
Section 3, Program Component Review:
Comments/Commendations:
Score:
6. Are adequate resources (for example, answer keys, student response sheets, scoring guides,
and so forth) provided to accurately evaluate and score student responses on all assessments?
 The answer keys provide explanations as well as specific answers for the
various assessments.
 The materials provide test generator software in a user-friendly format.
 The assessments include scoring guides, and other formats to evaluate and/or
score student responses.

Comments/Commendations:
Score:
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Program Title & Publisher:
Program Component Review:
Total Score:
ASSESSMENT
INDIVIDUAL SUMMARY STATEMENTS FOR ASSESSMENT:
Section 3 - Program Component Review
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UNIVERSAL ACCESS
UNIVERSAL ACCESS
Based on district/school needs:
1. What help is provided to identify specific errors and misconceptions in student learning?
 Resources that help teachers identify and clarify common misunderstandings
for each standard are included along with suggestions for addressing these
issues.
 The assessments provide a means for teachers to identify errors and
misconceptions in student learning.
 Resources are included to help teachers clarify exactly what part of each
standard students do and do not understand (i.e., cross references to support
materials).
 Comments/Commendations:
Score:
2. What help is provided to identify the underlying reasons for student errors and
misunderstandings?
 Resources to distinguish between English Learners’ challenges with language
or with content.
 Resources to help distinguish between academic language deficiencies and
content issues.
 Strategies help teachers in the teaching of reading for mathematical content.
 Activities and investigations promote mathematical reasoning.
 Activities include progress monitoring and summative assessments requiring
students to demonstrate mastery of the standard(s).
 Comments/Commendations:
Score:
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3=
EXEMPLARY
1 = Does NOT
meet needs
Section 3, Program Component Review:
2 = MEETS
needs
The goal of this section is to examine the Universal Access strategies and resources available for
teachers to use to help struggling students master the standards within the context of an instructional unit
and recommended pacing plan.
3=
EXEMPLARY
UNIVERSAL ACCESS
2 = MEETS
needs
1 = Does NOT
meet needs
Section 3, Program Component Review:
Based on district/school needs:
3. Does your school have adequate materials, tools, and manipulatives to support the activities
and strategies presented?
 Materials including tools and manipulatives are easily accessible and support
the activities and instructional strategies presented.
 Materials needed are appropriate to reinforce conceptual understanding,
procedures, and problem solving.
 Comments/Commendations:
Score:
4. Are there sufficient instructional strategies and resources to meet the identified needs of all of
your students (for example, diverse learners, struggling students, and advanced learners)?
Instructional strategies and resources:
 Provide effective and equitable opportunities for English Learners by
addressing: speaking, listening, reading, and writing.
 Provide multiple entry points for students with limited reading, comprehension,
and/or language skills.
 Include accommodations for students with disabilities in order to address their
Individualized Education Program (IEP).
 Include “extended activities” to reinforce/enrich the learning for all students.
 Include activities that are engaging and relevant to students’ lives.
 Include variety of quality materials for independent study, practice, and review.
 Include curriculum guides that make connections helping to deliver a balanced
mathematics program.
 Comments/Commendations:
Score:
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Based on district/school needs:
5. Are there opportunities for students to make connections in the unit of study?
 There are opportunities to make connections between mathematical strands.
 There are opportunities to make connections to prior learning during instruction,
including suggestions for reaching students who are functioning below grade
level.
 There are opportunities to apply mathematics in authentic contexts.
 Comments/Commendations:
Score:
6. Is there support to help teachers identify unit design and instructional strategies for content
development and student mastery of concepts within the unit? Include:
 Standards are designated.
 Specific outcomes and standards based objectives are stated.
 Appropriate progress monitoring assessment and summative assessments are
not only language dependent.
 A sufficient number of appropriate activities that support student mastery.
 Clear, concise daily lesson plans, with appropriate pacing,
 A wide range of research-based differentiated instructional strategies with
questions that focus on higher-level thinking, intentional instruction of academic
language, structured cooperative groupings, etc.
 A wide range of instructional strategies for intervention based on need.
 Research-based instructional strategies for the development of academic
language specific to the needs of mathematics are included within the
instructional unit (for example, Frayer Model, Direct Vocabulary Instruction,
Graphic Organizer, Concept Wheel, Semantic Word Map, etc.)
 Comments/Commendations:
Score:
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3=
EXEMPLARY
UNIVERSAL ACCESS
2 = MEETS
needs
1 = Does NOT
meet needs
Section 3, Program Component Review:
Based on district/school needs:
3=
EXEMPLARY
UNIVERSAL ACCESS
2 = MEETS
needs
1 = Does NOT
meet needs
Section 3, Program Component Review:
7. Does the material provide time options and pacing guides for instruction?
 Materials included in each instructional unit contain an appropriate pacing guide
that allows for individual student mastery of the standards.
 Ancillary teaching materials contain appropriate, alternative pacing guides that
accommodate the additional time required for strategic and intensive students.
 Materials offer suggestions for prioritizing key standards in order to teach
procedures, concepts, and problem solving.
 Comments/Commendations:
Score:
8.
Does the teacher’s edition offer sufficient suggestions for presenting the material successfully
to all learners?
 Ancillary teaching materials contain numerous research-based instructional
strategies for universal access to accommodate a diverse student population
(i.e., English Learners, Advanced Learners / Gifted and Talented Students,
Students with Disabilities, etc.).
 Ancillary teaching materials contain numerous strategies for integrating other
content disciplines (i.e., English/Language Arts, Science, Music and Art) into
instructional units in an effort to meet the needs of students.
 Comments/Commendations:
Score:
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Program Title:
PROGRAM COMPONENT REVIEW:
Total Score:
UNIVERSAL ACCESS
INDIVIDUAL SUMMARY STATEMENTS FOR UNIVERSAL ACCESS:
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DISTRICT SUMMARY CHART
REVIEW OF PROGRAM COMPONENTS
Program Title & Publisher:
Total Score:
SUMMARY STATEMENTS FOR SECTION #3:
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Glossary of Terms
Academic Vocabulary Development
Language used in formal contexts for academic subjects. It is language that is connected to literacy and
academics including the use of technical and academic terms.
Academic Performance Index (API)
State legislation established the Academic Performance Index (API), which summarizes a school's academic
performance and progress on statewide assessments. The API is used also as an additional indicator for federal
Adequate Yearly Progress (AYP) requirements.
Academic Yearly Performance (AYP)
The federal No Child Left Behind (NCLB) Act of 2001 requires all schools and districts to measure academic
success according to how well the school and district meets common performance targets. This determines
whether or not each public school and LEA is making Adequate Yearly Progress (AYP).
Assessment
An orderly process of gathering, analyzing, interpreting, and reporting student performance.
Benchmark
A common goal all students should reach. A common performance task using identical protocols that are given
to groups of students for comparative purposes.
Blueprints
Test blueprints indicate the number of questions per standard and the percentage of questions per strand assessed
on the California Standards Tests (CSTs).
Cognitive skills
Cognitive skills are any mental skills that are used in the process of acquiring knowledge; these skills include
reasoning, perception, and intuition. Any effort on the part of the teacher or the instructional materials to help
students process information in meaningful ways and become independent learners.
Concept Maps
A technique for representing knowledge in graphs.
Curriculum Mapping
A procedure for collecting data referenced directly to the calendar about the operational curriculum in a school
or district.
Curriculum Guides
Guides for curriculum connecting state standards to classroom instruction.
Differentiated Instruction
Differentiated Instruction is a teaching theory based on the premise that instructional approaches should vary
and be adapted to individual and diverse students. The intent of differentiating instruction is to maximize each
student’s growth and individual success by meeting each student where he or she is, and assisting in the learning
process.
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Direct Instruction
Refers to a skills-oriented, highly scripted method for teaching that emphasizes the use of small group, face-toface instruction by teachers and aides, using carefully articulated lessons in which cognitive skills are broken
down into small units.
Disaggregated Data
Disaggregated data means looking at test scores by specific subgroups of students. Patterns and trends and other
important information are uncovered by viewing disaggregated data.
District Profile
Data gathered by a school district showing information about teacher and learner needs, state testing, resources
and materials unique to that district.
English Learners
Students who are learning English as a second or additional language.
Entry-Level Assessment
Assessment measuring the extent of students’ existing knowledge and skills; helps teachers determine the
content that needs to be reviewed.
Evaluation
The process of judging achievement and growth of student learning by interpreting assessment data.
Extended Activities
Learning activities that extend beyond the lesson.
Guided Practice
Teacher supports the practice of a new concept with students. Part of the direct instruction model.
Individualized Education Program (IEP)
An Individualized Education Program (IEP) describes the special education and related services specifically
designed to meet the unique educational needs of a student with a disability.
Inquiry
Process of gaining information through questioning techniques and use of a variety of instructional methods
(such as, hands-on exploration or an investigation
Intervention
Stepping in to prevent failure in student academic progress.
Mathematics Framework
The Mathematics Framework is the blueprint for mathematics curriculum, instruction, professional
development, assessment, and instructional materials in California. The framework outlines the implementation
of the mathematics content and provides guidance for mathematics instruction in elementary, middle, and high
schools.
Misconceptions
Beliefs of students based on incorrect understanding or knowledge of mathematics concepts.
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Multiple Measures
Different types of assessments, for example, informal observations, portfolios, mathematics notebooks, student
tests, end-of-unit tests.
Pacing Guides
Recommended time frames for instructional delivery.
Pedagogy
The art or science of teaching. The discipline that focuses on how to structure material for promoting the
learning of students.
Progress Monitoring Assessment
Strategies and tools to assess students in various ways during a specific unit while students are doing a variety of
activities.
Student monitoring system:
Any point during the unit a teacher will have fairly accurate information as to the level of knowledge, skills, and
achievement for each student.
Assessment measuring the extent to which students have mastered (or are mastering) mathematics content
sufficiently to move forward in the logical progression of instruction.
Remediation Strategies
Instruction that is designed to correct an area of deficiency for a student.
Scaffolding
Adult/teacher support for learning and student performance of instructional tasks. Scaffolding can be removed,
as learners are able to demonstrate behaviors on their own.
Scope and Sequence
Documents that provide guidance on how the essential understandings, knowledge, skills, processes and
standards may be introduced to students in a logical, sequential, and meaningful manner.
Stakeholder Any persons or organizations that have a vested interest in the educational system.
Students with Disabilities
Students evaluated according to state and federal regulations as having mental retardation, a hearing impairment
(including deafness), a speech or language impairment, a visual impairment (including blindness), an emotional
disturbance, an orthopedic impairment, autism, traumatic brain injury, an other health impairment, a specific
learning disability, deaf-blindness, or multiple disabilities, and who needs special education and related services.
Summative Assessment
The final collection, analysis and reporting of information about student achievement at the end of a given time
frame.
Teacher Ancillaries
Extra resource materials that support state-adopted textbook programs.
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Universal Access
Differentiated instruction meeting the needs of all learners through
instruction delivered individually or in small group settings. Strategies
proven through research to be effective.
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