A Data-Driven Review of Instructional MaterialsCurriculum & Instruction Steering Committee A Data-Driven Review of Instructional Materials Mathematics Adoption Toolkit 1 Mathematics

Mathematics Adoption Toolkit 1

CCSESA California County SuperintendentsEducational Services Association

Curriculum & InstructionSteering Committee

A Data-Driven Review ofInstructional Materials


Mathematics Adoption ToolkitForeword

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 Larry ChampionCounty Superintendent, Riverside County Associate SuperintendentOffice of Education Tehama County Office of EducationPast President, CCSESA, California Past Chair, Curriculum and InstructionCounty Superintendents Steering CommitteeEducational Services Association

Mary Jane Burke Joyce WrightCounty Superintendent, Assistant Superintendent,Marin County Office of Education Sacramento County Office of EducationPresident, CCSESA, California Chair, Curriculum and InstructionCounty Superintendents Steering Committee


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 DirectorProfessional Development and Curriculum Support

Developed by the Mathematics Subcommittee,Curriculum and Instruction Steering CommitteeCalifornia County Superintendents Education Services Association© 2007 All rights reserved


Mathematics Adoption ToolkitTable 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 ToolkitIntroduction

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


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.

MathematicsContent

InstructionalProgram

Assessment UniversalAccess

Section 1: Developing the District Lens Yes Yes Yes Yes

- Task #1 – CA Expectations for Math Students Yes Yes Yes Yes

- Task #2 – District’s Expectations for Math Students Yes Yes

- Task #3 – District’s Needs for Student Population Yes Yes

- Task #4 – Assessment Data for Math Yes Yes

- Task #5 – District’s Learning Configurations Yes Yes

- Task #6 – District’s Needs for Teacher Population Yes Yes

- Task #7 – District’s Current Instructional Resources Yes

- Task #8 - Resources Supporting Mathematics Yes

Section #2: Standard Sampling 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 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 #2-


#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


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.


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 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

Section #1: Develop District Lens

Section #2: Standards Sampling

Section #4: Further Comparison

Section #5: Make a Decision

Section #5: Make a DecisionSection #3: Program Components

Section #5: Make a Decision

Section #6: Implementation


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

FACILITATOR’S GUIDE


Mathematics Adoption ToolkitFacilitator’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.


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 ToolkitAdoption Process Options

Section #1 (3 hours):

Developing the District Lens

Section #2 (3 - 6 hours):

Standards Sampling – Partial or Full

Section #3 (6 hours):

Review Program Components

Eliminate Programs

Section #4: Additional Review Options

Pilot ProgramsBlind Test of LessonsSurvey StudentsExecutive Committee

Section #5 (3 hours)

Making a Decision

Section #5 (3 hours)

Making a DecisionEliminate Programs

Eliminate ProgramsSection #5 (3 hours)

Making a Decision


Mathematics Adoption ToolkitFacilitator’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 ACTIVITIES MATERIALS

1. Establish a timeline. 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 ofEducation’s timeline for adoption, refer to:

www.cde.ca.gov/ci/cr/cf/timeline05to08adoptions.asp

2. Identify and gather stateadopted publishermaterials.

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 areavailable at the regional Learning ResourceDisplay 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, andconvene 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 perspectivemembers including teachers, administrators,parents, community members, highereducation faculty.

Letter of invitation explaining the process andtime commitment.


- Members of local school board- Representatives from higher education faculty.

Grade level or course groupings.4. Collect district data to

ensure match ofmaterials to districtneeds.

Data sources that should be considered and organized forSection #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.

Data previously collected for other purposese.g., for the science adoption

Collect data and enter onto web ahead oftime or collect and print

Gender:http://dq.cde.ca.gov/dataquest/ (Enrollment)http://www.jftk-ca.orghttp://star.cde.ca.gov/star2006/Viewreport.aspEthnicity:http://dq.cde.ca.gov/dataquest/ (Enrollment)http://www.jftk-ca.orghttp://star.cde.ca.gov/star2006/Viewreport.aspSocio-Economically Disadvantaged:http://dq.cde.ca.gov/dataquest/ APIBasehttp://www.jftk-ca.orgEnglish Learners:http://dq.cde.ca.gov/dataquest/ CELDThttp://dq.cde.ca.gov/dataquest Language Censushttp://www.jftk-ca.orghttp://star.cde.ca.gov/star2006/Viewreport.aspStudents with Disabilities:http://dq.cde.ca.gov/dataquest/ SpecEdhttp://www.jftk-ca.orghttp://star.cde.ca.gov/star2006/Viewreport.aspGifted and Talented:http://dq.cde.ca.gov/dataquest/ Enrollmenthttp://star.cde.ca.gov/star2006/Viewreport.aspMobility:http://dq.cde.ca.gov/dataquest/ APIBase2006Prevalent Languages:http://dq.cde.ca.gov/dataquest Language CensusCST:http://star.cde.ca.gov/star2006/Viewreport.asphttp://dq.cde.ca.gov/dataquest/APIBasehttp://www.jftk-ca.orgCELDT:http://dq.cde.ca.gov/dataquest/CELDTDistrict Technology:http://www1.edtechprofile.org



5. Publish resources forcommittee members.

Prepare materials for committee members 1. Overview of Adoption Process a. Timeline for adoption b. List of adopted publishers c. Graphic of process2. District data3. How to access website4. CA Mathematics Framework5. CA Blueprint for STAR6. Mathematics Released Items7. Toolkit worksheets: print or Electronic copies8. Contact information for committee members9. 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 decision-

making 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


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 ACTIVITIES MATERIALS

Section #1:Developing the DistrictLens.

Pages: 32-48

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.

Mathematics framework, hard copy orelectronic.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,

overheads, pens, etc.


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 Universal Program Access

Student Needs

Teacher Needs

Identify the nonnegotiable priorities. These describe the elementsany adopted program must have.

This chart should be referred to before the beginning of eachmeeting 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 donot need to be addressed.

Using the website or using a Word document, you may turn off anyquestions that do not pertain to your district (See: TechnologySupport Document).

Note: At this point you may choose to move to Section #2, #3 or #4.

overheads, pens, etc.

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


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.


• 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 atthe Mathematics.

Pages: 49-57

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 astandard. For example, choosing “division of positive fractions’ fromthe sixth grade standard: 2.1 “Solve problems involving addition,subtraction, multiplication, and division of positive fractions andexplain why a particular operation was used for a given situation”.

Brainstorm what the ideal instruction for this partial standard wouldbe.

Review with committee the questions in Section #2 to developcommon understanding of intent and meaning.

May use the folder with completed standards sampling to show howto complete forms.

Point out that there may be relevant information before and after thetarget 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 theirprogram(s) while simultaneously comparing programs with othergroup members. It takes about 2 hours to complete one publisherper 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.

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 separateworksheet for each standard and eachprogram reviewed. Worksheet p. 48-56

For electronic Word templates see:http://www.ccsesa.org

Chart of worksheet, District SummaryChart to compile results of individualworksheets.

Chart paper, pens Reference: folder of completed

standards sampling for sixth gradedivision of fractions.

Framework, Chapter 2 ContentStandards and Chapter 3, Grade LevelConsiderations


Add comments in text, + for area of strength, ? for question orconcern, and then score each question: 1 = does NOT meet districtneed, 2 = MEETS district needs, or 3 = EXEMPLARY.

A synthesis of findings for each question may add importantelaborations not specifically identified in question

Find the mode – the score that occurs most frequently - for eachsection

Step 4: Compile modes for four topics from each reviewer on District

Summary Chart for Standards Sampling p.49-57Step 5:

Review results of compilation and consider each program in terms ofthe district priorities. Committee members will explain where theyfound evidence or why they rated the question the way they did.

Use the District Summary Chart to notice if mode is consistentlystrong or weak across grade levels.

Decide which programs will continue to be reviewed and whichprograms will be eliminated from review.

Note: At this point you may choose to move to Section #5: Making aDecision or to continue on to Section #3: Reviewing ProgramComponents 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


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

(Standards Sampling)

What is the base model as listed on the Specs & Data

Sheets.

Program Organization What are the seating configurations? Does it have 2-

doors 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.


Section #3: ProgramComponent Review:Matching District Needswith InstructionalMaterials.

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 meetinglocation)

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 districtneeds, or 3 = EXEMPLARY.

Write summary statements for each of four topicsStep 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 whichprograms need further review. Try to eliminate all but 2 or 3.

Note: At this point you may choose to move to Section #5: Making aDecision or to continue on to Section #4: Options for Further Review.

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 itemswww.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.

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.


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 ReviewOptions: Piloting, BlindTest, Student Survey,Executive Committee.

Options: Blind Test

- Duplicate a similar lesson from each program and mask thename of the program.

- Teachers analyze each lesson for strengths andweaknesses

-

Blind Test: Copies of same lessonfrom each program with identificationof 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.

Piloting: CDE guidelines for pilotinghttp://www.cde.ca.gov/ci/cr/cf/imagen.asp

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.

Student materials from program(s)under consideration.

Survey questions.:

Directions: Look through the studentmathematics book. Review two entirelessons.


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 studentstake turns discussing the book, and answering thequestions about the book.

6. When students are comfortable, they may work on theirown. Allow 20 –45 minutes.

Source - Dos Palos-Oro Loma Unified School District

1. Were there pictures, graphs,diagrams, or examples?

2. If there were pictures, graphs,diagrams, examples, were theyhelpful?

3. Was the book too easy, just right, ortoo difficult?

4. Rate the lesson from 1 – 5. 1 = notvery good, 2 = just okay, 3 = good,4 = really good, 5 = excellent.

5. Retell three important facts from thelesson. Was this easy to do?

6. Describe what you like from thelessons.

7. Describe what you didn’t like fromthe lessons.

(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 exitexam, conducts a more thorough search of possible programs forbest match.

Section #5: Making a DecisionAt this point you have eliminated all the programs that do not meet your district criteria and you have “test driven” the two programs thatcome 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 ConsensusHonor everyone’s time, effort, and energy. It’s time to get the “family” to agree on which car to purchase. Remind everyone thatit’s time for the entire family (teenagers, mom, dad, grandparents) to come to agreement on which model will best meeteveryone’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 supportEITHER 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 thedistrict.


- 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. Thisprogram 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

Source: Miguel Carrillo, Ed.D, Poway School DistrictGoal: The group will come to consensus on the most appropriate choice ofprogram after all points of view have been heard. Everyone in the group willsupport the choice of the group, even if it was not their first choice.

Chart of District Priorities Data from reviews of Section 2, 3 and 4

is summarized in a report and sharedwith committee members.

1 Establish GroupNorms

Committee sitting in grade level groups will generate group normssuch 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

Chart paper to list agreed upon norms

2 Review History ofProcess

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

3 IndividualPrioritization ofPrograms

Each committee member reviews their notes on the evidencepersonally collected regarding the positives and the concerns foreach program. From an individual perspective, each committeemember indicates his or her current level of support for EACHprogram.

Teacher’s editions of each programfor 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 program3 This material is OK with me. I am willing to go along with thischoice2 I have reservations and I am not yet ready to support thismaterial1 I am opposed to this set of materialsFist I veto this proposal regardless of the will of the group

A reviewer could indicate 5 for both programs. Or a membercould indicate a level 5 support for Brand A and level 3 for BrandB. (Some may be confused thinking they need to split the 5between the two publishers)

Target a level of support between 3 and 5. If there are fists, 1s, or2s, concerns have not been heard well enough.

Straw Poll ChartNote: You will need one chart for each program.

Straw Poll Program A

5 4 3 2 1 Fist

Individual Support

Grade Level Consensus

Across Grade Consensus - 1

Across Grade Consensus - 2


Grade LevelConsensus

Each grade level group appoints a recorder. Then, the groupsdiscuss the positives and concerns. When every member of thegroup agrees on a positive or a concern, the recorder writes:

• 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 largersample. Record on wall chart.

Light green and red or pink post-its anda dark ink pen for each group.

Four positive/concerns charts for eachprogram 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:

InstructionalProgram A

Math ContentProgram A

Universal AccessProgram A

AssessmentProgram A

Universal AccessProgram B

InstructionalProgram B

AssessmentProgram B

Math ContentProgram B


Large GroupConsensus

Synthesize chart information across grades moving from a gradelevel perspective to a K-5 or 6-8 perspective.

If any post-it comments are duplicates, put them on top ofeach other, so it is one comment but you can still see that thiswas observed by multiple grades.

Go over each chart with the whole group. Ask for additionalstrengths or concerns. If the group agrees that this commentgoes across all grade levels, add post-its on the appropriatecharts.

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 strengthsthan the other, or they may have similar strengths, but onehas 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 supportprovided by the publisher.

Straw poll and Positive/Concernscharts.

If the decision is notyet 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).

Reconfirmcommitment toprogram

Even though this might not have been the first choice of eachindividual committee member, there is consensus that this is the bestprogram for the district.


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. Younow need to address the needs of students and teachers beyond just selecting a textbook. It’s time to begin the planning process forsuccessful 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

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 newadoption

Input from Executive Committee on how to use the program to meethigh priority district needs.



Templates for Section #1

Developing

the District Lens


SECTION 1 - DEVELOPING THE DISTRICT LENSTASK #1: California’s Mathematics Expectations for Students

Section 1 of the Mathematics Adoption Toolkit involves eight tasks. Each task is keyed to the fourtopics: Mathematics Content, Assessment, Instructional Program, and Universal Access. Task #1 isthe 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 CaliforniaDepartment of Education Mathematics Framework.

District Lens, Task #1 - MATHEMATICS CONTENT

Questions to Consider CA Mathematics Framework 2006

1. What is the depth ofknowledge that is expectedfor students?

Students should:• develop fluency in basic computational and procedural skills, an

understanding of mathematics concepts, and the ability to usemathematical 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 2 3 4 5 6 7 8 9 10Limited Developing Successful Exemplary

2. What mathematicalreasoning skills arestudents expected toknow and to be able todo?

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:



District Lens, Task #1 – INSTRUCTIONAL PROGRAM


3. What are the keycomponents of an effectivemathematics program?

a. Assessment

b. Quality Instruction

See Assessment Strand, page 36

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. 9District progress on quality instruction:

1 2 3 4 5 6 7 8 9 10 Limited Developing Successful Exemplary

c. MaximizedInstructional

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.10District progress on maximizing instructional time:


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 ofall three.

• provide ample opportunities for students to explain their thinking,verbally and in writing, formally and informally.

• supply ideas or tools for accommodating diverse studentsperformance within any given classroom. They offer suggestions forre-teaching a concept, providing additional practice for strugglingstudents, or condensing instruction so that advanced students canconcentrate on new material.

Framework, Ch. 1, pp. 9-11Also: p.207, 211 and 217

District progress on instructional resources:



e. ProfessionalDevelopment

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. 247-251District progress on professional development:


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. 13District progress on administrative practices:


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:



4. What are the expectationsfor the types and uses oftechnology?

The students’ use of technology builds on the skills and understandingsneeded to master basic mathematics skills. The uses of technology promotestudents’ understanding of mathematical concepts, quantitative reasoning,and achievement through the solving of problems, by testing conjectures,accessing data, and verifying solutions.

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:


District Lens, Task #1 - ASSESSMENT


5. What are the keycomponents of an effectiveassessment 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:


6. What are the types anduses of assessment that thedistrict is expected toimplement?

Regular and accurate assessment of student progress is essential. Thetypes of assessments that are the most crucial to student achievement are:

• Entry-level assessment.• Progress monitoring.• Summative evaluation.


District progress toward using all types of assessments:



District Lens, Task #1 – UNIVERSAL ACCESS


7. What are the expectationsfor supporting all studentsmastering the standards?

• Alignment ofInstruction

• Diagnostic Teaching,Differentiation,Grouping, Acceleratingfor At-Risk Students

• Planning for SpecialNeeds Students

• English Learners

• Advanced Learners

Procedures and processes are in place to:• assess student understanding at the start of instruction, frequently

during instruction, and use results for placement and programplanning

• Determine skills and understandings a students already possesses,and those the student needs to learn next

• diagnose the nature and severity of student difficulties• differentiate curriculum or instruction or both for all learners• use flexible grouping strategies• implement intervention strategies

• Plan for adapting to individual needs through careful organization ofresources and instruction

• Address English fluency

provide a combination of acceleration and enrichmentFramework, Ch. 6, pp. 229-239

District systems in place to support all students becoming proficient in mathematics:


Individual Summary Statements Task #1, California Expectations for students of mathematics:Implications for Adopting Mathematics Instructional Materials


SECTION 1 - DEVELOPING THE DISTRICT LENSTASK #2: District’s Mathematics Expectations for Students

This task examines how the District uses data to establish expectations for students, monitorsachievement of students, and develops district curriculum guides to support those expectations. Thegoals 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 currentcurriculum guide and/or map alignedwith the state’s mathematics contentstandards? What changes, if any, willbe made to this document? If noguides/maps, what processes are beingimplemented to generate them?

2. What is the district philosophy for theuse of curriculum guides and/or maps?

3. What are the district’s expectations forpreparing students for Algebra 1 andhigh school graduation?



4. How much instructional time is allottedto implement district expectations inmathematics?

5. How are teachers and/or grade levelteams implementing the guide and/ormap?

Individual Summary Statements Task #2, District Expectations for Students:Implications for Adopting Mathematics Instructional Materials


SECTION 1 - DEVELOPING THE DISTRICT LENSTASK #3: District Needs for Student Population

This task examines how the District uses data to establish particular needs of specific studentpopulations. The goals of this task are to examine the district’s strengths and areas of need.

District Lens, Task #3 – MATHEMATICS CONTENT


1. Analyze the unique mathematicsneeds of the following populations?How will you match their needs withthe newly adopted materials?

a. Gender

b. Ethnicity

c. Socio-economically Disadvantaged

d. English Learner

e. Students with Disabilities

f. Gifted and Talented

g. Other




2. What is the student mobility rateand how might it impact studentachievement in mathematics?

3. What are the most prevalentlanguages represented? Will yourmath textbook adoption considerprimary language support as anessential component?

Individual Summary Statements Task #3, District Needs for Students:Implications for Adopting Mathematics Instructional Materials


SECTION 1 - DEVELOPING THE DISTRICT LENSTASK #4: State and District Data Related to Mathematics

This task examines how the District uses state data and district assessment programs to identifyachievement of particular student populations.

District Lens, Task #4 – ASSESSMENT


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 assessmentsvalidate these findings?

3. Looking at the numbers andpercentages of students who areadvanced and proficient, how do wemeet their needs? What should we doto support their learning?

4. Looking at the numbers andpercentages 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 theirlearning?

5. Does the data indicate studentdeficiency in reading skills that mightimpact mathematics instruction andoverall student achievement?

6. CELDT: English Learnersa. Looking at numbers and percentage

of students at each level of theCalifornia English LanguageDevelopment Test (CELDT), how dowe meet their needs? What shouldwe do to support their learning?

b. In what strands do EL studentsexcel? Struggle?

Areas of strength:

Areas of struggle:


7. Does the district use progressmonitoring to guide teacher instructionand summative assessments tovalidate student mastery ofmathematics concepts and skills? Arethese assessments teacher generatedor does the district rely on publisherresources? Will they be updated orreplaced by this adoption process?

8. What types of assessments arecommonly used in the classroom? Arethese assessments teacher-generatedor does the teacher rely on publisherresources?

9. What other district programs addressstudent needs for remediation oracceleration?

Individual Summary Statements Task #4, State and District Data:Implications for Adopting Mathematics Instructional Materials


SECTION 1 - DEVELOPING THE DISTRICT LENSTASK #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 atyour district’s structures that impact mathematics instruction.



Task #1. What special needs must be

considered for the different schoolconfigurations in the district (e.g.,

K-8, K-5 or K-6, 6-8 or 7-8, self-contained, combination classes,departmentalized, houses, etc.)?

2. What are the implications fortextbook selection for schools withinthe district that are being monitoredby state and/or federal schoolimprovement initiatives?



3. How will you plan for differentiationof instruction with the newlyadopted materials for schoolswithin the district with a highconcentration of special educationstudents, English learners, oradvanced learners?

Special education students:

English learners:

Advanced learners:

Individual Summary Statements for Task #5, Instructional Program:Implications for Adopting Mathematics Instructional Materials


SECTION 1 - DEVELOPING THE DISTRICT LENSTASK #6: District Needs for Teachers

The goal of this section is to examine the district’s strengths and areas of need. This task is toconsider the long-range professional development needs of district teachers.

District Lens, Task #6 – MATHEMATICS CONTENT


1. How will you provide mathematicscontent training for teachers tobecome more knowledgeable of themathematics they teach and theways to teach?

2. What mathematics guidance donew teachers receive from thedistrict or from a BTSA supportprovider?



3. How will your long term professionaldevelopment plans accommodateteachers who move from one gradelevel to another?

4. Does the district/site have mathcoaches? If not, what actions andresources are needed to institutecoaching for the newly adoptedmath textbooks?

5. What types of on-goingmathematics professionaldevelopment (e.g., SB 472,coaching, differentiation, lessonstudy) does the district provide? Ifnone, what actions and resourcesare needed to implement ongoingstaff development?

6. What non-district professionaldevelopment opportunities areavailable for teachers?


7. How will you support new teacherswith professional development afteryour math textbook adoption? Willthe support of veteran teachers lookmuch different than that of newteachers?

8. How will your long term professionaldevelopment plans accommodateteachers who move from one gradelevel to another?

Individual Summary Statements Task #6, District Needs for Teachers:Implications for Adopting Mathematics Instructional Materials


SECTION 1 - DEVELOPING THE DISTRICT LENSTASK #7: District Current Instructional Resources

This task examines the instructional resources available to support the implementation of themathematics program. The goal of this section is to examine the district’s strengths and areas ofneed.



1. What is the district philosophy onthe use of instructional resources(ancillary materials, manipulatives,tools, and technology) to supportmathematics? Will this be animportant consideration in theadoption process?

2. To what extent are ancillarymaterials, manipulatives, and toolsbeing used to develop conceptualunderstanding?

3. What professional development isavailable on the effective use ofthese materials? Will this be animportant consideration in theadoption process?

4. What kinds of technology hardwareand software are in place to supportthe mathematics program? What isthe compatibility with the computerplatforms in the district?

Individual Summary Statements Task #7, District Instructional Resources:Implications for Adopting Mathematics Instructional Materials


SECTION 1: DEVELOPING THE DISTRICT LENSTASK #8: Resources to Support Mathematics

This task examines community resources available to support the mathematics program. The goal ofthis section is to examine the district’s strengths and areas of need.



1. What local informal mathematicslearning opportunities cansupplement the instructionalmaterials?

2. Will supplemental service providersutilize the instructional materials?

3. Are district mathematics volunteersusing the instructional materialsalong with the teachers?

4. What student events, programs, orparent education opportunities doesthe district provide to extendmathematics learning?

5. What organizations in thecommunity sponsor student eventspromoting mathematics?

Individual Summary Statements for Task #8, Resources:Implications for Adopting Mathematics Instructional Materials


DISTRICT SUMMARY CHARTDistrict Lens: Needs of Students and Teachers

Task #1

Task #2

Task #3

Task #4

Task #5

Task #6

Task #7

Task #8




Standards Sampling


SECTION 2: STANDARDS SAMPLINGCalifornia Content Standards for Mathematics

In an effective and well-designed mathematics program, students move steadily from whatthey already know to a mastery of skills, knowledge, and understanding. Students progressfrom an ability to explain, and then justify their thinking to being able to derive formal proofs.


This activity is to do a side-by-side comparison of standards development to determine which materials best meet the learningneeds of your students. The sampling of three standards provides a good indicator of match. In conducting the sampling, referto 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 multipleconcepts, choose just one concept as you focus for sampling. In elementary grades, sample standards might include a standard fromNumber Sense critical to subsequent mathematics understandings, another standard from Measurement and Geometry showing ahigh 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 perstandard, 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 ispresented. 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 andwhich materials no not merit further review.


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:


Section 2 – Standard Sampling

MATHEMATICS CONTENT

Score: 1 = Does NOT meet district needs

2 = Meets district needs3 = Exemplary

+ S

tren

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? C

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cern

S

core

1. Is the math content superficial or does it deepenconceptual understanding, procedural fluency,problem solving, and mathematical reasoning?

Evidence:

2. How well does “Teacher Background” prepare a newteacher or a teacher new to the grade level to:

• Present the concept?

• Build procedural fluency?

• Build mathematical reasoning?

• Make connections between conceptualunderstanding, procedural fluency, problemsolving, and mathematical reasoning?

3. What suggestions are provided to prevent or correctthe development of misconceptions as studentslearn?

4. How does the program support the teacher infacilitating mathematical discourse about thisconcept?

Mode:



INSTRUCTIONAL PROGRAM


2 = Meets district needs 3 = Exemplary

+ S

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1. When the concept is first introduced, what connectionsare made to students’ lives and prior knowledge?

Evidence:

2. What materials are available to help with the learningof vocabulary essential to understanding this standard:

• Definitions with visuals and examples?

• Pronunciations?

• Words used in context and in sentences?

• Suggestions for teaching and practicing bothacademic language (prove, analyze) and contentvocabulary (denominator, divide)?

3. How well do the different types of student worksupport:

• Developing conceptual understanding? Is thereevidence of a progression from concrete to pictorialto more abstract means of learning concepts?

• Learning and practicing the necessary skills andprocedures? Is there evidence of developing skillsin the context of problem solving andinvestigations?

• Developing mathematical reasoning?

• Applying their understanding to solve problems?


4. What kinds of practice of the standard are there forstudents to:

• Immediately practice the skill or concept?

• Revisit and apply what has been learned later inthe program?

• Revisit and apply what has been learned in adifferent context (e.g., area model to practicemultiplication, metric measurement to practicecomputation with decimals)?

Evidence:

5. How does technology support a balanced curriculumof this standard for:

• Conceptual understanding?

• Skills and procedures?

• Mathematical reasoning?

• Applying their understanding to solve problems?

6. Are the technology-based activities engaging forstudents?

Mode:



ASSESSMENT


2 = Meets district needs 3 = Exemplary +

Str

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th?

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rn

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1. What support is available to help teachers check for student misconceptions?

Evidence:

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 assessstudent procedural knowledge, conceptualunderstanding, and mathematical reasoning?

Mode:



UNIVERSAL ACCESS


2 = Meets district needs 3 = Exemplary

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1. What support is provided for English LanguageLearners (e.g., visual aides, advanced or graphicorganizers such as word webs or concept maps,manipulatives, reference charts, word walls, etc.)?

Evidence:

2. What support is provided for Special Educationstudents (e.g., modified or alternative tasks, advancedgraphic organizers, tactile or auditory support, etc.)?

3. What opportunities are provided for advanced learnersto deepen or extend their understanding of the standard(e.g., complex tasks, extension of learned skills, links toother content areas, special challenges, etc.)?

4. How well do the Universal Access strategies presentthe concept in an alternative form (e.g., hands-on,different context, etc.)?

Mode:


DISTRICT SUMMARY CHARTStandards Sampling

Program Title and Publisher:

Summary for Section #2 1 = Does not meet district needs2 = Meets district needs3 = Exemplary

MathematicsContent

InstructionalProgram Assessment

UniversalAccess

• 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):

Mode:




Reviewing

Program Components


Section 3 - Program Component ReviewMATHEMATICS CONTENT

Where the Standards Sample examined the materials from a very sharp focus, The Program ComponentReview examines the materials from a chapter or unit focus. The Program Component Review examines apublisher’s presentation of mathematics content and the standards in light of identified district needs. Thegoal is to determine if the program will adequately support the learning of procedural skills, conceptualunderstanding, and problem solving in becoming proficient in mathematics. Refer to the District SummaryChart of Needs of Students & Teachers.

Section 3, Program Component Review:

MATHEMATICS CONTENT

Based on school / district needs: 1 =

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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 sequencedwith key standards revisited over time.

The standards are addressed in a manner that will support students in becoming adeptat 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 thevocabulary in the standards and framework.

Instructional strategies are provided to create opportunities for students to usemathematical vocabulary with a focus on precision.

The definitions are easy for students to understand. Materials use cognates, real lifeexamples, realia, posters, etc. to support student use of vocabulary.

The vocabulary words are referenced within the text: glossary with a pronunciationguide, within the index, used in a sentence, and includes a visual representation.

Summary statements:

Score:



MATHEMATICS CONTENT


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3. Are the mathematics reasoning standards addressed so that students can both master them asindividual strategies and apply them to their mathematics content standards?

The mathematical reasoning standards needed in this lesson/unit are directlyaddressed 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 particularproblem by generalizing to other situations.

Summary statements:

Score:

4. Do the charts, graphs, diagrams, pictures and so forth appropriately and adequately supportthe 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 studentunderstanding of content standards.

Summary statements:

Score:



MATHEMATICS CONTENT


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5. Are connections delineated between grade-level mathematical strands?

Connections are made to prior learning in the development of thestandard(s).

Content is structured to provide opportunities to apply mathematics inauthentic contexts.

Summary statements:

Score:

6. Does the teacher’s edition provide adequate, adult-level background information (conceptsand examples) to equip the teacher to teach the standard?

Clear and complete adult-level explanations of the concepts, principles, andtheories are provided to refresh or enhance knowledge of the topic.

Instructional material provides additional resources for further backgroundinformation.

Alternative algorithms from other cultures and why they work are included.

Summary statements:

Score:


Program Title & Publisher: Program Component Review:

MATHEMATICS CONTENT

Total Score:

INDIVIDUAL SUMMARY STATEMENTS FOR MATHEMATICS CONTENT:


Section 3 - Program Component ReviewINSTRUCTIONAL PROGRAM

This section examines the publisher’s presentation of mathematics content in light of identified districtneeds. 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 =

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1. Does the material present the content in multiple ways to promote student understanding ofthe standards? Instructional material includes opportunities for students to receive direct

instruction and guided practice.

Instructional material provides multiple opportunities for students to engagein mathematical reasoning.

Instructional material includes activities/tools for the development of precisemathematical language.

Comments/Commendations:

Score:

2. Do the activities and problems promote student understanding of the standards and all theircomponents? 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 summativeassessments requiring students to demonstrate mastery of the standards.


Score:





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3. Does your school have adequate materials, tools, and manipulatives to support the activitiesand strategies presented?

Materials are easily accessible and support the activities and instructionalstrategies presented.

Materials needed are appropriate to reinforce conceptual understanding,procedures, and problem solving.


Score:

4. Are there sufficient instructional strategies and resources to meet the identified needs of all ofstudents (e.g., diverse learners, struggling students, and advanced learners)?

Instructional strategies and resources address the needs of EnglishLearners.

Instructional strategies and resources provide multiple entry points forstudents with limited reading or comprehension skills.

Instructional strategies and resources include accommodations for studentswith an Individualized Education Program (IEP).

Instructional strategies and resources include “extended activities” toreinforce/enrich the learning for all students (e.g., writing activities, structuredcooperative grouping, class discussion, inquiry activities, materials forindependent study, practice, and review).

Instructional strategies and resources include activities that connect contentto real-life application.

Curriculum guides delineate how content can be organized to deliver abalanced mathematics program.


Score:





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5. 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, includingsuggestions for reaching students who are functioning below grade level.

Application of the mathematics is made within authentic contexts.


Score:

6. Is there support to help teachers identify unit design and instructional strategies for contentdevelopment 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 learningobjectives 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 instructionalintervention are included i.e., alternative algorithms, structured cooperativegroupings, writing, mathematical discussions, etc.

Research-based instructional strategies for the development of academiclanguage specific to the needs of mathematics (e.g., Frayer Model, DirectVocabulary Instruction, Graphic Organizers, Concept Wheel, etc.).


Score:





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7. Does the material provide time options and pacing guides for instruction with focus on keystandards (see CST Blueprints)?

Materials included in each instructional lesson/unit contain an appropriatepacing guide that allows for student mastery of the standards.

Ancillary teaching materials contain appropriate, alternative pacing guidesthat accommodate limited instructional time.

Materials offer suggestions for prioritizing standards when time to teachmathematics is limited.

Materials offer several suggestions for pacing to accommodate a variety ofstudent needs as well as school / district schedules.


Score:

8. Does the teacher’s edition offer sufficient suggestions for presenting the material effectively toall learners?

Ancillary teaching materials contain numerous research-based instructionalstrategies to accommodate a diverse student population (e.g., EnglishLearners, Advanced Learners/Gifted and Talented Students, Students withDisabilities, and so forth).

Ancillary teaching materials contain suggestions for integrating other contentdisciplines (e.g., English/Language Arts, Science, Art, Music) into instructionalunits.


Score:




Total Score:

INDIVIDUAL SUMMARY STATEMENTS FOR INSTRUCTIONAL PROGRAM:


Section 3 - Program Component ReviewASSESSMENT

The goal of this section is to examine the publisher’s presentation of student assessment for entry-level assessment, progress monitoring, and summative evaluation in light of identified district needs inorder to differentiate instruction to more adequately support the teachers and students in the district.


ASSESSMENT


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1. Do the materials offer multiple measures to assess student mastery of the contentmathematical reasoning standards?

High quality multiple-choice items, formatted like state assessment items, areprovided.

Various types of assessments, such as multiple-choice, short-answer, essay,project options, portfolio use, and open-ended types, are provided and mirrorinstructional strategies in the program.

Assessments measure mathematical reasoning.

Performance assessments with scoring guides are provided to assessmathematical reasoning.


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 thematerials 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.


Score:



ASSESSMENT


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3. Do the materials provide assessments that measure the progress of students toward mastery ofthe content standards and mathematical reasoning standards?

There are a variety of progress-monitoring assessments that measure studentprogress and reflect a balanced mathematics program.

Varied progress monitoring assessments are available to support dailyinstruction.

The assessments include opportunities for students to monitor their ownprogress.


Score:

4. Do the materials provide assessments that accurately measure student mastery of thestandards after the completion of a unit of instruction (summative assessments)?

The summative assessments are correlated to specific mathematics contentand content standards and reflect a balanced mathematics program.

Varied summative assessments are available to measure student mastery ofmathematical content and content standards.

The assessments measure mastery of mathematical reasoning standards.


Score:



ASSESSMENT


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5. Do the assessments provide the information teachers need to make instructional decisions?

The assessments provide sufficient information to ascertain studentmisconceptions.

The assessments provide sufficient information to determine appropriateinterventions 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 EnglishLearners.

The varieties of assessments provide specific information regarding theprogress and needs of students with disabilities.

The variety of assessments provides specific information regarding theprogress and needs of students who are advanced learners.


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 thevarious assessments.

The materials provide test generator software in a user-friendly format.

The assessments include scoring guides, and other formats to evaluate and/orscore student responses.


Score:



ASSESSMENT

Total Score:

INDIVIDUAL SUMMARY STATEMENTS FOR ASSESSMENT:


Section 3 - Program Component ReviewUNIVERSAL ACCESS

The goal of this section is to examine the Universal Access strategies and resources available forteachers to use to help struggling students master the standards within the context of an instructional unitand recommended pacing plan.


UNIVERSAL ACCESS


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1. What help is provided to identify specific errors and misconceptions in student learning?

Resources that help teachers identify and clarify common misunderstandingsfor each standard are included along with suggestions for addressing theseissues.

The assessments provide a means for teachers to identify errors andmisconceptions in student learning.

Resources are included to help teachers clarify exactly what part of eachstandard students do and do not understand (i.e., cross references to supportmaterials).


Score:

2. What help is provided to identify the underlying reasons for student errors andmisunderstandings?

Resources to distinguish between English Learners’ challenges with languageor with content.

Resources to help distinguish between academic language deficiencies andcontent 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 requiringstudents to demonstrate mastery of the standard(s).


Score:



UNIVERSAL ACCESS


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3. Does your school have adequate materials, tools, and manipulatives to support the activitiesand strategies presented?

Materials including tools and manipulatives are easily accessible and supportthe activities and instructional strategies presented.

Materials needed are appropriate to reinforce conceptual understanding,procedures, and problem solving.


Score:

4. Are there sufficient instructional strategies and resources to meet the identified needs of all ofyour students (for example, diverse learners, struggling students, and advanced learners)?

Instructional strategies and resources:

Provide effective and equitable opportunities for English Learners byaddressing: 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 theirIndividualized 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 balancedmathematics program.


Score:



UNIVERSAL ACCESS


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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 gradelevel.

There are opportunities to apply mathematics in authentic contexts.


Score:

6. Is there support to help teachers identify unit design and instructional strategies for contentdevelopment 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 arenot 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 withquestions that focus on higher-level thinking, intentional instruction of academiclanguage, structured cooperative groupings, etc.

A wide range of instructional strategies for intervention based on need.

Research-based instructional strategies for the development of academiclanguage specific to the needs of mathematics are included within theinstructional unit (for example, Frayer Model, Direct Vocabulary Instruction,Graphic Organizer, Concept Wheel, Semantic Word Map, etc.)


Score:



UNIVERSAL ACCESS


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7. Does the material provide time options and pacing guides for instruction?

Materials included in each instructional unit contain an appropriate pacing guidethat allows for individual student mastery of the standards.

Ancillary teaching materials contain appropriate, alternative pacing guides thataccommodate the additional time required for strategic and intensive students.

Materials offer suggestions for prioritizing key standards in order to teachprocedures, concepts, and problem solving.


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 instructionalstrategies 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 othercontent disciplines (i.e., English/Language Arts, Science, Music and Art) intoinstructional units in an effort to meet the needs of students.


Score:


Program Title: PROGRAM COMPONENT REVIEW:

UNIVERSAL ACCESS

Total Score:

INDIVIDUAL SUMMARY STATEMENTS FOR UNIVERSAL ACCESS:


DISTRICT SUMMARY CHARTREVIEW OF PROGRAM COMPONENTS

Program Title & Publisher: Total Score:

SUMMARY STATEMENTS FOR SECTION #3:


Glossary of Terms

Academic Vocabulary DevelopmentLanguage used in formal contexts for academic subjects. It is language that is connected to literacy andacademics 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 academicperformance and progress on statewide assessments. The API is used also as an additional indicator for federalAdequate 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 academicsuccess according to how well the school and district meets common performance targets. This determineswhether 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 givento groups of students for comparative purposes.

Blueprints

Test blueprints indicate the number of questions per standard and the percentage of questions per strand assessedon the California Standards Tests (CSTs).

Cognitive skills

Cognitive skills are any mental skills that are used in the process of acquiring knowledge; these skills includereasoning, perception, and intuition. Any effort on the part of the teacher or the instructional materials to helpstudents 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 schoolor 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 varyand be adapted to individual and diverse students. The intent of differentiating instruction is to maximize eachstudent’s growth and individual success by meeting each student where he or she is, and assisting in the learningprocess.


Direct Instruction

Refers to a skills-oriented, highly scripted method for teaching that emphasizes the use of small group, face-to-face instruction by teachers and aides, using carefully articulated lessons in which cognitive skills are brokendown into small units.

Disaggregated Data

Disaggregated data means looking at test scores by specific subgroups of students. Patterns and trends and otherimportant information are uncovered by viewing disaggregated data.

District Profile

Data gathered by a school district showing information about teacher and learner needs, state testing, resourcesand 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 thecontent 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 specificallydesigned 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 FrameworkThe Mathematics Framework is the blueprint for mathematics curriculum, instruction, professionaldevelopment, assessment, and instructional materials in California. The framework outlines the implementationof the mathematics content and provides guidance for mathematics instruction in elementary, middle, and highschools.

MisconceptionsBeliefs of students based on incorrect understanding or knowledge of mathematics concepts.


Multiple Measures

Different types of assessments, for example, informal observations, portfolios, mathematics notebooks, studenttests, 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 thelearning of students.

Progress Monitoring Assessment

Strategies and tools to assess students in various ways during a specific unit while students are doing a variety ofactivities.

Student monitoring system:Any point during the unit a teacher will have fairly accurate information as to the level of knowledge, skills, andachievement for each student.Assessment measuring the extent to which students have mastered (or are mastering) mathematics contentsufficiently 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 andstandards 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 emotionaldisturbance, an orthopedic impairment, autism, traumatic brain injury, an other health impairment, a specificlearning 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 timeframe.

Teacher Ancillaries

Extra resource materials that support state-adopted textbook programs.

Universal Access

Differentiated instruction meeting the needs of all learners through instruction delivered individually orin small group settings. Strategies proven through research to be effective.
