Math Tool Kit Adoption

A Data-Driven Review of Instructional Materials

California County

CCSESA Superintendents

Educational Services Association

Mathematics Adoption Toolkit

Curriculum & Instruction Steering Committee

1

Mathematics Adoption Toolkit Foreword

On behalf of the County Superintendents of the State of California, we are pleased to introduce the Mathematics Adoption Toolkit developed by the Mathematics Subcommittee of the Curriculum and Instruction Steering Committee with support from the California Mathematics Council. Standards-based materials that meet the needs of students are essential for their achievement in mathematics. The Mathematics Adoption Toolkit offers a clear, data-driven process for reviewing mathematics instructional materials to help district personnel make informed, objective recommendations to local Boards of Education to best meet local needs.

The California County Superintendent Educational Services Association (CCSESA) is an organization consisting of the County Superintendents of Schools from the 58 counties in California working in partnership with the California Department of Education. The Curriculum and Instruction Steering Committee (CISC) is a subcommittee of CCSESA, consisting of county office associate superintendents, focusing on curriculum, instruction, and professional development.

The County

Superintendents of California are pleased to provide support to California schools for the mathematics instructional materials selection process.

Dr. David Long County Superintendent, Riverside County Office of Education Past President, CCSESA, California County Superintendents Educational Services Association

Larry Champion Associate Superintendent Tehama County Office of Education Past Chair, Curriculum and Instruction Steering Committee

Mary Jane Burke County Superintendent, Marin County Office of Education President, CCSESA, California County Superintendents

Joyce Wright Assistant Superintendent, Sacramento County Office of Education Chair, Curriculum and Instruction Steering Committee

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Contributing Authors Doreen Heath Lance, Chair

Sonoma County Office of Education

April Cherrington

San Mateo County Office of Education

Joanie Commons

UCSD, Cajon Valley Union School District, CMC

Babette DeCou

Paso Robles Public Schools, CMC Representative

Linda Dilger

Monterey County Office of Education

Luke Dilger

Monterey County Office of Education

Joan Easterday

Sonoma County Office of Education

Tim Gill

Lake County Office of Education

Satinder Singh

San Joaquin County Office of Education

Frances Basich Whitney

Santa Cruz County Office of Education

Debbie Williams

San Joaquin County Office of Education

Kathy Woods

Madera County Office of Education, CMC

Special Thanks Linda Menvielle

Chair, CISC Mathematics Subcommittee Assistant Superintendent for Instructional Services, Imperial County Office of Education

Harold Asturias

President, California Mathematics Council

Dean Gilbert

Chair, Science Adoption Toolkit, CISC Science Subcommittee

Members of the CISC Mathematics Subcommittee County Superintendents of Public Instruction Paul Giganti

Cover design

Department of Education California Phil La Fontaine

CDE Division Director Professional Development and Curriculum Support

Developed by the Mathematics Subcommittee, Curriculum and Instruction Steering Committee California County Superintendents Education Services Association ďƒŁ 2007 All rights reserved

Mathematics Adoption Toolkit

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Mathematics Adoption Toolkit Table of Contents

Table of Contents Foreword

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1

Introduction and Overview

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4

Facilitator’s Guide

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10

District Lens

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17

Standard(s) Sampling

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19

Program Components Review

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22

Additional Options

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24

Making A Decision

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26

Planning Forward

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30

Templates Section #1

Developing the District Lens

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32

Section #2

Standards Sampling

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49

Section #3

Reviewing Program Components

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58

Glossary

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78

Williams Settlement

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81

Mathematics Adoption Toolkit

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Mathematics Adoption Toolkit Introduction As a State, Are We Ready for 2014?

With the advent of No Child Left Behind, education has been held accountable for its work more closely than any other time in history. This mathematics adoption will be the adoption that sees us – students and educators – through to the year 2014! While all adoptions are serious business in education, the adoption of instructional materials for mathematics may be a key factor for schools and districts challenged to meet required levels of proficiency for all students by 2014.

Participation on a district adoption committee can be an exciting process, enabling educators to impact a district’s choice of instructional materials. Our goal is to support your efforts by helping you establish a focus toward best meeting the needs of students and teachers in your district. The task you are about to undertake will demand effort and availability of resources – time and staff to review programs. These resources vary from district to district. For this reason, the Toolkit can be implemented in a variety of ways, ensuring the facilitation of a successful adoption process, one focused on meeting the needs of students and teachers in your district.

The members of the

Curriculum and Instruction Steering Committee (CISC) urge schools and districts to craft a careful plan to analyze the myriad of State Board of Education (SBE) adopted programs for mathematics.

An Overview of the Mathematics Adoption Toolkit The Mathematics Adoption Toolkit is designed to support the selection of grades K-8 instructional materials for core programs, Algebra Readiness, and Intervention, but can also support a grades 9 – 12 adoption process The Toolkit is organized around accountability questions guiding the work in California schools: What do you want your students to know? (Mathematics Content) How will you know your students “know it”? (Assessment) How will you make sure your students “know it”? (Instructional Strategies) How will you make sure ALL students “know it”? (Universal Access) The Toolkit is divided into three worksheet sections (Developing the District Lens, Standard Sampling, and Program Component Review) each section is subdivided into four topics: Mathematics Content, Instructional Program, Assessment, and Universal Access. Section #4 offers options for further review. These sections and topics will help you thoroughly analyze the selected mathematics programs. Section #5, presents a process for coming to consensus on the choice for adoption. The Mathematics Adoption Toolkit

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review and ultimate selection of a mathematics program are your first steps in preparing your district for the year 2014.

Chart: Mathematics Adoption Toolkit: A Complete Adoption Process.

Mathematics Content Yes

Instructional Program Yes

Assessment Yes

Universal Access Yes

- Task #1 – CA Expectations for Math Students - Task #2 – District’s Expectations for Math Students - Task #3 – District’s Needs for Student Population - Task #4 – Assessment Data for Math - Task #5 – District’s Learning Configurations - Task #6 – District’s Needs for Teacher Population - Task #7 – District’s Current Instructional Resources - Task #8 - Resources Supporting Mathematics Section #2: Standard Sampling

Yes Yes Yes Yes

Yes Yes

Yes

Yes

Section 1: Developing the District Lens

Yes Yes

Yes

Yes Yes Yes

Yes

Yes

Yes

Yes Yes

Section #3: Program Components

Yes

Yes

Yes

Yes

Section #4: Further Options for Review

Yes

Yes

Yes

Yes

Section #5: Coming to Consensus

Yes

Yes

Yes

Yes

The

Yes

Mathematics Adoption Toolkit is based on the premise that a district’s adoption should

reflect its unique and specific needs. The most appropriate adoption for one district might not be the most appropriate for another.

Therefore, creating the district lens for analyzing the materials

(completing Section #1) is critical to making the best selection for your students and teachers.

However, if a district recently reviewed its needs and resources in the science materials adoption process, your adoption committee could update information relevant to mathematics needs and proceed to Section #2.  Section #1: Developing the District Lens The school or district adoption committee develops a lens through which to view and evaluate the various program materials.

Establishing a profile of the district’s needs and

resources creates this lens. The Toolkit provides a series of eight tasks analyzing state expectations in mathematics instruction, district expectations for mathematics instruction, student performance data, and the needs of your teacher population. The data needed for this section is, for most schools and districts, readily available and should be provided as informational packets to the committee. For schools and districts without ready access to data, an avenue for compiling the documentation can be accessed via an internet link to DataQuest http://dq.cde.ca.gov/dataquest/ Completing the District Lens will enable the school/district to determine the type of instructional program it needs and Toolkit sections #2Mathematics Adoption Toolkit

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#4 will help focus the evaluation of these programs based on district needs for students and teachers.

Developing the District Lens is a very important part of the process. It is not only an important initial step, it is powerful professional development for the committee members to “ground” themselves in the framework and specific needs of their district. While publishers may develop their own “toolkits” these have limited value in the sense that they are “lens free” and do not take into consideration the very specific and often challenging needs of a district. It is in a school’s/district’s best interest to thoroughly investigate their unique needs to determine the program that has the greatest likelihood of addressing those challenges. (See: pp.17-19, 32-48) An important tip for this stage - Start now!! It is not necessary to wait to see what the State Board of Education (SBE) adopts in order to clarify what critical components need to be in the program that best meet the needs of your students and staff. Once the SBE adopts a list of instructional materials, you are in a position to begin the work of investigating programs.

Once the committee has established school/district priorities for a mathematics program via the lens, it is ready to begin the work of reviewing the programs that the SBE has adopted. All programs adopted by the SBE are considered to meet the state requirements for instructional materials outlined in the framework. This was the work of the Instructional Materials Advisory Panel (IMAP) composed of teachers, educators, and a member of the Content Review Panel (CRP) during the summer of 2007. The panels have determined if the programs meet or do not meet the criteria including mathematical accuracy. The SBE votes after reviewing the recommendations of the Curriculum Commission who is advised by the IMAP and the CRP. Your committee work is to determine the quality of the program in best meeting your district needs. The Toolkit suggests different options for the analysis of instructional materials.

To start this stage, the committee evaluates the grade level configurations (K-5, K-6, K-8, 6-8, etc.) of the recommended instructional materials. It may be that some programs are eliminated at this point, without further investigation, due to the fact that the grade level configurations of the program do not meet the needs of the district.  Section #2 - Standards Sampling: Taking a Deeper Look at Mathematics Of great concern in the selection of a mathematics program is the ability of that program to support the instruction required to prepare all students for grade level proficiency and Algebra I. In an attempt to judge the quality of mathematics instruction, the committee will want to perform a deeper analysis of the instruction in key mathematical concepts and standards that Mathematics Adoption Toolkit

6

prepare students for further mathematics. (See: pp.19-22, 49-57). This is an opportunity to review programs through the lens of the standards that are challenging to teach in your district.

The Standard Sampling analysis will inform the committee of the strength of the mathematics critical in the selection of instructional materials that will take our schools to the year 2014. Information gleaned from the Standards Sampling indicating a strong balance of mathematics - procedural fluency, conceptual understanding, problem solving, and mathematical reasoning - will serve as a means for identifying programs you want to investigate further as the committee works to identify the best program for your school/district.  Section #3 - Analyzing Program Components: Matching District Needs to Instructional Materials.

Following the Standards Sampling, the committee will begin a formal review of the program components that make up the instructional program – a series of questions are provided to guide the program component review as committee members investigate and evaluate the four topics:

Mathematics Content, Instructional Strategies, Assessment, and

Universal Access.

Each time committee members investigate the programs, they will start by reviewing the district lens so that district priorities guide the analyses of the program components. An exciting feature of this Toolkit is that the feedback by reviewers for the program components can be done online. This allows the person facilitating the process to compile data on the programs, monitor committee member progress, prompt if needed, and develop a report based on the rubric scores assigned by the committee members for each component of each instructional material investigated. (See: pp. 17-19, 58-77)  Section #4 - Additional Review Options: Piloting, Blind Review, Student Surveys and Executive Committee.

Some school districts, after determining the top scoring programs for their students and staff, will choose to undergo a pilot phase of the programs before making a recommendation to its local school board.

Another option is to conduct a blind review. Teachers compare the same lesson from all programs under consideration. The name of the program is masked. Teachers compare the lessons looking for strengths and weaknesses.

Student surveys are used to develop a picture of how students make sense of mathematics while using the textbook.

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After identifying areas of top priority in the district lens, some committees may choose to convene a subcommittee of experts in an area(s) of high priority. For example, if English Language Learners are a top priority, instructors of second language learners may be convened to evaluate materials from that perspective. (See: pp. 24-26)

Certainly the prior steps are crucial in making an informed decision for program selection geared to meet the proficiency needs of our students by 2014. However, we are aware that not all districts have the resources needed to complete this ideal process. For that reason, we have suggested alternate pathways for determining the program that will best meet the needs of the students and teachers in your district.

For example, your district may choose to use Section #2, Standards

Sampling to gather evidence and then proceed to Section #5, Making a Decision. The graphic shows different options for using the Toolkit.

Section #1: Develop District Lens

Section #2: Standards Sampling

Section #5: Make a Decision

Section #3: Program Components

Section #5: Make a Decision

Section #4: Further Comparison

Section #5: Make a Decision

Section #6: Implementation

 Section 5: Making a Decision – Coming to Consensus The committee members tally and summarize comments about the four topics analyzed through the templates that guide this process. They review the results from a grade level and school wide perspective looking for program strengths and weaknesses.

The committee

comes to consensus about a program that all committee members will support throughout its implementation. (See: Facilitator’s Guide, pp. 26-30).

The qualitative and quantitative results from this work will be documented on a report to help arrive at the recommendation for adoption by your district. A helpful component of the Toolkit is the report that is generated electronically. This report neatly summarizes the Mathematics Adoption Toolkit

8

information and the scores of the programs and is an ideal document to submit to the local board in the recommendation packet.  Section 6: Next Steps, Implementation The next phase takes us to effective implementation of the selected program. With the critical role that this mathematics adoption is going to play as we prepare all students for proficiency in mathematics, we must update our instructional practices with this new program’s implementation.

A

complete

mathematics

program

will

include

staff

development,

implementation of instructional materials, and evaluation and analysis of student progress. No mathematics adoption will be a perfect match for your district needs, so you will need to be cognizant of gaps between what your students are expected to know and what they actually learn. Additional professional development will be needed to close these gaps.

While your committee is convened, take the time to brainstorm ways the district can support the serious and expedient implementation of its new adoption. This may include aligning current systems with the new program, e.g., benchmark assessments. The success of the adoptions is measured in its strategic and purposeful execution.

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Mathematics Adoption Toolkit

FACILITATOR’S GUIDE

Mathematics Adoption Toolkit

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Mathematics Adoption Toolkit Facilitator’s Guide

Facilitator’s Guide to the Mathematics Adoption Toolkit As a facilitator you will guide the process of identifying district needs and matching them to state-adopted instructional materials. The purpose of this Toolkit is to support schools and districts in conducting a data driven adoption process that identifies a balanced instructional program for students. Balanced instruction is the use of universal access strategies to provide students with experiences in conceptual understanding, procedural fluency, and problem solving while using mathematical reasoning (Mathematics Framework for California Schools, pp. 4-5).

Data is used to analyze and identify district needs and determine priorities in choosing a new mathematics program (See: pp.17-19, 32-48). Your school/district most likely has collected and organized this data for other purposes that will facilitate an easy transfer of information. Identifying district priorities for adoption should be completed before reviewers begin examining the mathematics programs.

The Mathematics Adoption Toolkit will guide your adoption committee as it gathers evidence, and will provide a structure for informed decision making. The size and resources available to a school or district may impact the degree of use of the Toolkit. Regardless of such constraints, any utilized portion of the Toolkit will provide valuable resources to a school or district seeking an instructional program that best meets the needs of its students and teachers.

OVERVIEW OF TOOLKIT SECTIONS

This Toolkit has six sections: Developing The District Lens, Standards Sampling, Program Components, Additional Review Options, Making a Decision, and Next Steps: Implementation. All sections are organized around four topics: Mathematics Content (What do you want your students to know? – color coded red); Instructional Program (How will you make sure your students “know it”? – color coded green); Assessment (How will you know if your students “know it”? – color coded blue); and Universal Access (How will you make sure ALL students “know it”? – color coded orange).

The first section of the Toolkit involves developing a clear picture of district needs: in effect, creating a “District Lens”. To accomplish these first steps, you will need a thorough understanding of Section #1: Developing A District Lens.

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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.

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Mathematics Adoption Toolkit Adoption Process Options

Section #1 (3 hours): Developing the District Lens

Section #2 (3 - 6 hours): Standards Sampling – Partial or Full

Eliminate Programs

Section #5 (3 hours) Making a Decision

Section #3 (6 hours): Review Program Components

Eliminate Programs

Section #5 (3 hours) Making a Decision

Section #4: Additional Review Options Pilot Programs Blind Test of Lessons Survey Students Executive Committee Eliminate Programs

Mathematics Adoption Toolkit

Section #5 (3 hours) Making a Decision

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Mathematics Adoption Toolkit Facilitator’s Guide Advance Preparation The 2007 Mathematics Adoption Toolkit is organized to help you, the adoption process facilitator, and your team identify the Basic grade level, Intervention, and Algebra Readiness programs best suited to the needs of your students and teachers. The Facilitator’s Guide illustrates how working through the sections in the Toolkit can produce customized program selections tailored to meeting the needs of all students as well as providing support and instructional clarity to teachers. The intent of these tools is to create a process by which decisions can be made objectively, based on collected data and program findings.

The facilitator needs to coordinate the logistics, as well as, the process for the adoption process. The following section provides an outline of work that will help the process to run smoothly.

TASK 1.

Establish a timeline.

ACTIVITIES

MATERIALS

Consider:  When the district board needs the recommendation.  Amount of time the process will require.  Configuration of time for work – release, after-school, etc.  Scheduling meeting rooms.

 For information on the CA Department of Education’s timeline for adoption, refer to: www.cde.ca.gov/ci/cr/cf/timeline05to08adoptions.asp

2.

Identify and gather state adopted publisher materials.

Consider:  Which programs has the state approved?  How will you acquire and store the materials?  How will the committee members access the materials?

 Materials submitted for state adoption are available at the regional Learning Resource Display Centers (LRDC): www.cde.ca.gov/ci/cr/cf/lrdc.asp  Information of state processes and publisher: www.cde.ca.gov/ci/cr/cf/imagen.asp  Publisher materials and contact information: http://www.cde.ca.gov/ci/ma/im/

3.

Identify, recruit, and convene the committee.

Collaborate with district leadership to consider:  Variety of stakeholders who will actively participate: - Classroom teachers (elementary and secondary).

- EL, Special Ed. Advanced Learner teachers.

- Teachers with AB466 or SB472 training in math.

- Administrators - Parents and other community members.

 Lists and contact information for perspective members including teachers, administrators, parents, community members, higher education faculty.  Letter of invitation explaining the process and time commitment.

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4.

Collect district data to ensure match of materials to district needs.

- Members of local school board - Representatives from higher education faculty.  Grade level or course groupings.

Data sources that should be considered and organized for Section #1, District Lens are:  Student assessment data including CELDT report.  Student demographic data.  Teacher data (expertise, credential type, years in present assignment).  School configuration data.  Resources, technology, equipment, and tools in district.  Curriculum guidelines, pacing guides, or curriculum maps.

Suggestion:  Provide hardcopies of relevant data reports to create packets for participants.  Hardcopy could be inserted with the individual tasks in Section #1 as relevant.  Or, consider entering the data ahead of time into the website.

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 Data previously collected for other purposes e.g., for the science adoption  Collect data and enter onto web ahead of time or collect and print Gender: http://dq.cde.ca.gov/dataquest/ (Enrollment) http://www.jftk-ca.org http://star.cde.ca.gov/star2006/Viewreport.asp Ethnicity: http://dq.cde.ca.gov/dataquest/ (Enrollment) http://www.jftk-ca.org http://star.cde.ca.gov/star2006/Viewreport.asp Socio-Economically Disadvantaged: http://dq.cde.ca.gov/dataquest/ APIBase http://www.jftk-ca.org English Learners: http://dq.cde.ca.gov/dataquest/ CELDT http://dq.cde.ca.gov/dataquest Language Census http://www.jftk-ca.org http://star.cde.ca.gov/star2006/Viewreport.asp Students with Disabilities: http://dq.cde.ca.gov/dataquest/ SpecEd http://www.jftk-ca.org http://star.cde.ca.gov/star2006/Viewreport.asp Gifted and Talented: http://dq.cde.ca.gov/dataquest/ Enrollment http://star.cde.ca.gov/star2006/Viewreport.asp Mobility: http://dq.cde.ca.gov/dataquest/ APIBase2006 Prevalent Languages: http://dq.cde.ca.gov/dataquest Language Census CST: http://star.cde.ca.gov/star2006/Viewreport.asp http://dq.cde.ca.gov/dataquest/APIBase http://www.jftk-ca.org CELDT: http://dq.cde.ca.gov/dataquest/CELDT District Technology: http://www1.edtechprofile.org

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5.

Publish resources for committee members.

Prepare materials for committee members

1. Overview of Adoption Process a. Timeline for adoption b. List of adopted publishers c. Graphic of process 2. District data 3. How to access website 4. CA Mathematics Framework 5. CA Blueprint for STAR 6. Mathematics Released Items 7. Toolkit worksheets: print or Electronic copies 8. Contact information for committee members 9. District pacing guide, benchmark assessments and results.

A Closer Look - Section by Section The primary intent of the Toolkit is to identify District needs for both students and teachers, and provide process steps to match these needs to a mathematics program best situated to support them. Each Toolkit section represents a different phase in the decisionmaking process, comparable to how you might work through a major purchase. The process steps in the Facilitator’s Guide have been worked around the scenario of buying a car. Section #1 (District Lens) identifies needs by creating a District “lens” – a filter that articulates student needs, as well as needs of teachers. Section #2 (Standards Sampling), #3 (Program Component Review), and #4 (Additional Review Options) provide several options for analyzing and comparing programs against the priorities for adoption. Section #5 (Coming to Consensus) outlines a consensus process whereby the accumulated data from Sections #1 through #4 are used to make final decisions and a customized selection.

Section #1: Creating the District Lens Warm-Up Activity: Creating a Mindset for Process You are getting ready to purchase a new car. Before walking onto a car lot and being influenced by a creative salesperson, and well before forking over a down payment, you do your homework and create a “shopping list”. You are determined to find the “best” car for your money; a car that will meet your needs and stand the test of time and use. In doing your homework, you establish what it is you have to have in a car. Some choices are essential (e.g., 4-wheel drive if you live where it snows; or air Mathematics Adoption Toolkit

17

conditioning if you live in the desert) and other choices are optional (e.g., a moon roof, or burl wood dash accents). Yet one person’s essential choice is another’s options. It is important to know your bottom line before you encounter the pressure of the car salesperson. 

Have team members generate a list of essential car features. In a quick popcorn share-out, discuss which features are essential, which are optional, and why. Is there agreement? Any differences of options?



Relate responses to the Toolkit process step, Creating the District Lens. As with the lists just generated, essential features versus those that are optional are not uniformly agreed upon.

Consider the magnitude of the textbook purchases your District is about to make. Unlike a car that decreases in value as soon as it’s driven off the lot, the textbook program you purchase must help increase the mathematical knowledge and understanding of all students!!

While all adoptions are serious business in education, the adoption of instructional materials for mathematics may be a key factor for schools and districts challenged to meet required levels of proficiency for all students by 2014.

Summary / Outcome: Establish district needs for all students and for teachers. It is crucial time be given at the onset to create the District Lens, as all subsequent decisions should reflect a true accounting of your learner populations and teacher needs. The data should guide the work done in all process steps as well as help prioritize essential program features in the “shopping list”. These priorities become your adoption itinerary!!!

SECTION Section #1: Developing the District Lens.

Pages: 32-48

Mathematics Adoption Toolkit

ACTIVITIES

MATERIALS

Task #1:  Become familiar with Mathematics CA. Framework (balanced program and reasoning standards)  The rating bar is for individual use and not recorded on website.

Task #2:  Identify district’s progress toward meeting state expectations for mathematics instruction.

Task #3 - 7:  Use district-generated data to identify student and staff needs.

Task #8:  Identify the availability of local mathematics resources.

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

Mathematics framework, hard copy or electronic. http://www.cde.ca.gov/ci/ma/cf/index.asp

    

Worksheets – pages 32-48 For electronic templates see: http://www.ccsesa.org District data compiled and/or entered in Advance Preparation #4 (above), Local benchmark assessment and results Meeting supplies: chart paper,

Summary  Key findings – compile summary statements (ah ha’s) from committee members into a district summary chart  Use a chart to prioritize district needs for students and teachers.

District Summary Chart: Content

Assessment

Instructional Program

overheads, pens, etc.

Universal Access

Student Needs Teacher Needs  

Identify the nonnegotiable priorities. These describe the elements any adopted program must have.

This chart should be referred to before the beginning of each meeting and be the basis of all decision-making.

As facilitator with your district leaders:  Examine the other sections of the Toolkit and determine which questions best address your district needs. And which questions do not need to be addressed.  Using the website or using a Word document, you may turn off any questions that do not pertain to your district (See: Technology Support Document).

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

Section #2: Standards Sampling District strengths and areas of needs have been identified in Section #1. The team is now ready to begin narrowing the field of program choices. The process shifts toward hands-on experiences with the Teacher’s Edition (TE) to determine which programs demonstrate the most robust mathematics course of instruction to meet the needs of students and teachers. Standards Sampling will allow you to evaluate program quality, depth, and integrity as you trace a standard’s introduction, development, and assessment as it is presented in the TE. The TE is the only portion of the program to be examined at this time: the TE is often the only universally

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19

purchased program component. More often than not, the TE is the only part of the program readily available to teachers several years into an adoption.

The Instructional Materials Advisory Panels (IMAP) and the Content Review Panels (CRP) established that all adopted programs meet the minimal criteria for 1) mathematical content/alignment with standards; 2) program organization; 3) assessment; 4) universal access; and, 5) instructional planning and support. Standards Sampling creates an opportunity to evaluate a program’s TE and its treatment of 2 or 3 “big ticket” standards you deem critical to student understanding. Help the team understand that an adopted program at worse meets minimal requirements; the team’s work should focus on identifying the extent of content development. The goal here is to create a side-by-side comparison of each program’s TE materials to narrow the field to those programs that best match the needs of students and teachers. In the words of one mathematics educator, “…if the math isn’t ‘good’, then nothing else matters!’”

Comparing Specs & Data Sheets: Establishing Program Depth and Complexity Armed with your list of priorities, you continue doing homework to find the car that best matches your needs. You are ready to begin narrowing the list of possible choices by comparing vehicle specifications. You can do a side-by-side comparison of vehicle Specs & Data sheets to assess performance and efficiency features, handling and braking features, exterior and aerodynamics features, as well as interior features. How well each vehicle does against this comparison will help to narrow the field of choices before you step on to a sales lot and into a car for a test drive.

Standards Sampling Process 

Select 2 to 3 standards to sample. Be strategic in choosing which standards: -

Select a standard(s) that the data that shows students struggle with, or

-

Select a standard(s) teachers have identified as difficult to teach, or

-

Select a standard(s) that threads through several grade levels. This type of sampling allows for tracking the development of concept(s) across grades.



A sampling of three standards is optimum, but if this is not possible, 1 or 2 comprehensive samples will inform your process.

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

Using only a program’s TE, analyze how the standard is introduced, developed, reviewed, enhanced, and assessed. The needs identified by the District Lens should be used as the guiding criteria throughout every part of the analysis.

Summary/Outcome: Identify programs that show the strongest development of critical standards with the Teacher’s Edition (TE). This sampling will highlight the likelihood of a program meeting student and teacher needs. The goal is to narrow the adoption list of prospective programs that will be taken to the next level of examination. Sampling is limited to the TE as this may be the only universally purchased program component: it is often the only tool a teacher has access to several years into an adoption.

Section #2: Standards Sampling: Taking a Deeper Look at the Mathematics.

Pages: 49-57

Mathematics Adoption Toolkit

Step 1:  Identify 3 challenging standards per grade level to use in sampling.

In choosing what to sample, you will most likely choose one part of a standard. For example, choosing “division of positive fractions’ from the sixth grade standard: 2.1 “Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation”.  Brainstorm what the ideal instruction for this partial standard would be.  Review with committee the questions in Section #2 to develop common understanding of intent and meaning.  May use the folder with completed standards sampling to show how to complete forms.  Point out that there may be relevant information before and after the target lesson(s).

Step 2:  Decide which members will review which programs at which grade level.  Teachers may do this work independently, or a grade level group may work together, individually gathering evidence on their program(s) while simultaneously comparing programs with other group members. It takes about 2 hours to complete one publisher per standard.

Step 3:  Complete one set of worksheets pp. 49-57 (per standard) for each publisher  Identify where in the program this partial standard is taught. Fill in the worksheet noting where the materials the standard is addressed.

This will be important to use during discussions.

21

 Chart of District Priorities  Teacher’s edition for each program to be considered.  Standards Sampling worksheets or electronic version, word or website – each reviewer will need a separate worksheet for each standard and each program reviewed. Worksheet p. 48-56  For electronic Word templates see: http://www.ccsesa.org  Chart of worksheet, District Summary Chart to compile results of individual worksheets.  Chart paper, pens  Reference: folder of completed standards sampling for sixth grade division of fractions.  Framework, Chapter 2 Content Standards and Chapter 3, Grade Level Considerations

  

Add comments in text, + for area of strength, ? for question or concern, and then score each question: 1 = does NOT meet district need, 2 = MEETS district needs, or 3 = EXEMPLARY. A synthesis of findings for each question may add important elaborations not specifically identified in question Find the mode – the score that occurs most frequently - for each section

Step 4:  Compile modes for four topics from each reviewer on District Summary Chart for Standards Sampling p.49-57 Step 5:  Review results of compilation and consider each program in terms of the district priorities. Committee members will explain where they found evidence or why they rated the question the way they did.  Use the District Summary Chart to notice if mode is consistently strong or weak across grade levels.  Decide which programs will continue to be reviewed and which programs will be eliminated from review.

Note: At this point you may choose to move to Section #5: Making a Decision or to continue on to Section #3: Reviewing Program Components or Section #4: Options for Further Review.

Section #3: Program Components Review The list of prospective programs has been pared down to the most promising candidates. Now comes the time to conduct a deeper, more thorough investigation of each program. Section #2 Standards Sampling provided team members time to deconstruct the Teacher’s Edition (TE). The Program Components Review enables the team to conduct a deeper analysis by deconstructing all of the other remaining program components. The analysis should answer the question: “Do the materials meet the needs of our students and teachers?”

Base Model vs. Options Packages You’ve reviewed the Specs & Data Sheets. It’s time to begin exploring the available options packages. You know what the base models possess – the safety features, seating configurations, performance expectations, handling and braking standards. Now Mathematics Adoption Toolkit

22

it’s time to consider the options packages. When buying a car, the options packages can make a huge difference with features such as comfort and maneuverability.

-

Section #2 Standards Sampling explored a program’s TE: you know what the “base model” has to offer in comparison to the other programs.

-

Now it’s time to investigate the different “options packages” available in the ancillary materials that accompany the TE. You can liken the five general program categories to different aspects of the options packages:

General Program Categories

Car Analogy: Options Packages

Mathematics Content / Alignment with Standards What is the base model as listed on the Specs & Data (Standards Sampling) Sheets.

Program Organization What are the seating configurations? Does it have 2doors or 4 doors? Moveable seats? What is its cargo capacity?

Universal Access Does the program offer advice for alternative forms of transportation (walking paths, bike, bus, train, airplane, boat)?

Instructional Planning and Support Does the options package offer different fuel choices (gas, diesel, ethanol, electric, hybrid)?

Summary/Outcomes: The Program Components Review will give team members a chance to review all of the ancillary materials that accompany the TE. Each of these components must be thoroughly examined for content and usage. The goal here is to refine the list of programs to 2 or 3 very strong candidates to be considered for piloting during the next phase of the process.

Mathematics Adoption Toolkit

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Section #3: Program Component Review: Matching District Needs with Instructional Materials.

Pages: 58-77

Step 1:  Decide whether each committee member will review independently or in a group setting.  Options of: each member will review ONE program for all components, or EACH program reviewed for one component.  Direct on how committee members can access all materials for review. (check out, central location in district, LRDC, at meeting location) Step 2:  Each member keeps notes taken during process which will be used in Section #5 – Making a Decision  Complete either a print or electronic worksheet for each program scoring: 1 = does NOT meet district needs, 2 = MEETS district needs, or 3 = EXEMPLARY.  Write summary statements for each of four topics Step 3:  Facilitator collect data from committee  Scores need to be compiled  Summary statements need to be collected for District Summary Chart for Review of Program Components  Duplicate results, or if web based, tabulation is automatic, but reports will also need to be printed out for committee review.

Summary:  Committee needs to review and discuss results.  Maintain the focus on meeting the needs of students and teachers identified in the District Priorities Chart while deciding which programs need further review. Try to eliminate all but 2 or 3.

   

District Priorities Chart Complete sets of programs for teacher review Mathematics Framework CST blueprints



www.cde.ca.gov/scrpts/texis.exe/webinator/ search?query=Blueprints&submit=GO CST released items

  

www.cde.ca.gov/ta/tg/sr/css05rtq.asp Worksheets for Section #3 For electronic templates see: http://www.ccsesa.org District Summary Chart for Review of Program Components.

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

Section #4: Additional Review Options Congratulations! You have successfully narrowed the list to 2 or 3 very strong programs that best match the needs of your students and teachers. The team is ready to begin piloting programs. The pilot will allow teachers to “kick the tires” and get a feel for how the program handles.

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Taking a Test Drive Now it’s time to take the car around the block for a test drive. Does it make it up a steep hill? How does it handle on the open road? In traffic? What does the stereo system sound like at full blast (okay, maybe our students would do this)! What’s the gas mileage really like? Do all the bells and whistles work? Which bells and whistles did you use? Were they useful?

-

Find the “test drivers” for each grade level. Who will pilot? Are there additional personnel who should be included for pilot purposes (English Learner specialists, BTSA teachers and leaders, CAHSEE prep teachers, etc.)?

-

Determine the length of pilot

-

Will the test drive be a pilot or blind test? Will students be surveyed?

Summary/Outcome: Field tests of the 2 or 3 strongest programs will provide real-time information regarding implementation in the classroom. Piloting will allow teachers to reconcile the research with real-time investigations. It may be determined that additional analysis is needed with more pilots, blind testing, etc. Once recommendations are made, plans for short- and long-term professional development can be drafted.

Section #4: Additional Review Options: Piloting, Blind Test, Student Survey, Executive Committee.

Options:  Blind Test - Duplicate a similar lesson from each program and mask the name of the program.

- Teachers analyze each lesson for strengths and weaknesses



Blind Test: Copies of same lesson from each program with identification of program masked.





Pilot Programs - See CA Department of Education guidelines - Committee teachers teach lessons from Brand A for 4 weeks and then teach lessons from Brand B for 4 weeks.

Student Survey  Students in small groups review two lessons and respond to survey questions.

Teachers: 1. Lay out publisher’s materials, one set at a time.

2. Have students work individually or in small groups of 3 or 4.

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



Student materials from program(s) under consideration.



Survey questions.: Directions: Look through the student mathematics book. Review two entire lessons.

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

2. If there were pictures, graphs, diagrams, examples, were they helpful?

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

4. Rate the lesson from 1 – 5. 1 = not very good, 2 = just okay, 3 = good, 4 = really good, 5 = excellent.

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

6. Describe what you like from the lessons.

7. Describe what you didn’t like from the lessons.

3. Go over directions and survey questions with students.

4. Demonstrate how to browse through materials with an objective in mind.

5. Demonstrate the group discussion, or Grand Conversation, method of discussion where students take turns discussing the book, and answering the questions about the book.

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

Source - Dos Palos-Oro Loma Unified School District

 

(Science Adoption Toolkit p. 63) http://www.ccsesa.org.

Committee of those who reflect district’s highest priority, e.g., English Learners, or Support for New Teachers, or high school exit exam, conducts a more thorough search of possible programs for best match.

Section #5: Making a Decision At this point you have eliminated all the programs that do not meet your district criteria and you have “test driven” the two programs that come closest to meeting your district’s needs. Now it is time to identify the program that everyone on the committee can fully support.

Coming to Consensus Honor everyone’s time, effort, and energy. It’s time to get the “family” to agree on which car to purchase. Remind everyone that it’s time for the entire family (teenagers, mom, dad, grandparents) to come to agreement on which model will best meet everyone’s needs. It’s time for some negotiations between each other, as well as with the dealership.

-

Team member negotiations – review the strengths and areas of need within the district as prioritized by the District Lens.

Review the non-negotiable needs. A consensus process decision means each team member agrees they can support EITHER program A or program B, as both programs met district prioritized needs and both showed well during the pilot.

Team members must understand they have a responsibility in supporting the adoption as it is implemented throughout the district.

Mathematics Adoption Toolkit

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-

Textbook Company negotiations – can the “dealership” offer any incentives? Price might be a defining aspect to consider, as well as any deals that can be negotiated into the contract.

Summary/Outcomes: The Adoption Team comes to consensus on one program that is recommended for adoption by the district. This program has been selected based on district data and analysis and has been found to best meet the needs of students and teachers.

Section #5: Making a Decision: Coming to Consensus

1 Establish Group Norms

2 Review History of Process

3 Individual Prioritization of Programs

Mathematics Adoption Toolkit

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

Committee sitting in grade level groups will generate group norms such as:  Let everyone be heard  Assume best intentions  Be present and prepared  Base decisions on evidence collected from multiple perspectives  Select a program to meet the needs of the district’s students and teachers.  Do not comment on another’s perspective—this is what they did or did not see in light of their own personal experience Briefly discuss the process of:  Developing the district lens: Identifying needs and priorities of our students and teachers.  Identifying the priorities and criteria for investigating mathematics programs  Standards Sampling  Investigating program components  Piloting programs Each committee member reviews their notes on the evidence personally collected regarding the positives and the concerns for each program. From an individual perspective, each committee member indicates his or her current level of support for EACH program.

27

 Chart of District Priorities  Data from reviews of Section 2, 3 and 4 is summarized in a report and shared with committee members.

Chart paper to list agreed upon norms

  

Teacher’s editions of each program for reference.

Notes Straw Poll Wall Chart (below)

Straw Poll (record results on the wall chart).

5 I can support this program fully. I will champion it.

4 I strongly agree with this program 3 This material is OK with me. I am willing to go along with this choice 2 I have reservations and I am not yet ready to support this material 1 I am opposed to this set of materials Fist I veto this proposal regardless of the will of the group A reviewer could indicate 5 for both programs. Or a member could indicate a level 5 support for Brand A and level 3 for Brand B. (Some may be confused thinking they need to split the 5 between the two publishers) Target a level of support between 3 and 5. If there are fists, 1s, or 2s, concerns have not been heard well enough.

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

Straw Poll Program A 5

4

3

2

Individual Support Grade Level Consensus Across Grade Consensus - 1 Across Grade Consensus - 2

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1

Fist

Grade Level Consensus

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

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

Positive aspects of each program on a green post-it Concerns for each program on a pink post-it Grade level and publisher on each post-it.

Take a Straw Poll to see if level of support has shifted after this larger sample. Record on wall chart.

Four positive/concerns charts for each program being considered:  Mathematics Content  Instructional Program  Assessment  Universal Access.

See examples below.

Positives / Concerns Charts Prepare 4 charts (Mathematics Content, Instructional Program, Assessment, Universal Access) for each program considered: Math Content Program A

Instructional Program A

Assessment Program A

Universal Access Program A

Math Content Program B

Instructional Program B

Assessment Program B

Universal Access Program B

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Large Group Consensus

Synthesize chart information across grades moving from a grade level perspective to a K-5 or 6-8 perspective.  If any post-it comments are duplicates, put them on top of each other, so it is one comment but you can still see that this was observed by multiple grades.  Go over each chart with the whole group. Ask for additional strengths or concerns. If the group agrees that this comment goes across all grade levels, add post-its on the appropriate charts.  Discuss proportion of pink to green post-its  Take a third straw poll for each publisher now from a whole program perspective. Record on chart.  If there are any fists, 1s, or 2s for either publisher, give those members a chance to express their concerns.  Fourth and final straw poll. Record on chart.  Make a decision. It may be very clear just from the number of each color of post-its that one program has more strengths than the other, or they may have similar strengths, but one has more concerns. If both programs are equal at this point, now is the time to consider any differences, or extra items “free” with the program, or the level of professional support provided by the publisher.

If the decision is not yet clear

Options:  Prioritize the criteria on all the charts.  Which criteria is a deal breaker? How does each program rate?  What are the second most important criteria? How does each program rate?  Evaluate each program in terms of the most immediate needs of district (e.g., number of new teachers needing support).

Reconfirm commitment to program

Even though this might not have been the first choice of each individual committee member, there is consensus that this is the best program for the district.

Mathematics Adoption Toolkit

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Straw poll and Positive/Concerns charts.

Section #6: Planning forward Congratulations!! The district made a decision and your Board of Education has approved the adoption.

As you have seen, no program is complete or perfect, but because of your thorough analysis, you have selected the best program. You now need to address the needs of students and teachers beyond just selecting a textbook. It’s time to begin the planning process for successful implementation.

Now it’s time to put teachers in the driver’s seat as we develop a successful implementation plan.

Closure/summary: You’re in the driver’s seat. The journey begins.

Section #6: Next Steps: Implementation

Mathematics Adoption Toolkit

Staff Development  Committee input on staff development needs for: - Effective implementation - Assessment to notice student trends and gaps  Input on what district structures e.g., benchmark assessments, pacing guides, will need to be upgraded to be coherent with new adoption  Input from Executive Committee on how to use the program to meet high priority district needs.

31

Mathematics Adoption Toolkit

Templates for Section #1

Developing the District Lens

Mathematics Adoption Toolkit

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SECTION 1 - DEVELOPING THE DISTRICT LENS TASK #1: California’s Mathematics Expectations for Students Section 1 of the Mathematics Adoption Toolkit involves eight tasks. Each task is keyed to the four topics: Mathematics Content, Assessment, Instructional Program, and Universal Access. Task #1 is the preliminary work needed to establish the district’s strengths and area of need. The goal of Task #1 is to assess your district’s progress toward accomplishing the goals identified in the California Department of Education Mathematics Framework.

District Lens, Task #1 - MATHEMATICS CONTENT Questions to Consider 1. What is the depth of knowledge that is expected for students?

CA Mathematics Framework 2006 Students should:  develop fluency in basic computational and procedural skills, an understanding of mathematics concepts, and the ability to use mathematical reasoning to solve problems.  communicate precisely.  develop logical thinking.  make connections.  apply mathematics.  develop an appreciation for the beauty and power of mathematics.

Framework Ch. 1, pp. 2-3

District progress toward achieving student depth of mathematical knowledge:

1 Limited

2

2. What mathematical reasoning skills are students expected to know and to be able to do?

3 4 Developing

5

6

7 Successful

8

9

10 Exemplary

Students must:  Develop the habits of logical thinking.  Recognize and critically question all assumptions.

Mathematical reasoning involves:  Explaining arithmetic facts.  Solving problems and puzzles at all levels.  Understanding algorithms and formulas.  Justifying basic results in all areas of mathematics.

Framework, Ch. 3, p. 110

District progress on student’s application of mathematical reasoning skills:

1 Limited

2

Mathematics Adoption Toolkit

3 4 Developing

5

6

7 Successful

8

9

10 Exemplary

33

District Lens, Task #1 – INSTRUCTIONAL PROGRAM Questions to Consider

CA Mathematics Framework 2006

3. What are the key components of an effective mathematics program? a. Assessment b.

See Assessment Strand, page 36

Quality Instruction

In an effective mathematics program, teachers:  possess in-depth understanding of the content standards and the mathematics.  are able to select research-based instructional strategies.  effectively organize instruction.  use the results of assessment to guide instruction.  use instructional grouping options and strategies Framework Ch. 1, p. 9 District progress on quality instruction:

1 Limited

2

3

4 Developing

5

6

7 8 Successful

9

10 Exemplary

c. Maximized Instructional Time

In an effective mathematics program:  Adequate time is allocated (50 – 60 minutes).  Additional instructional time is allocated for students who are performing substantially below grade level.  Instructional time is maximized and protected from interruption.  Learning time is extended through homework.

Framework, Ch. 1, p.10 District progress on maximizing instructional time:

1 Limited

2

3

4 Developing

5

6

7 8 Successful

9

10 Exemplary

d. Instructional Resources

In an effective mathematics program, instructional resources should:  emphasize depth of coverage.  balance basic computational and procedural skills, conceptual understanding, and problem solving and stress the interdependency of all three.  provide ample opportunities for students to explain their thinking, verbally and in writing, formally and informally.  supply ideas or tools for accommodating diverse students performance within any given classroom. They offer suggestions for re-teaching a concept, providing additional practice for struggling students, or condensing instruction so that advanced students can concentrate on new material.

Framework, Ch. 1, pp. 9-11 Also: p.207, 211 and 217 District progress on instructional resources:

1 Limited

2

Mathematics Adoption Toolkit

3

4 Developing

5

6

7 8 Successful

9

10 Exemplary 34

e. Professional Development

In an effective mathematics program:  teachers receive excellent preservice training.  staff development is a long-term, planned investment.  professional development should be ongoing and focused on: - maximizing instructional time.

- raising teacher proficiency in mathematics.

- balancing the curriculum.

- expanding the understanding of student differences.

- knowing which standards provide the core mathematics foundation for all students at each grade level.

- developing strategies to help parent involvement.

Framework, Ch. 1, pp. 12-13; Ch. 8, pp. 247-251 District progress on professional development:

1 Limited

2

3

4 Developing

5

6

7 8 Successful

9

10 Exemplary

f. Administrative practices

In an effective mathematics program:  mathematics achievement is among the highest priorities.  long-term and short-term goals for the school, each grade level, and individuals are outlined clearly and reviewed frequently.  mathematics specialists are considered for teaching most or all of the mathematics classes or to coach other teachers.  instructional groups can be realigned frequently (master schedule).

Framework, Ch. 1, p. 13 District progress on administrative practices:

1 Limited

2

3

4 Developing

5

6

7 8 Successful

9

10 Exemplary

g. Community Involvement

In an effective mathematics program:  parent input is used for program planning.  materials are organized so that parents, siblings, and community members can provide extended learning experiences.  community connections are used to provide examples of how and why mathematics is important.

Framework, Ch. 1, p. 13 District progress on community involvement:

1 Limited

2

Mathematics Adoption Toolkit

3

4 Developing

5

6

7 8 Successful

9

10 Exemplary

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

4. What are the expectations for the types and uses of technology?

Types of technology include:  electronic tools  databases  programming language  simulations.

Framework, Ch. 9, pp.253-259 District progress toward making technology available for students and teachers to use:

1 Limited

2

3

4 Developing

5

6

7 8 Successful

9

10 Exemplary

District Lens, Task #1 - ASSESSMENT Questions to Consider

CA Mathematics Framework 2006

5. What are the key components of an effective assessment program?

In an effective mathematics program, assessment:  aligns with and guides instruction  measures the specific content it was designed to measure (validity)  provides information that is used to inform instruction Framework, Ch. 1, pp. 8-9

District progress toward components of an effective assessment program:

1 Limited

2

6. What are the types and uses of assessment that the district is expected to implement?

3 4 Developing

5

6

7 8 Successful

9

10 Exemplary

Regular and accurate assessment of student progress is essential. The types of assessments that are the most crucial to student achievement are:  Entry-level assessment.  Progress monitoring.  Summative evaluation.

Framework, Ch. 5, pp. 221-4

District progress toward using all types of assessments:

1 Limited

2

Mathematics Adoption Toolkit

3 4 Developing

5

6

7 8 Successful

9

10 Exemplary 36

District Lens, Task #1 – UNIVERSAL ACCESS Questions to Consider 7.

CA Mathematics Framework 2006

What are the expectations for supporting all students mastering the standards?

Procedures and processes are in place to:  assess student understanding at the start of instruction, frequently during instruction, and use results for placement and program planning  Determine skills and understandings a students already possesses, and those the student needs to learn next



Alignment of Instruction



Diagnostic Teaching, Differentiation, Grouping, Accelerating for At-Risk Students

   

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



Planning for Special Needs Students



Plan for adapting to individual needs through careful organization of resources and instruction



English Learners



Address English fluency



Advanced Learners



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

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

1 Limited

2

3 4 Developing

5

6

7 Successful

8

9

10 Exemplary

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

Mathematics Adoption Toolkit

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SECTION 1 - DEVELOPING THE DISTRICT LENS TASK #2: District’s Mathematics Expectations for Students This task examines how the District uses data to establish expectations for students, monitors achievement of students, and develops district curriculum guides to support those expectations. The goals of this task are to examine the district’s strengths and areas of need.

District Lens, Task #2 - MATHEMATICS CONTENT Questions to Consider

Current District Conditions

1. Does the District have a current curriculum guide and/or map aligned with the state’s mathematics content standards? What changes, if any, will be made to this document? If no guides/maps, what processes are being implemented to generate them?

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

3. What are the district’s expectations for preparing students for Algebra 1 and high school graduation?

District Lens, Task #2 – INSTRUCTIONAL PROGRAM Questions to Consider

Current District Conditions

4. How much instructional time is allotted to implement district expectations in mathematics?

5. How are teachers and/or grade level teams implementing the guide and/or map?

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

Mathematics Adoption Toolkit

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SECTION 1 - DEVELOPING THE DISTRICT LENS TASK #3: District Needs for Student Population This task examines how the District uses data to establish particular needs of specific student populations. The goals of this task are to examine the district’s strengths and areas of need.

District Lens, Task #3 – MATHEMATICS CONTENT Questions to Consider 1.

Current District Conditions

Analyze the unique mathematics needs of the following populations?

How will you match their needs with the newly adopted materials?

a. Gender

b. Ethnicity

c. Socio-economically Disadvantaged

d. English Learner

e. Students with Disabilities

f. Gifted and Talented

g. Other

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District Lens, Task #3 – UNIVERSAL ACCESS Questions to Consider

Current District Conditions

2. What is the student mobility rate and how might it impact student achievement in mathematics?

3. What are the most prevalent languages represented? Will your math textbook adoption consider primary language support as an essential component?

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

Mathematics Adoption Toolkit

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SECTION 1 - DEVELOPING THE DISTRICT LENS TASK #4: State and District Data Related to Mathematics This task examines how the District uses state data and district assessment programs to identify achievement of particular student populations.

District Lens, Task #4 – ASSESSMENT Questions to Consider

Current District Conditions

1. CST: What pattern of strengths and weaknesses does the CST assessment data reveal? Is this trend consistent over the course of a single year and/or multiple years?

2. Do district benchmark assessments validate these findings?

3. Looking are the numbers and percentages of students who are advanced and proficient, how do we meet their needs? What should we do to support their learning?

4. Looking at the numbers and percentages of students in strategic (Basic to Below Basic) or intensive (Below Basic to Far Below Basic) programs, how do we meet their needs?

What should we do to support their learning?

5. Does the data indicate student deficiency in reading skills that might impact mathematics instruction and overall student achievement?

6. CELDT: English Learners a. Looking at numbers and percentage of students are at each level of the California English Language Development Test (CELDT), how do we meet their needs? What should we do to support their learning? b. In what strands do EL students excel? Struggle?

Mathematics Adoption Toolkit

Areas of strength:

Areas of struggle:

41

7. Does the district use progress monitoring to guide teacher instruction and summative assessments to validate student mastery of mathematics concepts and skills? Are these assessments teacher generated or does the district rely on publisher resources? Will they be updated or replaced by this adoption process?

8. What types of assessments are commonly used in the classroom? Are these assessments teacher-generated or does the teacher rely on publisher resources?

9. What other district programs address student needs for remediation or acceleration?

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

Mathematics Adoption Toolkit

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SECTION 1 - DEVELOPING THE DISTRICT LENS TASK #5: District Learning Configuration The goal of this section is to examine the district’s strengths and areas of need. This task is to look at your district’s structures that impact mathematics instruction.

District Lens, Task #5 – INSTRUCTIONAL PROGRAM Questions to Consider

Current District Conditions

Task # 1. What special needs must be considered for the different school configurations in the district (e.g., K-8, K-5 or K-6, 6-8 or 7-8, selfcontained, combination classes, departmentalized, houses, etc.)?

2. What are the implications for textbook selection for schools within the district that are being monitored by state and/or federal school improvement initiatives?

District Lens, Task #5 – UNIVERSAL ACCESS Questions to Consider 3. How will you plan for differentiation of instruction with the newly adopted materials for schools within the district with a high concentration of special education students, English learners, or advanced learners?

Current District Conditions Special education students:

English learners:

Advanced learners:

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

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SECTION 1 - DEVELOPING THE DISTRICT LENS TASK #6: District Needs for Teachers The goal of this section is to examine the district’s strengths and areas of need. This task is to consider the long-range professional development needs of district teachers.

District Lens, Task #6 – MATHEMATICS CONTENT Questions to Consider

Current District Conditions

1. How will you provide mathematics content training for teachers to become more knowledgeable of the mathematics they teach and the ways to teach?

2. What mathematics guidance do new teachers receive from the district or from a BTSA support provider?

District Lens, Task #6 – INSTRUCTIONAL PROGRAM Questions to Consider

Current District Conditions

3. How will your long term professional development plans accommodate teachers who move from one grade level to another?

4. Does the district/site have math coaches? If not, what actions and resources are needed to institute coaching for the newly adopted math textbooks?

5. What types of on-going mathematics professional development (e.g., SB 472, coaching, differentiation, lesson study) does the district provide? If none, what actions and resources are needed to implement ongoing staff development?

6. What non-district professional development opportunities are available for teachers?

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District Lens, Task #6 – UNIVERSAL ACCESS Questions to Consider

Current District Conditions

7. How will you support new teachers with professional development after your math textbook adoption? Will the support of veteran teachers look much different than that of new teachers?

8. How will your long term professional development plans accommodate teachers who move from one grade level to another?

9. Does the district/site have math coaches? If not, what actions and resources are needed to institute coaching for the newly adopted math textbooks?

10. What types of on-going mathematics professional development (e.g., SB 472, coaching, differentiation, lesson study) does the district provide? If none, what actions and resources are needed to implement ongoing staff development?

11. What non-district professional development opportunities are available for teachers?

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

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SECTION 1 - DEVELOPING THE DISTRICT LENS TASK #7: District Current Instructional Resources This task examines the instructional resources available to support the implementation of the mathematics program. The goal of this section is to examine the district’s strengths and areas of need.

District Lens, Task #7 – INSTRUCTIONAL PROGRAM Questions to Consider

Current District Conditions

1. What is the district philosophy on the use of instructional resources (ancillary materials, manipulatives, tools, and technology) to support mathematics? Will this be an important consideration in the adoption process?

2. To what extent are ancillary materials, manipulatives, and tools being used to develop conceptual understanding?

3. What professional development is available on the effective use of these materials? Will this be an important consideration in the adoption process?

4. What kinds of technology hardware and software are in place to support the mathematics program? What is the compatibility with the computer platforms in the district?

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

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SECTION 1: DEVELOPING THE DISTRICT LENS TASK #8: Resources to Support Mathematics This task examines community resources available to support the mathematics program. The goal of this section is to examine the district’s strengths and areas of need.

District Lens, Task #8 – UNIVERSAL ACCESS Questions to Consider

Current District Conditions

1. What local informal mathematics learning opportunities can supplement the instructional materials?

2. Will supplemental service providers utilize the instructional materials?

3. Are district mathematics volunteers using the instructional materials along with the teachers?

4. What student events, programs, or parent education opportunities does the district provide to extend mathematics learning?

5. What organizations in the community sponsor student events promoting mathematics?

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

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DISTRICT SUMMARY CHART District Lens: Needs of Students and Teachers

Task #1

Task #2

Task #3

Task #4

Task #5

Task #6

Task #7

Task #8

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Mathematics Adoption Toolkit

Templates for Section #2

Standards Sampling

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SECTION 2: STANDARDS SAMPLING California Content Standards for Mathematics In an effective and well-designed mathematics program, students move steadily from what they already know to a mastery of skills, knowledge, and understanding. Students progress from an ability to explain, and then justify their thinking to being able to derive formal proofs.

Framework, Ch. 1, pp. 8-13 This activity is to do a side-by-side comparison of standards development to determine which materials best meet the learning needs of your students. The sampling of three standards provides a good indicator of match. In conducting the sampling, refer to the District Chart of Needs for Students and Teachers.

1. Choose three standards important to the success of student mathematical achievement. Since most standards include multiple concepts, choose just one concept as you focus for sampling. In elementary grades, sample standards might include a standard from Number Sense critical to subsequent mathematics understandings, another standard from Measurement and Geometry showing a high number of items on the CST blueprint, and a third standard from Algebra and Functions.

2. For each selected standard, complete the Sampling survey for each textbook program reviewed. You will need one survey form per standard, per program for each committee/group conducting the review.

3. Use the table of contents, index, pacing guide, and/or standards map to find all places in the program where the identified standard is presented. Note the location and page reference (e.g., Teacher Edition p. 210; Student Edition p. 210; Language Supplement p. 48).

4. As you gather evidence take notes and mark whether it is evidence of strength “+” or concern “?”.

Answer each questions outlined below. Assign points to each element using the following rubric: 1 = Does not meet district needs

2 = Meets district needs

3 = Exemplary

5. Compare the results of this analysis to determine which programs meet the district needs well enough to merit further review and which materials no not merit further review.

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STANDARD SAMPLING of California Mathematics Content Standards Program Title and Publisher:

Program Type: CORE INTERVENTION ALGEBRA READINESS

Content Standard(s): Grade

Strand

Number

Standard

Program Component(s): Page number and component where standard instruction and support are found (e.g., ELD p. 278).

Teacher Edition: Student Edition: Supplement(s): Technology: Other:

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

2. How well does “Teacher Background” prepare a new teacher or a teacher new to the grade level to:  Present the concept?  Build procedural fluency?  Build mathematical reasoning?  Make connections between conceptual understanding, procedural fluency, problem solving, and mathematical reasoning?

3. What suggestions are provided to prevent or correct the development of misconceptions as students learn?

4. How does the program support the teacher in facilitating mathematical discourse about this concept?

Mode:

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Score

MATHEMATICS CONTENT

+ Strength ? Concern

Score: 1 = Does NOT meet district needs 2 = Meets district needs 3 = Exemplary

Section 2 – Standard Sampling

1 = Does NOT meet district needs 2 = Meets district needs 3 = Exemplary

INSTRUCTIONAL PROGRAM Evidence: 1. When the concept is first introduced, what connections are made to students’ lives and prior knowledge?

2. What materials are available to help with the learning of vocabulary essential to understanding this standard:  Definitions with visuals and examples?  Pronunciations?  Words used in context and in sentences?  Suggestions for teaching and practicing both academic language (prove, analyze) and content vocabulary (denominator, divide)?

3. How well do the different types of student work support:  Developing conceptual understanding? Is there evidence of a progression from concrete to pictorial to more abstract means of learning concepts?  Learning and practicing the necessary skills and procedures? Is there evidence of developing skills in the context of problem solving and investigations?  Developing mathematical reasoning?  Applying their understanding to solve problems?

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Score

Score:

+ Strength ? Concern

Section 2 – Standard Sampling

4. What kinds of practice of the standard are there for students to: 

Immediately practice the skill or concept?



Revisit and apply what has been learned later in the program?



Revisit and apply what has been learned in a different context (e.g., area model to practice multiplication, metric measurement to practice computation with decimals)?

Evidence:

5. How does technology support a balanced curriculum of this standard for:  Conceptual understanding?  Skills and procedures?  Mathematical reasoning?  Applying their understanding to solve problems?

6. Are the technology-based activities engaging for students?

Mode:

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Score: 1 = Does NOT meet district needs 2 = Meets district needs 3 = Exemplary

ASSESSMENT Evidence: 1.

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

2.

How well do the progress monitoring assessments inform instruction of this concept (e.g., distracters in the multiple choice items provide information on student understanding and/or misconceptions)?

3.

How well do the assessments adequately assess student procedural knowledge, conceptual understanding, and mathematical reasoning?

Mode:

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Score

+ Strength ? Concern

Section 2 – Standard Sampling

1 = Does NOT meet district needs 2 = Meets district needs 3 = Exemplary

UNIVERSAL ACCESS Evidence: 1. What support is provided for English Language Learners (e.g., visual aides, advanced or graphic organizers such as word webs or concept maps, manipulatives, reference charts, word walls, etc.)?

2. What support is provided for Special Education students (e.g., modified or alternative tasks, advanced graphic organizers, tactile or auditory support, etc.)?

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

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

Mode:

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Score

Score:

+ Strength ? Concern

Section 2 – Standard Sampling

Program Title and Publisher:

DISTRICT SUMMARY CHART Standards Sampling Summary for Section #2

1 = Does not meet district needs 2 = Meets district needs 3 = Exemplary



Kindergarten Content Standard(s):



First Grade Content Standard(s):



Second Grade Content Standard(s):



Third Grade Content Standard(s):



Fourth Grade Content Standard(s):



Fifth Grade Content Standard(s):



Sixth Grade Content Standard(s):



Seventh Grade Content Standard(s):



Eighth Grade Content Standard(s):

Mathematics Instructional Content Program

Assessment

Universal Access

Mode:

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Mathematics Adoption Toolkit

Templates for Section #3

Reviewing Program Components

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Section 3 - Program Component Review MATHEMATICS CONTENT

MATHEMATICS CONTENT Based on school / district needs:

1. In this unit, are the standards addressed comprehensively leading students to mastery?  The standards are clearly identified in each lesson/unit of study.  The lesson/unit identifies the skills, the concepts, and opportunity to problem solve.  The outcomes and standards-based objectives are identified and logically sequenced with key standards revisited over time.  The standards are addressed in a manner that will support students in becoming adept at problem solving. 

Summary statements:

Score: 2. Is the key mathematics vocabulary adequately identified and addressed?  The essential vocabulary in the instructional material is clearly aligned with the vocabulary in the standards and framework.  Instructional strategies are provided to create opportunities for students to use mathematical vocabulary with a focus on precision.  The definitions are easy for students to understand. Materials use cognates, real life examples, realia, posters, etc. to support student use of vocabulary.  The vocabulary words are referenced within the text: glossary with a pronunciation guide, within the index, used in a sentence, and includes a visual representation. 

Summary statements:

Score:

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3= EXEMPLARY

1 = Does NOT meet needs

Section 3, Program Component Review:

2 =MEETS needs

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

Based on school / district needs:

3= EXEMPLARY

MATHEMATICS CONTENT

2 =MEETS needs

1 = Does NOT meet needs

Section 3, Program Component Review:

3. Are the mathematics reasoning standards addressed so that students can both master them as individual strategies and apply them to their mathematics content standards?  The mathematical reasoning standards needed in this lesson/unit are directly addressed in a variety of problem situations.  Students make decisions about how to approach problems.  Students use strategies, concepts, and skills in finding solutions.  Students determine if a solution is complete and move beyond a particular problem by generalizing to other situations. 

Summary statements:

Score:

4. Do the charts, graphs, diagrams, pictures and so forth appropriately and adequately support the teaching of the identified standards?  The lesson/unit asks students to read, interpret, and create diagrams, charts, and graphs.  The charts, graphs, diagrams, and so forth adequately support student understanding of content standards. 

Summary statements:

Score:

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Based on school / district needs:

5. Are connections delineated between grade-level mathematical strands?  Connections are made to prior learning in the development of the standard(s).  Content is structured to provide opportunities to apply mathematics in authentic contexts. 

Summary statements:

Score: 6. Does the teacher’s edition provide adequate, adult-level background information (concepts and examples) to equip the teacher to teach the standard?  Clear and complete adult-level explanations of the concepts, principles, and theories are provided to refresh or enhance knowledge of the topic.  Instructional material provides additional resources for further background information.  Alternative algorithms from other cultures and why they work are included. 

Summary statements:

Score:

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3= EXEMPLARY

MATHEMATICS CONTENT

2 =MEETS needs

1 = Does NOT meet needs

Section 3, Program Component Review:

Program Title & Publisher:

Program Component Review:

Total Score:

MATHEMATICS CONTENT INDIVIDUAL SUMMARY STATEMENTS FOR MATHEMATICS CONTENT:

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Section 3 - Program Component Review INSTRUCTIONAL PROGRAM

INSTRUCTIONAL PROGRAM

3= EXEMPLARY

1 = Does NOT meet needs

Section 3, Program Component Review:

2 = MEETS needs

This section examines the publisher’s presentation of mathematics content in light of identified district needs. The goal is to determine if the program will adequately support the learning of procedural skills, conceptual understanding, and problem solving in becoming proficient in mathematics.

Based on district/school needs: 1. Does the material present the content in multiple ways to promote student understanding of the standards?  Instructional material includes opportunities for students to receive direct instruction and guided practice.  Instructional material provides multiple opportunities for students to engage in mathematical reasoning.  Instructional material includes activities/tools for the development of precise mathematical language. 

Comments/Commendations:

Score: 2. Do the activities and problems promote student understanding of the standards and all their components?  Activities and problems are directly aligned to standards.  Activities and problems build on prior learning.  Activities and problems form a basis for subsequent learning.  Activities and problems promote mathematical reasoning.  Activities and problems include progress monitoring and summative assessments requiring students to demonstrate mastery of the standards. 

Comments/Commendations:

Score:

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3= EXEMPLARY

INSTRUCTIONAL PROGRAM

2 = MEETS needs

1 = Does NOT meet needs

Section 3, Program Component Review:

Based on district/school needs: 3. Does your school have adequate materials, tools, and manipulatives to support the activities and strategies presented?  Materials are easily accessible and support the activities and instructional strategies presented.  Materials needed are appropriate to reinforce conceptual understanding, procedures, and problem solving. 

Comments/Commendations:

Score: 4. Are there sufficient instructional strategies and resources to meet the identified needs of all of students (e.g., diverse learners, struggling students, and advanced learners)?  Instructional strategies and resources address the needs of English Learners.  Instructional strategies and resources provide multiple entry points for students with limited reading or comprehension skills.  Instructional strategies and resources include accommodations for students with an Individualized Education Program (IEP).  Instructional strategies and resources include “extended activities” to reinforce/enrich the learning for all students (e.g., writing activities, structured cooperative grouping, class discussion, inquiry activities, materials for independent study, practice, and review).  Instructional strategies and resources include activities that connect content to real-life application.  Curriculum guides delineate how content can be organized to deliver a balanced mathematics program. 

Comments/Commendations:

Score:

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INSTRUCTIONAL PROGRAM Based on district/school needs: 5.

3= EXEMPLARY

1 = Does NOT meet needs 2 = MEETS needs

Section 3, Program Component Review:

Are there opportunities for students to make connections in the unit of study?  Connections are made between mathematical strands.  Connections are made to prior learning during instruction, including suggestions for reaching students who are functioning below grade level.  Application of the mathematics is made within authentic contexts.



Comments/Commendations:

Score: 6. Is there support to help teachers identify unit design and instructional strategies for content development and student mastery of concepts?

Within the lesson and/or unit:  Standards are designated.  Specific outcomes and standards based objectives are stated.  Appropriate progress monitoring & summative assessments are included.  A sufficient number of activities that support student mastery of the learning objectives are included.  Clear, concise daily lesson plans, with appropriate pacing, are included.  Wide ranges of differentiated instructional strategies are included.  A wide range of recommended instructional strategies for instructional intervention are included i.e., alternative algorithms, structured cooperative groupings, writing, mathematical discussions, etc.  Research-based instructional strategies for the development of academic language specific to the needs of mathematics (e.g., Frayer Model, Direct Vocabulary Instruction, Graphic Organizers, Concept Wheel, etc.). 

Comments/Commendations:

Score:

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Based on district/school needs: 7. Does the material provide time options and pacing guides for instruction with focus on key standards (see CST Blueprints)?

3= EXEMPLARY

INSTRUCTIONAL PROGRAM

2 = MEETS needs

1 = Does NOT meet needs

Section 3, Program Component Review:

 Materials included in each instructional lesson/unit contain an appropriate pacing guide that allows for student mastery of the standards.  Ancillary teaching materials contain appropriate, alternative pacing guides that accommodate limited instructional time.  Materials offer suggestions for prioritizing standards when time to teach mathematics is limited.  Materials offer several suggestions for pacing to accommodate a variety of student needs as well as school / district schedules. 

Comments/Commendations:

Score: 8. Does the teacher’s edition offer sufficient suggestions for presenting the material effectively to all learners?  Ancillary teaching materials contain numerous research-based instructional strategies to accommodate a diverse student population (e.g., English Learners, Advanced Learners/Gifted and Talented Students, Students with Disabilities, and so forth).  Ancillary teaching materials contain suggestions for integrating other content disciplines (e.g., English/Language Arts, Science, Art, Music) into instructional units. 

Comments/Commendations:

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Program Title & Publisher:

Program Component Review:

Total Score:

INSTRUCTIONAL PROGRAM

INDIVIDUAL SUMMARY STATEMENTS FOR INSTRUCTIONAL PROGRAM:

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Section 3 - Program Component Review ASSESSMENT

ASSESSMENT

Based on district/school needs: 1. Do the materials offer multiple measures to assess student mastery of the content mathematical reasoning standards?  High quality multiple-choice items, formatted like state assessment items, are provided.  Various types of assessments, such as multiple-choice, short-answer, essay, project options, portfolio use, and open-ended types, are provided and mirror instructional strategies in the program.  Assessments measure mathematical reasoning.  Performance assessments with scoring guides are provided to assess mathematical reasoning.  Comments/Commendations:

Score: 2. Do the materials provide assessments that diagnostically measure the extent of students’ existing knowledge and skills (entry-level or pre-instructional assessment)?  Specific and various types of entry-level assessments are included in the materials and reflect balance as defined by the mathematics framework.  Entry-level assessments provide useful information for planning instruction.

- Pre-assessing prerequisite skills - Pre-assessing upcoming chapter content  Entry-level assessments include mathematical reasoning as well as content. 

Comments/Commendations:

Score:

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3= EXEMPLARY

1 = Does NOT meet needs

Section 3, Program Component Review:

2 = MEETS needs

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

Based on district/school needs:

3= EXEMPLARY

ASSESSMENT

2 = MEETS needs

1 = Does NOT meet needs

Section 3, Program Component Review:

3. Do the materials provide assessments that measure the progress of students toward mastery of the content standards and mathematical reasoning standards?  There are a variety of progress-monitoring assessments that measure student progress and reflect a balanced mathematics program.  Varied progress monitoring assessments are available to support daily instruction.  The assessments include opportunities for students to monitor their own progress. 

Comments/Commendations:

Score: 4.

Do the materials provide assessments that accurately measure student mastery of the standards after the completion of a unit of instruction (summative assessments)?  The summative assessments are correlated to specific mathematics content and content standards and reflect a balanced mathematics program.  Varied summative assessments are available to measure student mastery of mathematical content and content standards.  The assessments measure mastery of mathematical reasoning standards.

 Comments/Commendations:

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Based on district/school needs: 5. Do the assessments provide the information teachers need to make instructional decisions?





The assessments provide sufficient information to ascertain student misconceptions.



The assessments provide sufficient information to determine appropriate interventions and/or remediation to meet students’ needs.



A variety of assessments, including those that are not language dependent, provide specific information regarding the progress and needs of English Learners.



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



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

3= EXEMPLAR Y

ASSESSMENT

2 = MEETS needs

1 = Does NO meet needs

Section 3, Program Component Review:

Comments/Commendations:

Score: 6. Are adequate resources (for example, answer keys, student response sheets, scoring guides, and so forth) provided to accurately evaluate and score student responses on all assessments?  The answer keys provide explanations as well as specific answers for the various assessments.  The materials provide test generator software in a user-friendly format.  The assessments include scoring guides, and other formats to evaluate and/or score student responses. 

Comments/Commendations:

Score:

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Program Title & Publisher:

Program Component Review:

Total Score:

ASSESSMENT

INDIVIDUAL SUMMARY STATEMENTS FOR ASSESSMENT:

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UNIVERSAL ACCESS

UNIVERSAL ACCESS

Based on district/school needs: 1. What help is provided to identify specific errors and misconceptions in student learning?  Resources that help teachers identify and clarify common misunderstandings for each standard are included along with suggestions for addressing these issues.  The assessments provide a means for teachers to identify errors and misconceptions in student learning.  Resources are included to help teachers clarify exactly what part of each standard students do and do not understand (i.e., cross references to support materials).  Comments/Commendations:

Score: 2. What help is provided to identify the underlying reasons for student errors and misunderstandings?  Resources to distinguish between English Learners’ challenges with language or with content.  Resources to help distinguish between academic language deficiencies and content issues.  Strategies help teachers in the teaching of reading for mathematical content.  Activities and investigations promote mathematical reasoning.  Activities include progress monitoring and summative assessments requiring students to demonstrate mastery of the standard(s).  Comments/Commendations:

Score:

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3= EXEMPLARY

1 = Does NOT meet needs

Section 3, Program Component Review:

2 = MEETS needs

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

3= EXEMPLARY

UNIVERSAL ACCESS

2 = MEETS needs

1 = Does NOT meet needs

Section 3, Program Component Review:

Based on district/school needs: 3. Does your school have adequate materials, tools, and manipulatives to support the activities and strategies presented?  Materials including tools and manipulatives are easily accessible and support the activities and instructional strategies presented.  Materials needed are appropriate to reinforce conceptual understanding, procedures, and problem solving.  Comments/Commendations:

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

Instructional strategies and resources:  Provide effective and equitable opportunities for English Learners by addressing: speaking, listening, reading, and writing.  Provide multiple entry points for students with limited reading, comprehension, and/or language skills.  Include accommodations for students with disabilities in order to address their Individualized Education Program (IEP).  Include “extended activities” to reinforce/enrich the learning for all students.  Include activities that are engaging and relevant to students’ lives.  Include variety of quality materials for independent study, practice, and review.  Include curriculum guides that make connections helping to deliver a balanced mathematics program.  Comments/Commendations:

Score:

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Based on district/school needs: 5. Are there opportunities for students to make connections in the unit of study?  There are opportunities to make connections between mathematical strands.  There are opportunities to make connections to prior learning during instruction, including suggestions for reaching students who are functioning below grade level.  There are opportunities to apply mathematics in authentic contexts.  Comments/Commendations:

Score: 6. Is there support to help teachers identify unit design and instructional strategies for content development and student mastery of concepts within the unit? Include:  Standards are designated.  Specific outcomes and standards based objectives are stated.  Appropriate progress monitoring assessment and summative assessments are not only language dependent.  A sufficient number of appropriate activities that support student mastery.  Clear, concise daily lesson plans, with appropriate pacing,  A wide range of research-based differentiated instructional strategies with questions that focus on higher-level thinking, intentional instruction of academic language, structured cooperative groupings, etc.  A wide range of instructional strategies for intervention based on need.  Research-based instructional strategies for the development of academic language specific to the needs of mathematics are included within the instructional unit (for example, Frayer Model, Direct Vocabulary Instruction, Graphic Organizer, Concept Wheel, Semantic Word Map, etc.)  Comments/Commendations:

Score:

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3= EXEMPLARY

UNIVERSAL ACCESS

2 = MEETS needs

1 = Does NOT meet needs

Section 3, Program Component Review:

Based on district/school needs:

3= EXEMPLARY

UNIVERSAL ACCESS

2 = MEETS needs

1 = Does NOT meet needs

Section 3, Program Component Review:

7. Does the material provide time options and pacing guides for instruction?  Materials included in each instructional unit contain an appropriate pacing guide that allows for individual student mastery of the standards.  Ancillary teaching materials contain appropriate, alternative pacing guides that accommodate the additional time required for strategic and intensive students.  Materials offer suggestions for prioritizing key standards in order to teach procedures, concepts, and problem solving.  Comments/Commendations:

Score: 8.

Does the teacher’s edition offer sufficient suggestions for presenting the material successfully to all learners?  Ancillary teaching materials contain numerous research-based instructional strategies for universal access to accommodate a diverse student population (i.e., English Learners, Advanced Learners / Gifted and Talented Students, Students with Disabilities, etc.).  Ancillary teaching materials contain numerous strategies for integrating other content disciplines (i.e., English/Language Arts, Science, Music and Art) into instructional units in an effort to meet the needs of students.

 Comments/Commendations:

Score:

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Program Title:

PROGRAM COMPONENT REVIEW:

Total Score:

UNIVERSAL ACCESS INDIVIDUAL SUMMARY STATEMENTS FOR UNIVERSAL ACCESS:

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DISTRICT SUMMARY CHART REVIEW OF PROGRAM COMPONENTS Program Title & Publisher:

Total Score:

SUMMARY STATEMENTS FOR SECTION #3:

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Glossary of Terms Academic Vocabulary Development Language used in formal contexts for academic subjects. It is language that is connected to literacy and academics including the use of technical and academic terms.

Academic Performance Index (API) State legislation established the Academic Performance Index (API), which summarizes a school's academic performance and progress on statewide assessments. The API is used also as an additional indicator for federal Adequate Yearly Progress (AYP) requirements.

Academic Yearly Performance (AYP) The federal No Child Left Behind (NCLB) Act of 2001 requires all schools and districts to measure academic success according to how well the school and district meets common performance targets. This determines whether or not each public school and LEA is making Adequate Yearly Progress (AYP).

Assessment An orderly process of gathering, analyzing, interpreting, and reporting student performance.

Benchmark A common goal all students should reach. A common performance task using identical protocols that are given to groups of students for comparative purposes.

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

Cognitive skills Cognitive skills are any mental skills that are used in the process of acquiring knowledge; these skills include reasoning, perception, and intuition. Any effort on the part of the teacher or the instructional materials to help students process information in meaningful ways and become independent learners.

Concept Maps A technique for representing knowledge in graphs.

Curriculum Mapping A procedure for collecting data referenced directly to the calendar about the operational curriculum in a school or district.

Curriculum Guides Guides for curriculum connecting state standards to classroom instruction.

Differentiated Instruction Differentiated Instruction is a teaching theory based on the premise that instructional approaches should vary and be adapted to individual and diverse students. The intent of differentiating instruction is to maximize each student’s growth and individual success by meeting each student where he or she is, and assisting in the learning process.

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

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

District Profile Data gathered by a school district showing information about teacher and learner needs, state testing, resources and materials unique to that district.

English Learners Students who are learning English as a second or additional language.

Entry-Level Assessment Assessment measuring the extent of students’ existing knowledge and skills; helps teachers determine the content that needs to be reviewed.

Evaluation The process of judging achievement and growth of student learning by interpreting assessment data.

Extended Activities Learning activities that extend beyond the lesson.

Guided Practice Teacher supports the practice of a new concept with students. Part of the direct instruction model.

Individualized Education Program (IEP) An Individualized Education Program (IEP) describes the special education and related services specifically designed to meet the unique educational needs of a student with a disability.

Inquiry Process of gaining information through questioning techniques and use of a variety of instructional methods (such as, hands-on exploration or an investigation Intervention Stepping in to prevent failure in student academic progress.

Mathematics Framework The Mathematics Framework is the blueprint for mathematics curriculum, instruction, professional development, assessment, and instructional materials in California. The framework outlines the implementation of the mathematics content and provides guidance for mathematics instruction in elementary, middle, and high schools.

Misconceptions Beliefs of students based on incorrect understanding or knowledge of mathematics concepts.

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Multiple Measures Different types of assessments, for example, informal observations, portfolios, mathematics notebooks, student tests, end-of-unit tests.

Pacing Guides Recommended time frames for instructional delivery.

Pedagogy The art or science of teaching. The discipline that focuses on how to structure material for promoting the learning of students.

Progress Monitoring Assessment Strategies and tools to assess students in various ways during a specific unit while students are doing a variety of activities.

Student monitoring system: Any point during the unit a teacher will have fairly accurate information as to the level of knowledge, skills, and achievement for each student.

Assessment measuring the extent to which students have mastered (or are mastering) mathematics content sufficiently to move forward in the logical progression of instruction.

Remediation Strategies Instruction that is designed to correct an area of deficiency for a student.

Scaffolding Adult/teacher support for learning and student performance of instructional tasks. Scaffolding can be removed, as learners are able to demonstrate behaviors on their own.

Scope and Sequence Documents that provide guidance on how the essential understandings, knowledge, skills, processes and standards may be introduced to students in a logical, sequential, and meaningful manner.

Stakeholder Any persons or organizations that have a vested interest in the educational system.

Students with Disabilities Students evaluated according to state and federal regulations as having mental retardation, a hearing impairment (including deafness), a speech or language impairment, a visual impairment (including blindness), an emotional disturbance, an orthopedic impairment, autism, traumatic brain injury, an other health impairment, a specific learning disability, deaf-blindness, or multiple disabilities, and who needs special education and related services.

Summative Assessment The final collection, analysis and reporting of information about student achievement at the end of a given time frame.

Teacher Ancillaries Extra resource materials that support state-adopted textbook programs.

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

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