April 3, 2006

Dear Publishers of Kindergarten Through Grade Eight Mathematics Instructional
Materials:
##### 2007 MATHEMATICS PRIMARY ADOPTION

PUBLISHER QUESTIONS AND ANSWERS

(PUBLISHER BULLETIN 2006-01)

###### Criterion Category 1: Mathematics content/alignment with the standards

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###### Criterion Category 2: Program organization

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###### Criterion Category 3: Assessment

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###### Criterion Category 5: Instructional planning and support

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###### Algebra Readiness Programs

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###### Intervention Programs

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###### Other Adoption Processes/Procedures

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PUBLISHER QUESTIONS AND ANSWERS

(PUBLISHER BULLETIN 2006-01)

A publisher briefing for the 2007 Mathematics Primary Adoption, kindergarten through grade eight, was held on November 8, 2005. At that briefing, Curriculum Commissioners and California Department of Education staff provided an overview of the Mathematics Framework and “Criteria for Evaluating Instructional Materials.” Several questions were collected prior to or during the briefing. This document responds to those questions.

The following questions and answers relate to the instructional materials evaluation criteria for the 2007 Mathematics Adoption and are organized around these topics:

- Five criterion categories in Chapter 10, “Criteria for Evaluating Mathematics Instructional Materials,” of the Mathematics Framework
- Algebra Readiness programs
- Mathematics Intervention programs
- Other Adoption processes/procedures

Is there any expectation that data analysis or probability topics should appear in Algebra 1 course material?

The only standards required for an Algebra I program are the California mathematics standards for Algebra I. Category 1, criterion 2, states “programs support comprehensive teaching of the California Mathematics Standards…as detailed, discussed and prioritized” in Chapters 2 and 3 of the Mathematics Framework. These are the only standards required for an Algebra I program; however, some seventh grade standards may be included as appropriate for review purposes.

For Category 1, criterion 5, are there specific standards identified at each course level that are targeted for the requirement that "a foundation for mastery of later standards must be built"?

Chapter 3, “Grade-Level Considerations,” in the Mathematics Framework provides guidance on developing a foundation for the mastery of later standards. Refer to the sections of the chapter that address the Key Standards, Elaboration, and Grade-Level Accomplishments.

Is there a model for publishers to refer to concerning placement of California standards on the student page?

The publisher has flexibility regarding placement of the standards in its program; however, the full text of all of the standards must be present where the student can see them in the materials. Standards must be included for material in grades four through eight and may be included for material for kindergarten through grade three.

Category 2, criterion 6, states, “For grades four through eight, the relevant grade-level standards must be explicitly stated in both the teachers’ and the students’ editions.”

How will the validity and reliability of assessment measures be judged? Must all assessments be reliable and valid content?

Programs must include assessments with valid content that measure student progress. Valid and reliable assessments provide useful assessment data to help guide decisions about instructional practices.

Category 3, criterion 4, states: “Assessments, such as lesson quizzes and chapter and unit tests, which have valid content and measure individual student progress both at regular intervals and at strategic points of instruction, are provided. The assessments are based on research and are designed to:

- Measure each student’s skills and knowledge.
- Monitor students’ progress toward meeting the standards.
- Provide summative evaluations of individual student achievement.
- Identify students who are not making reasonable progress.
- Monitor students’ conceptual understanding, use of basic skills and procedures, and

problem-solving ability. - Monitor students’ reasoning, from informal explanations to formal proofs.
- Provide multiple methods of assessing what students know and are able to do.
- Help the teacher determine the effectiveness of instruction.
- Help the teacher keep parents and students informed about students’ progress.”

Category 3, criterion 5, states: “Suggestions are given on how to use assessment data to guide decisions about instructional practices and how to modify an instructional program so that all students continually progress toward meeting or exceeding the standards.”

Can entry-level or other forms of assessment be delivered online?

Yes, any assessments can be delivered online if submitted as part of the instructional program. Most important, Web site and/or technology-based materials that are an integral component of a submitted program must remain unchanged throughout the period of the adoption.

Further directions regarding online components of programs will be included in the Publishers Invitation to Submit, 2007 Mathematics Adoption document to be distributed at the Invitation to Submit meeting scheduled for January 9, 2007. Publishers will be required to submit a statement of Assurance Regarding Technology-Based Materials that the content of the program that was evaluated will not change during the duration of the adoption cycle.

For an example of these requirements from a previous adoption, refer to the Publishers Invitation
to Submit, 2006 Science Adoption document available online at
Publishers Invitation to Submit 2006 Science Primary Adoption

[http://www.cde.ca.gov/ci/sc/im/documents/science-its122005.doc] DOC; 1MB; 199pp.). (Refer to page 15 and Attachment L.)

What access formats (for online components) must/may be provided?

Recognizing that the range of performance and ability of students varies greatly, producers and publishers must apply universal design strategies when creating learning resources. Directions related to “access formats” for online components of programs will be included in the Publishers Invitation to Submit, 2007 Mathematics Adoption document that will be distributed at the Invitation to Submit meeting scheduled for January 9, 2007.

For an example of these requirements from a previous adoption, refer to the Publishers Invitation
to Submit, 2006 Science Adoption document available online at
Publishers Invitation to Submit 2006 Science Primary Adoption

[http://www.cde.ca.gov/ci/sc/im/documents/science-its122005.doc] (DOC; 1MB; 199pp.). (Refer to pages 15-17).

Noteworthy are requirements in Senate Bill 842, Karnette, Chapter 800 of the Statutes of 2003, which added Section 60061.8 to the Education Code (effective January 1, 2004). Publishers of basic instructional materials for the 2007 Mathematics Primary Adoption will be required to modify their materials as may be necessary to comply with this section. Requirements specifically mention video products, Internet resources, and digital multimedia programs.

In addition, design resources to help make materials more accessible to more students are available on the Clearinghouse for Specialized Media and Technology (CSMT) Web site at Clearinghouse For Specialized Media and Technology [http://www.cde.ca.gov/re/pn/sm/] or by contacting CSMT at 916-445-5103.

In what ways will submitted course materials be evaluated against the instructional strategies (such as the three-phase model of instruction) found in Chapter 4?

Instructional strategies will be evaluated for alignment with the evaluation criteria. Most of these requirements are listed in criterion Category 5: Instructional Planning and Support, and these are consistent with guidance included in the Mathematics Framework, Chapter 4,“Instructional Strategies.”

For example: Category 5, criterion 5, requires “Strategies to anticipate, identify, address, and correct common student errors and misconceptions.”

Category 5, criterion 7, requires “Different kinds of lessons and alternative ways in which to explain concepts, offering teachers choice and flexibility in implementing the program.”

Category 5, criterion 9, requires “Review and practice problems, as described in Chapter 4, ‘Instructional Strategies,’ in this framework, which are distributed in the program to enhance students’ understanding and to promote generalization and transfer of skills and knowledge.”

When referring to “materials” in Chapter 10 of the Mathematics Framework, may those materials include online teacher support materials?

Yes, teacher support materials can be delivered online if submitted as part of the instructional program. Most important, Web site and/or technology-based materials that are an integral component of a submitted program must remain unchanged throughout the period of the adoption.

Further directions regarding online components of programs will be included in the Publishers Invitation to Submit, 2007 Mathematics Adoption document to be distributed at the Invitation to Submit meeting scheduled for January 9, 2007. Publishers will be required to submit a statement of Assurance Regarding Technology-Based Materials that the content of the program that was evaluated will not change during the duration of the adoption cycle.

For an example of these requirements from a previous adoption, refer to the Publishers Invitation to Submit, 2006 Science Adoption document available online at Publishers Invitation to Submit 2006 Science Primary Adoption . [http://www.cde.ca.gov/ci/sc/im/documents/science-its122005.doc] (DOC; 1MB; 199pp.) (Refer to page 15 and Attachment L.)

For Algebra Readiness, what instructional settings are anticipated beyond the full year of instruction? For example, do they include pull-out sessions or additional class periods for students concurrently enrolled in a pre-algebra or an Algebra 1 course?

How and when to use algebra readiness materials is a local decision. Chapter 10 of the Mathematics Framework states, “Districts will decide, based on individual assessment data, whether each student uses one or a combination of basic grade-level, intervention, or algebra readiness materials.”

Category 5, Instructional Planning and Support, criterion 20, states “…programs must have suggestions for how to use the materials in different instructional settings.”

Refer to Appendix E for information on alternative uses of intervention materials in different instructional settings. This information is based on data from a 2004 survey of local educational agencies (LEAs) in which LEAs reported conducting intervention programs before or after school hours, during an inter session or summer session, during the regular school hours by providing additional instructional time, and in a tutorial setting.

What support is envisioned for intensive students who are reentering the basic grade- level program, especially in light of the expectation that intervention is not a fixed-term course?

Category 4, Universal Access, requires programs to provide support for “intensive students” (students performing two or more years below grade level) in the basic grade-level program.

Category 4, criterion 2, states programs should include: “Suggestions on how to help strategic or intensive students learn the key concepts in mathematics in the basic program and have access to grade-level content.”

Category 4, criterion 1, states programs should include: “Suggestions for reinforcing or expanding the curriculum to meet the needs of benchmark, strategic, and intensive students” and “Special help for students who are below grade level, including clearer explanations, with ample opportunities for review and practice or other assistance to help accelerate students’ performance to grade level.”

Should mathematics intervention programs be organized to target specific grade levels or be organized by volumes that include instruction on all the standards for each grade level emphasized in Appendix E, allowing implementation of the volumes at any grade level? If the math intervention program targets a specific grade level, should the intervention include instruction and practice from lower grade levels (i.e., should standards for Number Sense for grade two be included in intervention for grade four)? How should a publisher determine the standards that should be included at each grade level?

The mathematics intervention program must be organized around the six topical volumes indicated in Appendix E (Volume I – Place Value and Basic Number Skills; Volume II– Fractions and Decimals; Volume III – Ratios, Rates, and Percents; Volume IV – The Core Processes of Mathematics; Volume V – Functions and Equations; and Volume VI – Measurement). It should provide instruction and practice in all of the standards from various grades (including the lower grades) listed in the chart on page 341 of Appendix E, titled “The Subsets of Mathematics Content Standards, by Grade Level.”

Category 2, Program Organization, criterion 1, states: “For the intervention programs, materials must be organized around the six volumes and the subset of standards specified in Appendix E. No specific order of topics within these volumes is required, and volumes may be split into smaller units for publication.”

Appendix E states materials should: “Reflect the interests and the ages of the students (e.g., materials used to teach a foundational skill or concept to students in grade eight should reflect the interests of a teenager).”

Here is an example of how to use the mathematics intervention materials for a student at a specific grade level. Assume you have a fifth grade student who is below grade level in the areas of Fractions and Decimals (Volume II of the Mathematics Intervention program). This student might benefit from instruction that focuses on the subset of the Number Sense standards from grades two, three, four and possibly grade five that are the focus of Volume II; however, he/she should not receive instruction in the subset of Number Sense standards from grades six and seven (those standards can be covered in future years as part of his/her basic grade-level program).

Are the mathematics intervention programs submitted for adoption required to include optional teaching strategies in each lesson?

Lessons should include adequate support for teachers to implement the program.

Requirements for all programs (including intervention programs) in Category 5, Instructional Planning and Support, state: “The materials should be designed to help teachers implement a mathematics program that ensures opportunities for all students to learn the essential skills and knowledge called for in the California Mathematics Standards and the Mathematics Framework.”

Category 5, criterion 5, requires programs to include “Strategies to anticipate, identify, address, and correct common student errors and misconceptions.”

Category 5, criterion 7, requires programs to include “Different kinds of lessons and alternative ways in which to explain concepts, offering teachers choice and flexibility in implementing the program.”

Category 5, criterion 20, applies to intervention and algebra readiness programs and requires that “Instructional materials provide an adequate sample of the range of examples that illustrate each concept.”

Are the math intervention programs submitted for adoption required to include optional instruction in alternate processes or algorithms?

No, programs are not required to include instruction in alternate processes or algorithms. Programs are required to include instruction that helps students understand why standard algorithms work and when and how to use them.

Appendix E states: “From a practical perspective, the algorithms for the addition and subtraction of whole numbers are important because they replace the need to count forwards and backwards by ones to determine sums and differences. The standard algorithms are applications of the definitions of mathematical operations to numbers in place value notation. They are not always the most efficient method of problem solving, but they are sufficiently robust that they can be applied in every case. The standard algorithms model the mathematical strategy of breaking complicated problems into smaller solvable components and help to develop later algebraic concepts of working with polynomials…. It is important for students to understand how familiar algorithms work, recognize the different situations in which operations are called for strategically in problem solving, and have sufficient practice with different types of problems that they can generalize and apply them to new and novel situations.”

What is the role of English learners regarding “Unique/ Appropriate” mathematics intervention instructional strategies – and how should they be identified within submitted math intervention?

Mathematics intervention programs should include support for English learners in the areas of the academic language of instruction and the specialized vocabulary of mathematics.

Category 5, Instructional Planning and Support, criterion 20, applies to intervention and algebra readiness programs only and states: “Instructional materials provide assistance in the specialized vocabulary of mathematics and in the academic language of instruction, including instructional strategies in the teacher’s edition for approaches appropriate for English learners.”

Chapter 6, Universal Access, criterion 4, requires “Instructional materials designed to help meet the needs of students whose reading, writing, listening, and speaking skills fall below grade level. (Materials should help students understand and use appropriate academic language in mathematics.)”

Appendix E states: “Particular attention should be given to the needs of English learners, including the academic language of instruction and the specialized vocabulary of mathematics. If students do not understand the academic language of instruction and assessment, they will not be successful in mathematics.” Appendix E goes on to list several areas that should be addressed in the program.

How does the mathematics intervention program work? Do students participate in the regular core classroom instruction plus have additional time for intervention in a pull-out program? The criteria state that students should be in an intensive intervention program for two hours a day, is this in addition to their core program or does it replace the core time?

How and when to use intervention materials is a local decision.

Chapter 10 states: “The criteria require that instructional materials address the learning needs of students and that programs be submitted in one of three categories: basic grade level, intervention, and algebra readiness. Districts will decide, on the basis of individual assessment data, whether each student uses one or a combination of basic grade-level, intervention, or algebra readiness materials.”

Refer to Appendix E for information on alternative uses of intervention materials in different instructional settings. This information is based on data from a 2004 survey of LEAs in which LEAs reported conducting intervention programs before or after school hours, during an inter session or summer session, during the regular school hours by providing additional instructional time, and in a tutorial setting.

Is the goal of the intensive intervention program to accelerate the student to the strategic intervention level (two years below) or on-grade level standards?

The goal is to accelerate student achievement so that they can succeed in the basic grade-level program.

Category 1, Mathematics Content / Alignment with Standards, criterion 12, states: “Intervention programs are designed to accelerate the progress of students in mathematics in the shortest possible time so that they can begin to make progress, using the basic grade-level programs. To serve this purpose, intervention programs must provide targeted and explicit instruction on the subset of mathematics standards indicated in Appendix E and be free of unrelated or unnecessary content. (See ‘A Mathematics Intervention Program (Grades Four through Seven)’ in Appendix E for further explanation.)”

At what point does a student exit the Intensive Intervention program?

Assessment data should indicate when a student is ready to exit the program.

Category 3, Assessment, criterion 6, states: “In the intervention program frequent diagnostic assessments are provided to tailor instruction to
the standards with which students are having difficulty. The program should include an initial
assessment to determine students’ placement in a program (e.g., referenced to the six volumes or

sections within each volume to be used or both), diagnostic assessments to identify areas of
strengths and weaknesses, formative assessments to demonstrate students’ progress toward
meeting identified benchmarks, and a summative assessment to determine whether a student has
mastered the materials.”

Appendix E states: “The embedded assessments should provide a plan for each
student that identifies which section of the six volumes need to be covered and when
students are ready to move on to the next section or to exit the program.”

Can the core program submission reference the intensive intervention program?

Yes, the core (basic) grade-level program can reference the mathematics intervention program; however, it is not required. The criteria state that all programs “…must be stand-alone products and will be reviewed separately.”

What is your recommendation for grade three students who score more than two grade levels below grade level standards?

Basic grade-level programs should provide some support for “intensive students” (students performing two or more years below grade level).

Category 4, Universal Access, criterion 2, requires programs to include “Suggestions on how to help strategic or intensive students learn the key concepts in mathematics in the basic program and have access to grade-level content.”

Also refer to the answer for Question 9.

When mathematics intervention programs include suggested modifications, must the suggestions be included at point of use or can they be included at an alternate site in the teacher’s edition?

The criteria do not specify where suggested modifications should be located; however, suggestions should be available to help the teachers implement the program as needed.

Category 5, Instructional Planning and Support, criterion 7, requires programs to include “Different kinds of lessons and alternative ways in which to explain concepts, offering teachers choice and flexibility in implementing the program.”

Can the intervention program cover grades four through six rather than four through seven?

No, the mathematics intervention program must include materials for students in grades four through seven and must be organized around the six topical volumes indicated in Appendix E. It should provide instruction and practice in all of the standards from the various grades listed in the chart on page 341 of Appendix E, titled “The Subsets of Mathematics Content Standards, by Grade Level.”

(For additional information, refer to the example provided as part of the answer to Question 10.)

Does everything in the framework apply to intervention? How will the mathematics intervention materials be reviewed? By an elementary committee, a middle school committee, or a combination of both?

Most information that specifically addresses mathematics intervention programs is included in Chapter 10 or Appendix E of the framework.

Chapter 10 states that unless otherwise noted, the information in categories 1 through 5 of the criteria apply to all three types of programs (including mathematics intervention programs).

For purposes of the education content review, each program will be assigned to a review panel for evaluation. The panel will consist of Instructional Materials Advisory Panel (IMAP) members and the Content Review Panel (CRP) members. IMAP members are primarily classroom teachers and CRP members are content experts with an advanced degree in mathematics or a related subject matter field. There will be panels designated specifically to look at mathematics intervention materials.

[In the mathematics intervention program] what "benchmarks" are supposed to be identified by the formative assessments? Does the publisher identify these benchmarks or are there specific benchmarks identified by CDE? Are the "benchmarks" the state standards?

Formative assessments should measure progress towards student mastery of the required subset of mathematics standards included in the chart in Appendix E, titled “The Subsets of Mathematic Content Standards, by Grade Level.” Specific benchmarks should align with the program material and help educators tailor instruction to the standards with which students are having difficulty.

Category 3, criterion 6, states: “In the intervention program frequent diagnostic assessments are provided to tailor instruction to the standards with which students are having difficulty. The program should include an initial assessment to determine students’ placement in a program (e.g., referenced to the six volumes or sections within each volume to be used or both), diagnostic assessments to identify areas of strengths and weaknesses, formative assessments to demonstrate students’ progress toward meeting identified benchmarks, and a summative assessment to determine whether a student has mastered the materials…. Teachers editions should help educators select and use assessment tools that provide student data to help educators meet the instructional needs of students.” (Refer to this criterion for examples of assessment data.)

Also in reference to the Mathematics Intervention program, Category 5, Instructional Planning and Support, criterion 20, states: “Instructional materials include extensive diagnostic components to guide instruction. Diagnosis may often apply to the many smaller, embedded concepts and skills and not to a whole standard.”

In what ways will submitted course materials be evaluated against Categories 2 through 5 (Program Organization, Assessment, Universal Access, and Instructional Planning and Support)? Will the evaluation be "holistic," or will specific checklists or rating procedures be developed? Will the categories be weighted?

Materials will be evaluated “holistically” against the criteria in categories 2 through 5. The categories are not weighted; however, materials that fail to meet Category 1, Mathematics Content/Alignment with the Standards, will not be considered satisfactory for adoption. Only those programs that meet all criteria in category 1 and that have strengths in each of categories 2 through 5 will be deemed worthy of adoption.

Are publishers encouraged to use exemplars exactly as they are presented in Chapter 2 and Appendix D in developing course materials?

The sample problems in Appendix D are provided as examples and not intended to be used exactly as stated in the program.

Other sample problems are available online at 2003 Through 2008 CST Released Test Questions [http://www.cde.ca.gov/ta/tg/sr/css05rtq.asp] as part of the released test questions from the 2003, 2004, and 2005 California Standards Tests (CSTs).

When will the California standards mapping document be available to publishers to begin work on the project?

The standards maps for the 2007 Mathematics Adoption will be available in late spring 2006.

Is Spanish an alternate format that can be submitted anytime after the adoption as an alternate format, or is there a timeframe for Spanish submission and review?

Alternate formats in languages other than English will be accepted for review following the State Board adoption of the English edition.

What is the anticipated per pupil funding allotment?

Each year the state budget includes funding for the purchase of instructional materials.
The Instructional Materials Funding Realignment Program (IMFRP) provides a per-pupil amount
for students in kindergarten through grade twelve. Each year the per-pupil amount varies
depending on the total funding available and the annual enrollment. For 2005-06 the IMFRP
totaled $360,997,000, or $52.79 per pupil. Information on the IMFRP is available online at
IMFRP Information [http://www.cde.ca.gov/ci/cr/cf/imfrpintro.asp].

Districts also receive funding for the purchase of instructional materials through the state lottery.
Proposition 20, which passed in 2000, provided that half of any increase in lottery revenue above
the base year of 1997-98 be restricted for the purchase of instructional materials. This amount
varies each year, depending on the total annual lottery revenue, and is allocated at the end of the
fiscal year. For the 2004-05 fiscal year, districts received a total of $22.34 per unit of average
daily attendance. Information on lottery allocations is available online at
Lottery [http://www.cde.ca.gov/fg/aa/lo/].

Please be advised there will be a formal Invitation to Submit Meeting held on January 9, 2007, in the California Department of Education building at 1430 N Street, Sacramento, CA 95814. Publishers will be notified of the time of the meeting through fax or mail, and an announcement will also appear on the Curriculum Frameworks and Instructional Resources (CFIR) Web site at Instructional Materials [http://www.cde.ca.gov/ci/ma/im/].

The adopted timeline for the 2007 Mathematics Primary Adoption is enclosed as Attachment A [http://www.cde.ca.gov/ci/ma/im/math0601bullatta.asp] Please review the dates carefully.

If you have additional questions regarding the 2007 Mathematics Primary Adoption, please
contact Mary Sprague, Lead Consultant for the 2007 Mathematics Adoption, Curriculum
Frameworks Office, at ~~916-319-0510~~, or Suzanne Rios, Administrator, Instructional Resources
Office, at ~~916-319-0665~~. [Please note, the preceding phone numbers are no longer applicable. For more information, please contact the Curriculum Frameworks and Instructional Resources Division at 916-319-0881.]

Sincerely,

Thomas Adams, Director

Curriculum Frameworks and Instructional Resources Division

TA:ms

Enclosure

cc

Glee Johnson, State Board President

Deborah Keys, Chair, Curriculum Development and Supplemental Materials Commission

Sue Stickel, Deputy Superintendent, Curriculum & Instruction Branch

Curriculum Development and Supplemental Materials Commission Members

Dale Shimasaki, Association of American Publishers