four researchers will be rating assessments and · web viewfor example, tables a1 through a5...

Alignment in Math and Science

Alignments between St. Michael’s Episcopal Day School’s assessment materials and

the state, national and international content standards for Grades 4, 6, 7 and 8 in

math and science

Fereshteh Hejri, PhD

Advance Research & Data Analyses Center

Jamal Abedi, PhD

University of California Davis and

Advance Research & Data Analyses Center

In collaboration with:

Allison HarrisMalini PrakashVeena Nambiar

Jennifer LambrosIrini Okhremtchouk

Sarah Ryen

October, 2007

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TABLE OF CONTENTSIntroduction and Perspectives ...................................................................................................3Content Areas and Grades Assessed ........................................................................................5Results of the Alignments..........................................................................................................6Summary and Discussion.........................................................................................................10Appendix A (Sample Rating sheet).........................................................................................13Appendix B, Table A series.....................................................................................................15Appendix C, Table B series...................................................................................................140

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Alignments between St. Michael’s Episcopal Day School’s assessment materials and

the state, national and international content standards for Grades 4, 6, 7 and 8 in

math and science

Introduction and Perspectives

The purpose of this study was to conduct alignments between St. Michael’s

Episcopal Day School’s assessment materials and the state, national and international

content standards. A team of experts with the relevant background and experience in this

area conducted the alignment study. We used two of the alignment components that

Webb (1999) proposed. These are: (1) Categorical Concurrence and (2) Depth-of-

Knowledge Consistency. In Categorical Concurrence, we compared the level of

alignment between school materials and the state, national and international standards to

see if they cover the same content categories. The school assessment contents are judged

to be aligned with the standards (state, national and international) if the same or

consistent categories of content appear in both documents. Similarly, the Depth-of-

Knowledge Consistency is confirmed if what is elicited from students on the assessments

is as demanding cognitively as what students are expected to know and do as stated in the

state and national standards.

Six researchers from the office of Advance Research & Data Analyses Center

examined the assessment materials in math and science for grade 4, 6, 7 and 8 (grade 5

was not included due to logistical issues) and conducted the alignment between the

content of the School materials and state, national, and international standards for math

and science. The international standards in math and science were available for grades 4

and 8 only.

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For each standard, two researchers independently rated the level of alignment of

School assessments with the standard’s specific goals for students using a 5-point Likert-

Scale system ranging from 1 to 5, 5 representing the highest level of alignment. This

provided objectivity that is needed in the evaluation of the degree of alignment.

Discrepancies between judges were resolved either by the peer discussion or by the

intervention of the supervisor. The two ratings were then averaged for more reliable

rating outcomes. Researchers (judges) had prepared for rating by reading the expanded

descriptions of each standard and familiarizing themselves with the assessment content,

in addition to participating in group training sessions and a series of conference calls for

training purposes and for discussing issues concerning alignments.

During the rating process, researchers carefully studied the description of the

standards to determine whether or not the assessments tested the skills specified in the

standards. Researchers used alignment sheets that were designed to allow them to mark a

rating from 1 (least aligned) to 5 (most aligned) for each standard and for each specific

skill to be mastered. Researchers rated the assessments in the context of whether or not

school tested their students for the skills they were expected to learn during the whole

school year in accordance with the standards.

After rating the assessments, researchers submitted summaries of their work for

the day, including suggestions or questions addressed by the group to the project

supervisor. Researchers maintained regular contact through e-mail, and also through the

use a communication log to record their work, communications with St. Michael’s

administrators, or any information pertinent to the project. To improve the efficiency,

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accuracy, and quality of their work, researchers met as a group several times during the

alignment process to share their ideas, observations, methods and concerns.

Content areas and grades assessed

This alignment study was conducted on math and science content areas in grades

4, 6, 7 and 8. These particular content areas were chosen for this study because of

existing state and national standards for all of these four grades plus international

standards for grades 4 and 8. International standards were obtained from international

assessments such as the Third International Math and Science Studies Study (TIMSS,

“http://timss.bc.edu) and Programme for International Student Assessment (PISA, see,

PISA website at www.pisa.oecd.org for more information and for international

standards). National standards for math were obtained from National Council of

Teachers of Mathematics (NCTM: www.nctm.org) and for science from the National

Science Education Standards (NSES). For more information about the national science

standards see “www.nap.edu”. For state, the state standards were obtained from the

California Department of Education website.

The judges used a rating sheet for each standard. Appendix A shows a sample

rating sheet. The rating sheet included all standards and sub-standards for the content

areas being assessed (math and science). As indicated earlier, judges carefully reviewed

the standards (state, national and international) and then examined the School’s

assessment materials for existence of those standards. The Likert-scale scoring system

allowed the judges to specify the degree of alignment in addition to the existence of the

content standard. When a particular standard was identified in the assessment materials,

the judges then determined the level of strength of the alignment for that standard. For

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example, the level of alignment could vary from a low level (ratings of 1 to 2) to high

level (rating of 5).

Results of the Alignments

The results of the alignments study in math and science for grades 4, 6, 7 and 8

were summarized into two series of tables at different levels of details: (1) in a more

detail format by each category of content standards and subcategories within each of the

main categories and (2) in a more general format by categories of content standards

averaging over the subcategories of standards. For example, for grade 4, the state content

standards include five areas: (1) Number Sense, (2) Algebra and Functions, (3)

Measurement and Geometry, Statistics, (4) Data Analysis, and Probability, and (5)

Mathematical Reasoning. Under the first content area (Number Sense), there were four

main categories of standards as follows:

1. Students understand the place value of whole numbers and decimals to two

decimal places and how whole numbers and decimals relate to simple fractions.

Students use the concepts of negative numbers.

2. Students extend their use and understanding of whole numbers to the addition

and subtraction of simple decimals:

3. Students solve problems involving addition, subtraction, multiplication, and

division of whole numbers and understand the relationships among the operations:

4. Students know how to factor small whole numbers:

Under each of these main categories there were several subcategories of standards. For

example, under the first categories there were the following subcategories:

1.1 Read and write whole numbers in the millions,

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1.2 Order and compare whole numbers and decimals to two decimal places.

1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand,

ten thousand, or hundred thousand.

1.4 Decide when a rounded solution is called for and explain why such a solution may

be appropriate.

1.5 Explain different interpretations of fractions, for example, parts of a whole, parts

of a set, and division of whole numbers by whole numbers; explain equivalents of

fractions (see Standard 4.0).

1.6 Write tenths and hundredths in decimal and fraction notations and know the

fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or .50; 7/4 = 1

3/4 = 1.75).

1.7 Write the fraction represented by a drawing of parts of a figure; represent a given

fraction by using drawings; and relate a fraction to a simple decimal on a number line.

1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in

temperature, in "owing").

1.9 Identify on a number line the relative position of positive fractions, positive

mixed numbers, and positive decimals to two decimal places (see the California

Department of Education website at www.cde.ca.gov).

Tables A1 to A153 present the detailed alignment ratings in math and science by

main categories and subcategories for grades 4, 6, 7, and 8. As indicated above, the

alignment was conducted at the state and national levels for all grades used in this study

(grades 4, 6, 7, and 8). In addition, for grades 4 and 8 alignment between school content

standards and international content standards were also conducted. For other grades in

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this study (grade 6 and 7) the international standards were not available. Tables B1 to

B20 present a summary of alignment data that were presented in Tables A1 to A153.

These summaries were obtained by averaging the ratings over subcategories of content

standards.

In these tables, two judges rated each category/subcategory for alignment between

school’s assessment content with Categorical Concurrence and Depth-of-Knowledge

Consistency. The judges conducted their ratings for the two dimensions of alignment

(Categorical Concurrence and Depth-of-Knowledge) and reported their average ratings in

an integer format (without decimals). The main reason for combining the ratings of the

two dimensions was to ease the interpretation of the results.

The alignment results were reported for math first and then for science for each of

the four grades (grades 4, 6, 7, and 8). Within each content areas, the alignments were

reported for states, then national and then international standards. For example, Tables

A1 through A5 presents the alignment results for state math in grade 4; Tables A6

through A10 present the results for national math for grade 4 and Tables A11 through

A14 show the results for international math for grade 4. The results of alignment for

science for grade 4 then follow these tables. Tables A15 through A18 present the

alignment results for state science for grade 4; Tables A19 through A25 show the results

for national science for grade 4 and Tables 26 through 29 summarize the alignment

results for international science for grade 4. Next are tables reporting the results of

alignments for grade 6 in math and science followed by tables for grade 7 and then for

grade 8. For all the grades we followed the same format of reporting: first math then

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science and within each content area, first state results, then national results and then

international results (if available).

Since this study involved multiple grades, multiple content and multiple

standards, it would be difficult to discuss the results at the subcategory and category and

even at the content levels by each of the four grades subject of this study. The results of

alignment studies are reported in 1153 tables (Tables A1 to A153 and are summarized in

another 20 tables (Tables B1 to B20). Therefore it is quite clear that detail reporting of

these results would be difficult and time consuming. We will discuss the findings of this

study at the general level. Readers will then have the chance to go through details of

analyses by reviewing and inspecting the data reported in Tables A and B series.

In general, the results of alignment study suggest high level of consistency

between judges. That is the level of interrater reliability between the judges was

extremely high. This suggests that the two independent ratings by two independent

judges produced almost identical results which provide evidences on the reliability and

validity of the outcome of this study. On the alignment aspects of the study, the outcomes

were mixed. For a large majority of standards, the judges provided high ratings

suggesting high level of alignment between School’s content standards and state, national

and international standards. However, in a few cases, judges did not find School’s

assessments contend to be highly aligned with the outside standard criteria.

To provide a clear picture of the level of alignment between School’s content

standards and state, national and international content standards, we use the summary

alignment data presented in the Table B series. The average ratings for grade 4 standards

over all main categories and subcategories and over the two independent raters and two

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dimensions of alignment are 3.38 for state math (Table B1), 3.10 for national math (Table

B2), and 4.00 for international math (Table B3). For the science content area for grade 4

the average ratings are: 4.3 (Table B4) for state, 3.9 for national (Table B5), and 3.2 for

international standards (Table B6). As these findings show, the average ratings range

from 3.10 to 4.3 well above the midpoint of 2.5 in the Likert-Scale rating system used for

this study. Similar trends of ratings can be seen for other grades in both math and science

standards. For example, for grade 6 the average ratings are 3.25 for state math (Table

B7), and 3.2 for national math (Table B8). Once again, these average ratings are all above

the midpoint of 2.5 ratings. For grade 6 science, however, there are some low ratings. The

average ratings for state science for grade 6 is 2.4 (Table B9) and 3.3 for the national

science (Table B10). To explain the reasons behind the relatively low average rating of

some of the standards, we elaborate on the state science ratings for grade 6. The data in

Table B9 suggests that the ratings for some of the categories of state science standards

are quite high but for some other categories are low. For example for the category labeled

as “Focus on earth sciences (ecology-life sciences)”, the average ratings was 3.67 as

compared with an average rating of 1.58 for ratings on the category labeled as “Thermal

Energy” (Table B9). Similar trend of alignment can be seen for other grades. These

findings suggest that low level of alignment could be caused by missing of one or more

subcategories of standards.

Summary and Discussion

In this study, the content of St. Michael’s Episcopal Day assessment materials

were compared with the content standards from the State of California, and the national

and international assessments standards and their level of alignments was examined. In

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general, the levels of alignment between assessment materials of St. Michael’s Episcopal

Day School and state, national and international content standards were well above the

midpoint of 2.5 in a 5-point rating scales. The results of these analyses clearly suggest

that:

The two independent judges produced ratings that were quite consistent

In a majority of cases, the alignment between the School’s content standards and

the state, national and international content standards are strong

The average ratings in most of the cases were well above the midpoint of 2.5 in a

5-point Likert-Scale rating system.

In cases with the overall low ratings, the average ratings were different across the

categories and subcategories of standards suggesting that only a few categories or

subcategories cause the low ratings.

The finding from this alignment study suggest that in preparing the assessment

materials, the St. Michael’s Episcopal Day School included materials for Grades 4, 6, 7

and 8 in math and science that are consistent with the state, national and international

contents. While the results of this study were generally consistent and indicate high level

of alignments but in a few cases low alignment ratings were observed. We believe that

the low ratings are not due to the lack of alignment but they are due to the School’s

content coverage policy and practice. We examined the content standards defined by

state, national and international experts and found some differences between these

standards. We are not at the position to judge which standards should or should not be

covered at the School. We suggest that the School policy makers and curriculum planners

review the standards carefully and identify those with low ratings (ratings below 2) and

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then decide if those standards should be included into the School curriculum or more

emphases should be given to those standards. We know it would be a big challenge for

individual districts and schools within the districts to include all standards that are

included in the state and national and international standards.

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Appendix ACalifornia State Standards in Math

Grade 8 Rating FormAlignment: Categorical Concurrence

Degree of Alignment________________________________________________

Not aligned

Most aligned

Content Standard 1 2 3 4 5Algebra I1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable.

Standard 1.1 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

California State Standards in MathGrade 8 Rating Form

Alignment: Categorical Concurrence Degree of Alignment

________________________________________________Not

alignedMost

alignedContent Standard 1 2 3 4 5

3.0 Students solve equations and inequalities involving absolute values.

4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.

5.0 Students solve multistep problems, including word problems, involving linear

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equations and linear inequalities in one variable and provide justification for each step.

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Appendix B

Table A1California State Math, Grade 4

Degree of Alignment

Content Standard Rater 1 Rater 2 Total

Number Sense1.0 Students understand the place value of whole numbers and decimals:

3 5 8

Standard 1.1 4 4 8Standard 1.2 5 4 9Standard 1.3 4 4 8Standard 1.4 5 3 8Standard 1.5 4 5 9Standard 1.6 5 5 10Standard 1.7 2 3 5Standard 1.8 5 3 8Standard 1.9 3 2 52.0 Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals:

4 3 7

Standard 2.1 4 5 9Standard 2.2 2 3 53.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations:

4 4 8

Standard 3.1 5 5 10Standard 3.2 4 3 7Standard 3.3 5 4 9Standard 3.4 5 4 94.0 Students know how to factor small whole numbers:

2 2 4

Standard 4.1 4 3 7Standard 4.2 1 1 2

Average 3.69

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Degree of Alignment

Content Standard Rater 1 Rater 2 TotalAlgebra and Functions1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences:

3 4 7

Standard 1.1 5 5 10Standard 1.2 5 5 10Standard 1.3 5 4 9Standard 1.4 4 5 9Standard 1.5 1 1 22.0 Students know how to manipulate equations:

1 2 3

Standard 2.1 1 2 3Standard 2.2---------------------------------------

1 2 3

Average 3.11

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Degree of Alignment

Content Standard Rater 1 Rater 2 TotalMeasurement and Geometry 2 2.5 4.51.0 Students understand perimeter and area:Standard 1.1 4 3 7Standard 1.2 1 1 2Standard 1.3 1 1 2Standard 1.4 5 5 102.0 Students use two-dimensional coordinate grids to represent points and graph lines and simple figures:

2 2.5 4.5

Standard 2.1 4 3 7Standard 2.2 2 3 5Standard 2.3 2 3 53.0 Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems:

3 2.5 5.5

Standard 3.1 5 3 8Standard 3.2 1 1 2Standard 3.3 3 4 7Standard 3.4 5 3 8Standard 3.5 3 4 7Standard 3.6 2 3 5Standard 3.7 1 1 2Standard 3.8--------------------------------------------

5 4 9

Average 2.79

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Degree of Alignment

Content Standard Rater 1 Rater 2 TotalStatistics, Data Analysis, and Probability 1.0 Students organize, represent, and interpret numerical and categorical data and clearly communicate their findings:

4 3 7

Standard 1.1 2 3 5Standard 1.2 5 4 9Standard 1.3 5 4 92.0 Students make predictions for simple probability situations:

5 3 8


Average 3.85

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Degree of Alignment

Content Standard Rater 1 Rater 2 TotalMathematical Reasoning 1.0 Students make decisions about how to approach problems:

3 3 6

Standard 1.1 4 3 7Standard 1.2 2 3 52.0 Students use strategies, skills, and concepts in finding solutions:

3 3.5 6.5

Standard 2.1 4 4 8Standard 2.2 3 4 7Standard 2.3 3 4 7Standard 2.4 4 5 9Standard 2.4 4 3 7Standard 2.6 3 2 53.0 Students move beyond a particular problem by generalizing to other situations:

3 3.5 6.5

Standard 3.1 4 3 7Standard 3.2 4 4 8Standard 3.3------------------------------------

3 4 7

Average 3.20

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Table A6National Math Grade 4

Degree of Alignment

Content Standard Rater1 Rater 2 Average Number and Operations Standard1.0 Understand numbers, ways of representing numbers, relationships among numbers, and number systemsStandard 1.1 5 4 9Standard 1.2 4 3 7Standard 1.3 5 5 10Standard 1.4 5 4 9Standard 1.5 5 4 9Standard 1.6 5 3 8Standard 1.7 1 1 22.0 Understand meanings of operations and how they relate to one anotherStandard 2.1 5 4 9Standard 2.2 5 4 9Standard 2.3 5 3 8Standard 2.4 3 3 63.0 Compute fluently and make reasonable estimatesStandard 3.1 2 1 3Standard 3.2 5 4 9Standard 3.3 3 3 6Standard 3.4 5 4 9Standard 3.5 2 3 5Standard 3.6--------------------------------------------------

5 4 --------------

Average 3.73

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Degree of AlignmentContent Standard Rater1 Rater 2 Average Algebra Standard1.0 Understand patterns, relations, and functions

3 4 7

Standard 1.1 3 5 8Standard 1.22.0 Represent and analyze mathematical situations and structures using algebraic symbols

4 3 7

Standard 2.1 5 4 9Standard 2.2 5 3 8Standard 2.3 3 2 53.0 Use mathematical models to represent and understand quantitative relationships

5 3 8

Standard 3.1 5 3 84.0 Analyze change in various contexts

2 3 5

Standard 4.1 1 3 4Standard 4.2--------------------------------------------------

3 3 6

Average 3.13

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Degree of AlignmentContent Standard Rater

1 Rater 2 Average

Geometry Standard1.0 Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

3 3.5 6.5

Standard 1.1 5 5 10Standard 1.2 4 5 9Standard 1.3 2 3 5Standard 1.4 2 4 6Standard 1.5 2 2 42.0 Specify locations and describe spatial relationships using coordinate geometry

2 3 5

Standard 2.1 3 2 5Standard 2.2 3 5 8Standard 2.3 2 4 63.0 Apply transformations and use symmetry to analyze mathematical situations

2 3 5

Standard 3.1 3 2 5Standard 3.2 2 3 5Standard 3.3 4 3 74.0 Use visualization, spatial reasoning, and geometric modeling to solve problems

2 1.3 3.3

Standard 4.1 4 3 7Standard 4.2 1 1 2Standard 4.3 1 1 2Standard 4.4 2 1 3Standard 4.5 4 2 6Standard 4.6---------------------------------------------------

2 1 3

Average 2.6

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Degree of AlignmentContent Standard Rater1 Rater 2 Average Measurement Standard1.0 Understand measurable attributes of objects and the units, systems, and processes of measurement

4 3 7

Standard 1.1 5 3 8Standard 1.2 5 3 8Standard 1.3 4 2 6Standard 1.4 5 3 8Standard 1.5 1 2 32.0 Apply appropriate techniques, tools, and formulas to determine measurementsStandard 2.1 2 2 4Standard 2.2 5 3 8Standard 2.3 4 2 6Standard 2.4 4 5 9Standard 2.5 3 5 8Average 3.45

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Degree of AlignmentContent Standard Rater1 Rater 2 Average Data Analysis and Probability Standard1.0 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

3 2 5

Standard 1.1 3 3 6Standard 1.2 2 2 4Standard 1.3 2 3 5Standard 1.4 4 3 72.0 Select and use appropriate statistical methods to analyze data

3 2 5

Standard 2.1 4 3 7Standard 2.2 3 2 5Standard 2.3 1 2 33.0 Develop and evaluate inferences and predictions that are based on data

1 2 3

Standard 3.1 1 2 34.0 Understand and apply basic concepts of probability

3 2 5

Standard 4.1 2 1 3Standard 4.2 4 3 7Standard 4.3Total

2 1 3

Average 2.35

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Table A11International Math, Grade 4

Degree of Alignment

Content Standard Rater 1 Rater 2 Total1.0 Number: Whole NumbersStandard 1.1 5 4 9Standard 1.2 5 3 8Standard 1.3 3 5 8Standard 1.4 5 5 10Standard 1.5 5 3 8Standard 1.6 5 5 10Standard 1.7 5 5 10Standard 1.8 3 2 52.0 Number: Fractions and DecimalsStandard 2.1 4 5 9Standard 2.2 5 5 10Standard 2.3 5 5 10Standard 2.4 5 5 10Standard 2.5 4 5 9Standard 2.6 5 3 8Standard 2.7 5 5 103.0 Number: Number Sentences with Whole NumbersStandard 3.1 5 5 10 Standard 3.2 5 5 104.0 Number: Patterns and RelationshipsStandard 4.1 1 1 2Standard 4.2 1 1 2Standard 4.3 1 2 3Standard 4.4--------------------------------------------------

1 1 2---------------

Average 3.88

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Degree of Alignment

Content Standard Rater 1 Rater 2 TotalGeometric Shapes and Measures1.0 Geometric Shapes and Measures: Lines and AnglesStandard 1.1 5 5 10Standard 1.2 5 4 9Standard 1.3 5 5 102.0 Geometric Shapes and Measures: Two- and Three-dimensional ShapesStandard 2.1 5 5 10Standard 2.2 4 5 9Standard 2.3 5 4 9Standard 2.4 1 1 2Standard 2.5 5 5 10Standard 2.6 5 4 93.0 Geometric Shapes and Measures: Location and MovementStandard 3.1 5 5 10Standard 3.2 5 5 10Standard 3.3 5 4 9Average 4.46

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Degree of Alignment

Content Standard Rater 1 Rater 2 Total1.0 Data Display: Reading and InterpretingStandard 1.1 4 3 7Standard 1.2 1 1 2Standard 1.3 5 5 102.0 Data Display: Organizing and RepresentingStandard 2.1 3 2 5Standard 2.2--------------------------------------------------

5 4 9

Average 3.30

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Degree of Alignment

Content Standard Rater 1 Rater 2 TotalThe Cognitive Domain1.0 KnowingStandard 1.1 5 5 10Standard 1.2 5 5 10Standard 1.3 5 5 10Standard 1.4 5 3 8Standard 1.5 5 5 10Standard 1.6 5 5 102.0 ApplyingStandard 2.1 5 5 10Standard 2.2 5 3 8Standard 2.3 4 3 7Standard 2.4 4 3 7Standard 2.5 5 3 83.0 ReasoningStandard 3.1 3 2 5Standard 3.2 4 3 7Standard 3.3 5 3 8Standard 3.4 5 3 8Standard 3.5--------------------------------------------------

5 4 9---------------

Average 4.22

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Table A15California State Science Grade 4

Degree of Alignment


Physical Sciences 1. Electricity and magnetism are related effects that have many useful applications in everyday life. As a basis for understanding this concept: Standard a 5 5 10Standard b 5 4 9Standard c 5 5 10Standard d 4 4 8Standard e 5 4 9Standard f 5 5 10Standard g 4 4 8Average 64:7x2=4.8

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Degree of Alignment

Content Standard Rater 1 Rater 2 TotalLife Sciences2. All organisms need energy and matter to live and grow. As a basis for understanding this concept:

5 5 10

Standard a 5 5 10Standard b 5 5 10Standard c 5 5 103. Living organisms depend on one another and on their environment for survival. As a basis for understanding this concept: Standard a 5 5 10Standard b 4 4 8Standard c 3 3 6Standard d 1 1 2Average 66:8x2=4.1

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Degree of Alignment

Content Standard Rater 1 Rater 2 TotalEarth Sciences4. The properties of rocks and minerals reflect the processes that formed them. As a basis for understanding this concept:

5 4 9

Standard a 5 5 10Standard b 5 4 95. Waves, wind, water, and ice shape and reshape Earth's land surface. As a basis for understanding this concept:

5 5 10

Standard a 4 5 9Standard b 5 4 9Standard c 5 5 10Average 66:7x2=4.7

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Degree of Alignment

Content Standard Rater 1 Rater 2 TotalInvestigation and Experimentation 6. Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations. Students will:

4 4 8

Standard a 4 3 7Standard b 2 2 4Standard c 5 5 10Standard d 3 3 6Standard e 4 4 8Standard f 5 5 10Average 53:7x2=3.8

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Table A19NSES National Science Grade 4

Degree of Alignment

Content Standard Rater 1 Rater 2 Total1.0 Science as Inquiry

Standard 1.1 5 5 10Standard 1.2 5 5 10Average 20:2x2=5


Degree of Alignment


2.0 Physical ScienceStandard 2.1 2 3 5Standard 2.2 1 1 2Standard 2.3 5 5 10Average 17:3x2=2.8

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Degree of Alignment


3.0 Life ScienceStandard 3.1 4 4 8Standard 3.2 2 3 5Standard 3.3 5 5 10

Average 23:3x2=3.8


Degree of Alignment


4.0 Earth and Space ScienceStandard 4.1 5 5 10Standard 4.2 2 1 3Standard 4.3 5 5 10Average 23:3x2=3.8

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Degree of Alignment

Content Standard Rater 1 Rater 2 Total5.0 Science and Technology

Standard 5.1 4 4 8Standard 5.2 4 4 8Standard 5.3 4 2 6Average 22:3x2=3.7


Degree of Alignment

Content Standard Rater 1 Rater 2 Total6.0 Science in Personal and Social Perspectives

Standard 6.1 1 1 2Standard 6.2 4 3 7Standard 6.3 5 5 10Standard 6.4 5 5 10Standard 6.5 5 5 10Average 39:5x2=3.9

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Degree of Alignment

Content Standard Rater 1 Rater 2 Total7.0 History and Nature of Science

Standard 7.1 4 4 8Average 8:1x2=4


Degree of Alignment

Content Standard Rater 1 Rater 2 Total1.0 Unifying Concepts and Processes

Standard 1.1 5 4 9Standard 1.2 5 4 9Standard 1.3 5 4 9Standard 1.4 4 5 9Standard 1.5 3 2 5Average 41:5X2=4.1

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Table A26TIMSS International Science Grade 4

Degree of Alignment

Content Standard Rater 1 Rater 2 TotalLife Science1.0 Life Science: Characteristics and Life Processes of Living ThingsStandard 1.1 5 5 10Standard 1.2 2 3 5Standard 1.3 1 1 22.0 Life Science: Life Cycles, Reproduction, and HeredityStandard 2.1 2 2 4Standard 2.2 1 1 23.0 Life Science: Interactions with the EnvironmentStandard 3.1 3 3 6Standard 3.2 2 2 44.0 Life Science: EcosystemsStandard 4.1 5 5 10Standard 4.2 5 5 10Standard 4.3 5 5 105.0 Life Science: Human HealthStandard 5.1 1 1 2Standard 5.2 1 1 2Average 67:12x2=2.8

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Degree of Alignment

Rater 1 Rater 2 TotalContent Standard

Physical Science1.0 Physical Science: Classification and Properties of MatterStandard 1.1 4 4 8Standard 1.2 4 4 8Standard 1.3 1 2 3Standard 1.4 3 2 5Standard 1.5 1 1 22.0 Physical Science: Physical States and Changes in MatterStandard 2.1 1 1 2Standard 2.2 1 1 2Standard 2.3 3 2 53.0 Physical Science: Energy Sources, Heat, and TemperatureStandard 3.1 4 5 9Standard 3.2 2 2 44.0 Physical Science: Light and SoundStandard 4.1 2 3 5Standard 4.2 1 1 25.0 Physical Science: Electricity and MagnetismStandard 5.1 5 5 10Standard 5.2 5 5 106.0 Physical Science: Forces and MotionStandard 6.1 2 3 5Standard 6.2 1 1 2Average

82:16x2=2.6

38



Degree of Alignment


Earth Science1.0 Earth Science: Earth’s Structure, Physical Characteristics, and ResourcesStandard 1.1 5 5 10Standard 1.2 4 3 7Standard 1.3 2 1 3Standard 1.4 3 3 6Standard 1.5 5 5 102.0 Earth Science: Earth’s Processes, Cycles, and HistoryStandard 2.1 3 3 6Standard 2.2 1 1 2Standard 2.3 5 5 103.0 Earth in the Solar SystemStandard 3.1 1 1 2Standard 3.2 1 1 2Average

58:10x2=2.9

39



Degree of AlignmentRater 1 Rater 2 Total

Content StandardThe Cognitive Domain1.0 KnowingStandard 1.1 5 5 10Standard 1.2 5 5 10Standard 1.3 5 5 10Standard 1.4 4 4 8Standard 1.5 5 5 102.0 ApplyingStandard 2.1 5 5 10Standard 2.2 5 5 10Standard 2.3 5 5 10Standard 2.4 5 5 10Standard 2.5 4 3 7Standard 2.6 5 5 103.0 ReasoningStandard 3.1 4 4 8Standard 3.2 3 3 6Standard 3.3 5 4 9Standard 3.4 5 4 9Standard 3.5 5 5 10Standard 3.6 4 5 9Standard 3.7 5 4 9Standard 3.8 4 4 8

173:19x2=4.6Average

40


Table A 30California State Math Grade 6



Number Sense1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages.

3 4 7

Standard 1.1 4 5 9Standard 1.2 2 4 6Standard 1.3 3 5 8Standard 1.4 3 3 62.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division.

3 5 8

Standard 2.1 3 4 7Standard 2.2 3 5 7Standard 2.3 5 5 10Standard 2.4 3 4 7

Average 76: 20=3.8

41



Degree of Alignment_____________________________________________Rater 1 Rater 2 Total

Content StandardAlgebra & Functions1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.

4 4.5 8.5

Standard 1.1 5 4 9Standard 1.2 5 4 9Standard 1.3 4 5 9Standard 1.4 4 5 92.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions.

5 4 9

Standard 2.1 5 5 10Standard 2.2 5 3 8Standard 2.3 5 4 93.0 Students investigate geometric patterns and describe them algebraically.

5 5 10


Average 110:24=4.58

42





Measurement and Geometry1.0 Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems.

5 5 10

Standard 1.1 5 5 10Standard 1.2 5 5 10Standard 1.3 5 5 102.0 Students identify and describe the properties of two-dimensional figures.

1 1 2

Standard 2.1 1 1 2Standard 2.2 1 2 3Standard 2.3 1 1 2

Average 49:16=3.06

43





Statistics, Data Analysis, and Probability1.0 Students compute and analyze statistical measurements for data sets.

2 2 4

Standard 1.1 3 5 8Standard 1.2 1 1 2Standard 1.3 1 1 2Standard 1.4 1 2 32.0 Students use data samples of a population and describe the characteristics and limitations of the samples.

1 1 2

Standard 2.1 1 2 3Standard 2.2 1 2 3Standard 2.3 1 3 4Standard 2.4 1 1 2Standard 2.5 1 1 23.0 Students determine theoretical and experimental probabilities and use these to make predictions about events.

1 1.5 2.5

Standard 3.1 1 3 4Standard 3.2 1 1 2Standard 3.3 1 1 2Standard 3.4 1 1 2Standard 3.5 1 2 3

Average 50.5:34=1.49

44





Mathematical Reasoning1.0 Students make decisions about how to approach problems.

4 4 8

Standard 1.1 4 4 8Standard 1.2 3 4 7Standard 1.3 5 4 92.0 Students use strategies, skills, and concepts in finding solutions.

3 3.5 6.5

Standard 2.1 2 4 6Standard 2.2 5 3 8Standard 2.3 3 4 7Standard 2.4 3 5 8Standard 2.5 4 3 7Standard 2.6 1 2 3Standard 2.7 1 2 33.0 Students move beyond a particular problem by generalizing to other situations.

3 3.5 6.5


Average 108:32=3.38

45


Table A35NCTM National Math Grades 6

Degree of Alignment

Content Standard Rater 1 Rater2 Total

Number and Operations Standard 5 4 9

1.0 Understand numbers, ways of representing numbers, relationships among numbers, and number systemsStandard 1.1 5 5 10Standard 1.2 4 4 8Standard 1.3 4 5 9Standard 1.4 5 3 8Standard 1.5 5 4 9Standard 1.6 2 2 4Standard 1.7 5 3 82.0 Understand meanings of operations and how they relate to one another

4 4 8

Standard 2.1 4 4 8Standard 2.2 5 4 9Standard 2.3 3 5 83.0 Compute fluently and make reasonable estimates

3 2 5

Standard 3.1 3 2 5Standard 3.2 1 3 4Standard 3.3 3 3 6Standard 3.4 5 3 8Average 126:34=3.71

46






Degree of Alignment

Rater 1 Rater2 TotalContent Standard

Algebra Standard1.0 Understand patterns, relations, and functions

4 3.5 7.5

Standard 1.1 3 4 7Standard 1.2 5 3 8Standard 1.3 4 4 82.0 Represent and analyze mathematical situations and structures using algebraic symbols

5 5 10

Standard 2.1 5 4 9Standard 2.2 4 5 9Standard 2.3 5 5 10Standard 2.4 5 5 103.0 Use mathematical models to represent and understand quantitative relationships

4 4 8

Standard 3.1 5 4 94.0 Analyze change in various contexts 2 3 5Standard 4.1 2 2 4Average 104.5:26=4.02

47







Degree of Alignment

Content Standard Rater 1 Rater2 TotalGeometry Standard1.0 Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

4 4.5 8.5

Standard 1.1 4 4 8Standard 1.2 5 5 10Standard 1.3 1 3 42.0 Specify locations and describe spatial relationships using coordinate geometry and other representational systems

4 2

Standard 2.1 4 2 6Standard 2.2 4 2 63.0 Apply transformations and use symmetry to analyze mathematical situations

4 3.5 7.5

Standard 3.1 4 3 7Standard 3.2 4 4 84.0 Use visualization, spatial reasoning, and geometric modeling to solve problems

3 4 7

Standard 4.1 3 5 8Standard 4.2 4 4 8Standard 4.3 1 2 3Standard 4.4 5 4 9Standard 4.5 3 5 8Average 108:30=3.6

48







Degree of Alignment

Content Standard Rater 1 Rater2 TotalMeasurement Standard1.0 Understand measurable attributes of objects and the units, systems, and processes of measurement

5 4 9

Standard 1.1 5 5 10Standard 1.2 5 3 8Standard 1.3 3 4 72.0 Apply appropriate techniques, tools, and formulas to determine measurements

3 4 7

Standard 2.1 2 4 6Standard 2.2 4 3 7Standard 2.3 4 5 9Standard 2.4 4 5 9Standard 2.5 5 4 9Standard 2.6 1 2 3

Average 84:22=3.82

49






Degree of Alignment

Content Standard Rater 1 Rater2 TotalData Analysis and Probability Standard1.0 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

3 3.5 6.5

Standard 1.1 1 3 4Standard 1.2 4 4 82.0 Select and use appropriate statistical methods to analyze data

5 4 9

Standard 2.1 5 3 8Standard 2.2 5 5 103.0 Develop and evaluate inferences and predictions that are based on data

4 2 6

Standard 3.1 5 3 8Standard 3.2 5 3 8Standard 3.3 1 3 44.0 Understand and apply basic concepts of probability

1 1.5 2.5

Standard 4.1 1 2 3Standard 4.2 1 1 2Standard 4.3 1 2 3Average 82:28=2.93

50







Degree of Alignment

Content Standard Rater 1 Rater2 TotalProblem Solving StandardStandard 1.1 5 3 8Standard 1.2 5 4 9Standard 1.3 2 3 5Standard 1.4 4 3 7Average 29:8=3.63

Table A 41NCTM National Math Grades 6

Degree of Alignment

Content Standard Rater 1 Rater2 TotalReasoning and Proof StandardStandard 1.1 2 3 5Standard 1.2 2 4 6Standard 1.3 1 2 3Standard 1.4 1 2 3Average 17:8=2.13

51



Degree of Alignment

Content Standard Rater 1 Rater2 TotalCommunication StandardStandard 1.1 4 2 6Standard 1.2 3 1 4Standard 1.3 1 1 2Standard 1.4 4 2 6Average 18:8=2.25


Degree of Alignment

Content Standard Rater 1 Rater2 TotalConnections StandardStandard 1.1 4 3 7Standard 1.2 1 2 3Standard 1.3 5 4 9

19:6=3.17


Degree of Alignment

Content Standard Rater 1 Rater2 TotalRepresentation StandardStandard 1.1 4 2 6Standard 1.2 4 4 8Standard 1.3 3 2 5Average 19:6=3.17

52


Table A 45California State Science Grade 6


Content Standard Rater 1 Rater 2 AverageFocus on Earth ScienceStandard 1: Plate Tectonics and Earth’s StructurePlate tectonics accounts for important features of Earth's surface and major geologic events.

2 3.5 5.5

Standard 1.a 3 5 8Standard 1.b 1 3 4Standard 1.c 2 4 6Standard 1.d 2 4 6Standard 1.e 3 5 8Standard 1.f 1 2 3Standard 1.g 1 2 3Average 43.5:16=2.72

53



Degree of Alignment

________________________________________________

Content Standard Rater 1 Rater 2 AverageFocus on Earth ScienceStandard 2: Shaping Earth’s SurfaceTopography is reshaped by the weathering of rock and soil and by the transportation and deposition of sediment.

2 3.5 5.5

Standard 2.a 2 4 6Standard 2.b 2.5 4 6.5Standard 2.c 1 3 4Standard 2.d 1 3 4

Average 26:10=2.6

54




Content Standard Rater 1 Rater 2 AverageFocus on Earth ScienceStandard 3: Heat (Thermal Energy) (Physical Sciences)Heat moves in a predictable flow from warmer objects to cooler objects until all the objects are at the same temperature.

1 2.5 3.5

Standard 3.a 1.5 3 4.5Standard 3.b 1 1 2Standard 3.c 1 2 3Standard 3.d 1 3 4

Average 17:10=1.7

55




Content Standard Rater 1 Rater 2 TotalFocus on Earth ScienceStandard 4: Energy in the Earth SystemMany phenomena on Earth's surface are affected by the transfer of energy through radiation and convection currents.

2 3.5 5.5

Standard 4.a 1 2 3Standard 4.b 1 3 4Standard 4.c 2 5 7Standard 4.d 3 3 6Standard 4.e 1.5 4 5.5

Average 31:12=2.58

56




Content Standard Rater 1 Rater 2 TotalFocus on Earth ScienceStandard 5: Ecology (Life Sciences)Organisms in ecosystems exchange energy and nutrients among themselves and with the environment.

1 2 3

Standard 5.a 1 3 4Standard 5.b 1 2 3Standard 5.c 1 2 3Standard 5.d 1 1 2Standard 5.e 1 3 4

Average 19:12=1.58

57




Content Standard Rater 1 Rater 2 TotalFocus on Earth ScienceStandard 6: ResourcesSources of energy and materials differ in amounts, distribution, usefulness, and the time required for their formation.

2 2.5 4.5

Standard 6.a 1 3 4Standard 6.b 2 3 5Standard 6.c 2 2 4

Average 17.5:8=2.19

58




Content Standard Rater 1 Rater 2 TotalFocus on Earth ScienceStandard 7: Investigation and ExperimentationScientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations.

4 4 8

Standard 7.a 5 4 9Standard 7.b 4 5 9Standard 7.c 5 4 9Standard 7.d 3 4 7Standard 7.e 4 4 8Standard 7.f 1 3 4Standard 7.g 4 4 8Standard 7.h 1 3 4

Average 66:18=3.67

59


Table A52National Science Grade 6

Degree of Alignment

Content Standard Rater 1 Rater 2 Total1.0 Science as Inquiry

Standard 1.1 5 4 9Standard 1.2 5 4 9Average 18:4=4.5


Degree of Alignment


2.0 Physical ScienceStandard 2.1 2 3 5Standard 2.2 4 4 8Standard 2.3 1 1 2

Average 15:6=2.5

60



Degree of Alignment


3.0 Life ScienceStandard 3.1 1 2 3Standard 3.2 1 1 2Standard 3.3 1 1 2Standard 3.4 1 3 4Standard 3.5 1 2 3Average 14:10=1.4

61


Table A 55National Science Grade 6

Degree of Alignment


4.0 Earth and Space ScienceStandard 4.1 4 5 9Standard 4.2 5 5 10Standard 4.3 5 3 8 27:6=4.5

62



Degree of Alignment

Content Standard Rater 1 Rater 2 Total5.0 Science and Technology

Standard 5.1 1 3 4Standard 5.2 2 3 5Average 9:4=2.25

63



Degree of Alignment


Standard 6.1 1 1 2Standard 6.2 4 2 6Standard 6.3 5 3 8Standard 6.4 4 4 8Standard 6.5 4 2 6Average 30:10=3

64



Degree of Alignment



65



Degree of Alignment



66




Rater1 Rater 2 TotalContent Standard

Number Sense1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:

5 4 9

Standard 1.1 5 5 10Standard 1.2 5 4 9Standard 1.3 5 4 9Standard 1.4 5 4 9Standard 1.5 5 5 10Standard 1.6 5 5 10Standard 1.7 5 3 82.0 Students use exponents, powers, and roots and use exponents in working with fractions.

5 4 9


Average 127:28=4.54

67





Algebra & Functions1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs.

5 3.5 8.5

Standard 1.1 5 5 10Standard 1.2 5 5 10Standard 1.3 5 4 9Standard 1.4 3 1 4Standard 1.5 5 4 92.0 Students interpret and evaluate expressions involving integer powers and simple roots.

5 4 9

Standard 2.1 5 5 10Standard 2.2 5 3 83.0 Students graph and interpret linear and some nonlinear functions.

3 3 6

Standard 3.1 1 1 2Standard 3.2 1 3 4Standard 3.3 5 5 10Standard 3.4 5 3 84.0 Students solve simple linear equations and inequalities over the rational numbers.

5 3.5 8.5


Average 133:34=3.91

68





Measurement and Geometry1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems.

4 3.5 7.5

Standard 1.1 4 4 8Standard 1.2 3 3 6Standard 1.3 4 4 82.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale.

4 4.5 8.5

Standard 2.1 5 5 10Standard 2.2 5 4 9Standard 2.3 5 5 10Standard 2.4 3 4 73.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures.

4 4 8


Average 132:32=4.13

69





Statistics, Data Analysis, and Probability1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program.

5 4.5 9.5

Standard 1.1 5 5 10Standard 1.2 5 5 10Standard 1.3 5 4 9Average 38.5:8=4.81

70


Table A64California State Math Grade 7



Mathematical Reasoning1.0 Students make decisions about how to approach problems.

5 4 9

Standard 1.1 5 4 9Standard 1.2 5 5 10Standard 1.3 5 3 82.0 Students use strategies, skills, and concepts in finding solutions.

4 3 7

Standard 2.1 5 3 8Standard 2.2 5 3 8Standard 2.3 5 4 9Standard 2.4 2 4 6Standard 2.5 5 4 9Standard 2.6 5 3 8Standard 2.7 5 3 8Standard 2.8 5 3 83.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations.

5 4.5 9.5


Average 144.5:34=4.25

71



Degree of Alignment


Number and Operations Standard 8

1.0 Understand numbers, ways of representing numbers, relationships among numbers, and number systems

4 4

Standard 1.1 4 5 9Standard 1.2 2 5 7Standard 1.3 4 3 7Standard 1.4 3 5 8Standard 1.5 4 5 9Standard 1.6 4 5 9Standard 1.7 5 5 102.0 Understand meanings of operations and how they relate to one another

3 5 8


3 4 7


Average 137:34=4.03

72






Degree of Alignment

Content Standard Rater 1 Rater 2 TotalAlgebra Standard 81.0 Understand patterns, relations, and functions

3 5

Standard 1.1 3 5 8Standard 1.2 3 5 8Standard 1.3 2 5 72.0 Represent and analyze mathematical situations and structures using algebraic symbols

3 5 8

Standard 2.1 5 5 10Standard 2.2 3 5 8Standard 2.3 4 5 9Standard 2.4 2 5 73.0 Use mathematical models to represent and understand quantitative relationshipsStandard 3.1 5 5 104.0 Analyze change in various contextsStandard 4.1 3 5 8Average 91:22=4.14

73







Degree of Alignment

Content Standard Rater 1 Rater 2 TotalGeometry Standard1.0 Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

4 4 8


4 5


1 2 3


3 5 8


74







Degree of Alignment

Content Standard Rater 1 Rater 2 TotalMeasurement Standard1.0 Understand measurable attributes of objects and the units, systems, and processes of measurement

3 5 8

Standard 1.1 3 5 8Standard 1.2 4 5 9Standard 1.3 3 5 82.0 Apply appropriate techniques, tools, and formulas to determine measurementsStandard 2.1 1 3 4Standard 2.2 4 5 9Standard 2.3 4 4 8Standard 2.4 3 4 7Standard 2.5 2 4 6Standard 2.6 2 4 6

Average 73:20=3.65

75






Degree of Alignment

Content Standard Rater 1 Rater 2 TotalData Analysis and Probability Standard1.0 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

3 5 8


3 4 7


3 4 7


4 3 7


76







Degree of Alignment

Content Standard Rater 1 Rater 2 TotalProblem Solving StandardStandard 1.1 4 5 9Standard 1.2 4 5 9Standard 1.3 3 5 8Standard 1.4 2 3 5Average 31:8=3.88


Degree of Alignment

Content Standard Rater 1 Rater 2 TotalReasoning and Proof StandardStandard 1.1 1 2 3Standard 1.2 3 5 8Standard 1.3 3 5 8Standard 1.4 2 4 6Average 25:8=3.13


Degree of Alignment

Content Standard Rater 1 Rater 2 TotalCommunication StandardStandard 1.1 3 2 5Standard 1.2 2 1 3Standard 1.3 1 1 2Standard 1.4 1 1 2Average 12:8=1.5

77



Degree of Alignment

Content Standard Rater 1 Rater 2 TotalConnections StandardStandard 1.1 3 5 8Standard 1.2 2 4 6Standard 1.3 4 4 8Average 22:6= 3.67


Degree of Alignment

Content Standard Rater 1 Rater 2 TotalRepresentation StandardStandard 1.1 3 5 8Standard 1.2 3 5 8Standard 1.3 2 4 6Average 22:6=3.67

78





Focus on Life ScienceStandard 1: Cell BiologyAll living organisms are composed of cells, from just one to many trillions, whose details usually are visible only through a microscope.

1 1 2

Standard 1.a 1 1 2Standard 1.b 1 2 3Standard 1.c 1 1 2Standard 1.d 1 1 2Standard 1.e 1 1 2Standard 1.f 1 1 2Average 15: 14=1.07

79


Table A 76California State Standards in Science Grade 7



Focus on Life ScienceStandard 2: GeneticsA typical cell of any organism contains genetic instructions that specify its traits. Those traits may be modified by environmental influences.

1 2 3

Standard 2.a 3 4 7Standard 2.b 1 1 2Standard 2.c 1 1 2Standard 2.d 1 3 4Standard 2.e 1 1 2Average 20:12=1.67

80





Focus on Life ScienceStandard 3: EvolutionBiological evolution accounts for the diversity of species developed through gradual processes over many generations.

2.5 2 4.5


Average 24.5:12=2.04

81



Degree of Alignment

________________________________________________Rater 1 Rater 2 Total

Content StandardFocus on Life ScienceStandard 4: Earth and Life History (Earth Sciences)Evidence from rocks allows us to understand the evolution of life on Earth

1 1 2

Standard 4.a 1 1 2Standard 4.b 1 1 2Standard 4.c 1 1 2Standard 4.d 1 1 2Standard 4.e 1 1 2Standard 4.f 1 1 2Standard 4.g 1 1 2

Average 16:16=1

82





Focus on Life ScienceStandard 5: Structure and Function in Living SystemsThe anatomy and physiology of plants and animals illustrate the complementary nature of structure and function.

2 2 4


Average 33:16=2.06

83





Focus on Life ScienceStandard 6: Physical Principles in Living Systems (Physical Sciences)Physical principles underlie biological structures and functions.

1 1 2

Standard 6.a 1 1 2Standard 6.b 1 1 2Standard 6.c 1 1 2Standard 6.d 1 1 2Standard 6.e 1 1 2Standard 6.f 1 1 2Standard 6.g 1 1 2Standard 6.h 1 1 2Standard 6.i 1 1 2Standard 6.j 1 1 2

Average 22:22=1

84





Focus on Life ScienceStandard 7: Investigation and ExperimentationScientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations.

3 2 5


Average 33:12=2.75

85


Table A 82National Science Grade 7Science as Inquiry

Degree of Alignment


1.0 Science as Inquiry 5 4 9

Standard 1.1 5 4.5 9.5Standard 1.2 5 4 9

27.5:6=4.58


Degree of Alignment


2.0 Physical Science 2.5 3 5.5Standard 2.1 1 2 3Standard 2.2 2 3 5Standard 2.3 3 4 7

Average 20.5:8=2.56

86



Degree of Alignment


3.0 Life Science 4.5 3 7.5Standard 3.1 5 4 9Standard 3.2 4 3 7Standard 3.3 5 4 9Standard 3.4 4 4 8Standard 3.5 5 4 9

Average 49.5:12=4.13

87



Degree of Alignment


4.0 Earth and Space Science1.5 3 4.5


Average 12.5:8=1.56


Degree of Alignment

Content Standard Rater 1 Rater 2 Total5.0 Science and Technology 2 3 5


Average 15:6=2.5

88



Degree of Alignment


3.5 3 6.5Standard 6.1 2 1 3Standard 6.2 4 3 7Standard 6.3 2 3 5Standard 6.4 4 4 8Standard 6.5 4 3.5 7.5

Average 37:12=3.08


Degree of Alignment


4.5 4 8.5Standard 7.1 5 3 8Standard 7.2 4 2 6Standard 7.3 4 3 7

Average 29.5:8=3.69

89



Degree of Alignment


5 4 9Standard 1.1 5 5 10Standard 1.2 5 4 9Standard 1.3 4 3 7Standard 1.4 5 4 9Standard 1.5 5 4 9

Average 53:12=4.42

90





Algebra I1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable.

4 5 9

Standard 1.1 2 4 62.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

4 5 9

Average 24:6=4

91





3.0 Students solve equations and inequalities involving absolute values.

4 5 9

4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.

5 5 10

5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

3 5 8

Average 27:6=4.5

92





6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).

5 5 10

7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.

5 5 10

Average 20:4=5

93





8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.

2 4 6

9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.

3 5 8

10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.

4 5 9

Average 23:6=3.83

94





11.0 Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.

5 5 10

12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.

5 5 10

13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.

3 3 6

Average 26:6=4.33

95





Algebra I14.0 Students solve a quadratic equation by factoring or completing the square.

5 5 10

15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.

5 4 9

Average 19:4=4.75

96





16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.

3 4 7

17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.

3 4 7

Average 14:4=3.5

97





18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.

3 5 8

19.0 Students know the quadratic formula and are familiar with its proof by completing the square.

4 5 9

Average 17:4=4.25

98





21.0 Students graph quadratic functions and know that their roots are the x- intercepts.

3 5 8

22.0 Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.

4 4 8

Average 16:4=4

99





23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.

4 5 9

24.0 Students use and know simple aspects of a logical argument.

1.5 3.5 5


Average 30:10=3

100





25.0 Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements:

3 3.5 6.5


Average 27.5:8=3.44

101



Degree of Alignment


Number and Operations Standard 1.0 Understand numbers, ways of representing numbers, relationships among numbers, and number systems

4 3 7

Standard 1.1 5 4 9Standard 1.2 5 3 8Standard 1.3 3 2 5Standard 1.4 5 3 8Standard 1.5 5 3 8Standard 1.6 4 2 6Standard 1.7 5 4 92.0 Understand meanings of operations and how they relate to one another

4 4 8


3 3.5 6.5


Average 124.5:34=3.66

102






Degree of Alignment


Algebra Standard1.0 Understand patterns, relations, and functionsStandard 1.1 3 5 8Standard 1.2 2 4 6Standard 1.3 4 5 92.0 Represent and analyze mathematical situations and structures using algebraic symbols

5 5 10

Standard 2.1 5 4 9Standard 2.2 5 5 10Standard 2.3 5 5 10Standard 2.4 5 5 103.0 Use mathematical models to represent and understand quantitative relationships

4 5 9

Standard 3.1 4 5 94.0 Analyze change in various contexts 4 5 9Standard 4.1 3 5 8

Average 107:24=4.45

103







Degree of Alignment


Geometry Standard1.0 Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

2 3 5


4 2 6


1 2 3


3 2.5 5.5


Average 87.5:32=2.73

104







Degree of Alignment


Measurement Standard1.0 Understand measurable attributes of objects and the units, systems, and processes of measurement

2 3.5 5.5

Standard 1.1 2 3 5Standard 1.2 2 4 6Standard 1.3 3 3 62.0 Apply appropriate techniques, tools, and formulas to determine measurements

3 3 6


Average 64.5: 22=2.93

105






Degree of Alignment


Data Analysis and Probability Standard1.0 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

3 4 7


4 4.5 8.5


4 4 8


3 3.5 6.5


Average 100:28=3.57

106







Degree of Alignment


Problem Solving StandardStandard 1.1 5 5 10Standard 1.2 4 5 9Standard 1.3 4 5 9Standard 1.4 2 3 5

Average 33:8=4.13


Degree of Alignment


Reasoning and Proof StandardStandard 1.1 4 5 9Standard 1.2 3 5 8Standard 1.3 3 5 8Standard 1.4 3 5 8

Average 33:8=4.13

107



Degree of Alignment


Communication StandardStandard 1.1 1 2 3Standard 1.2 1 1 2Standard 1.3 1 1 2Standard 1.4 1 2 3

Average 10:8=1.25


Degree of Alignment


Connections StandardStandard 1.1 4 5 9Standard 1.2 3 5 8Standard 1.3 5 5 10

Average 27:6=4.5


Degree of Alignment


Representation StandardStandard 1.1 5 5 10Standard 1.2 5 4 9Standard 1.3 3 5 8

Average 27:6=4.5

108


Table A 111TIMSS International Math Grade 8


Content StandardNumber 1.0 Number: Whole NumbersStandard 1.1 5 4 9Standard 1.2 4 5 9Standard 1.3 5 3 8Standard 1.4 5 4 9Standard 1.5 4 4 82.0 Number: Fractions and DecimalsStandard 2.1 5 5 10Standard 2.2 5 4 9Standard 2.3 5 5 10Standard 2.4 5 4 9Standard 2.5 5 4 9Standard 2.6 5 4 9Standard 2.7 4 5 93.0 Number: IntegersStandard 3.1 5 4 9Standard 3.2 5 5 104.0 Number: Ratio, Proportion, and PercentStandard 4.1 5 5 10Standard 4.2 4 5 9Standard 4.3 5 5 10Standard 4.4 4 4 8

Average 156: 18=8.67

109



Degree of Alignment

Content Standard Rater 1 Rater 2 TotalAlgebra1.0 Algebra: PatternsStandard 1.1 1 2 3Standard 1.2 1 2.5 3.52.0 Algebra: Algebraic ExpressionsStandard 2.1 5 4 9Standard 2.2 5 4 9Standard 2.3 5 5 10Standard 2.4 5 4 93.0 Algebra: Equations/Formulas and FunctionsStandard 3.1 5 4 9Standard 3.2 5 5 10Standard 3.3 5 5 10Standard 3.4 5 4 9Standard 3.5 5 4 9Standard 3.6 5 4 9

Average 99.5:24=4.15

110




Content StandardGeometry1.0 Geometry: Geometric ShapesStandard 1.1 1 2 3Standard 1.2 1.5 3 4.5Standard 1.3 4 3 7Standard 1.4 1 2 3Standard 1.5 1 2 3Standard 1.6 2 3 5Standard 1.7 1 2 3Standard 1.8 5 5 10Standard 1.9 5 4 92.0 Geometry: Geometric MeasurementStandard 2.1 2 3 5Standard 2.2 1 2 3Standard 2.3 1 2 3Standard 2.4 4 3 73.0 Geometry: Location and MovementStandard 3.1 5 4 9Standard 3.2 2 3 5Standard 3.3 1 2 3

Average 82.5:32=2.58

111




Content StandardData and Chance1.0 Data and Chance: Data Organization and RepresentationStandard 1.1 2 3 5Standard 1.2 2 3 5Standard 1.3 1 2 32.0 Data and Chance: Data InterpretationStandard 2.1 1 2 3Standard 2.2 3 4 7Standard 2.3 1 2 33.0 Data and Chance: ChanceStandard 3.1 1 2 3Standard 3.2 1 2 3Standard 3.3 1 2 3

Average 35: 18=1.94

112




Content StandardThe Cognitive Domain1.0 KnowingStandard 1.1 5 4 9Standard 1.2 5 4 9Standard 1.3 5 5 10Standard 1.4 2 3 5Standard 1.5 2 1 3Standard 1.6 4 3 72.0 ApplyingStandard 2.1 5 5 10Standard 2.2 3 3 6Standard 2.3 5 4 9Standard 2.4 4 4 8Standard 2.5 5 4 93.0 ReasoningStandard 3.1 3 4 7Standard 3.2 3 3 6Standard 3.3 5 4 9Standard 3.4 3 3 6Standard 3.5 3 3 6

Average 119:32=3.72

113




Content Standard Rater 1 Rater 2 TotalFocus on Physical ScienceStandard 1: MotionThe velocity of an object is the rate of change of its position.

4 5 9

Standard 1.a 5 5 10Standard 1.b 5 5 10Standard 1.c 5 5 10Standard 1.d 5 5 10Standard 1.e 5 5 10Standard 1.f 3 5 8

Average 67:14=4.79

114




Content Standard Rater 1 Rater 2 TotalFocus on Physical ScienceStandard 2: ForcesUnbalanced forces cause changes in velocity.

5 4 9


Average 72:16=4.5

115





Focus on Physical ScienceStandard 3: Structure of MatterEach of the more than 100 elements of matter has distinct properties and a distinct atomic structure. All forms of matter are composed of one or more of the elements.

5 4 9

Standard 3.a 5 3 8Standard 3.b 5 5 10Standard 3.c 5 3 8Standard 3.d 5 5 10Standard 3.e 5 4 9Standard 3.f 5 5 10

Average 64:14=4.57

116




Content Standard Rater 1 Rater 2 TotalFocus on Physical Science 1 1 2Standard 4: Earth in the Solar SystemThe structure and composition of the universe can be learned from studying stars and galaxies and their evolution.

1 1


Average 12:12=1

117




Content Standard Rater 1 Rater 2 TotalFocus on Physical ScienceStandard 5: ReactionsChemical reactions are processes in which atoms are rearranged into different combinations of molecules.

5 4 9


Average 56:12=4.67

118




Content Standard Rater 1 Rater 2 TotalFocus on Physical Science 4 3 7Standard 6: Chemistry of Living Systems (Life Sciences)Principles of chemistry underlie the functioning of biological systems.

4 4 8


Average 37:8=4.63

119




Content Standard Rater 1 Rater 2 TotalFocus on Physical Science 5 4 9Standard 7: Periodic TableThe organization of the periodic table is based on the properties of the elements and reflects the structure of atoms.

5 5 10


Average 48:10=4.8

120




Content Standard Rater 1 Rater 2 TotalFocus on Physical Science 5 5 10Standard 8: Density and BuoyancyAll objects experience a buoyant force when immersed in a fluid.

5 5

Standard 8.a 5 4 9Standard 8.b 5 4 9Standard 8.c 5 5 10Standard 8.d 5 5 10

Average 48:10=4.8

121




Content Standard Rater 1 Rater 2 TotalFocus on Life Science 4 3 7Standard 9: Investigation and ExperimentationScientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations.

4 4 8


Average 69:18=3.83

122



Degree of Alignment

Content Standard1.0 Science as Inquiry Rater 1 Rater 2 Total


Average 18:4=4.5

123



Degree of Alignment

Content StandardRater 1 Rater 2 Total

2.0 Physical ScienceStandard 2.1 5 4 9Standard 2.2 3 5 8Standard 2.3 4 5 9

Average 26:6=4.33


Degree of Alignment

Content StandardRater 1 Rater 2 Total

3.0 Life ScienceStandard 3.1 2 2 4Standard 3.2 1 1 2Standard 3.3 2 3 5Standard 3.4 3 4 7Standard 3.5 1 3 4

Average 22:10=2.2

124



Degree of Alignment

Content Standard

4.0 Earth and Space ScienceRater 1 Rater 2 Total


Average 6:6=1

125



Degree of Alignment

Content Standard5.0 Science and Technology Rater 1 Rater 2 Total


15:4=3.75

126



Degree of Alignment

Content Standard6.0 Science in Personal and Social Perspectives

Rater 1 Rater 2 Total


127



Degree of Alignment

Content Standard7.0 History and Nature of Science Rater 1 Rater 2 Total



Degree of Alignment

Content Standard1.0 Unifying Concepts and Processes Rater 1 Rater 2 Total


39:10=3.9

128


Table A 133TIMSS International Science Grade 8



Focus on Biology 1 1 2Standard 1.0: Biology: Characteristics, Classification, and Life Processes of Organisms

1 1 2

Standard 1.1 1 1 2Standard 1.2 2 1 3Standard 1.3 1 1 2Standard 1.4 1 1 2Average 13:12=1.1

129



Degree of Alignment______________________________________________


Focus on Biology 1 1 2Standard 2.0: Biology: Cells and Their Functions

1 1 2

Standard 2.1 1 1 2Standard 2.2 1 1 2Standard 2.3 1 1 2Standard 2.4 1 1 2Average 12:12=1


Degree of Alignment

________________________________________________Rater 1 Rater 2 Total

Content StandardFocus on Biology 1 1 2Standard 3.0: Biology: Life Cycles, Reproduction, and Heredity

1 1 2


Average 10:10=1

130





Focus on BiologyStandard 4.0: Biology: Diversity, Adaptation, and Natural Selection

1 1 2


Average 6:6=1



Content Standard Rater 1 Rater 2 TotalFocus on BiologyStandard 5.0: Biology:EcosystemsStandard 5.1 1 1 2Standard 5.2 1 1 2Standard 5.3 1 1 2Standard 5.4 1 1 2Standard 5.5 1 1 2

Average 10:10=1

131





Focus on BiologyStandard 6.0: Biology:Human Health

1 1 2


Average 6:6=1



Content Standard Rater 1 Rater 2 TotalFocus on ChemistryStandard 1.0: Chemistry: Classification and Composition of MatterStandard 1.1 3 5 8Standard 1.2 3 5 8Standard 1.3 3 5 8Standard 1.4 4 5 9

Average 33:8=4.13

132




Content Standard Rater 1 Rater 2 TotalFocus on ChemistryStandard 2.0: Chemistry: Properties of MatterStandard 2.1 2 1 3Standard 2.2 4 5 9Standard 2.3 3 5 8Standard 2.4 4 5 9

Average 29:8=3.63




Focus on ChemistryStandard 3.0: Chemistry: Chemical ChangeStandard 3.1 5 5 10Standard 3.2 5 5 10Standard 3.3 4 4 8Standard 3.4 4 5 9

Average 37:8=4.63

133




Content Standard Rater 1 Rater 2 TotalFocus on PhysicsStandard 1.0: Physics: Physical States and Changes in MatterStandard 1.1 4 5 9Standard 1.2 3 5 8Standard 1.3 3 5 8Standard 1.4 4 5 9Average 34:8=4.25



Content Standard Rater 1 Rater 2 TotalFocus on PhysicsStandard 2.0: Physics: Energy Transformations, Heat, and TemperatureStandard 2.1 3 4 7Standard 2.2 4 5 9Standard 2.3 3 5 8Average 24:6=4

134




Content Standard Rater 1 Rater 2 TotalFocus on PhysicsStandard 3.0: Physics: LightStandard 3.1 3 5 8Standard 3.2 5 5 10Standard 3.3 3 5 8

Average 26:6=4.33



Content Standard Rater 1 Rater 2 TotalFocus on Earth ScienceStandard 1.0: Earth Science: Earth’s Structure and Physical FeaturesStandard 1.1 1 2 3Standard 1.2 1 1 2Standard 1.3 1 1 2

Average 7:6=1.17

135




Content Standard Rater 1 Rater 2 TotalFocus on Earth ScienceStandard 2.0: Earth Science: Earth’s Processes, Cycles, and HistoryStandard 2.1 1 1 2Standard 2.2 1 1 2Standard 2.3 1 1 2Standard 2.4 1 1 2Standard 2.5 4 5 9Standard 2.6 1 1 2Average 19:12=1.58



Content Standard Rater 1 Rater 2 TotalFocus on Earth ScienceStandard 3.0: Earth Science: Earth’s Resources, Their Use and ConservationStandard 3.1 3 4 7Standard 3.2 1 1 2Standard 3.3 1 1 2

Average 11:3=3.7

136




Content Standard Rater 1 Rater 2 TotalFocus on Earth ScienceStandard 4.0: Earth Science: Earth in the Solar System and the UniverseStandard 4.1 1 1 2Standard 4.2 1 1 2Standard 4.3 1 1 2Standard 4.4 1 1 2

Average 8:8=1



Content Standard Rater 1 Rater 2 TotalFocus on PhysicsStandard 4.0: Physics: SoundStandard 4.1 1 1 2Standard 4.2 1 1 2

Average 4:4=1



Content Standard Rater 1 Rater 2 TotalFocus on PhysicsStandard 5.0: Physics:Electricity and MagnetismStandard 5.1 3 4 7Standard 5.2 2 3 5

Average 12:4=3

137




Content Standard Rater 1 Rater 2 TotalFocus on PhysicsStandard 6.0: Physics:Forces and MotionStandard 6.1 5 5 10Standard 6.2 4 5 9Standard 6.3 5 5 10Standard 6.4 4 5 9Standard 6.5 3 5 8

Average 46:10=4.6



Content Standard Rater 1 Rater 2 TotalCognitive DomainStandard 1.0: KnowingStandard 1.1 5 5 10Standard 1.2 4 5 9Standard 1.3 4 5 9Standard 1.4 3 4 7Standard 1.5 5 5 10

Average 45:10=4.5

138




Content Standard Rater 1 Rater 2 TotalCognitive DomainStandard 2.0: ApplyingStandard 2.1 5 5 10Standard 2.2 4 5 9Standard 2.3 3 5 8Standard 2.4 3 5 8Standard 2.5 4 5 9Standard 2.6 5 5 10

Average 54:12=4.5



Content Standard Rater 1 Rater 2 TotalCognitive DomainStandard 3.0: ReasoningStandard 3.1 4 5 9Standard 3.2 2 4 6Standard 3.3 5 5 10Standard 3.4 2 4 6Standard 3.5 4 5 9Standard 3.6 3 5 8Standard 3.7 5 4 9Standard 3.8 3 5 8

Average 65: 16=4.06

139


Appendix C

Table B1California State Math, Grade 4

Rater 1 Rater2 TotalContent Standard- Number Sense 3.8 3.6 3.69Content Standard- Algebra and Functions

2.9 3.3 3.11

Content Standard- Measurement and Geometry

2.8 2.75 2.8

Content Standard -Statistics, Data Analysis, and Probability

4.4 3.3 3.85

Content Standard -Mathematical Reasoning

3.4 3.5 3.45

Total (All Standards) 3.38

140


Table B 2National Math, Grade 4

Rater 1 Rater2 TotalContent Standard- Number and Operations Standard

4.1 3.35 3.75

Content Standard- Algebra Standard 3.54 3.27 3.13Content Standard-Geometry Standard 2.6 2.75 2.6Content Standard-Measurement Standard

3.9 3 3.45

Content Standard-Data Analysis and Probability Standard

2.5 2.7 2.35


141


Table B3International Math, Grade 4

Rater 1 Rater2 TotalContent Standard-Number 3.95 3.8 3.88Content Standard- Geometric Shapes and Measures

4.6 4.3 4.46

Content Standard- Data Display: Reading and Interpreting

3.8 3 3.30

Content Standard-The Cognitive Domain

4.7 3.75 4.22


142


Table B 4California State Science, Grade

Rater 1 Rater2 TotalContent Standard (Physical Sciences 4.7 4.4 4.55Content Standard(Life Sciences 4.1 4.1 4.1Content Standard(Earth Sciences 4.9 4.6 4.75Content Standard(Investigation and Experimentation

3.9 3.7 3.8


143


Table B 5NSES National Standards in Science, Grade 4

Rater 1 Rater2 TotalContent Standard (Science as Inquiry) 5 5 5Content Standard(Physical Science) 2.7 3 2.85Content Standard(Life Science) 3.7 4 3.85Content Standard(Earth and Space Science)

4 3.7 3.85

Content Standard(Science and Technology)

4 3.3 3.65

Content Standard(Science in Personal and Social Perspectives)

4 3.8 3.9

Content Standard(History and Nature of Science)

4 4 4

Content Standard(Unifying Concepts and Processes)

4.4 3.8 4.1


144


Table B 6TIMMS International Standards in Science, Grade 4

Rater 1 Rater2 TotalLife Science 2.75 2.8 2.8Physical Science 2.5 2.6 2.55Earth Science 3 2.8 2.9The Cognitive Domain 4.6 4.5 4.6Total (All Standards) 3.20

145


Table B 7California State Math Grade 6

Rater 1 Rater2 TotalNumber Sense 3.2 4.4 3.8Algebra & Functions 4.8 4.5 4.5Measurement and Geometry 3 3.1 3.06Statistics, Data Analysis, and Probability 1.2 1.8 1.49Mathematical Reasoning 3.3 3.5 3.4Total (All Standards) 3.25

146


Table B 8NCTM National Standards in Math, Grades 6

Rater 1 Rater2 Total

Number and Operations Standard 3.9 3.5 3.7

Algebra Standard 4.1 4 4.02Geometry Standard 3.6 3.6 3.6Measurement Standard 3.7 3.9 3.82

Data Analysis and Probability Standard 3 2.9 2.93

Problem Solving Standard 4 3.25 3.63Reasoning and Proof Standard 1.5 2.75 2.13Communication Standard 3 1.5 2.25Connections Standard 3.3 3 3.17Representation Standard 3.6 2.7 3.17Total (All Standards) 3.20

147


Table B 9

California State Science Grade 6

________________________________________________

Rater 1 Rater 2 Total

Focus on Earth Science (Plate Tectonics and Earth’s Structure)

1.7 3.5 2.6

Focus on Earth Science (Shaping Earth’s Surface)

1.1 2.3 1.7

Focus on Earth Science (Shaping Earth’s Surface)

1.75 3.4 2.58

Focus on Earth Science Heat (Thermal Energy)

1 2.2 1.58

Focus on Earth Science (Energy in the Earth System)

1.75 2.6 2.19

Focus on Earth Science (Ecology -Life Sciences)

3.4 3.9 3.67


148


Table B 10National Science Grade 6

Rater 1 Rater2 TotalContent Standard(Science Inquiry) 5 4 4.5Content Standard(Physical Science) 2.3 4 2.5Content Standard(Life Science) 1 1.8 1.4Content Standard (Earth and Space Science)

4.7 4.3 4.5

Content Standard (Science and Technology)

1.5 3 2.25

Content Standard (Science in Personal and Social Perspectives)

3.6 2.4 3

Content Standard (History and Nature of Science)

4.3 4 4.16

Content Standard (Unifying Concepts and Processes)

4.2 4.2 4.2

Content Standard (Focus on Earth Science)

1.9 3.6 2.72


149



Rater 1 Rater2 TotalContent Standards :Number Sense 5 4.1 4.54Algebra & Functions 4.3 3.5 3.91Measurement and Geometry 4.25 4 4.13Statistics, Data Analysis, and Probability 5 4.6 4.81Mathematical Reasoning 4.8 3.7 4.25Total (All Standards) 4.35

150


Table B 12NCTM National Math Grades 7

Rater 1 Rater2 TotalNumber and Operations Standard 3.4 4.6 4.03Algebra Standard 3.3 5 4.14Geometry Standard 3.01 4.5 3.73Measurement Standard 2.9 4.4 3.65Data Analysis and Probability Standard 3.2 4.1 3.68Problem Solving Standard 3.25 4.5 3.88Reasoning and Proof Standard 2.25 4 3.11Communication Standard 1.75 1.25 1.5Connections Standard 3 4.3 3.67Representation Standard 2.7 4.7 3.67Total (All Standards) 3.50

151


Table B 13California State Science Grade 7

Rater 1 Rater2 TotalContent Standard (Focus on Life Science)

1 1.1 1.07

Content Standard (Focus on Life Science)

1.3 2 1.67


2.1 2 2.04


1 1 1.00


2.1 2 2.06


1 1 1.00


3 2.5 2.75


152



Rater 1 Rater2 TotalContent Standard (Science as Inquiry) 5 4.2 4.58Content Standard (Physical Science) 2.12 3 2.56Content Standard (Life Science) 4.6 3.7 4.13Content Standard (Earth and Space Science)

1.13 2 1.56

Content Standard (Science and Technology)

2.3 2.7 2.5

Content Standard (Science in Personal and Social Perspectives)

3.25 3 3.08

Content Standard (History and Nature of Science)

4.4 3 3.69

Content Standard (Unifying Concepts and Processes)

4.8 4 4.42


153



Rater 1 Rater2 TotalContent Standard 3.3 4.7 4.00Content Standard 4 5 4.5Content Standard 5 5 5.00Content Standard 3 4.7 3.83

Content Standard 4.3 4.3 4.3Content Standard 5 4.5 4.75Content Standard 3 4 3.5Content Standard 3.5 5 4.25Content Standard 3.5 4.5 4.00Content Standard 2.3 3.7 3.00Content Standard 3.25 3.6 3.44Total (All Standards) 4.05

154


Table B 16NCTM National Math Grades 8

Rater 1 Rater2 TotalNumber and Operations Standard 3.9 3.4 3.66Algebra Standard 4.1 4.8 4.45Geometry Standard 2.9 2.6 2.73Measurement Standard 2.7 3.1 2.93Data Analysis and Probability Standard 3.1 4.1 3.57Problem Solving Standard 3.75 4.5 4.13Reasoning and Proof Standard 3.25 5 4.13Communication Standard 1 1.5 1.25Connections Standards 4 5 4.5Representation Standard 4.3 4.7 4.5Total (All Standards) 3.60

155


Table B 17TIMMS International Math Grade 8

Rater 1 Rater2 TotalNumber 4.2 4.3 4.25Algebra 4.3 4 4.15Geometry 2.3 2.8 2.58Data and Chance 1.4 2.4 1.94The Cognitive Domain 3.9 3.6 3.72Total (All Standards) 3.33

156


Table B 18California State Science Grade 8

________________________________________________

Rater 1 Rater 2 Total Focus on Physical Science Focus on Physical Science

4.6 5 4.79

Content Standard - Focus on Physical Science

5 4 4.50


5 4.14 4.57


1 1 1.00


5 4.8 4.67


4 3.2 3.70


5 4.6 4.80


5 4.6 4.00

Content Standard - Focus on Life Science

3.9 3.8 3.83


157



Rater 1 Rater2 TotalContent Standard (Science as Inquiry) 4 5 4.50Content Standard (Physical Science) 4 4.7 4.33Content Standard(Life Science) 1.8 2.6 2.2Content Standard(Earth and Space Science)

1 1 1.00

Content Standard(Science and Technology)

3 4.5 3.75

Content Standard(Science in Personal and Social Perspectives)

2.8 3.8 3.40

Content Standard(History and Nature of Science)

3.3 4 3.67

Content Standard(Unifying Concepts and Processes)

3.2 4.6 3.90


158


Table B 20TIMMS International Science Grade 8

Rater 1 Rater2 TotalContent Standard (Focus on Biology) 1.2 1 1.10Content Standard (Focus on Biology) 1 1 1.00Content Standard (Focus on Biology) 1 1 1.00Content Standard (Focus on Biology) 1 1 1.00Content Standard (Focus on Biology) 1 1 1.00Content Standard (Focus on Biology) 1 1 1.00Content Standard (Focus on Chemistry)

3.25 5 4.13

Content Standard (Focus on Chemistry)

3.25 4 3.63

Content Standard (Focus on Chemistry)

4.5 4.75 4.63

Content Standard (Focus on Physics) 3.5 5 4.25Content Standard (Focus on Physics) 3.3 4.7 4.00Content Standard (Focus on Physics) 3.7 5 4.33Content Standard (Focus on Earth Science)

1 1.3 1.17


1.5 1.7 1.58


1.7 2 1.85


1 1 1.00

Content Standard (Focus on Physics) 1 1 1.00Content Standard (Focus on Physics) 2.5 3.5 3.00Content Standard (Focus on Physics) 4.2 5 4.60Content Standard (Cognitive Domain) 4.2 4.8 4.50Content Standard (Cognitive Domain) 4 5 4.50Content Standard (Cognitive Domain) 3.5 4.6 4.06Total (All Standards) 2.65

159

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