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Carolina Institute for Public Policy

Middle School Math: What are North Carolina Teachers Teaching in the DSSF Pilot Districts

and Elsewhere?

April 2009

Middle School Math: What are North Carolina

Teachers Teaching in the DSSF Pilot Districts

and Elsewhere?

April 2009

by

Kelly M. Purtell, UNC-Chapel Hill

Rebecca A. Zulli, UNC-Chapel Hill

Charles L. Thompson, East Carolina University

Gary T. Henry, UNC-Chapel Hill

Acknowledgements

We wish to thank the local educators in the 77 middle schools who participated in this study by

completing the survey of grades 6-8 mathematics content coverage. Without the time and

information that they generously provided, we could not have completed this examination of

middle grades mathematics content coverage.

We also wish to thank the teachers from the middle school math department at Woods Charter

School for helping us to develop a preliminary mapping of the survey items to the appropriate

NC Standard Course of Study. We also wish to recognize Dr. Everly Broadway, Section Chief

for K-12 Mathematics at the North Carolina Department of Public Instruction and Robin Barbour

and Mary Russell, consultants within the K-12 Mathematics section, for the expert guidance they

provided by reviewing our mapping of the survey items to the appropriate NC Standard Course

of Study.

In addition, we wish to thank the staff of Compass consulting who handled the administration of

the survey and Patrick DeHaye from the Andrew Young School of Policy Studies at Georgia

State University who was responsible for scanning the surveys and creating the clean data files

for this investigation.

Table of Contents

Executive Summary 1

Introduction 1

Data 2

Survey Construction & Organization 3

Findings 4

Conclusion 8

References 10

Tables

Table 1 School Demographics (School Year 2006-07) 3

Table 2 Content Coverage in Participating Middle Schools 4

Table 3 Content Coverage in DSSF and Matched Middle Schools 5

Table 4 Grade 6 Content Coverage 6



Appendix

Survey of Instructional Content for Grades 6-8 Mathematics 11

Executive Summary

One of the strongest indicators of high school success is middle grades mathematics achievement.

Without opportunities to learn the content specified in the North Carolina Standard Course of

Study, students are unlikely to succeed in high school. In this study, we examine the extent to

which mathematics teachers in middle schools with substantial educational disadvantages,

including those in the Disadvantaged Student Supplemental Fund pilot districts, are teaching the

NC Standard Course of Study.

A primary goal of this study was to examine math content coverage in middle schools located in

Disadvantaged Student Supplementary Fund (DSSF) pilot districts and compare the coverage in

those schools to a group of similar middle schools in districts not receiving pilot DSSF funds.

On a survey tailored to the NC Standard Course of Study in mathematics, middle school math

teachers reported how much time they spent covering a number of different math topics

throughout the 2007-08 school year. These items were designed to provide an overview of how

much time teachers are spending on material that is expected to be covered in grades 6-8

including how much time they are spending on remedial material, which is expected to be

covered in earlier grades. Coverage of on-grade items was examined in terms of both overall

coverage and coverage of each of the five specific competency goals outlined in the Standard

Course of Study. In addition to examining coverage differences between DSSF and non-DSSF

classrooms, we also investigated differences in coverage by teacher characteristics, such as years

of experience and licensure.

The primary differences we found are:

There were virtually no significant differences in reported content coverage between

DSSF and non-DSSF schools.

Teachers with elementary licenses (in the 6th

grade) and middle school math licenses (in

the 7th

grade) reported higher levels of overall content coverage and higher coverage of

certain specific competency goals. There were no licensure-related findings in the 8th

grade.

Teachers who themselves had higher standardized test scores (e.g., scores on PRAXIS

exams) reported lower coverage of remedial material in both the 7th

and 8th

grade.

Introduction

This report presents findings from a study designed to shed light on the amount and type of

content being covered in middle school mathematics classrooms in districts receiving

Disadvantaged Student Supplemental Funds and a set of similar middle schools in non-DSSF

districts. The Disadvantaged Student Supplementary Fund (DSSF) was established as a pilot

program in 2004 by Governor Easley and the North Carolina State Board of Education. The

pilot took place in 16 of the most disadvantaged school districts in the state and was designed to

increase learning and student achievement, particularly among academically disadvantaged

students. During the 2004-05 school year, the program provided $22.4 million to the 16 pilot

districts. The pilot program continued with slightly increased funding for the 2005-06 school

year. In school year 2006-07, the Governor recommended expanding the program statewide, and

the General Assembly appropriated $49.5 million for this purpose. The program allowed

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districts flexibility in using the funds to attract and retain qualified, competent teachers and to

provide enhanced instructional opportunities to students at risk of academic failure.

This brief report is one in a series designed to document the impact DSSF has exerted on

participating schools. This report focuses specifically on the mathematics content being covered

by teachers in the middle grades. In other reports, we have established that DSSF pilot funding

had an effect on student achievement (Henry, Thompson, Fortner, Rickman and Zulli, 2008). In

this report, we investigate a potential explanation for the effect—that is the teachers provided

more opportunities to learn mathematics content. Because DSSF was designed to allow districts

to recruit and retain teachers as well as to provide teachers with professional development

activities, there is reason to assess the possibility that teachers in DSSF schools may have

different patterns of content coverage than teachers in non-DSSF schools. That is, teachers in

DSSF districts may have been taught and encouraged to improve their students’ opportunities to

learn tested content by teaching the North Carolina Standard Course of Study more thoroughly,

or with a set of emphases better attuned to the demands of the State’s End–of-Grade tests.

Three primary questions guided this report:

1) What does math content coverage look like in the middle school grades? That is, how

much time do teachers report spending on material contained in the North Carolina

Standard Course of Study?

2) Are there differences in math content coverage between teachers in DSSF schools and

non-DSSF schools?

3) Do teachers with different qualifications (e.g., years of experience, level of education)

vary in their math content coverage?

This report will provide an overview of the data collected, a description of the survey used, and a

detailed look at the findings.

Data

Data for this report comes from mathematics content coverage surveys that were completed by

middle school math teachers (grades 6-8) in 38 DSSF schools and 39 non-DSSF schools where

student achievement levels were similar to the DSSF schools in the year before the

Disadvantaged Student Supplemental Fund was initiated. By choosing schools whose pre-DSSF

performance levels were similar to the DSSF schools’ pre-pilot performance levels, we set the

stage to ask whether the DSSF schools provided more coverage of mathematics content than

similar middle schools elsewhere in the state after the pilot was initiated, and if so, whether

differences in the patterns of content coverage could account for the greater progress. That is,

one very basic way in which DSSF might improve student performance would be to improve

students’ opportunities to learn – to spur better coverage of the knowledge and skills on which

students are tested. This report was designed to address only the first issue: whether there were

differences in content coverage. Data on the school’s 2007-08 student performance were not yet

available when we carried out the analyses for this report.

In the spring of 2008 a total 86 schools (44 schools in districts receiving DSSF pilot funds and 42

schools in districts not receiving DSSF pilot funds) schools agreed to participate in a survey

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effort which combined the collection of the Carolina Dimensions of Schooling Survey (CDOSS)

along with the surveys of mathematics and language arts content coverage. In each of the

participating schools all teachers received the CDOSS. For those teachers who taught

mathematics within the participating schools, a content coverage survey was included as an

insert inside the CDOSS. Nine of the 86 schools that agreed to participate in the survey effort

failed to provide any completed math content coverage surveys. Six of these schools were in

DSSF pilot districts and the other three were in non-DSSF pilot districts). Additionally, fifteen

schools from non-DSSF districts that were initially asked to participate in the survey opted not to

participate. In these cases, alternate schools with similar performance levels were added until

agreement to participate was obtained from 42 schools from non-DSSF pilot districts.

Within participating schools, all 6th

-8th

grade math teachers were asked to complete the math

content coverage survey. A total of 458 teachers completed the survey in April 2008 and

reported on coverage during the 2007-08 academic year. The overall response rate for the survey

(including non-participation by both teachers and schools) was 56%. The rate of completion

among teachers was 67%. Information on the characteristics of teachers who completed the

survey was obtained through administrative records provided by the N.C .Department of Public

Instruction. The demographic characteristics of the participating DSSF schools, the matched

schools, and all middle schools in North Carolina are shown below in Table 1.

Table 1: School Demographics (School Year 2006-07)

School

Characteristics

DSSF

Schools

Match

Schools

Other Middle

Schools

All Middle

Schools in N.C.

Income Averages Free Lunch 57.55% 49.94% 34.35% 37.23%

Reduced Price Lunch 8.87% 9.40% 8.36% 8.47%

Ethic Composition

White 26.47% 37.91% 55.88% 54.95%

Black 51.99% 46.43% 29.91% 30.67%

Asian 0.34% 1.41% 1.65% 1.61%

Hispanic 5.34% 9.23% 7.12% 7.13%

Multi-racial 1.14% 1.98% 2.25% 2.22%

American Indian 14.72% 0.43% 1.49% 1.73%

Survey Construction & Organization

Understanding the extent to which middle school teachers cover the content in terms of the NC

Standard Course of Study is important because the Standard Course of Study specifies what each

student should know and be able to do in mathematics and what material will be on the End-of-

Grade exams. The study survey was based on the instructional content portion of the Survey of

Enacted Curriculum (SEC) for Mathematics, which was developed from 1998-2000 through a

collaboration between state education specialists and researchers led by the Council of Chief

State School Officers (CCSSO). The original SEC was modified in order to align it with the

North Carolina Standard Course of Study. The survey was also reviewed by a small number of

NC middle school teachers, whose feedback helped ensure an accurate mapping. After the

survey was administered, items were mapped onto the 6th

grade Standard Course of Study, the 7th

grade Standard Course of Study, the 8th

grade Standard Course of Study. In addition, items that

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represented remedial material for each grade were identified for analysis. This mapping was

conducted by members of our research team, in conjunction with local middle school teachers

and mathematics consultants at NC DPI. Items were organized to provide an overview of how

much time teachers are spending on material that is expected to be covered in their grade and

how much time they are spending on material that is expected to be covered in earlier grades.

Coverage of on-grade items were examined in terms of both overall coverage and coverage of

the five broad goal areas into which specific objectives are grouped in the Standard Course of

Study for each of the middle grades. The five goal areas (―competency goals‖) are: 1) Numbers

& Operations, 2) Measurement, 3) Geometry, 4) Data Analysis & Probability and 5) Algebra.

Remedial content items were placed into three categories: 1) Elementary Remedial (items

contained in the Standard Course of Study for elementary grades, but not middle school grades),

2) 6th

Grade Remedial (items contained in the 6th

grade Standard Course of Study, but considered

remedial in grades 7 and 8), and 3) 7th

Grade Remedial (items contained in the 7th

grade Standard

Course of Study, but considered remedial for grade 8).

Findings

To answer our initial question, we first investigated what teachers across grades reported

covering. Teachers responded on a scale of 0-3, where 0=None (not covered); 1=Slight

Coverage (less than 1 class/lesson); 2=Moderate coverage (1 to 5 classes/lessons); 3=Sustained

Coverage (more than 5 classes/lessons). Table 2 shows the average coverage levels across the

middle grades. Teachers in all three grades report spending more time on on-grade instruction

than on remedial material. Also, it is important to note that teachers report higher coverage of

algebra (goal 5) in later grades, which would be expected based on the proportion of algebra

questions on the End-of-Grade exams for those grades.

Table 2: Content Coverage in Participating Middle Schools

6th grade 7th grade 8th grade

Overall coverage of Standard Course of Study 2.05 2.22 2.24

Competency Goal #1 (Numbers & Operations) 2.38 2.33 2.23

Competency Goal #2 (Measurement) 2.10 2.44 2.24

Competency Goal #3 (Geometry) 2.19 2.12 2.10

Competency Goal #4 (Data Analysis & Probability) 1.77 2.12 2.10

Competency Goal #5 (Algebra) 1.89 2.26 2.37

Elementary Remedial Coverage 1.91 1.78 1.62

Grade 6 Remedial Coverage 1.70 1.66

Grade 7 Remedial Coverage 2.16

Next, we investigated differences in content coverage between teachers in DSSF schools and

teachers in matched schools. Table 3 shows the average teacher content coverage by school and

DSSF status. As noted earlier, there were no significant differences in coverage between the two

sets of schools.

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Table 3: Content Coverage in DSSF and Matched Middle Schools

6th grade 7th grade 8th grade

DSSF Match DSSF Match DSSF Match

Overall coverage of Standard Course of Study 2.06 2.03 2.30 2.18 2.31 2.16

Competency Goal #1 (Numbers &Operations) 2.42 2.33 2.38 2.30 2.29 2.14

Competency Goal #2 (Measurement) 2.18 2.02 2.51 2.41 2.38* 2.12*

Competency Goal #3 (Geometry) 2.23 2.13 2.20 2.08 2.19 2.02

Competency Goal #4 (Data Analysis & Probability) 1.71 1.84 2.20 2.07 2.12 2.11

Competency Goal #5 (Algebra) 1.89 1.91 2.35 2.23 2.44 2.29

Elementary Remedial Coverage 1.90 2.03 1.82 1.75 1.62 1.58

Grade 6 Remedial Coverage 1.79 1.66 1.69 1.60

Grade 7 Remedial Coverage 2.16 2.14

*Indicates a given coefficient is significant at the .05 level

To address our third question, we examined the impact of teacher characteristics on content

coverage using multiple regression techniques. In these analyses, the effect of each teacher

characteristic is unique, above and beyond the effects of the other predictors in the model. The

teacher characteristics we examined are: 1) years of teaching experience, 2) area of teacher

licensure, 3) whether the teacher attended a highly competitive undergraduate institution

(according to Barron’s rankings), 4) whether the teacher held an advanced degree (beyond a

bachelor’s degree), and 5) teacher’s average test scores on entrance exams such as the PRAXIS.

Teacher test scores are not shown in the tables because it is a continuous variable, but results will

be discussed in the text. National Board Certification was not examined because too few

teachers were board certified to analyze. Because coverage of the Standard Course of Study

could be influenced by the total number of students and the ability level of the students within a

particular class, we included class size and the teacher’s expectation for their students’

achievement on the EOG exam as control variables.

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Table 4: Grade 6 Content Coverage

0-2

yrs ex

perien

ce

3-1

0 y

rs. Exp

erience

11

-20

yrs ex

perien

ce

21

+ y

rs exp

erience

Elem

entary

Licen

se On

ly

MS

Math

Licen

se On

ly

Bo

th L

icenses

Neith

er Licen

se

Hig

hly

Co

mp

. Inst.

No

n-H

igh

ly C

om

p. In

st.

Ad

van

ced D

egree

No

Ad

van

ced D

egree

Overall Coverage of Standard

Course of Study 1.93 2.14 2.05 2.04 2.14* 2.00 2.15* 1.66 2.16 2.02 2.16 2.03

Numbers & Operations 2.26 2.45 2.34 2.44 2.45* 2.37* 2.40 2.06 2.39 2.36 2.39 2.37

Measurement 1.99* 2.18 2.10 2.09 2.16 2.03 2.17 1.92 2.23 2.06 2.23 2.10

Geometry 2.01 2.30 2.20 2.16 2.29* 2.15 2.24 1.76 2.29 2.16 2.29 2.18

Data & Probability 1.60 1.93 1.77 1.76 1.93* 1.69 2.00* 1.13 1.99* 1.74 1.99 1.75

Algebra 1.89 1.90 1.95 1.83 1.95 1.85 1.97 1.71 2.00 1.88 2.00 1.88

Elem. Remedial Coverage 1.71* 1.97 1.92 1.96 1.98 1.77 1.89 1.81 1.96 1.87 1.96 1.90


In the 6th

grade, we examined the impact of having an elementary education license or a middle

school math license because both are valid licenses for the 6th

grade, and holders of both types of

licenses would be considered to be teaching in-field in the 6th

grade. We find that teachers with

elementary licenses, middle school math licenses, and teachers with both licenses tended to

cover more of the tested material than teachers who did not hold either of the two licenses.

Teachers who are licensed in these areas may be more knowledgeable about the material that

needs to be covered to prepare students for the EOG exam.

Teachers who had 0-2 years teaching experience reported significantly lower coverage of goal 2

(Measurement) and on remedial items. Because the findings are only for these categories, it is

difficult to interpret what is leading to these differences. Additionally, teachers who attended a

highly competitive undergraduate institution reported significantly higher coverage of goal 4

(Data Analysis & Probability) than teachers who did not. Goal 4 represents 20-25% of the 6th

grade EOG exam and is an important set of topics for 6th

teachers to cover.

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0-2

yrs ex

perien

ce

3-1

0 y

rs. exp

erience

11

-20

yrs ex

perien

ce

21

+ y

rs exp

erience

Elem

entary

Licen

se On

ly

MS

Math

Licen

se On

ly

Bo

th L

icenses

Neith

er Licen

se

Hig

hly

Co

mp

. Inst.

No

n-H

igh

ly C

om

p. In

st.

Overall Coverage of Standard

Course of Study 2.09 2.24 2.24 2.32 2.29* 1.53 2.19 2.22 2.30 2.21

Numbers & Operations 2.26 2.30 2.36 2.44 2.38* 1.86 2.25 2.34 2.36 2.33

Measurement 2.43 2.46 2.40 2.49 2.53* 1.53 2.44 2.44 2.53 2.43

Geometry 1.83 2.14 2.21 2.26 2.19* 1.41 2.05 2.12 2.19 2.11

Data & Probability 2.04 2.15 2.15 2.14 2.19 1.42 2.13 2.10 2.20 2.11

Algebra 2.06 2.32 2.21 2.42* 2.35* 1.47 2.26 2.28 2.35 2.26

Elementary Remedial Coverage 1.55 1.75 1.83 1.95 1.81* 1.46 1.61 1.78 1.81 1.77

Grade 6 Remedial Coverage 1.59 1.62 1.82 1.91 1.76* 1.18 1.57* 1.72 1.74* 1.71

* Indicates a given coefficient is significant at the .05 level

Similar to the 6th

grade findings, teachers of 7th

grade students licensed in middle school math

reported greater coverage of both on-grade and remedial items. Students in these classrooms are

likely exposed to more material that is prescribed in the Standard Course of Study and this may

enhance their exam performance, but they are exposed to more remedial material as well.

Seventh grade teachers with higher standardized test scores reported lower coverage of both

elementary and grade 6 remedial items. Teachers who attended a highly competitive

undergraduate university and teachers with an advanced degree also reported lower coverage of

grade 6 remedial items. It may be that teachers with these academic characteristics are better

able to tailor their coverage to include only material that is in the 7th

grade Standard Course of

Study. Another finding in the 7th

grade is that teachers with more than 20 years of experience

report higher coverage of goal 5 (algebra). Otherwise, years of experience exerted no significant

effect on coverage.

As indicated in the table on the following page, there are few findings in the 8th

grade. Similar to

the 7th

grade finding, teachers with higher standardized test scores report lower coverage of

elementary remedial items, and may be tailoring their coverage to grade level more than other

teachers. Additionally, 8th

grade teachers who have taught more than 20 years report higher

coverage of elementary items. As there is no overall relationship between experience and

coverage, it is difficult to interpret this isolated finding.

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0-2

yrs ex

perien

ce

3-1

0 y

rs. exp

erience

11

-20

yrs ex

perien

ce

21

+ y

rs exp

erience

Elem

entary

Licen

se On

ly

MS

Math

Licen

se On

ly

Bo

th L

icenses

Neith

er Licen

se

Hig

hly

Co

mp

. Inst.

No

n-H

igh

ly C

om

p. In

st.

Overall coverage of Standard

Course of Study 2.36 2.12 2.24 2.39 2.28 2.01 2.30 2.24 2.25 2.23

Numbers & Operations 2.42 2.08 2.16 2.36 2.23 2.14 2.14 2.24 2.24 2.20

Measurement 2.39 2.17 2.23 2.26 2.27 2.07 2.43 2.23 2.19 2.29

Geometry 2.27 1.96 2.26 2.07 2.14 1.85 2.42 2.05 2.07 2.11

Data & Probability 2.12 2.03 2.07 2.39 2.15 1.86 2.07 2.13 2.25 2.06

Algebra 2.49 2.21 2.40 2.59 2.42 2.03 2.40 2.38 2.37 2.36

Elementary Remedial Coverage 1.73 1.53 1.52 1.74* 1.57 1.82 1.71 1.58 1.53 1.62

Grade 6 Remedial Coverage 1.66 1.61 1.56 1.83 1.63 1.76 1.68 1.64 1.63 1.64

Grade 7 Remedial Coverage 2.24 2.06 2.12 2.33 2.16 2.13 2.22 2.14 2.14 2.15


Conclusion

Overall, we find that middle school math teachers are reporting coverage of material that is

consistent with the NC Standard Course of Study. Our analyses provides little evidence that

teachers in DSSF schools are reporting more coverage of the NC Standard Course of Study than

are teachers in schools which were performing at similar levels before the DSSF pilot was

initiated.

One consistent finding is that teachers with a middle school math license (or an elementary

license in the 6th

grade) report more coverage of the Standard Course of Study. It is important to

note that most of the teachers who participated in the study had a middle school math license so

the group of teachers we are comparing them to is quite small. Thus, this set of findings should

be interpreted cautiously. Although the number of teachers without a middle school license is

small, it is interesting that we found similar patterns in both the 6th

and 7th

grade.

Another important finding is that teachers with higher test scores, advanced degrees, or degrees

from more highly competitive undergraduate institution covered less remedial material. We

cannot directly test why they report lower coverage but one plausible hypothesis is that they are

better able to focus only on the material specified for that grade. Although we controlled for

class size and expected achievement levels, we cannot rule out another possibility – that teachers

with these characteristics are assigned to students who do not need as much coverage of remedial

material.

A central question left to be answered is whether the differences in content coverage influence

student achievement. Furthermore, the patterns of coverage, not just the overall level of

coverage, may be more closely linked to student performance on the EOG exam. For example,

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higher coverage of algebra material may be more important to student performance in 8th

grade

than material contained in the other competency goals, but it is impossible to be certain about the

impact of these patterns without explicit analysis of the link between content coverage and data

on student achievement. Thus, our findings should be interpreted as only a first step towards

understanding content coverage in North Carolina middle schools and the implications of

coverage for student achievement.

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References

Henry, Thompson, Fortner, Rickman and Zulli, (2008) The Impact of the Disadvantaged Student

Supplemental Fund on High School Student Performance in Pilot Districts. Chapel Hill, NC:

Carolina Institute for Public Policy.

Council of Chief State School Officers, Wisconsin Center for Education Research, & Learning

Point Associates/NCREL. (2003). Survey Instruments: Survey of Classroom Practices and

Instructional Content in Mathematics, Science, and English Language Arts [Elementary, Middle,

High school versions]. Washington, DC: Council of Chief State School Officers.

If you teach more than one math class (i.e., different group of students), please respond only for the first class that you teacheach week. If that is a split class (i.e., the class contains more than one group for math instruction and each group is taughtseparately), respond for only one group.

Indicate the grade level of the majority of the students in the target class.

How many students are in the target class?

What percentage of the students in the target class are NOT CAUCASIAN? (Estimate to the nearest 10%)

How many weeks total will the target mathematics class/course meet this school year?

During a typical week, approximately how many hours will the target class spend in mathematics instruction (i.e., contacthours)?

What percentage of the students in the target class ARE FEMALE? (Estimate to the nearest 10%)

6th 7th 8th

10 or less 11 to 15 16 to 20 21 to 25 26 to 30 31 or more

Less than 10% 10% 20% 30% 40% 50% 60% 70% 80% More than 90%


1 to 12 weeks 13 to 24 weeks 25 to 36 weeks More than 36 weeks

1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours 9 hours 10+ hours

TARGET CLASS DESCRIPTION

What is the average length of each class period for the target mathematics class?

Estimate the achievement level of the majority of the students in the target class based on how you expect them to perform onthe end-of-grade test for Mathematics.

What percentage of students in the target class are Limited English Proficient (LEP) (estimate to the nearest 10%)?

To the best of your knowledge, which of the following factors is considered most in scheduling students into this class?

30 to 40 minutes

41 to 50 minutes

51 to 60 minutes

61 to 90 minutes

91 to 120 minutes

varies due to block scheduling or integrated instruction

High achievement levels

Average achievement levels

Low achievement levels

Mixed achievement levels


Ability or prior achievement

Heterogeneity of race, ethnicity, gender, etc.

Limited English Proficiency

Clustering of 4-6 gifted or EC students per class

Teacher recommendation

Random selection

Parent request

Student selects

No one factor more than another

Other

Survey of Instructional Contentfor Grades 6-8 Mathematics

The following pages request information regarding topic coverage and your expectations for students in the targetmathematics class for the current school year. If you teach more than one math class (i.e., different group of students),respond only for the first class that you teach each week. The content matrix that follows contains lists of discrete topicsassociated with mathematics instruction. The categories and the level of specificity are intended to gather informationabout content across a wide variety of programs. It is not intended to reflect any recommended or prescribed content forthe grade level.Indicate the amount of time spent on each topic covered in the target class.

For the groups where the "None" bubble has NOT been filled in, indicate the amount of coverage devoted to each individualtopic by filling in the appropriately numbered circle in the "Time on Topic" column using the following codes:

0 = None (not covered)1 = Slight coverage (less than 1 class/lesson)2 = Moderate coverage (1 to 5 classes/lessons)3 = Sustained coverage (more than 5 classes/lessons)

Factors, multiples, divisibility

Estimation (e.g., sums, differences, products,quotients)

Exponential, scientific, calendar notation

Number comparison and order (e.g., relativesize, inverse, opposites, equivalent forms, scale)

Operations

Order of operations

Relationships between operations (e.g. effectson size)

Mathematical properties (e.g., identity,commutative, associative, distributive)

Time onTopic

Mathematics Topics

Number Sense/ Properties/Relationships

Whole numbers

Decimals

Odds, evens, primes, composites

Number representations (model, number,number word)

Number line

None

3210

Rational numbers

Irrational numbers

Real numbers

Negative numbers

Fractions

Ratio, Proportion

Percents

END OF SURVEYThank you for your participation!

Add, subtract, multiply, divide whole numbers

OperationsNone

Time onTopic

Add, subtract, multiply, divide decimal numbers

Add, subtract, multiply, divide fractions

Add, subtract, multiply, divide irrational numbers

Add, subtract, multiply, divide negative numbers

Equivalence of decimals, fractions, percents

3210

Representations of fractions (e.g., concrete andsymbolic representations, models, diagrams)

Computational strategies (e.g., mentalcomputation, estimation, calculators orcomputers, paper and pencil)

Judge/evaluate reasonableness of solutions

Ratio, proportion

Equivalent/non-equivalent fractions

Begin by reviewing the entire list of topics identified in the topics column of each table, noting how topics are grouped.Review each of the individual topics (e.g., Whole numbers, Rational numbers) within a given group (e.g., NumberSense/Properties/Relationships). If none of the individual topics listed within that group were taught, fill in the "None"bubble in the "Time on Topic" column. Then proceed to the next group.

1680

7

Algebraic Concepts (cont.)3210

Time onTopic

Linear, non-linear relations

Rate of change/slope/line

Quadratic equations

Factoring

Operations on polynomials

Linear, non-linear functions

Inverse relationships (e.g., addition andsubtraction, squares and square roots)

Squares roots and radicals

Operations with radicals

Complex numbers

Multiple representations (e.g., verbal, written,tabular, graphic, algebraic) of expressions,equations, inequalities, functions

Inequalities

Systems of inequalities

Absolute value

Sequences, patterns

Use of variables or symbols

One-step equations

Multi-step equations

Algebraic Concepts

3210

None

Time onTopic

Algebraic expressions

Algebraic formulas

Systems of equations

Direction/location/navigation

Time (e.g., elapsed time)

Measurement concepts and theory (e.g.,standard units, unit size)

Use of measuring instruments

Metric (SI) system

Mass (weight, ounces, pounds, grams, kilograms)

Capacity (cups, pints, quarts, gallons, liters)

Length (miles, kilometers)

Temperature (Fahrenheit, Celsius)

Indirect measurement

Perimeter, circumference

Surface area

Area

Volume

Angles

Rate/speed

Measurement

3210

None

Time onTopic

Conversions

Scaling (e.g., drawing objects to scale, usingscale drawings to solve problems)

Accuracy, precision

Points, lines, rays, segments, and vectors

Line/segment relationships (e.g., parallel,perpendicular, intersecting, bisecting)

Coordinate plane

Plane figures

Patterns

Congruence

Symmetry

Geometric Concepts

3210Basic terminology or vocabulary

None

Time onTopic

Similarity

Ratio, proportionality, equality

Triangles

Quadrilaterals

Circles

Angles and angle relationships

Polygons

Polyhedra

Geometric models

2-dimensional figures and relationships

3-dimensional figures and relationships

Transformations (e.g., reflections, rotations,translations, dilations)

Pythagorean Theorem

Simple trigonometric ratios

Research/Statistics/Probability

Time onTopic

None

3210Experiments

Instruments (e.g., surveys, protocols)

Data collection and organization

Data analysis (one or multiple data sets)

Summarize data in table or a graph, report data

Mean, median, mode

Range, inter-quartile range, frequency distribution

Line of best fit

Quartiles, percentiles

Sample

Combinations and permutations

Sampling

Outliers

Variability, variance, standard deviation

Experimental probability

Theoretical probability

Fundamental counting principle, counting strategies

Simple probability/single events

Compound probability/compound events

Independent/dependent events

Tables

Classification(s), Venn diagrams

Bar graphs, histograms

Pie charts, circle graphs

Pictographs

Line graphs

Stem and leaf plots

Scatter plots

Box plots

Multiple representations of data

Data displays

Time onTopic

None

3210Tree diagrams, lists

Frequency distribution tables

Line plots

Instructional Technology

Use of calculators

Graphing calculators

Computers and internet

Time onTopic

3210

None

1680

7

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