Post on 21-Aug-2018
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
Table 5 Grade 7 Content Coverage 7
Table 6 Grade 8 Content Coverage 8
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
Page 2 of 13
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
Page 3 of 13
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
Page 4 of 13
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.
Page 5 of 13
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.
Page 6 of 13
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
*Indicates a given coefficient is significant at the .05 level
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.
Page 7 of 13
Table 5: Grade 7 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.
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.
Page 8 of 13
Table 6: Grade 8 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.
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
*Indicates a given coefficient is significant at the .05 level
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,
Page 9 of 13
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.
Page 10 of 13
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%
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
Less than 10% 10% 20% 30% 40% 50% 60% 70% 80% More than 90%
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
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