Š 2001 School Renaissance Institute, Inc. All Rights Reserved.
L0388.0201.RN.5700
For more information about the Instituteâs Renaissance Independent Research Reports, or to submit a report for distribution, please contact:
School Renaissance Institute ⢠Educational Research Department
PO Box 45016 ⢠Madison, WI 53744-5016
(800) 200-4848
Helping Educators Improve Schools Through Technology and Research.
Summary of Independent
Math Research
Regarding Accelerated Math
ÂŽ
Math Management Software
and Math Renaissance
ÂŽ
Professional Development
Helping Educators Improve Schools Through Technology and Research.
Table of Contents
Introduction
...........................................................................................................................................1
Part 1: Internal Research
............................................................................................................2-4
Part 2: Independent Research
Section 1: Elementary and Intermediate Schools
Sudley Elementary School, Manassas, Virginia............................................................................5
Graham A. Barden Elementary School, Havelock, North Carolina .............................................6
Michigan Avenue Elementary School, Cleveland, Tennessee ......................................................7
Dyersburg Intermediate School, Dyersburg, Tennessee................................................................8
Changes in Mathematics Achievement and Instructional Ecology Resulting from
Implementation of a Learning Information System .............................................................9-10
Enhancing the Learning of English Language Learners: Consultation and Curriculum
Based Monitoring System........................................................................................................11
Section 2: Middle and Junior High Schools
Mac Williams Middle School, Fayetteville, North Carolina ......................................................12
Using Accelerated Math to Enhance Instruction in a Mandated Summer School Program ......13
Section 3: High School
Buhler High School, Buhler, Kansas .....................................................................................14-15
Part 3: References and Further Reading
...........................................................................16-17
Introduction
In 1990, the National Governorâs Association and the President adopted the National Educational Goals, a
framework for educational improvement consisting of eight goals to be met by the year 2000. Goal Five states
that by the year 2000 United States students will be first in the world in mathematics and science (National
Education Goals Panel, 1995). However, recent test score results indicate that the United States has not
achieved this goal. In the Third International Mathematics and Science Study (TIMSS), eighth grade students
in the United States scored below the international average in math, and eighth-graders in 20 other countries
scored higher in math than American eighth-graders (Beaton et. al., 1996). In the 1999 follow-up study,
TIMSS-R, U.S. eighth-graders were still outperformed by eighth-graders in 14 other countries (Gonzales et.
al., 2000).
In order for U.S. students to compete worldwide, math skills are becoming increasingly important.
Nonetheless, our students still trail behind. Among the many factors impacting mathematics achievement, time
on taskâpractice timeâis one of the most important. Research demonstrates that increasing time spent on
academic tasks boosts achievement, especially in mathematics (Cotton and Wikelund, 1989). Students learn
more about a subject if they spend more time studying itâif they have more opportunity to learn (Berliner,
1990; Brophy, 1988). The TIMSS report agrees that time on task is important, but says that this time must be
spent efficiently with students academically engaged in mathematics tasks. In other words, simply allotting
more time to mathematics instruction and practice is not enough: the time must be used well.
In their Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics
(NCTM) concurs that time on task is important, but proposes that certain characteristics will make it more
effective. For example, NCTM asserts that teachers need frequent formative feedback from a variety of
assessment methods to diagnose learning problems promptly, and intervene with individualized attention
(NCTM, 2000). Furthermore, the NCTM report contends that students learn more and learn better when they
are able to take charge of their learning, set goals, are challenged by aptly chosen tasks, and can monitor their
own progress (NCTM, 2000).
Math Renaissance and its learning information systems components, Accelerated Math and STAR Math,
offer an effective way to manage time engaged in math tasks. Through a significant increase in available task-
level information, teachers are able to individualize instruction, provide more meaningful feedback to students,
and closely monitor academic progress. As a result, math achievement improves dramatically.
1
2
Study Description
The following is an overview of a recent School Renaissance Institute study conducted to examine Accelerated
Math usage and test score gains of a national sample of students in a range of grades with a variety of
backgrounds and math achievement levels. The Special Math Report is based on STAR Math and Accelerated
Math data which was voluntarily supplied by schools across the country. The study includes data from 1,160
students enrolled in grades three through nine during the 1999â2000 school year at 20 different elementary,
middle, junior high, and high schools.
Results
The study found that overall, these students experienced large gains in math achievement. Change in math
achievement levels over the school year was measured using STAR Math, a computer-adaptive, norm-
referenced mathematics test. STAR Math tracks student progress with normal curve equivalents (NCEs),
percentile ranks (PRs), and grade equivalents (GEs). Both PRs and NCEs illustrate math progress. When
students experience growth in achievement over time that is consistent with a national sample of students in
their own grade, their PRs and NCEs will remain unchanged from one STAR Math testing to a later one. When
students improve their math skills at a faster rate than their peers, their PRs and NCEs will increase over a
school year.
STAR Math results for the students in this study demonstrate remarkable PR and NCE increases
(See Figure 1). While the largest gains took place in grades three through six, strong gains were present up
through ninth grade. Overall, students gained, on average, 13 percentile points during approximately three-
quarters of a school year.
Part 1: Internal Research
3
The study also found that students engaging in a greater quality and quantity of math practice using
Accelerated Math experienced greater math achievement gains. The study measures the quality of math
practice by how well students score on Accelerated Math problems that cover the objectives they are
learning. Quantity of math practice is indicated by the number of problems attempted and the number of
objectives mastered.
The results in figure 2 show that achievement gains increased as percent correct increased on test, practice,
and review problems. Even students with low pretest scores showed greater gains on their post-tests when they
maintained higher average percent correct on Accelerated Math test problems.
0
5
10
15
20
25
30
<=65%
66â70%
71â75%
76â80%
81â85%
86â90%
91â95%
96â100%
All Students
Students below 50th percentile on pretest
Students with Higher Percent Correct on Accelerated Math
Test Problems Experienced More Math Achievement Growth
ST
AR Math Percentile Rank Change
Percent Correct on Accelerated Math Test Problems
0
10
20
30
40
50
60
70
80
3 (n=94)
4 (n=188)
5 (n=117)
6 (n=359)
7 (n=186)
8 (n=159)
9 (n=57)
All Grades
(n=1360)
Pretest
Post-test
Students Show Large Achievement Gains
After Using Accelerated Math
ST
AR Math Percentile Rank
Grade
Figure 1
Figure 2
Regarding the quantity of math practice, the study found that increases in objectives mastered led to increases
in math achievement (See Figure 3). Students who mastered more Accelerated Math objectives gained more
than twice as much as students mastering fewer objectives. As with percent correct, students who initially
scored at or below the 50th percentile on their pretests also greatly benefited from mastering more objectives.
The Special Math Report illustrates how students can benefit from sound implementation of Math Renaissance
techniques. Overall, students in the study showed significant test score improvements over the school year. In
fact, on average, students improved their math skills at an accelerated rate compared to a national peer sample.
Yet, students whose practice approached the quality and quantity goals recommended by Math Renaissance
experienced even greater gains.
1
The study indicates that students who scored higher on test, practice, and
review problems and students who mastered a higher number of objectives experienced greater gains in STAR
Math test scores, regardless of their initial math ability. This study strongly suggests dramatic possibilities
for improvements in mathematics learning when students attain the quality and quantity goals provided by
Math Renaissance.
7
18
20
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15
20
25
At or Below Median for Their Grade
Above Median for Their Grade
All Students
Students below 50th percentile on pretest
Students Mastering More Accelerated Math Objectives
Experience Greater Math Achievement Gains
ST
AR Math Percentile Rank Change
Number of Objectives Mastered
1
Math Renaissance currently recommends that students should maintain an average percent correct of 75% on practice problems, 80%
correct on review problems, and 85% on test problems. In addition, the goal for quantity of math practice is for a student to complete
a Standard Library in a school year (based on 36 weeks). Most students can accomplish this goal with a minimum of 30 minutes of
daily math practice; more math practice can result in students advancing to the next library within the school year.
4
Figure 3
Accelerated Math Implementation and Math Renaissance
Improves Math Performance
Information submitted by Jonathan Lind and Ann Lubas
Sudley Elementary School, Manassas, Virginia
Section 1: Elementary and Middle Schools
Renaissance Independent Research Reports
Study Description
Lind and Lubas gathered information for two fourth-
grade Accelerated Math classesâ17 and 23 students
respectivelyâand one fourth-grade non-Accelerated
Math control class of 27 students at Sudley
Elementary. Lind and Lubas team-taught Accelerated
Math classroom #1, while another instructor taught
Accelerated Math classroom #2. A different teacher
who did not use Accelerated Math or Math
Renaissance taught the control classroom. The
Stanford Achievement Test, ninth edition
(Stanford 9)
1
was administered to all students in
September 1998, and STAR Math was given in
November 1998. The graph on the right shows the
growth in math performance that occurred between
the two testing dates.
As shown in the graph, the growth in math
performance for the Accelerated Math classes is more
than double that of the control class. The score
increases are especially noteworthy since they were
obtained after just nine weeks of instruction.
Additional pretest/post-test information for an entire
year was collected for the previous yearâs fourth-
grade classes. Increased math performance for the
students who were instructed with Accelerated Math
and Math Renaissance techniques is again
demonstrated. The spring 1997 Stanford 9 figures
serve as the pretest, and the spring 1998 STAR Math
scores represent the post-test for 26 Accelerated
Math/Math Renaissance students and 25 control
students. As before, another fourth-grade instructor
who did not use Accelerated Math or Math
Renaissance techniques taught the control students.
The Accelerated Math/Math Renaissance students
were team-taught by Lind and Lubas. The table at
right outlines the results.
Results
Accelerated Math and Math Renaissance yield results
in both short and long windows of time. While
significant gains occurred after one quarter, the results
illustrate much larger increases in math performance
1
The Stanford 9 has a high +.71 correlation with STAR Math scores, thus offering validity for use of these two different instruments to
measure growth in math performance.
Sudley Elementary Fourth-Grade Math Results
from Spring 1997 to Spring 1998
(In Percentile Rankings)
Growth in Percentiles
10
15
20
25
30
35
40
16
35
36
Control
Classroom
AM
Classroom
#1
AM
Classroom
#2
Sudley Elementary Math Growth from September to November, 1998
Accelerated Math Classrooms Achieved Twice as Much Growth
as a Classroom with Regular Math Instruction
School Profile
Sudley Elementary School
Manassas, Virginia
Students: 476, Kâ12
Educator Backgrounds
Jonathan Lind and Ann Lubas are fourth- and fifth-grade teachers
at Sudley Elementary School in Manassas, Virginia. They have been
certified as Reading Renaissance Model Classroom Teachers since
February 1996, and have been using Accelerated Math and Math
Renaissance techniques since September 1997.
Race/Ethnicity:
Asian or Pacific Islander: 2%
Black/African American: 8%
Hispanic or Latino: 4%
White: 86%
5
for students who have had Accelerated Math and Math
Renaissance instruction over one full year. Greater-
than-average growth for the control students was either
nonexistent or only half that experienced by their
Accelerated Math/Math Renaissance counterparts.
AM/MR
Control
Stanford 9 (spring 1997)
56
36
STAR Math (spring 1998)
95
34
Difference (from 1997 to 1998)
+39
-2
Fifth-Grade Students in North Carolina Show Remarkable Math Gains
Source: Kathy Leffler, fifth-grade math teacher
Graham A. Barden Elementary School, Havelock, North Carolina
6
Renaissance Independent Research Reports
Study Description
Leffler began using Accelerated Math with her fourth-
grade class in April 1999. She moved to fifth grade with
the same group of students and continued using
Accelerated Math during the 1999â2000 school year.
She has a wide range of abilities in her class including a
student who is mentally handicapped, students who are
learning disabled, and students who are gifted.
When teaching math, Leffler starts each session by
introducing a new objective. She uses manipulatives
and cooperative groups to illustrate the objective
whenever possible. Students then complete a
related exercise from their assigned Accelerated Math
library so that Leffler can check for understanding. If
any students are having trouble with the objective,
Leffler integrates a power lesson into the math
session for those students. Finally, students receive
daily practice sheets to complete during math time
and for homework.
Leffler credits Accelerated Math with giving her more
information about her studentsâ strengths and
weaknesses and giving her the flexibility to provide
whole class, small group, or individualized instruction
as needed. She believes that Accelerated Math helps
students feel successful and that the challenge of
applying for Renaissance Certification motivated all
her students to work extremely hard to meet, and
sometimes exceed, their weekly individual math goals.
To track her studentsâ progress throughout the year,
Leffler administered STAR Math at the beginning of
the school year in August, halfway through the year
in December, and again at the end of the school yea
r.
Results
During the period between the first and last STAR
Math test administrations, Lefflerâs fifth-grade
classroom achieved dramatically accelerated growth.
The pretest and post-test results show that Lefflerâs 22
fifth-grade students improved, on average, by 2.5 years
in just eight months. The class started at an average
School Profile
Graham A. Barden Elementary School
Havelock, North Carolina
Students: 385, Kâ5
Socio-Economic Status:
Title I
Free or reduced lunch: 56%
Educator Background
Kathy Leffler has taught at Graham A. Barden Elementary
School for the past five years. She received her bachelorâs
degree in education from Northern Illinois University and is
currently working on her masterâs degree at East Carolina
University. She is a Renaissance Master Educator in Reading,
the highest honor School Renaissance Institute can bestow,
and has the distinction of being the first Renaissance Model
Educator in Math.
Race/Ethnicity:
American Indian or Alaskan
Native: 1%
Asian or Pacific Islander: 2%
Black/African American: 23%
Hispanic or Latino: 6%
White: 68%
grade equivalent of 4.7 and improved to an
average grade equivalent of 7.2. This means that
near the end of fifth grade, Lefflerâs students were
scoring, on average, more than a full year ahead of
their grade level.
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Graham A. Barden Elementary School
Havelock, North Carolina
Eight-Month Gains for Fifth-Grade Classroom
(22 students)
Math Renaissance Implementation Significantly Increases Percentile
Rankings in Tennessee
Sources: Patsy Owenby, Title I math teacher and Robert Taylor, principal
Michigan Avenue Elementary School, Cleveland, Tennessee
7
Renaissance Independent Research Reports
Study Description
Michigan Avenue, a Renaissance Model School in
reading, piloted Accelerated Math math management
program during the 1998â1999 school year. At that
time, Taylor and his staff effectively integrated
Accelerated Math into the schoolâs existing math
curriculum. In addition, Taylor, Owenby, and staff
received Math Renaissance training. Many of the
teachers successfully incorporated various intrinsic
and extrinsic motivational strategies, such as
classroom charts that track objectives mastered,
point clubs, and competition between individuals
or teams. Teachers discovered that individualized
goal setting was easy to establish for the varying
student skill levels.
To target these ranges of academic levels, Michigan
Avenue implements power lessons (five to fifteen
minute lessons) as a classroom instructional
technique. For example, one fifth-grade classroom
teacher has students in math libraries three through
six. The teacher places them in groups according to
the math libraries and then moves around the
classroom, teaching short lessons applicable to each
group. Peer tutoring and cooperative learning are also
implemented. Following the power lessons, students
tutor one another in order to master the relevant
objective(s) taught. Accelerated Math has also proven
successful with Resource (Special Education)
students at Michigan Avenue, with one student even
demonstrating the program to visitors.
Results
Throughout their inaugural period, Michigan Avenue
showed significant improvement in student
achievement, attitudes, and enthusiasm. Additionally,
STAR Math computer-adaptive assessment scores
between the late October 1998 pretest and the early
May 1999 post-test increased 19 percentiles for 226
students in grades three through five. Fourth-grade
students achieved an especially significant gainâ32
percentiles in six months.
School Profile
Michigan Avenue Elementary School
Cleveland, Tennessee
Students: 518, Kâ12
Socio-Economic Status:
Rural, Title I
Free or
reduced lunch: 58%
Educator Backgrounds
Patsy A. Owenby earned a masterâs in elementary
education from the University of Tennessee at Chattanooga
and has taught third grade at Michigan Avenue School for
more than 30 years. Currently, she is a Title I math teacher
and the Accelerated Math coordinator for the school.
Robert Taylor earned a M.Ed. from the University of
Tennessee at Chattanooga and has been an educator
for 23 years. As principal, he was active in bringing
Accelerated Reader and Reading Renaissance to Michigan
Avenue Schoolânow a certified Renaissance Model
School.
Race/Ethnicity:
Black/African American: 7%
White: 93%
STAR Math scores for 1999â2000 demonstrated a
gain of 32 percentiles for 237 students in grades
three through five. In particular, third-grade students
gained a substantial 44 percentiles. Two-year
percentile gains for grades three through five are
illustrated in the table below. Owenby believes that
Accelerated Math is one of the best math programs
that has ever been developed. Second grade is now
part of the program and plans are underway to
include first grade in 2001.
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Michigan Avenue Elementary School
Cleveland, Tennessee
STAR Math Percentile Rankings, 1998â2000
Tennessee Intermediate School Experiences Outstanding Results
With Math Renaissance
Source: Roger L. Wilson, sixth-grade math teacher
Dyersburg Intermediate School, Dyersburg, Tennessee
8
Renaissance Independent Research Reports
Study Description
Dyersburg Intermediate School installed Accelerated
Math in January 1999. Wilson, along with 46 staff
members, attended a Math Renaissance on-site
seminar on August 2, 1999. Soon afterward, he
pretested his students with STAR Math and began
implementing Accelerated Math/Math Renaissance
in his sixth-grade classroom. Using past Tennessee
Comprehensive Assessment Program (TCAP) scores
and STAR Math data, Wilson placed his sixth-grade
students in the proper math libraries.
In order to target pertinent math objectives, Wilson
starts each class with a 10 to 15 minute power lesson.
Following these short lessons, student comprehension
is assessed with either a short worksheet (four to five
problems), or working a problem on the chalkboard.
To diagnose and address specific problems, Wilson
reviews the studentsâ TOPS (The Opportunity to
Praise a Student) reports, makes comments, and
initials each copy. Students are further motivated and
challenged by âenrichmentâ worksheets which
Wilson distributes between assignments.
To keep his students motivated, Wilson employs
various Renaissance methods such as peer tutoring,
individual goal setting, grouping students who are
working on common objectives, and posting a chart
with number of objectives passed. Wilson believes
the interaction and cooperative learning from peer
tutoring has proven particularly successful.
Results
After six months of Math Renaissance
implementation, Wilsonâs sixth-grade classroom has
achieved powerful results. Wilson reports that more
than half of his 18-student classroom has mastered
over 200 objectives. In addition, his students now
enjoy math. Based on post-test STAR Math data,
Wilsonâs class showed very significant gains on all
metrics (see table).
School Profile
Dyersburg Intermediate School
Dyersburg, Tennessee
Students: 680, 4â6
Socio-Economic Status:
Rural I
Free or reduced lunch: 40%
Educator Background
Roger L. Wilson has taught in the Dyersburg City School
System for 23 years. He received his B.S. degree in
elementary education from Eastern Illinois University at
Charleston (1973) and did his graduate work in education
at the University of Tennessee at Martin.
Race/Ethnicity:
Black/African American: 21%
White: 79%
Dyersburg Intermediate School
Dyersburg, Tennessee
Six-Month Gains for Wilsonâs Sixth-Grade Classroom
(18 Students)
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Independent University Study
Summarized from: Changes in Mathematics Achievement and Instructional Ecology Resulting from
Implementation of a Learning Information System. Ysseldyke, J., Spicuzza, R., & McGill, S. (2000).
National Center on Educational Outcomes, University of Minnesota, Minneapolis, Minnesota.
Study Description
The purpose of this study was to determine the
effects of Accelerated Math on student achievement
and classroom ecology. Accelerated Math was
utilized in combination with a district adopted math
curriculum. During the period of February through
June 1999, Accelerated Math and Math Renaissance
techniques were implemented in nine fourth- through
eighth-grade classrooms in a Midwest urban district
with a special focus on fourth- and fifth-grade
classrooms. The number of students in the
experimental group (Accelerated Math students) was
205. The control group (non-Accelerated Math
students) consisted of 184 students. In addition, a
subset of 26 students, based on varying math skills
(high, middle, and low), was chosen for intensive
observation.
1
The researchers measured ecological
classroom behaviors for this subset of students.
1
The varying math levels of high, middle, and low were determined by STAR Math test scores from December 1998. Students who scored in the 80th
percentile were categorized as high, students who scored in the 40th to 60th percentile were identified as middle achievers, and those deemed low
achievers scored below the 20th percentile.
0
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2
3
4
5
6
7
NALT
STAR
Accelerated Math Group
Control Group
Differences in Gains on NALT and STAR
Math Accelerated Math Participants vs. Control Group
Achievement Measure
Figure 1
Results
On the Northwest Achievement Level Test (NALT)
students in grades four and five using Accelerated
Math gained an average of 6.65 normal curve
equivalents (NCEs) while all fourth
-
and fifth-graders
in the district gained an average of only 2.66 NCEs.
The gain for Accelerated Math users is statistically
significantly higher than the gain across the district.
The study also compared the NALT and STAR Math
gains of students in the Accelerated Math treatment
group to students in a representative control group.
Students who received the Accelerated Math
treatment significantly out-gained those who received
the standard district curriculum only. For example, on
STAR Math, the treatment group (N=187) gained 5.8
NCEs, while the control group (N=139) gained 1.7
NCEs. Data on the NALT and STAR Math
comparisons are show in Figure 1.
(continued on next page)
School Profiles
(Note: schools are unnamed for confidentiality purposes)
Students: 415, 4â8
Socio-Economic Status:
Free or reduced lunch: 67%
English as a Second Language: 12%
Minority: 70%
Additional test score analysis compared the gains of
students with differing initial skill levels. Among all
the Accelerated Math participants, students in the top
20% gained 3.5 NCEs while students in the median
group and the bottom 20% gained over 8 NCEs. In
contrast, among all the students in the district,
students in the top 20% experienced no NCE growth
while students in the median group and bottom 20%
experienced growth of only 2.6 and 3.3 NCEs,
respectively (See Figure 2).
Normal Curve Equivalent Scores on the Northwest
Achievement Level Test (NALT) for the Entire District and for
Accelerated Math Participants
District (N=15,502)
Accelerated Math
Participants (N=187)
NALT NALT
NALT
NALT
1998
1999
1998
1999
(pretest) (post-test) Gain (pretest) (post-test) Gain
Top 1/5
70.9
70.9
0.0
64.2
67.7
3.5
Median
46.3
48.9
2.6
43.6
52.4
8.8
Bottom 1/5
28.2
31.5
3.3
26.3
34.4
8.1
Figure 2
10
Accelerated Math students spent significantly more
classroom time academically engaged than students
receiving only the district adopted curriculum.
Students were receiving more individualized
instruction with Accelerated Math and teachers were
able to adapt instruction according to student needs.
In addition, low-achieving Accelerated Math
students had nearly the same amount of academically
engaged time (36% of classroom time) as high-
achieving non-Accelerated Math students (35%).
The addition of Accelerated Math with the adopted
curriculum produced a positive effect on student
behavior, because students were spending more time
on task. A full report of this study is available:
L0373.
Independent University Study
Summarized from: Enhancing the Learning of English Language Learners: Consultation and Curriculum
Based Monitoring Systems, Teelucksingh, E. (2000). University of Minnesota, Minneapolis, Minnesota.
11
Independent University Study
Study Description
This study compared the math performance of
English Language Learners (ELL) using Accelerated
Math along with Everyday Math (EM) to a group of
ELL students who received the district adopted
curriculum only (EM). Accelerated Math and Math
Renaissance techniques were implemented in nine
fourth- through eighth-grade classrooms in four
schools in an unnamed urban school district from
February through June 1999. STAR Math and the
Northwest Achievement Levels Test (NALT) were
used to measure achievement. STAR Math was
administered in January and May 1999. NALT was
administered in Spring 1998 and Spring 1999.
Results
Among fourth- and fifth-grade students who received
math instruction through Title I services, students
using Accelerated Math (N=25) gained an average of
6.57 normal curve equivalents (NCEs) on the
Northwest Achievement Levels Test (NALT) while
students not using Accelerated Math (N=70) gained
an average of 2.79 NCEs.
Across the four pilot schools in the district, ELL
students using Accelerated Math (N=50) along with
the district curriculum gained an average of 6.67
NCEs on the NALT while ELL students not using
Accelerated Math in the four pilot schools (N=151)
gained only 3.87 NCEs. On STAR Math, ELL
students using Accelerated Math (N=49) gained an
average of 4.79 NCEs, while ELL students not using
Accelerated Math lost 2.55 NCEs. (Note: Release
date is undetermined.)
School Profiles
Note: Districtwide data are unavailable, demographics
below are of focus group.
Accelerated Math group (N=26)
Socio-Economic Status:
Free or reduced lunch: 22
English Language Learners: 7
Race/Ethnicity
American Indian: 1
African American: 6
Hispanic: 17
White: 2
Control group (N=74)
Socio-Economic Status:
Free or reduced lunch: 41
English Language Learners:18
Race/Ethnicity
American Indian: 0
African American: 12
Asian: 1
Hispanic: 32
White: 29
Extraordinary Math Gains Reported by North Carolina Middle School
Source: Charlotte Crayton and Yvonne Wheeler
Mac Williams Middle School, Fayetteville, North Carolina
12
Renaissance Independent Research Reports
Study Description
Mac Williams Middle School began using Accelerated
Math and implementing Math Renaissance in the fall
of 1999. Yvonne Wheeler, who teaches five sections of
eighth grade, had attended a Math Renaissance
seminar in October. Using STAR Math data, Wheeler
placed her eighth-grade students in the appropriate
Accelerated Math math libraries, ranging from third
grade to algebra. She assigned her students the large
math practice sheets and gave them 25â30 minutes in
school to work on them. If they were unable to finish
the practice sheet during the allotted time, they took
them home to complete as a homework assignment.
She scheduled mastery tests twice a week.
Wheeler had students monitor their own progress by
completing personalized progress charts based on
data from Accelerated Math. She used the Status of
the Class Report to determine the content of the
power lessons that she gave every day. In her
classroom, math textbooks were used by students as
a resource and reference guide. She also used the
TOPS (The Opportunity to Praise a Student) Report
to intervene immediately and individualize
instruction. As an intervention technique, she used
peer helpers and cooperative learning groups. The
outcome of Wheelerâs classes was nothing short of
remarkable. The five-month percentile and grade-
equivalent gains for all of her sections are shown in
the following table.
School Profile
Mac Williams Middle School
Fayetteville, North Carolina
Students: 1200, 6â8
Socio-Economic Status:
Rural
Title I
Free or reduced lunch: 57%
Educator Backgrounds
Charlotte Crayton graduated from East Carolina University, Fayetteville, N.C., and has been an educator for 33 years. In her
position as Title I Facilitator and Technology Coordinator, she has been instrumental in bringing Accelerated Reader, Reading
Renaissance, Accelerated Math, and Math Renaissance to Mac Williams Middle School.
Yvonne Wheeler earned her degree from Campbell University, in Buies Creek, N.C., and has been teaching math and/or algebra
for 10 years, grades 7â9. She also has been a presenter in cooperative learning and introduction to technology. Presently, Wheeler
teaches eighth-grade general math and algebra. She received her Math Renaissance training in October 1999.
Race/Ethnicity:
American Indian: 5%
Hispanic or Latino: 1%
Asian or Pacific Islander: 1%
White: 63%
Black/African American: 30%
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Mac Williams Middle School, Fayetteville, North Carolina
Five-Month Gains for Wheelerâs Eighth-Grade Students
Section 2: Middle and Junior High Schools
Pretest
Summarized from Using Accelerated Math to Enhance Instruction in a Mandated Summer School Program.
Spicuzza, R. & Ysseldyke, J. (1999). National Center on Educational Outcomes, University of Minnesota,
Minneapolis, Minnesota.
13
Independent University Study
Study Description
Accelerated Math and Math Renaissance techniques
were used with 139 students in grades six through
eight during a 1998 six-week summer program in the
Minneapolis Public Schools. Two middle schools
within the Minneapolis Public Schools were chosen.
Five classrooms participated and teachers submitted
bids for involvement in the study. Notably, the
classroom conditions were very demanding: the
buildings were not air-conditioned and teacher
selection was not based on reading or math skills and
experience. This difficult environment remained
unaltered so that outcomes would be based on
ânaturalâ settings.
Results
The districtâs Northwest Achievement Level Test
(NALT) results indicate that Accelerated Math
students gained an average of 5.75 normal curve
equivalents (NCEs) immediately following the
summer school interventionâa gain nearly twice that
of the 3.2 NCEs achieved during the previous
academic year. The NCE gain was greater during the
3 month intervention period, than the previous entire
school year. Furthermore, very significant
commensurate gains of 2.64 NCEs were documented
on STAR Math during this six-week period. A full
report of this study is available: L0342.
School Profiles
Students: 139. 6â8
Free or reduced lunch: 67%
Minority: 70%
Site 1
A Spanish immersion school
Socio-Economic Status:
Limited English Proficiency: 37%
Site 2
Socio-Economic Status:
Limited English Proficiency: 39%
Special Education: 16%
0
1
2
3
4
5
6
Minneapolis Public Schools, Mineaspolis, MN
Acclerated Math Intervention Helps Students Achieve 80%
More Math Growth on Northwest Achievement Level Test
April 1997 to April 1998
(Period before
Accelerated
Math intervention)
April 1998 to July 1998
(Period including
Accelerated
Math intervention)
3 . 2
5 . 7 5
14
Renaissance Independent Research Reports
Using Accelerated Math to Enhance Student Achievement in High School
Mathematics Courses
Source: Terri J. Gaeddert, teacher and technology specialist
Buhler High School, Buhler, Kansas
Summarized from: Gaeddert, T. 2001. Using Accelerated Math to Enhance Student Achievement in High School Mathematics Courses.
Masterâs thesis. Wichita, KS: Friends University.
Study Description
This study evaluated the effectiveness of a learning
information system, Accelerated Math, in high school
pre-algebra, algebra, and geometry courses. For each
subject, the study compared changes in student
achievement, student attitudes, and parent attitudes
of a class using Accelerated Math to a class receiving
traditional instruction. The three-and-a-half month
study included 50 students in the intervention
(Accelerated Math) classes, 53 students in the control
(traditional instruction) classes, and 3 teachers. The
intervention and control classes for each subject had
the same teacher and studied the same topics.
Students in the control classes continued to receive
instruction through the traditional method of teacher
lecture followed by student assignments, while
students in the intervention classes were enrolled
in the appropriate Accelerated Math libraries and
progressed at their own rate through the appropriate
objectives. These students received most of their
instruction in small groups or individually from
the teacher.
At the beginning and end of the study, each student
was tested with the Stanford 9 Achievement Test
(SAT 9) and STAR Math computer-adaptive math
test. SAT 9 is a paper-and-pencil norm-referenced
test. Students in pre-algebra and algebra took
Task 1, while students in geometry took Task 2.
STAR Math is a computer-adaptive norm-referenced
test that uses Adaptive Branching technology to
accurately assess studentsâ mathematics skills in
15 to 20 minutes.
Results
Students in the classes using Accelerated Math scored
about the same as students in the control classes on
the SAT 9 and STAR Math pretests. However,
students using Accelerated Math experienced more
improvement in SAT 9 and STAR Math test scores
than students in classes using traditional instruction.
Across all three subjects, students in Accelerated
Math classes gained 12 percentile points on the SAT
9, while students in the control classes gained only
3.8 percentile points. Looking at grade equivalent
scores on the SAT 9, students in Accelerated Math
classes gained a full grade equivalent in just 3.5
months, while students in the control classes gained
only 0.3 grade equivalents. Similarly, on STAR Math
tests, students using Accelerated Math gained 9.5
percentile points while students in control classes
gained only 1.2 percentile points. Differences in test
score gains were particularly striking for students in
algebra and geometry. The graph which follows
shows percentile rank gains on the SAT 9 by class.
Students also responded to attitudinal surveys at the
beginning and end of the study. The pretest and post-
test surveys were identical except students using
Accelerated Math answered four additional questions
that specifically related to the Accelerated Math
program. The surveys asked students to indicate their
level of agreement or disagreement to statements
about attitudes toward math. Overall, on the survey
before Accelerated Math implementation, students in
the Accelerated Math classes responded more
negatively than students in the control classes to
statements such as âI learned more math this year
than last yearâ and âThe pace of this class is just
right.â However, at the end of the three-and-a-half
month study students using Accelerated Math showed
more improvement in attitudes toward math than
students in the control classes.
continued on next page
Section 3: High School
15
School Profile
Buhler High School
Buhler, Kansas
Students: 777, Grades 9â12
Socio-Economic Status:
Free or reduced lunch: 13%
Race/Ethnicity:
Asian or Pacific Islander: 1.4%
Black or African American: 1.7%
Hispanic or Latino: 2.3%
White: 94.6%
Educator Background
Terri Gaddert has 10 years of experience teaching
mathematics in grades 9â12. She received her bachelorâs
degree in secondary education from Chadron State College,
Chadron, Nebraska, in 1987. She has presented Applied
Mathematics workshops to teachers and administrators in
several states. She has been involved with business
partnerships, provided technical mathematics training for
company employees, and written problem-solving tests for
state competitions. In addition to teaching, Gaeddert is
currently serving as a technology specialist for her school,
and will receive her Master of Arts in Teaching from Friend
University, Wichita, Kansas, in 2001.
Renaissance Independent Research Reports
Parent surveys also indicated positive attitudes
toward Accelerated Math. Before implementation
of Accelerated Math, 25% of parents of
intervention group students and 33% of parents of
control group students agreed with the statement,
âMy child is learning math better this year than
last year.â After Accelerated Math
implementation, 56% of parents of intervention
group, 40% of parents of control group students
agreed with the statement.
The author of this study concludes that using a
computer managed learning system, in particular
Accelerated Math, can be beneficial for high
school students. Students in the intervention
group showed greater gains in basic mathematical
skills as well as algebraic and geometric skills.
Furthermore, students and parents believed they
did better with Accelerated Math than they did
with traditional instruction. In light of these
positive findings, the author recommends further
research in more schools as well as with more
advanced high school courses.
7.7
-10.0
10.7
3.8
11.9
4.4
16.2
12.0
14.4
5.5
8.2
4.2
-15
-10
-5
0
5
10
15
20
Pre-Algebra
Algebra
Geometry
Total
Control
Intervention
Difference
Buhler High School, Buhler, Kansas
Mean Percentile Rank (PR) GainsâStanford 9 Achievement Test
Mean
PR Gains
Math Subject Area
References and Further Readings
Educational Accountability & Foundations
Algozzine, B., Ysseldyke, J.E., & Elliott, J. Strategies and Tactics for Effective Instruction. Longmont:
Sopris West, 1997.
Cawelti, G. Handbook of Research on Improving Student Achievement. Arlington: Educational Research
Service, 1995.
Creemers, B. The Effective Classroom. London: Cassell, 1994.
Howe, M.J.A., Davidson, J.W., & Sloboda, J.A. âInnate Talents: Reality or Myth?â Behavioral and Brain
Sciences 21 no. 3 (1998): 399â442.
Sanders, W.L. & Rivers, J.C. Cumulative and Residual Effects of Teachers on Future Student Academic
Achievement. Research Progress Report. Knoxville: University of Tennessee Value-Added Research
and Assessment Center, 1996.
Information Theory & Formative Feedback
Bangert-Drowns, R.L., Kulik, C.-L.C., Kulik, J.A., & Morgan, M. âThe Instructional Effects of Feedback in
Test-Like Events.â Review of Educational Research 61 (1991): 213â238.
Berliner, D. âWhatâs All the Fuss About Instructional Time?â The Nature of Time in Schools. Edited by
M. Ben-Peretz & R. Bromme, 3â35. New York: Teachers College Press, 1990.
Brophy, J. âResearch Linking Teacher Behavior to Student Achievement: Potential Implications for
Instruction of Chapter 1 Students.â Educational Psychologist 23 (1988): 235â286.
Kluger, A.N. & DeNisi, A. âThe Effects of Feedback Interventions on Performance: A Historical Review,
a Meta-Analysis, and a Preliminary Feedback Intervention Theory.â Psychology Bulletin 119 (1996):
254â284.
Natriello, B. âThe Impact of Evaluation Processes on Students.â Educational Psychologist 22 no. 2
(1987): 155â175.
Paul, T.D. Learning Information Systems: Theoretical Foundations. Madison: Institute for Academic
Excellence, 1996.
Vygotsky, L.S. Thought and Language. Edited by E. Hanfmann & G. Vakar. Cambridge: MIT Press, 1962.
Mathematics
Beaton, A., Mullis, I., Martin, M., Gonzalez, E., Kelly, D., & Smith, T. Mathematics Achievement in the
Middle School Years: IEAâs Third International Mathematics and Science Study (TIMSS).
Chestnut Hill, MA: TIMSS International Study Center, 1996.
Cotton, K. & Wikelund, K.R. âEducational Time Factors.â School Improvement Research Series. Northwest
Regional Educational Laboratory, 1989. Available online: http://www.nwrel.org/scpd/sirs/4/cu8.html
16
Gonzales, P., Calsyn, C., Jocelyn, L., Mak, K., Kastberg, D, Arafeh, S., Williams, T., & Tsen, W. Pursuing
Excellence: Comparisons of International Eighth-Grade Mathematics and Science Achievement from
a U.S. Perspective, 1995 and 1999. NCES 2001-028. Washington, DC: U.S. Government Printing
Office, 2000.
Ina, V.S., Mullis, M.O., Eugenio, J.G., Gonzalez, K.D., Gregory, R.A., Garden, K.M., OâConnor, S.J., &
Chrostowski, T.A.S. TIMSS 1999 International Mathematics Report: Findings from IEAâs Repeat of
the Third International Mathematics and Science Study at Eighth Grade. Chestnut Hill, MA: TIMSS
International Study Center, 1999.
Loveless, T. & Diperna, P. The Brown Center Report on American Education: How Well Are American
Students Learning?: Focus on Math Achievement. Washington, DC: The Brookings Institution, 2000.
Available online: http://www.brook.edu/browncenter/bc%5Freport/2000/intro.htm
National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics.
Reston, VA: NCTM, 2000.
Reese, C.M., Miller, K.E., Mazzeo, J., & Dossey, J.A. NAEP 1996 Mathematics Report Card for the Nation
and the States. Washington, DC: Office of Educational Research and Improvement, U.S. Department
of Education, 1997. Available online: http://nces.ed.gov/nationsreportcard/96report/97488.shtml
Spicuzza, R. & Ysseldyke, J., & McGill, S. Changes in Mathematics Achievement and Instructional Ecology
in 4th and 5th Grade Classrooms Resulting from Implementation of a Learning Information System.
Minneapolis: National Center on Educational Outcomes, University of Minnesota, 2000.
Motivation & Affective Factors
Ausubel, D.P. Educational Psychology: A Cognitive View. New York: Holt, Rinehart and Winston, 1968.
Cameron, J. & Pierce, W.D. âReinforcement, Reward, and Intrinsic Motivation: A Meta-Analysis.â Review of
Educational Research 65 (1994): 363â423.
17
Reading Renaissance and Math Renaissance are registered trademarks of School Renaissance Institute, Inc. AR, ATOS, Duolog
Reading, Generation 21, Perfect Copy, Reading Practice, School Renaissance, STAR Early Literacy, Surpass, TKM, and TOPS are
trademarks of Advantage Learning Systems, Inc. Accelerated Reader, Accelerated Math, STAR Math, and STAR Reading are regis-
tered trademarks of Advantage Learning Systems, Inc.