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Ability Grouping
1
ABILITY GROUPING IN HETEROGENEOUS CLASSROOM: AN ACTION
RESEARCH STUDY OF NARROWING ACHIEVEMENT GAP
University of Maryland, Baltimore County
Ability Grouping
2
Table of Contents
pages
Abstract …………………………….…………………………… 3
Introduction ……………………………………………………... 4-6
Literature Review ……………………………………………….. 7-15
Classroom Structure …………………………………..... 11-15
Research Question and Hypothesis …………………………..... 16
Methodology …………………………………………………..... 17-27
Participants ……………………………………………. 18
Procedure and Instrumentation …………………………… 19-22
Data Collection …………………………………………. 23-24
Analysis ………………………………………………… 24-27
Summary ………………………………………………... 27
Implications …………………………………………………… 28
Limitations …………………………………………………… 29
Conclusion …………………………………………………… 30
Appendix A …………………………………………………… 34
Appendix B …………………………………………………… 35
Appendix C …………………………………………………… 36
Appendix D …………………………………………………… 37
Appendix E …………………………………………………… 39
Appendix F …………………………………………………… 41
Appendix G …………………………………………………… 42
Appendix H …………………………………………………… 44
Appendix I …………………………………………………… 45
Appendix J …………………………………………………… 46
Appendix K …………………………………………………… 47
Appendix L …………………………………………………… 50
Appendix M …………………………………………………… 51
Ability Grouping
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ABSTRACT
The impact of class size on student achievement remains an open question despite
hundreds of empirical studies and perception among parents, teachers, and policymakers
that larger classes are a significant detriment to student development. Teachers face
significant pedagogical challenges in organizing productive work for all ability level
students. This study offers an analysis of grouping students in smaller groups within the
heterogeneous classroom. The analysis focuses on two groups of seventh grade on-grade
level math students in a co-teaching class environment.
Ability Grouping
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1. INTRODUCTION
Ability level grouping is not a new concept. For almost a century, educators
continue to debate the pros and cons of its benefits and costs. Slavin (1990) cited that
discussions on the pros and cons of ability level grouping occurred in the 1920s and were
summarized in the early 1930s. This summary lists the advantages and disadvantages of
ability level grouping.
The advantages of ability level grouping include:
a. Allows students to make progress appropriate with their abilities.
b. Makes it possible to use instruction techniques that fit the needs of the
group.
c. Reduces failures.
d. Helps to maintain engagement.
e. Allows lower level ability pupils to participate when not eclipsed by other
students.
f. Makes teaching easier.
g. Makes individual instruction possible to small groups.
The disadvantages of ability level grouping include:
a. Lower level ability students need the presence of the higher level ability
students for stimulation and encouragement.
b. Attaches a stigma to lower level ability sections that can discourage the
students in these sections.
c. Causes teachers to experience time constraints for differentiating
instruction.
The reasons that I chose to study ability level grouping extend back to my
personal experience. I experienced ability level grouping first as a student and then as an
educator. As a student, I was placed in an ability-grouped classroom to take Algebra in
7th
grade. I was challenged in this class, my teacher encouraged me to ask questions and
explore high level thinking questions. As an educator, I observed that changing the
Ability Grouping
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placement of one student could have tremendous effects. Two years ago, when I taught a
30-minute remedial class everyday to students who scored basic in math and were failing
math during that school year was an eye opening for me. The 30 minutes I spent with
these 7 students everyday was the toughest teaching experience I ever had encountered.
They had no motivation to come to class and often commented that they were the ―dumb‖
group. However, when I had an intern last semester, he pulled a top performing group of
students (4-5 students) in my on-grade math classes to work on more challenging
problems. Meanwhile, I work with the rest of the class (about 15 students) to answer
questions with details and meaningful answers. I noticed that the second quarterly
assessment grades were much higher than the grades from the first quarterly assessment.
See figures 1 and 1.1. A 1-tail t-test was performed where the null hypothesis was the
quarter 1 quarterly assessment equals to the quarter 2 quarterly assessment; the
alternative hypothesis was the quarter 1 quarterly assessment was lower than the quarter
2 quarterly assessment. The p-values for periods 9 and 7 were .00617 and .00041,
respectively. The data has a 95% confidence interval of 1.9 to 6.1 mean point gain in
period 9 and .9 to 5.9 mean point gain in period 7. Therefore, the null hypothesis was
rejected and the alternative hypothesis was supported in both periods. Realizing that the
impact of changing one student‘s placement can affect an entire classroom gave me the
motivation for implementing ability level grouping. For these reasons, I chose to study
ability level grouping in the middle school environment.
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Figure 1
Period 9 First and Second Quarterly Assessment
0
5
10
15
20
25
30
Students
Po
ints E
arn
ed
Ou
t O
f 3
0 P
oin
ts
q1 per.9 9 20 18 22 22 17 15 6 22 9 10 22 17 19 9 8 22 22
q2 per.9 14 21 17 23 23 16 22 15 23 14 23 27 17 19 18 18 25 26
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Figure 1.1
Period 7 First and Second Quarterly Assessments
0
5
10
15
20
25
30
Students
Po
ints e
arn
ed
ou
t o
f 3
0
q1per. 7
q2 per. 7
q1per. 7 16 22 13 18 15 21 15 22 9 19 11 22 19 22 22 6 22 9
q2 per. 7 18 21 24 21 18 17 20 26 16 22 19 22 26 14 25 17 20 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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2. LITERATURE REVIEW
Introduction
Sustaining student achievement is on the minds of every school district and every
administrator in our current high-stakes accountability environment. Everyone is looking
for a ―silver bullet‖ that will magically meet the ever-increasing demands of
accountability requirements in No Child Left Behind (NCLB). It is also true that schools
in areas with few perceived challenges cannot remain at ―status quo‖ or ―business as
usual‖ levels in which the majority of students may be achieving. Schools across the
nation must now shift from their emphasis on the majority to the minority of their
students in significant subgroups now that every single student must be accounted for.
Furthermore, student achievement must now be sustained over time to keep pace with
expectations that are required NCLB, when, in 2014, the student-achievement target will
reach 100 percent proficiency.
Though some may scoff at the notion of actually reaching 100 percent, the truth is
that the majority of schools are not even reaching 50 percent of their students performing
proficiency. A looming wake-up call is coming down the line to schools that have been
on cruise control, thinking that they will not have to address those hidden subgroups of
students who are not achieving up to standards (Reksten 2009).
Since the Third International Mathematics and Science Study (TIMSS), there has
been more and more focus on how to improve mathematics education. Many dedicated
educators have made creative and valuable contributions that range from the global
(systemic reform) to the specific (innovative ways to use new materials in the classroom).
Even so, students‘ willingness and ability to learn, retain, recall, and apply math concepts
Ability Grouping
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and facts have not improved nearly as fast, or as much, as was expected or as is urgently
needed (Ben-Avie, Haynes, Ensign, & Steinfeld, 2003).
Having all students achieve the set standards in mathematics is considered a
national priority, as indicated in the Goals 2000: Educate America Act (PL 103-227).
Mathematics is the gatekeeper to a number of opportunities for occupational and
educational advancement (Jetter, 1993). Further, more state and district requirements
(e.g., Maryland, Virginia) are including high-school math assessments that students have
to pass to receive diplomas.
Background
Though math is vital to students' future, many students have difficulty with it.
According to the Third International Mathematics and Science Study (TIMSS)
(International Association for the Evaluation of Educational Achievement, 1996),
American eighth-grade students score significantly below the international average in
math and outperform only seven other nations (Bernstein, 1997). Further, American 12th
graders have an overall math average significantly below the international average.
Discrepancies in the nature of classroom activities across countries may help to
explain student performances. U.S. students spend 96% of their seatwork time practicing
routine procedures, whereas Japanese students engage in this type of exercise only 41%
of their seatwork time (Bernstein, 1997). In addition, Japanese students work on
problems that require the invention of new solutions, proofs, or creative procedures 44%
of the time, compared to U.S. students, who engage in similar activities less than 1%.
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Heterogeneous or homogeneous ability grouping:
There are two types of ability grouping, homogeneous and heterogeneous, in
education where teachers have been debating, for decades, whether one is more effective
than the other. If evidence suggests that a specific pattern of ability grouping tends to
enhance the nature and quality of instruction that can be provided in the classroom, then
the practice should be initiated or continued in the interest of maintaining quality
education. ―Homogeneous grouping refers to the organization of instructional classes on
the basis of student similarity in one or more specific characteristics. The criterion for
this classification may be age, sex, social maturity, I.Q., achievement, learning style, or a
combination of these or other variables. Homogeneous ability grouping, therefore, is one
of the many forms of homogeneous grouping, and generally refers to the use of
standardized measures of intelligence, aptitude, or achievement in a given subject area in
classifying students into separate ability categories and instructional class units.‖
(Esposito 1973, 165). Heterogeneous grouping ―may be achieved by either randomly
assigning all children in a grade or school to instructional classes, or by deliberately
assigning children to instructional classes, or by deliberately assigning children to
instructional classes such that a wide range of individual differences is present.
Heterogeneous ability grouping, therefore, refers to the organization of instructional
classes such that a rich mixture of children who differ with respect to test performance
level is assured.‖ (Esposito 1973, 165)
In the past, reforms such as back to the basics and individualized instructional
programs have attempted to address the issue of how to improve students' mathematics
performance. More recently, the National Council of Teachers of Mathematics (NCTM,
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1989, 1991, 1995) has outlined changes in curricular, assessment, and teaching practices
that emphasize complex math tasks requiring problem solving and mathematical
reasoning skills and deemphasize rote computation and memorization tasks.
Skills without understanding are meaningless.
Understanding without skills is inefficient.
Without problem solving, skills and understanding have little
utility. (Rectanus 2006, 13)
Understanding concepts, skill, and problem solving are three important areas of
math for middle school students. All are necessary and one does not necessarily come
before the others. (Rectanus 2006, 13)
In Ireson and Hallam (2009) review, found that students who were grouped into
ability level classes performed better in mathematical and science than those not grouped
into ability level classes. This contrasted a popular opinion that ability grouping showed
lower achievement in the lower level ability group classes. The results indicated that
students‘ self-concept but not their self-esteem and test anxiety impacted the student‘s
achievement.
However, William and Bartholomew (2004) confirmed that ability level grouping
increases achievement for students in higher ability level group while lowering
achievement in the lower level ability group. William and Bartholomew (2004)
investigated the influence that ability level grouping has on performance in mathematics.
Community support for ability level grouping is present. Students have shown
preferences for ability level grouping (Hallam & Ireson, 2006). The majority of students
in ability level groups are satisfied with their placement (Hallam & Ireson, 2007), and
teachers are supportive of teaching high ability grouped classes (Hallam, 2007). In
Ability Grouping
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addition, parents of students in the high ability level group are also supportive of ability
level grouping (Ruben, 2006).
Students who struggle in math class sometimes have difficulties primarily with
one or two topics. I‘ve known students who have trouble with number, operations,
computation, and algebra, yet are adept in geometry and spatial reasoning, and students
whose strengths and struggles are the reverse. I‘ve also taught students who have had
difficulties across all topics in math. And of course, many students bump into roadblocks
from time to time as new topics are introduced. Regardless of the specific difficulty,
there are general responses and interventions that benefit all students. (Rectanus 2006,
20).
One of the most difficult challenges facing educators is that we often have a wide
range of needs and ability within each classroom.
Ways to structure classroom
Zone of proximal development
Marian Small suggested ―one approach to meeting each student‘s needs is to
ensure that each student in the class has the opportunity to make a meaningful
contribution to the class community of learners and to provide tasks with in each
student‘s zone of proximal development.” The description of zone of proximal
development is ―distance between the actual development level as determined by
independent problem solving and the level of potential development as determined
through problem solving under adult guidance or in collaboration with more capable
peers‖ (Vygotsky, 1978, p. 86).
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―Instruction within the zone of proximal development allows students, whether
through guidance from the teacher or through working with other students, to access new
ideas that are close enough to what they already know to make the access feasible.
Teachers are not using educational time optimal if they either are teaching beyond a
student‘s zone of proximal development or are providing instruction on material the
student already can handle independently. Although other students in the classroom may
be progressing, the student operating outside his or her zone of proximal development is
often not benefiting from the instruction‖ (Small 2009, 3).
To ensure success in teaching the zone of proximal development method, first the
teacher must determine what that zone is by gathering diagnostic information to assess
the student‘s mathematical developmental level. Second, ―the teacher might also use
locally or personally developed diagnostic tools. Only after a teacher has determined a
student‘s level of mathematical sophistication, can he or she even begin to attempt to
address that student‘s needs‖ (Small 2009, 4).
Parallel tasks:
Parallel tasks are sets of tasks, usually two or three, designed to meet the needs of
students at different developmental levels. These tasks get at the same big idea and are
close enough in context that they can be discussed simultaneously. In other words, if a
teacher asks the class a question, it is pertinent to each student no matter which task that
student completed. Parallel tasks contribute to the creation of the classroom as learning
community in which all students are able to contribute to discussion of the topic being
studied (Murray &Jorgensen, 2007). Cluster grouping of a small number of students
within a heterogeneously grouped classroom can be used. This way, the students are
Ability Grouping
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grouped according to their prior experiences and knowledge about the topic. This allows
each group to be given tasks that involve a variety of opportunities for novices as well as
experienced students. When grouped in this manner, students are challenged and are
interested in the work rather than being bored by information they already have received
for frustrated by something they know nothing about. The knowledge base of an
individual is based on experiences. The novice or beginner needs more of the basic topic
information than the experienced learner does.
Peer partners:
Another effective grouping approach in mathematics involves working with peer
partners (Archer, Gleason, Englert, & Isaacson, 1995). For example, students work
together in pairs on an assignment/worksheet and provide peer assistance via the
following steps (Archer et al., 1995): Students solve the first problem independently.
1. Students check their respective answers with a key.
2. If one student errs, the other student illustrates how to solve the problem.
3. Students ask the instructor if they both erred.
―All children, however diverse, learn best when they learn together, sharing each
other‘s insight and experience, absorbing knowledge and recreating knowledge as they
collaborate, in the company of their teachers in a common pursuit‖ (Brighthouse, 2003,
45,1,p3). Having students assist each other with specific needs is a way to give them
responsibility for understanding what they know and how they can use the information.
The student who is tutoring is gaining from this experience. If you teach something, you
remember it and realize what you know and how you know it. The learner is gaining
Ability Grouping
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from the experience too, because it is an individualized instruction that is tailored to a
personal need. Students often communicate with each other using different words than
the teacher would, and sometimes their ways of explaining information may be easier for
the peer to understand.
Groupwork:
Groupwork is viewed suspiciously by many teachers, partly because of the
perceived loss of control they experience when they give students opportunities to talk
with each other (Doyle, 1983). Teachers are also reluctant to employ groupwork as they
have found that groups do not always work well together (Slavin, 1990). A common
problem in the effort of groupwork is an uneven distribution of work and responsibility
among students; some students doing more of the work and others choosing to opt out or
being forced out of discussions. Cohen and Lotan (1997) developed an approach to make
groupwork more effective and more equitable called ‗complex instruction‘. Productive
and flexible partner and group work are essential in a differentiated classroom. When
using cooperative learning the group comes to a consensus on a common goal or a
specific assignment. Those in the group are assigned specific roles to play for a
particular task. Both individual and group accountability are built in as an important part
of a cooperative learning experience.
‗Complex instruction’
This is a teaching method that is specifically designed to counter social and
academic status differences in groups, starting from the premise that status differences do
not emerge because of particular students but because of group interactions. The
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complex instruction approach has a number of strands that pertain to the learning of
respect and responsibility. In the first instance the authors recommend that classrooms
need to be ‗multidimensional‘ (Rosenholz &Wilson, 1980; Simpson, 1981). According
to the guidelines, one-dimensional classrooms are those in which only some practices are
valued; a one-dimensional mathematics classroom, for example, would be one in which
students are valued for executing procedures and nothing more. Multidimensional
classrooms expand the dimensions along which students are judged and encouraged. For
example, a multidimensional mathematics classroom could reward students for using
different methods, asking questions, representing ideas and having good discussions in
addition to the execution of procedures. The theory is that as classrooms become more
multidimensional more students have access to ideas and may be regarded as contributing
in important ways. When classrooms are multidimensional the authors propose that
teachers then apply a ‗multiple ability treatment‘. This involves explaining to students
that no one student will be ‗good on all these abilities‘ and that each student will be ‗good
on at least one‘ (Cohen & Lotan, 1997, p78).
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3. RESEARCH QUESTION AND HYPOTHESIS
Can achievement gap be narrowed through ability grouping in heterogeneous
classrooms?
This action research study will take a closer look at combining the parallel tasks
that proposed by Murray and Jorgensen (2007) and peer partners suggested by Archer,
Gleason, Englert, and Isaacson (1995). This researcher expects that students who put
with peers in similar ability groups with provided work that challenged their knowledge
base will perform better than students who work individually. For the purpose of this
study only, students who scored highest on the pre-test were identified as high achieving
students, and students who scored lowest were identified as low achieving students. The
remaining students were identified as average achievers. This identification was used to
place the experimental group in groups based on their performance on the pre-test.
Ability Grouping
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4. METHODOLOGY
This study was conducted at Bonnie Branch Middle School in Ellicott City. The
neighborhood surrounding the school is very wealthy with houses priced in the low
$750s. Our student population socioeconomic status ranges from homeless to overly
privileged. Among our students, 2.5% have limited English proficient, 11.1% are eligible
for free/reduced lunch, and 7.9% are categorized as special education. Our school‘s
student population is a little under 700 and made up of 61.1% White, 25.1% African
American, 8.9% Asian, 4.7% Hispanic, 0.1% Native American, and 0.1% unidentified –
see Table 1. The feeder elementary schools are Ilchester, Bellows Spring, and Phelps
Luck. Their high schools are Howard High or Long Reach High. To identify the effects
of small groups, this study will look at a group of convenience samples of two classes of
36 seventh grade students working on a mathematical concept – see Table 2 and 3.
Table 1
Bonnie Branch Middle School Population
Asian African
American
Caucasian Hispanic Native
American
Unidentified ESOL FARMS Special
Education
8.9% 25.1% 61.1% 4.7% .1% .1% 2.5% 11.1% 7.9%
Ability Grouping
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4.1 Participants
Table 2
Period 7 Class Make-up
Feeder Elementary School
Gender Socio-
economic
Ethnic
group
Phelps
Luck
Bellows
Spring
Ilchester Howard
County
elementary
schools
Others
13
boys
2 FARMs 9 AA
1 H
3 C
6 0 3 3 1
5 girls 1 FARMs 3 AA
2 C
0 0 2 2 1
Note. The acronyms for FARMs and ethnic groups in Tables 1 and 2 .
A = Asian
AA = African American
C = Caucasian
H = Hispanic
FARM = Students qualified for free and reduced meals
Table 3
Period 9 Class Make Up
Feeder Elementary School
Gender Socio-
economic
Ethnic
group
Phelps
Luck
Bellows
Spring
Ilchester Howard
County
elementary
schools
Others
10
boys
2 FARMs 2 AA
1 A
7 C
3 1 2 2 2
8 girls 2 FARMs 4 AA
1 A
3 C
2 3 1 0 2
The make up in both classes of African Americans was over represented in comparison
with the school‘s student population – 66% in 7th
period and 33% in 9th
period. The
number of Caucasian students was under represented in 7th
period. The population of
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FARMS students and Special Education students are also over represented in both
classes.
Table 4
Student Academic/Intervention Information
Period IEPs 504
accommodations
Basic
MSA
(2009)
(1st, 2
nd)
Quarter
Grades
Proficient
MSA
(2009)
(1st, 2
nd)
Quarter
Grades
7 4 1 4 A - (0,0)
B –(2,1)
C – (0, 2)
D – (2,1)
E – (0,0)
14 A – (4,3)
B – (4, 5)
C – (3, 2)
D – (1, 4)
E – (2, 0)
9 4 2 3 A – (0,0)
B – (0,1)
C – (0,1)
D – (3,1)
E – (0,0)
15 A – (4,2)
B – (4,4)
C – (4,6)
D – (1,2)
E – (1,1)
4.2 Procedure and Instrumentation
Due to external factors this research data collection began during the first week of MSA
testing. The first week of MSA testing this year was math, March 9th
and 10th
. Our
school schedules were modified during those two days. Each class period was shortened
to 25 minutes - almost half of a normal class period. I gave students a pre-test (Appendix
A), on March 10th
, which composed of five problems: finding the area of a rectangle, a
triangle, and calculating the surface area of a rectangular prism, cube and rectangular
pyramid. Pre-test data was gathered prior to the lessons to establish baseline data. The
lessons required 9 full class periods to complete, where students in 7th
period will work
with out intervention and students in 9th
period will work with small group intervention.
Small groups were formed based on the scores earned on the pre-test: group A - zero to
thirty percent; group B – forty to sixty percent; and group C – more than sixty percent.
Each pre-test problem worth two points; one point earned if students had the correct
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20
calculation and the other point earned by indicated the correct unit. An identical test was
given after the lessons to assess class averages. The post-test (Appendix A) was graded
based on a 4 point scale: 1 point for stating the correct formula, 1 point for completing
the correct work, 1 point for having the correct answer, and 1 point for stating the correct
unit.
A typical math lesson – Students spent the first five minutes copied the assigned
homework of the day, and completed the warm-up problems. I used this time to take care
of all administrative paper work. Upon the completion of the warm-up problems,
questions to the warm-up problems and homework from the previous night were
answered. From here, the new lesson was introduced – either by taking notes or hands-
on activities, with guided practice problems to ensure students get enough practice to
complete work on their own. To assess their understand of the lesson, students were
given the task of completing some problems on their own. Most often, it was individual
work process. Meanwhile, my co-teacher and I circulated the class to ensure that
students were on the right track.
A math lesson with intervention – Students completed the same tasks as their
counterparts during the first five minutes. Students checked their answers and asked
questions from the assigned homework problems. The direct instruction was also similar
to their counterparts – by taking notes or completing hands-on activities to introduce the
new lesson. Then, students were divided into groups. Each group had a task of problems
to complete. Groups A and B often had the same set of problems; however, group A had
the aid of a calculator regardless whether students had special accommodations or not.
Group C had the task of answering problems with fractions and open-ended type of
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21
questions. This process gave students an opportunity to discuss the problems among
themselves. Students were reshuffled during the first group work. The reshuffling was
determined based on the ease of effort or difficulty on the assigned work. This
experimental study was focused on students‘ improvement on the surface area unit. A
quiz was given (Appendix B) on the 5th
day to assess student comprehension; however, it
was not a factor to evaluate the study.
Table 5
47-minute class period (interventions occurred in the shaded regions)
Day (lesson)
Class Warm-up
(minutes)
Homework
check
(minutes)
Intro to
new
lesson
(minutes)
Modeling
(minutes)
Independent/group
work and closure
(minutes)
1 (area of rectangles
and triangles)
Appendices C and D
7 5 0 18 10 14 independent
Appendix D 9 5 0 14 10 18 group
2 (area of triangles)
Appendix L
7 5 10 10 5 17 independent
Appendix E 9 5 10 10 6 16 group
3 (area and perimeter
of triangles and
rectangles)
Appendix F
7 5 8 5 0 29 independent
Appendix F 9 5 7 5 0 30 group
4 (surface area of
rectangular prism)
Appendix M
7 5 5 15 12 10 independent
Appendix G 9 5 9 13 7 13 group
5 (surface area of
rectangular pyramid)
Appendices H and I
7 5 7 10 5 20 independent
Appendices H and I 9 5 8 12 5 17 group
6 (explore on
Explorelearning.com)
Appendix K
7 5 5 30 0 7 independent
Appendix K 9 5 4 30 0 8 group
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22
7 (combined work on
surface area of
rectangular prism,
triangular prism, and
rectangular pyramid)
Appendix J
7 5 0 4 0 38 independent
Appendix K 9 5 0 5 0 37 group
8 (assessment) 7 5 42 assessment
9 5 42 assessment
A set of 4 to 5 fraction problems involve adding, subtracting, multiplying, and
dividing were posted for 5-minute warm-up (Appendix M) everyday. The amount of
time spent on homework check depended on the number of questions and clarifications
needed from students. An introduction of a new lesson everyday was unnecessary.
There were days where students needed time to work and process the material. A review
of the previous lesson was completed on those days. Modeling of the concept in the
lesson was necessary for on-grade level students to think through the process of the
lesson. Given time for students to practice was imperative to learning. Students had the
opportunity to ask questions as they were solving the problems. When worked in groups
they had an opportunity to answer each other questions and learn from each other. When
worked individually they had the opportunity to process the material and had their
questions answered by teachers. Closures were either completing of an exit ticket or
summarizing the day‘s lesson.
One rule I established from the beginning that students needed to ask their
questions to two other people in their group before they raised their hands to ask a teacher
for help.
Ability Grouping
23
4.3 Data Collection
This was an experimental quantitative study. The convenient sampling
population was among my current students in 7th
grade on-grade students. The 18
students in Period 7 was the control group, without the small group intervention. The 18
students in Period 9 was the experimental group where they received the small group
intervention. The difference in the pre-test scores and post-test scores were compared
between periods 7 and 9. The data were compared based on the percentage increased
between the two classes, and the subgroups between the classes. Central of tendencies
and the t-test were used to analyze the data. I expected the class with intervention to have
a higher percentage increase than the control group. See Table 6.
Table 6
Scores of Pre-tests and Post-tests
Period 7 Control
Group
Period 9 Experimental
Group
pre-test post-test
points
gained pre-test post-test
points
gained
0 35 35 0 55 55
0 55 55 0 90 90
10 35 25 0 50 50
10 60 50 10 55 45
10 80 70 10 65 55
10 50 40 10 65 55
10 85 75 20 65 45
10 85 75 20 50 30
10 35 25 20 60 40
10 30 20 20 85 65
10 70 60 20 30 10
20 60 40 20 70 50
30 80 50 20 95 75
30 80 50 30 90 60
40 80 40 40 45 5
50 100 50 50 60 10
60 80 20 60 95 35
80 85 5 70 85 15
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Table 7
Pre-test summary
Period Students Scored
less than 50%
Students Scored
50% to 70%
Students Scored
more than 70%
7
(n=18)
15 2 1
9
(n=18)
15 3 0
As predicted, the majority of the students in Table 7 scored less than 50% on the pre-test.
Table 8
Post-test summary
Period Students Scored
less than 50%
Students Scored
50% to 70%
Students Scored
more than 70%
7
(n=18)
4 5 9
9
(n=18)
2 10 6
After the lessons with the intervention, more students scored fifty percent or greater in
the experimental group (period 9) than the control group (period 7). See Table 8.
4.4 Analysis
Table 9
Central of Tendencies of Pre/Post Tests
Period 7
Pre-test Post-test
Period 9
Pre-test Post-test
Mean 22.22% 65.83% 23.33% 67.22%
Median 10 75 20 65
Mode 10 80 20 65
Max 80 100 70 95
Min 0 30 0 30
Ability Grouping
25
Figure 2
Averages
Pre-test and Post-test
0
10
20
30
40
50
60
70
80
Perc
en
t
overall pre-test 22.77
per. 7 pre-test 22.22
per. 9 pre-test 23.33
overall post 66.52
per. 7 post-test 65.83
9 post 67.22
Pre-test Post-test
The data in Table 9 and Figure 2 showed that period 9 was a slightly stronger
group of students in both pre- and post-tests.
From the data:
H0: The difference in the improved mean scores in period 7 and period 9 is zero
7 9 0
HA: The difference in the improved mean scores is not zero
7 9 0
Period 7 Period 9
n1 = 18 n2 =18
y 1 65.83
y 2 67.22
s1 = 21.51 s2 = 18.96
Ability Grouping
26
A two-sample t-test was performed to compare two means. The comparison had
the p-value of 0.84 indicated 84 students out of 100 were not affected by the intervention.
Since the p-value was greater than .05 then it has an indication of no difference between
two groups.
A closer look at the students who scored fifty percent or less on the pretest made a
significant percentage gain than those scored greater than fifty percent in both classes –
see Figure 3. When the t-test was performed comparing the two classes among the fifty
percent or less groups, it has the p-value of .86. Again, the p-value indicated that there
was no significant difference in the two classes.
Figure 3
The data summary in Figure 4 showed students in period 9 scored a higher average gain
than period 7 in the overall average among students who scored 0% to 30% in the pre-
test. This is very encouraging to the study because if the trend continues then there is a
Average Gains of Subgrouping
0
20
40
60
80
100
120
Pre-test Scores
Av
era
ge
Pe
rce
nt
Ga
ined
period 7 45 59 60 80 80 100 80 85
period 9 65 62 63 90 45 10 95 85
0 10 20 30 40 50 60 70 80
Ability Grouping
27
possibility that the hypothesis can be supported. However, more studies needed to be
done.
Figure 4
Average Gains of Subgroups
0
20
40
60
Subgroups
Pe
rce
nt
Ga
ine
d
Period 7 47.9 28.75
Period 9 51.8 16.25
0% to 30% 40% to 80%
Summary:
Since the p-value was greater than .05 we failed to reject the H0 and not enough to
support the HA. The results cannot be inferred to the population because more time and a
broader sample were needed to collect more data on other math concepts as well.
Although the experiment did not show a significant improvement in student achievement
in comparison between the control group and the experimental group; however, there was
a steady gain in the low subgroup - see Figures 3 and 4. This experimental study was
completed on one unit assessment. If the time frame was longer and more objectives
were covered the results will show a more significant improvement in student
achievement between the two classes.
Ability Grouping
28
5. IMPLICATIONS
It is important that as educators in teaching the general population of students, a
critical eye be taken when making decisions about research because it often presents
conflicting directions. There are many social and political implications for general
education polarizing the advocates and experts on how to best educate the country‘s math
education. Clearly the educational community must find ways to encourage students to
pursue mathematics at higher levels, and to provide instruction that will increase their
mathematics abilities and mathematical achievement. From the result of this research
study – small groupings by common ability, a different grouping should be considered for
the next school year. Small groups in 9th
period math class showed some improvement in
achievement. From the start of the next school year, students will be placed in small
groups of 4 by one of the following categories:
1. Similar ability levels
2. One strong ability student, two average ability students, and one weak ability
student
3. Two average ability students and two weak ability students or two average ability
students and two strong ability students.
The group ratios will remain the same throughout the school year but the groups will get
mixed up frequently so that students will not have the perception of being labeled.
Ability Grouping
29
6. LIMITATIONS
There were several limitations in this research study. Firstly, the sample group was a
convenient sample of the two on-grade math classes of 36 students. The sample size of
was not large enough to accurately assessed student performance. Secondly, the topic
used to conduct the experiment was on surface area unit over the course of two weeks.
The data was collected based on one small section of mathematics in a short period of
time. Students who performed poorly on algebra objectives or computation skills most
often performed beautifully in geometry. Thirdly, due to the external factors of the study,
the pre-test was given on the day of math MSA. Students were tired and burned out from
sitting for more than two hours of taking a standardized test. Lastly, the data were
analyzed based on the average gained between pre- and post-test scores; students‘ pre-test
scores may not be accurately measured their true performance.
Ability Grouping
30
7. CONCLUSION
This case study provides an example of teaching in a heterogeneous
mathematics class, and begins to understand the importance of the role of teacher in
organizing a classroom system that supports student achievement. Further research is
needed to better understand aspects of the teacher‘s role and their relation to the
emergent patterns of various grouping methods, for example, how smaller groups
within different ability levels promote equal learning among group members. In
addition, we must consider the relationship between success in school and young
people‘s motivation and self-confidence. To promote mathematics achievement,
educators must find strategies that increase students‘ self-esteem and self-confidence
in their ability to do mathematics. We must adopt strategies that motivate students to
engage in mathematical activities to pursue further study in mathematics.
Ability Grouping
31
REFERENCES
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difficulties (pp. 161-194). Boston: Allyn & Bacon.
Ben-Avie, Michael, N. M. Haynes, J. Ensign, & T. R. Steinfeld (2003). How social and
emotional development add up – Getting results in math and science education.
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Bernstein, B. (1997). Message and meaning: The third international math and science
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draw a line in the sane and create a new ideal? FORUM, 45(1), pp.3-11.
Cheung, C., & Rudowicz, E. (2003). Academic outcomes of ability grouping among
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Cohen, E. (1994) Designing Groupwork (New York, Teachers College Press).
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Esposito, D. (1973, Spring). Homogeneous and heterogeneous ability grouping:
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of structured grouping practices. British Educational Research Journal, 32(4), 583-
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Mathematics achievement in the middle school years: LEA's third international
Ability Grouping
32
mathematics and science study (TIMSS). Chestnut Hill, MA: TIMSS International
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(1996). Within-class grouping: A meta-analysis. Review of Educational Research,
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that works (p. 87). Alexandria, VA: Association for Supervision and
Curriculum Development.
Murray, M., & Jorgensen, J. (2007). The differentiated math classroom: A guide for
teachers, K-8. Portsmouth, NH: Heinemann.
National Council of Teachers of Mathematics (NCTM) (1986). Position statement of
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school mathematics. Reston, VA: Author.
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Rectanus, C. (2006). So You Have To Teach Math. Sausalito, CA: Math Solutions
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Reksten, L. E. (2009). Sustaining extraordinary student achievement. Thousand
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Rosenholtz, S.J. & Wilson, B. (1980) The effect of classroom structure on shared
perceptions of ability, American Educational Research Journal, 17, pp. 175-182.
Ability Grouping
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Ruben, B. C. (2006). Tracking and detracking: Debates, evidence, and best practices for
a heterogeneous world. Theory into Practice, 45(1), 4-14.
Simpson, C. (1981) Classroom structure and the organization of ability, Sociology of
Education, 54, pp. 120-132.
Slavin, R.E. (1990) Achievement effects of ability grouping in secondary schools: a best
evidence synthesis, Review of Educational Research, 60(3), pp. 471-499.
Small, M. (2009). Good Questions: Great Ways to Differentiate Mathematics
Instruction. New York, New York: Teachers College Press .
Tomlinson, C. A. (2004). Differentiation in diverse settings. School Administrator,
61(7). 28-33.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological
processes. Cambridge, MA: Harvard University Press.
William, D., & Bartholomew, H. (2004). It‘s not which school but which set you‘re in
that maters: The influence of ability grouping practices on student progress in
mathematics. British Education Research Journal, 30(2), 279-293.
Ability Grouping
34
Appendix A - Pre-test and Post-test
Surface Area
1. Find the area of the rectangle below.
2. Find the area of triangle ABC below.
3. What is the total surface area, in square inches, of the
rectangular prism below?
4. Jack is building a wooden cube in his carpentry class. Each face has an area of 25
square centimeters. What is the total surface area of the cube?
5. Find the surface area of the rectangular pyramid below.
6 inches
5 inches
12 inches
16 m
36 m
A
C
B
3.5 m 10 m 13 m
15 m
5 m
10 m
7 m
9 m
Ability Grouping
35
Appendix B - Quiz
Find the area and perimeter of each figure. 5 points per problem.
1. 2.
base = _________ base = _________
height = ________ height = __________
Perimeter = _____________ Perimeter = _______________
Area = _________________ Area = ________________
3 cm 4 cm
6 cm
5 cm
7 m
7 m
Ability Grouping
36
Appendix C
How to find the area of a rectangle:
The area of a rectangle can be found by multiplying the base times the
height. The base and height of a rectangle must be perpendicular to each
other
If a rectangle has a base of length 6 inches and a height of 4 inches, its area
is 6x4=24 square inches
Jenny wanted to cover her 8 feet by 9 feet rectangular garden with a tarp due to the frost
freeze advisory for tonight. What is the smallest size tarp must she use?
6 in
24 in
4 in
8 in
5 ft 9 ft
Ability Grouping
37
Appendix D (excerpt from
http://www.mathgoodies.com/lessons/vol1/area_triangle.hmtl)
Notes and Guided Practice – Formulas on Triangles
The base and height of a triangle must be perpendicular to each other. In each of the
examples below, the base is a side of the triangle. However, depending on the triangle,
the height may or may not be a side of the triangle. For example, in the right triangle in
Example 2, the height is a side of the triangle since it is perpendicular to the base. In the
triangles in Examples 1 and 3, the lateral sides are not perpendicular to the base, so a
dotted line is drawn to represent the height.
Example 1: Find the area of an acute triangle with a base of 15 inches and a height of 4
inches.
Solution:
A =
1
2b h
A =
1
2· (15 in) · (4 in)
A =
1
2· 60 in
2
A = 30 in2
Example 2: Find the area of a right triangle with a base of 6 centimeters and a height of
9 centimeters.
Solution:
A =
1
2b h
A =
1
2· (6 cm) · (9 cm)
A =
1
2· (54 cm
2)
A = 27 cm2
Example 3: Find the area of an obtuse triangle with a base of 5 inches and a height of 8
inches.
Solution:
A =
1
2b h
A =
1
2· (5 in) · (8 in)
A =
1
2· (40 in
2)
A = 20 in2
4 in
15 in
10 in
8 in
11 cm ccm
9 cm ccm
6 cm ccm
8 in
5 in
12 in
Ability Grouping
38
Find the area of a triangle with a base of
16 feet and a height of 3 feet.
Find the area of a triangle with a base of 4
meters and a height of 14 meters.
Find the area of a triangle with a base of
18 inches and a height of 2 inches.
13 in 16 in
15 in
18 in
Ability Grouping
39
Appendix E
Groups A and B
Identify the base and the height in each figure
base = base =
height = height =
area = area =
base = base =
height = height =
area = area =
Group C
Identify the base and the height in each figure
base = base =
height = height =
area = area =
15 cm 10 cm
12 cm 30 m
10 m 15 m
30 m
10 m
15 m
24 ft
11 ft
14 ft
20 ft
15 cm 10
2
3 cm
12
1
2 cm 30.92
m
10.8 m 15.7 m
Ability Grouping
40
base = base =
height = height =
area = area =
30.02 m
10.9 m 15.81 m
24 ft
11
6
7 ft
14.5 ft
20
1
5 ft
Ability Grouping
41
Appendix F
Find the area and perimeter of the following triangles.
P = ___________ P = ___________ P = ___________
A = ___________ A = ___________ A = ___________
P = ___________ P = ___________
A = ___________ A = ___________
5 cm ccm
7 cm ccm
5 cm ccm
4 cm ccm
3 cm ccm
6 cm
5 cm ccm
4 cm ccm
5 cm ccm
5 cm ccm
7 cm ccm
20 in
25 in
29 in
20 in
55 in
29 in
22 in 25 in
Ability Grouping
42
Appendix G
Groups A and B – rectangles (www.mathplayground.com)
1. A square has a perimeter of 24 inches. What is the area of the square?
2. A square kitchen has an area 100 square feet. What is the kitchen‘s perimeter?
3. The length of a rectangular field is 75 meters. Its width is 15 meters. Sofie ran
around the track 3 times. How far did she run?
4. Molly and Ted built pens for their dogs. Molly made a pen 12 meters by 8
meters. Ted‘s pen is 15 meters by 6 meters. Who will need more fencing to build
the pen?
5. The area of square photo is 25 square inches. Angie decided to enlarge the photo
by doubling the sides. What will the new area be?
6. Bridget needs to make rectangular cards measuring 2 inches by 3 inches. She will
cut them from a square sheet of poster board measuring 1 foot on each side. What
is the greatest number of cards that Bridget can make?
Group C –rectangles (www.mathplayground.com)
1. The distance around a rectangular garden is 36 feet. One side measures 15 feet.
What is the area of the garden?
2. Mrs. bathroom measures 6 feet by 10 feet. She wants to cover the floor with
square tiles. The sides of the tiles are 6 inches. How many tiles will Mrs. need?
3. Mrs. used 80 meters of fencing to enclose a rectangular garden. The length of
the garden is 25 meters. How wide is the garden?
4. A rectangle has an area of 360 square centimeters. It is 20 centimeters long.
What is its perimeter?
5. A square garden has a perimeter of 48 meters. A pond inside the garden has an
area of 20 square meters. What is the area of the garden that is not taken up by
the pond?
6. A rectangular living room measures 12 feet by 10 feet. A carpet placed on the
floor leaves a border 2 feet wide all around it. What is the area of the border?
Ability Grouping
43
7. The square has sides that measure 15 cm. A rectangle has a length of 18 cm. The
perimeter of the square is equal to the perimeter of the rectangle. What is the area
of the rectangle?
8. Kevin can mow a square lawn that is 30 meters of each side in 45 minutes. If he
works at the same rate, how many minutes will it take Kevin to mow a square
lawn that measures 60 meters on each side?
9. Chloe agreed to wash all of the windows in Todd‘s giant art studio. There are 400
square panes of glass each measuring 2.5 feet on each side. Todd offered to pay
10 cents per square foot. Chloe said she would rather get paid 60 cents a pane.
Todd agreed and was happy that he was actually going to save money. How
much money will Todd save?
Ability Grouping
44
Appendix H
Color the top face in red, a side face in blue, and the front face in yellow.
top face: side face: front face:
base = base = base =
height = height = height =
Area = Area = Area =
Color the top face in green, a side face in blue, and the front side in red.
top face: side face: front face:
base = base = base =
height = height = height =
Area = Area = Area =
16 in
10 in
21 in
16 in
6 in
6 in
Ability Grouping
45
Appendix I
Find the surface area of the following figure:
13 cm
4 cm
10 cm
10 ft
6 ft
8 ft
5 ft
Ability Grouping
46
Appendix J - Review
Find the surface area
15 ft
8 ft
10 ft
5 ft
10 cm
2 cm
8 cm
9 ft
9 ft
9 ft
Ability Grouping
47
Appendix K – Gizmo Exploration
Surface Area of a Rectangular Prism
In this activity, you will find the surface area of a rectangular prism, first by using a net,
then by using lateral area.
1. In the Gizmo, next to Base, select Rectangle. Under Rectangle, slowly drag the
point on the top right corner of the base of the prism to change the dimensions of both
bases of the prism. Set the width to 8 and the length to 10. Set Height (h) to 4.0 using the
slider. (To quickly set a value, type a number in the box to the right of the slider and
press Enter.)
1. Look at the 3-D and unfolded views of the prism. How many faces does the prism
have? In which view is it easier to see each face, 3-D or unfolded? The unfolded
view is called a net. A net is a pattern you can fold into a three-dimensional
figure.
2. Identify the shape of each face of the prism. What are the dimensions of each
face? Find the area of each of the six faces of this prism. What are those areas?
3. Add the areas of all the faces. What is your answer? This sum is called the surface
area of the prism (often abbreviated S.A.). Click on Compute lateral area and then
click on Compute surface area to check your answer.
2. Turn off Compute lateral area. Be sure that Base is still set to Rectangle, and be sure
that width = 8, length = 10, and height = 4. You will now find surface area by finding the
lateral area (L.A.) and base area (B) separately and then adding them together. The lateral
area of a prism is the sum of the areas of the lateral faces (all the faces except the bases).
1. How many lateral faces does this prism have? What is the area of each lateral
face? What is the lateral area of the prism?
2. Now use the shortcut for finding the lateral area—multiply the perimeter of the
base by the height. Does this answer agree with your answer from the last step?
If not, double-check your work. Click on Compute lateral area to check your
work.
Ability Grouping
48
3. To finish finding surface area, you first need to know the total base area. How
many bases does the prism have? What is the area of each base?
4. Add the total base area to the lateral area to find the surface area. Click on
Compute surface area to check your answer.
Surface Area of a Triangular Prism
In this activity, you will find the lateral area and surface area of a triangular
prism.
Next to Base, select Triangle. Turn off Compute lateral area. Set Height (h) to 8.0.
Drag the vertices of the triangle to reshape the base. Notice the 3-D and unfolded views
of the triangular prism.
1. How many faces does a triangular prism have? How many faces are triangles?
How many are rectangles? Which ones are the lateral faces?
2. Find the lateral area of this triangular prism. Check your answer by clicking on
Compute lateral area.
3. The base area (B) has been calculated for you in the Gizmo. (This is tricky to do
on your own in this case.) What is the base area?
4. What is the surface area of the prism? Check your answer by clicking on Compute
surface area.
Surface Area of a Pyramid
In this activity, you will find the surface area of a regular pyramid. A regular pyramid has
a regular polygon for a base and congruent isosceles triangles for lateral faces.
1. In the Gizmo, next to Base, select Square. Under Square, drag the point on the top
right corner of the square to change the side length of the base. Set Side length (s) = 8.
Set Height (h) to 7.0 using the slider. (To quickly set a value, type a number in the box to
the right of the slider and press Enter.) Notice the regular pyramid in the Gizmo, shown
in 3-D and in unfolded view.
Ability Grouping
49
1. The base of this pyramid is a square. What is the length of one side of the base?
What is the perimeter of the base?
2. Each lateral face of the pyramid is an isosceles triangle. What is the slant height
(L) of each face?
3. The Lateral Area (L.A.) of a pyramid is the total of the area of the lateral faces
(the triangles). The shortcut to find the lateral area is to find one-half the product
of the perimeter of the base times the slant height, or L.A. = 1 over 2PL. What is
the lateral area of this pyramid? Round your answer to the nearest whole number.
Click on Compute lateral area to check your answer.
4. The Surface Area (S.A.) of a pyramid is the sum of the lateral area and the area of
the base (B), or S.A. = L.A. + B. What is the area of this square base?
5. What is the surface area of this pyramid, to the nearest square unit? Click on
Compute surface area to check your answer.
2. Turn off Compute lateral area. Next to Base, select Triangle. Set Side length (s) to 9
and set Height (h) to 8.0.
1. The formula for finding the lateral area is the same for all regular pyramids, L.A.
= 1 over 2PL. Find the lateral area for this triangular pyramid. Click on Compute
lateral area and use the Gizmo to check your work.
2. The surface area of any regular pyramid is found by S.A. = L.A. + B. The base
area (B) has been calculated for you in the Gizmo. (This is tricky to do on your
own in this case.) What is the base area?
3. What is the surface area of the pyramid? Click on Compute surface area to check
your answer.
Ability Grouping
50
Appendix L
Identify the base and the height in each figure
base = base =
height = height =
area = area =
base = base =
height = height =
area = area =
15 cm 10 cm
12 cm 30 m
10 m 15 m
30 m
10 m
15 m
24 ft
11 ft
14 ft
20 ft
Ability Grouping
51
Appendix M
Rectangles (www.mathplayground.com)
1. A square has a perimeter of 24 inches. What is the area of the square?
2. A square kitchen has an area 100 square feet. What is the kitchen‘s perimeter?
3. The length of a rectangular field is 75 meters. Its width is 15 meters. Sofie ran
around the track 3 times. How far did she run?
4. Molly and Ted built pens for their dogs. Molly made a pen 12 meters by 8
meters. Ted‘s pen is 15 meters by 6 meters. Who will need more fencing to build
the pen?
5. The area of square photo is 25 square inches. Angie decided to enlarge the photo
by doubling the sides. What will the new area be?
6. Bridget needs to make rectangular cards measuring 2 inches by 3 inches. She will
cut them from a square sheet of poster board measuring 1 foot on each side. What
is the greatest number of cards that Bridget can make?
7. The distance around a rectangular garden is 36 feet. One side measures 15 feet.
What is the area of the garden?
8. Mrs. ‘s bathroom measures 6 feet by 10 feet. She wants to cover the floor with
square tiles. The sides of the tiles are 6 inches. How many tiles will Mrs. need?
9. Mrs. Wrenn used 80 meters of fencing to enclose a rectangular garden. The
length of the garden is 25 meters. How wide is the garden?
10. A rectangle has an area of 360 square centimeters. It is 20 centimeters long.
What is its perimeter?
11. A square garden has a perimeter of 48 meters. A pond inside the garden has an
area of 20 square meters. What is the area of the garden that is not taken up by
the pond?
12. A rectangular living room measures 12 feet by 10 feet. A carpet placed on the
floor leaves a border 2 feet wide all around it. What is the area of the border?
13. The square has sides that measure 15 cm. A rectangle has a length of 18 cm. The
perimeter of the square is equal to the perimeter of the rectangle. What is the area
of the rectangle?
Ability Grouping
52
14. Kevin can mow a square lawn that is 30 meters of each side in 45 minutes. If he
works at the same rate, how many minutes will it take Kevin to mow a square
lawn that measures 60 meters on each side?
15. Chloe agreed to wash all of the windows in Todd‘s giant art studio. There are 400
square panes of glass each measuring 2.5 feet on each side. Todd offered to pay
10 cents per square foot. Chloe said she would rather get paid 60 cents a pane.
Todd agreed and was happy that he was actually going to save money. How
much money will Todd save?
Rubric for A Guide for Assessing the Capstone Project
* Please rate the student's competencies in each area using the scale of 1-3. Please provide feedback and recommendations in the text box provided. If not applicable, please select NA.
Criterion Performance Rating
Substandard Standard Proficient Score
Beginning
Is the question specific to the
teacher’s class?
1 The question does not
reflect the context of the classroom or the teacher;
rather it is generic to teaching.
2 The question reflects
the context of the class but is not specific to the
concerns or is unclear.
3 The question is critical for the teacher, linked directly to the context of the class.
3
Is the question of immediate value to the teacher or class performance?
1 The question does not lead to changes in the perspective of the teacher, offer possible changes in the class, or lead to new knowledge about the class.
2 The question could change perspective or classroom understand but is narrow or of limited value to class learning.
3 The question leads to a change in understanding of the class, suggests potential changes for the class or offers new knowledge to the teacher.
3
Developing the question(s)
Will the question yield practical advice, assist in decision-making,
and consider the diversity of the classroom?
1 The question does not offer change options for the
teacher, assist in decision making, or consider the diversity of the classroom.
2 The question offers change options for the
teacher, considers diversity, and assists with the decision
making within a narrow scope or of limited value to the growth of the class or teacher.
3 The question offers change options for the teacher, considers
the diversity of the classroom, and assists with decision-making.
3
Will the findings lead to an attainable solution for the
classroom?
1 The findings are not used to develop a realistic solution for this or other
classrooms
2 The findings can develop a realistic solution for this
classroom.
3 The findings can develop a realistic solution for this and other classrooms.
3
Has the teacher used collaborative models of reflection for establishing the question?
1 There is no evidence of the use of a critical friend or other sources of reflection used in the development of the question.
2 Some evidence of
collaborative reflection that supported the development of the
question
3 Evidence of collaborative reflection enhanced the development of the question.
2
Is the research literature consulted as part of the development of the question?
1 Literature has not been consulted or incorporated into the question
2 Evidence of a literature search and its application to the question is apparent.
3 The literature review is integrated into the question, demonstrating a clear understanding of the literature base and its application to the question.
3
Data CollectingIs the context
explained in enough detail for the reader to understand the issue?
1 The reader can not envision the classroom or
link the classroom context to the question.
2 The reader envisions the classroom and can
link the classroom context to the question.
3 The reader envisions the classroom and can link the
classroom context to the question and other classrooms.
3
Does the research involve multiple sources of information to answer the question?
1 Only one source of information is listed for the data collection and this source does not take into account the complexity of the issue in question.
2 Multiple sources of information are listed for the data collection, and the sources respond to the question.
3 Multiple sources of information are listed for the data collection, and the sources take into account the complexity of the issue in question.
3
Does the collected
evidence offer a data rich environment for the teacher to
examine the class including analysis in areas of diversity and the question?
1 Little is known about the
classroom from the data collected for the study.
2 Data collected
offers an understanding about the classroom
including areas of diversity in either qualitative or
quantitative terms.
3 Data collected offers a rich
understanding about the classroom including areas of diversity in both qualitative and
quantitative terms.
2
Has the teacher used collaborative efforts in the examination of the
1 There is no external analysis or review of the data. Neither participants
2 External analysis and review of the data involve either
3 External analysis and review of the data involve the participants and critical friends in the review.
3
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classroom data? nor critical friends are
included in the review.
participants or critical
friends in the review.
Analyzing DataDoes the analysis examine diverse subsets of the population such as gender, race or socioeconomic status where appropriate to the question?
1 The analysis does not examine diverse subsets of the population where appropriate to the question.
2 The analysis
examines diverse subsets of the population where
appropriate to the question.
3 The analysis offers an in-depth examination of diverse subsets of the population where appropriate to the question.
2
Does the analysis incorporate multiple
data sources into a coherent overview of the question?
1 The data collection sources can not answer the
question posed by the teacher.
2 Provided a correct explanation of the
results which caused the research to either
accept or reject the hypotheses.
3 Provided a thorough and precise explanation of the results
which cause the research to either accept or reject the hypotheses.
2
Does the analysis offer explanation that can change teacher/student behaviors or attitudes?
1 No explanation is offered for teacher or student behaviors or attitudes.
2 An explanation is offered for teacher or student behaviors or attitudes.
3 An explanation is offered for
teacher or student behaviors or attitudes that could lead to changes in future behaviors.
3
Reflecting on the Findings
Are the conclusions an accurate portrayal of the question and
findings?
1 An incorrect explanation of the results of the
research.The question was not addressed, and findings arenot accounted for, used
nofacts, concepts or principlesin the conclusion. An incomplete explanation ofthe classroom leaving out key facts, concepts or principles.
2 An explanation of the resultsof the results of
the research.The question was addressed,and findings
are accounted for. The teacher used facts,concepts, or principles in theconclusion.
3 A clear explanation of the results of the research. The
question was addressed, and findings are accounted for. The
teacher used facts, concepts or principles in the conclusion. A complete explanation of the
classroomaccounting for key facts, concepts or principles.
3
Do the conclusions
contribute to student learning which includes addressing
the diversity of the classroom?
1 There is no stated
linkage between the research and student learning or the linkage does
not appear coupled to learning or address the
diversity of the classroom.
2 There is linkage between the research and student learning
and the diversity of the classroom is addressed.
3 There is stated linkage
between the context, research question and student learning including considerations for the
diversity of the classroom.
2
Are there better ideas than before the study?
1 There is no change in the ideas of the teacher, or ideas appear to be similar in quality and impact.
2 There is change in the ideas of the teacher.
3 Change in the ideas of the teacher that improves the quality of the classroom learning.
2
Do the findings exemplify the classroom in
question?
1 There is no linkage between the findings and the class described in the
context section of the paper.
2 Linkage can be found between the findings and the class described
in the context section of the paper
3 Strong linkage between the findings and the class described
in the context section of the paper
3
What changes could be initiated next year to change the teacher behavior or the classroom?
1 No changes are stated or recommended by the author.
2 Changes are recommended by the author
3 Changes are recommended by the author that can be implemented over the coming year.
3
Sharing the FindingsAre the results transferable?
1 There are no stated or apparent transferability of the findings.
2 There is stated or apparent transferability of the findings.
3 There are stated or apparent transferability of the findings to a
wide variety of settings including diverse settings and populations.
3
Will the results permit
flexible application?
1 Results do not permit co-
construction for other settings or classes.
2 Results support co-
construction for other settings
3 Results support co-construction for other settings with high probability of success.
3
Total Score 54.0
Feedback and Recommendations
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