CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
The Use of Concept Mapping in the Modeling Physics Classroom and Its Effects on
Comprehension and Retention
Principal Investigator: Dr. Colleen Megowan
Co-Investigators: Melissa Girmscheid and Darrick Kahle
Arizona State University
This study was completed as Action Research required for the Master of Natural Science
degree with concentration in physics.
Submitted July 2014
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
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Table of Contents
Abstract ........................................................................................................................................... 3
Rationale ......................................................................................................................................... 3
Literature Review............................................................................................................................ 4
Method .......................................................................................................................................... 11
Procedure for Treatment ............................................................................................................... 17
Timeline ........................................................................................................................................ 22
Data Analysis ................................................................................................................................ 23
Results ............................................................................................Error! Bookmark not defined.
Reflections .................................................................................................................................... 58
Conclusion .................................................................................................................................... 67
Appendix A ................................................................................................................................... 71
References ..................................................................................................................................... 72
CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
Abstract
Implementing a concept mapping method in our class allowed students to face
what they know (metacognition) before investigations by drawing a concept map at the
start of each instructional unit. As the unit progressed they incorporated new knowledge
on the same diagram by way of concepts and visual models, simultaneously forming a
new physical representation of their thinking and a more comprehensive mental model.
We examined the progression of these concept maps for evidence of resolution of student
misconceptions, the integration of new ideas into existing conceptual models and
retention of introductory mechanics knowledge. The use of concept mapping produced
statistically significant gains in both scientific reasoning skills when compared to the
Modeling physics classroom as well as an increase in introductory physics knowledge
among students with lower initial scientific reasoning skills. In addition, qualitative data
is favorable with students reporting an increase in thought analysis and organization,
knowledge analysis and confidence with academic content.
Rationale
We, the investigators, taught high school physics using the Modeling Method of
Instruction developed at Arizona State University (Hestenes, 2010). While the Modeling
Method of Instruction provided our students with multiple concept representations, our
students still struggled to confront misconceptions that have been learned and cemented
through experience. Classroom discussion helped students to verbalize and analyze
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thoughts; however a difficulty arose when translating these discussions into written form.
As teachers we often witnessed students struggling to take notes that will be both useful
and comprehensive. We believed that by confronting the difficulties in organizing and
integrating thoughts and new concepts derived from class discussions and laboratory
activities, students would be able to actively monitor their learning in a simple and
practical way. The task at hand for our research team was to have students go one step
further from our baseline Modeling approach and incorporate concept mapping as a
metacognitive strategy, in the hope that they would achieve additional learning gains over
those realized by students who used only the Modeling Instruction representational
practices. Student-generated concept maps encompassed ideas, vocabulary, diagrams,
equations and graphs were produced during lab experiences, small-group conferencing
and class discussion. These maps promoted both personal learning and student
confidence in the model under investigation and served as the comprehensive
visualizations through which our students recorded preconceptions, confronted
misconceptions, and made connections with new material. Through this study we strived
to determine in what ways and to what extent concept mapping affected comprehension
and retention in the Modeling physics classroom.
Literature Review
Physics education begins long before students set foot in a physics classroom.
From being able to throw a ball with accuracy to gauging how to step on a moving object,
personal observations help us construct mental explanations about moving objects
(Norman, 1983). Making neural connections regarding motion, and seeking answers to
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
complicated questions begins well before a student walks through a classroom
(Vygotsky, Cole, John-Steiner, Scribner, & Souberman, 1978). Students often enter the
physics classroom with preconceived notions regarding mechanics (Halloun & Hestenes,
1985b). Although students enter the class with all of this physics experience, they also
inevitably bring an equal amount of misconceptions (Arons, 1997). One challenge in
education is student lack of cognitive skills necessary to explain the complexities of a
phenomenon (Collins, 2006). The goal is for students to develop a comprehensive
Newtonian level of knowledge (Halloun & Hestenes, 1985a&b). Through the course of a
physics class, students should evolve from simply experiencing concepts to gaining a
working model of observed phenomena by using multiple representations, and
demonstrate coherence of a concept by having all the necessary elements, operations,
relations and rules properly represented and connected with one another (Hestenes, 2010;
Lesh & Doerr, 2003).
Overcoming preconceptions has proven to be difficult for some students for many
reasons. Prior knowledge can determine how a student will accept and decipher
instruction while leading to unacceptable explanations (Roschelle, 1995). According to
McDermott, for students to discover and correct their own misunderstandings, instruction
should elicit students’ ideas, then confront students with errors in those ideas, and finally
offer students the opportunity to resolve the errors (McDermott, 1993). “A person's prior
knowledge is part of his or her personal identity in society. Conceptual change almost
always involves a transformation of identity- the specialization of concepts about motion
not only enables a child to think more like a scientist, but also allows a child to progress
towards becoming a scientist. Becoming a participant in a community can be a stronger
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motivation the gaining knowledge. This is a useful corrective to educators who focus on
the ‘right knowledge’ and forget to ask who a learner is becoming” (Roschelle, 1995).
Assessing student mastery of a concept begins by considering student
preconceptions. Concept maps are an excellent way to track students’ prior knowledge as
well as track learning progression and thoughts related to class material and assist
students in recognizing gaps in information that need to be addressed (Cañas, 2008).
Valid, as well as invalid ideas held by students can be identified through the use of
concept maps, pinpointing relevant knowledge before and after instruction in a manner as
effective as a clinical interview (Edwards & Fraser, 1983).
While many students recognize when a misconception has been addressed or
momentarily realize a connection between ideas, they rarely memorialize these events to
fit reality (Clement, 1982). Placing ownership in the hands of the student, to operate
independently, is an expectation well-established in traditional schooling, yet this
expectation is not met by many (Hake, 1998). Some students are able to recall past
events, and some students are not, and it is this difference that prevents these students
from actively rejecting a prior misconception or adopting a new one (Herman,
Caczmarczyk, Loui, & Zilles, 2008). By concept mapping periodically throughout a
class, students must confront misconceptions and are forced to memorialize, thus
producing and retaining connections between ideas (Novak & Gowin, 1984). According
to Novak and Gowin, concept maps break down the required material into small
segments, making learning easier for the student, and simplifying instructional planning
(Novak & Gowin, 1984). Concept maps externalize a person’s knowledge structure and
can serve to point out any conceptual misconceptions the person may have, and this
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explicit evaluation of knowledge and subsequent recognition of misconceptions allows
for finely targeted remediation (Novak & Gowin, 1984). Since concept maps are visual
images therefore they tend to be more easily remembered than text (Safdar, Hussain,
Shah, & Rifat, 2012).
Modeling Instruction was developed at Arizona State University by Dr. David
Hestenes and Malcolm Wells beginning with a framework designed in 1987 (Hestenes,
2010). “A key to the astounding success of science in discovering the inner workings of
natural phenomena has been the development of a powerful way of thinking called
modeling. To describe and understand the structure of things, from raindrops to animals,
and the regularities in natural processes, from evaporation to locomotion, scientists
create conceptual models of things and processes” (Hestenes, 1993). Scaffolding (Wood,
Bruner, & Ross, 1976) in Modeling has its own “flavor” it is, theoretically, student-led,
user-friendly, hands-on, group-based and mandates cognitive dissonance through student
enrichment activities that use whiteboards as a tool to increase Newtonian-centered
discourse (Megowan, 2007). Modeling Instruction done well produces discourse that is
consistent with an activity that is intrinsically motivating (Megowan, 2007).
In a study conducted in 1992, research showed that the use of Modeling
Instruction produced an increase in post-test scores and normalized gains amongst ninthgrade general physics students, a result that was supported by later studies on the
usefulness of Modeling (Hake, 1998). The work of H. Simon provides additional
validation for modeling, stating that the ability to create and use representations as
problem-solving tools is a “major intellectual achievement” that is often underestimated
in its significance for both science and instructional design (Simon, 1977). Teachers who
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understand modeling recognize not only the importance of representations in aiding
student comprehension, but they are also trained on how to model a concept in different
ways (Wells, Hestenes, & Swackhamer, 1995). If done correctly, Modeling Instruction
becomes student-led, demonstrating the next step by the student beyond comprehension
and into retention (Megowan, 2007).
Modeling provides easy access to the main ideas or nodes forming “the big
picture” by nature of whiteboard presentations during which ideas are submitted,
reviewed and dissected by students (Wells, Hestenes, & Swackhamer, 1995). Quite often
students completely misinterpret this “zoomed out” model as they are mentally
preoccupied on the intricacies making the model (Megowan, 2007). The use of concept
mapping aims to generate a more meaningful and self-regulated set of classroom
activities geared toward remembering meaningful vocabulary and concepts in a
hierarchical way so that interpretations of phenomena are represented physically on a
consistent basis (Novak, 1990).
Concept maps provide a medium for building important contextual language and
connections and making material more easily understood (Rafferty & Fleschner, 1993).
“The act of mapping is a creative activity, in which the learner must exert effort to clarify
meanings, identifying important concepts, relationships, and structure within a specified
domain of knowledge… and concept maps facilitate the process of knowledge creation
for individuals and for scholars in a discipline” (Novak & Cañas, 2004). Concept
mapping is a tool for representing the interrelationships among concepts in an integrated,
hierarchical manner (Novak, 1990). Concept maps should not simply list information
from text randomly, or even in a linear fashion (Novak, 1990). Rather, concept maps
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should depict the structure of knowledge in propositional statements that illustrate the
relationships among the concepts in a map (Novak & Gowin, 1984).
Meaningful learning, according to Ausubel, results when a person consciously
and explicitly ties new knowledge to relevant concepts or propositions that he or she
already possesses (Ausubel, 1963). Information is retained meaningfully by storing it in
long-term memory in association with similar, related pieces of information (Ausubel,
1963). In contrast, rote learning provides little or no attempt to make the information
meaningful or to understand it in terms of things one already knows (Ausubel, 1963). If
such information is stored in long-term memory at all, it is stored unconnected to, and
isolated from, other related information (Ausubel, 1963). Information stored in this
unconnected fashion becomes difficult to retrieve (Jegede, Alaiyemola, & Okebukola,
1990). The structure of the concept map merges the above plan of action with both
Robert Gagne‘s hierarchical thought and Richard C. Anderson's schema diagrams (Davis,
1991).
Novak’s work with concept mapping was based on the learning psychology of
David Ausubel (Novak & Gowin, 1984). The fundamental idea in Ausubel’s cognitive
psychology is that learning takes place by the assimilation of new concepts and
propositions into existing concept and propositional frameworks held by the learner
(Ausubel, 1963). This knowledge structure as held by a learner is also referred to as the
individual’s cognitive structure (Leake, et al., 2003).
It is the individual student who structures a fluid concept map with clear precise
language in an interconnected hierarchical drawing promoting newly learned information
who will have the ability to assimilate the material into a more complete model (Novak &
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Cañas, 2004). Novak's work stressed the importance of prior knowledge in being able to
learn new concepts: "The most important single factor influencing learning is what the
learner already knows. Ascertain this and teach accordingly" (Ausubel, 1978). Correcting
prior knowledge and misconceptions through the employment of experiential knowledge
will allow students to create a more comprehensive view of the Newtonian world
(Hestenes, 1992). “The Newtonian World must enter the student, for it is a conceptual
world which must be recreated in the mind of anyone who would know it. Each student
must literally reinvent the Newtonian World in his/her own mind to understand it”
(Hestenes, 1992).
Modeling is a research-based pedagogy that allows for understanding by way of
using multiple representations in multiple ways effectively (Hake, 1998). This method
encourages students to confront misconceptions and utilize the multiple representations in
student friendly conversations and white-boarding sessions (Wells, Hestenes, &
Swackhamer, 1995). However, we have found the success of modeling relies heavily on
the students being self-regulated learners (Wells, Hestenes, & Swackhamer, 1995) and
this is often not our reality.
We introduced concept mapping into our modeling class in order to supplement
the Modeling Method of Instruction. We believed this might help students to confront
and relinquish their misconceptions and memorialize the connections that they make
between different concepts and representations in physics. This allowed for a more
productive overall “flavor” of modeling that promoted more effective physics thinking
and learning.
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
Method
Data was collected from a combination of four high school Physics classes taught
by the investigators and compared to data collected from additional classrooms as
discussed below in the ‘Treatment Groups’ and ‘Comparison Groups’ sections. The
investigators taught at high schools within the metropolitan area of Phoenix, Arizona, one
in a West Valley suburban school of 2,100 students, the other at an East Valley suburban
school of 2,700 students. Our General Physics classes consisted of juniors and seniors for
whom Physics is their third high school science class. Prior to taking Physics, our
students had taken a general science course and a Biology course, in addition to passing a
basic course in algebra. We both used the Modeling method of teaching in our Physics
classes with a high emphasis placed on inquiry learning methods and student-led
learning.
The investigation for our research consisted of having our students using concept
maps throughout the school year as a way to better develop the physics models. Our
application for concept mapping started at the beginning of each instructional unit, which
began with a lab activity. Students individually constructed concept maps after being
exposed to the lab apparatus. Prompting questions such as “What can we change?” and
“What will change?” allowed the teacher to focus thinking on possible experimental
variables. Addressing preconceptions before a lab required students to confront their
model of how a system works. In addition, this process enabled the instructor to walk
around and perform a concept check while the pre-lab concept map was completed.
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Following this initial map creation, class discussion confronted possible variables
and students narrowed down possibilities, with direction from the teacher. It was the
intent that following this discussion students were prepared to design a procedure for
testing the desired variables and proceed with data collection. After data was collected,
evaluations made through graphical representations, and conclusions produced, the class
discussed findings using whiteboards. It was after this discussion that students
individually modified and updated their original concept maps to correct disproven
misconceptions and add new information.
As each instructional unit progressed, the concept maps were used as a personal
note-taking method. The Modeling Method of Instruction, while emphasizing student
accountability for learning, does not implicitly include student note-taking. New ideas
were formed during activities, group and class discussion with the intention that the
concept maps became a graphical method of note-taking and organization with which the
students became comfortable and could call upon to assist in their learning process. Our
students were given time to modify concept maps on those days that new information was
presented or their prior misconceptions were confronted. A color-coding system kept
track of modifications throughout the unit enabling the progression of student thought to
be tracked.
Demographics
For purposes of this research project, two lead investigators from
demographically divergent areas of the Phoenix Metropolitan area each identified classes
which would serve as the treatment groups. These classes underwent training in the
Concept Map methodology throughout their duration in the investigators’ classes. In
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addition, investigator 1 identified two classes at High School 1 (HS1) where she taught
and investigator 2 identified five physics classes at High School 2 (HS2) where he taught
to serve as comparison groups. For further evaluation, classes at three additional schools
were selected as comparison groups as identified below.
School Demographics
Investigator 1 taught at HS1 in a suburb on the west side of Phoenix, Arizona.
HS1 had an enrollment of approximately 2,100 in grades 9-12. This population was
approximately 67% Caucasian, 23% Hispanic, 5% Black, 3% Asian, 1% Hawaiian or
Pacific Islander and 1% Native American. Twenty-four percent of students received free
or reduced price lunch, a program that enables children to qualify based on their family
income status and important to note because this illustrates that about 1 in 4 students
come from economically disadvantaged households. During the investigational period
Investigator 1 taught two classes of general Physics with a total class enrollment of fifty
students.
Investigator 2 taught at HS2 in an eastern suburb of Phoenix. HS2 had an
enrollment of approximately 2,700 students in grades 9-12. This population was 53%
Caucasian, 23% Hispanic, 15% Black, 6% Asian and 3% Hawaiian or Pacific Islander.
Fifty percent of students received free or reduced lunch and HS2 was a Title I School.
During the investigational period Investigator 2 taught two classes of general Physics
with a total class enrollment of sixty-four students.
Treatment Groups
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Treatment Group Participants for Investigator 1. Classes at HS1 were on a
block schedule, meaning that students were in class for 90 minutes each day, with courses
lasting only one semester. The students at HS1 were split between two general physics
courses, one in the fall semester and one in the spring semester of the same school year.
Investigator 1 was the only physics teacher in the school and additionally taught an
Advanced Placement physics course in which the treatment was not applied. This class
was not used as a comparison group. The students in the general physics courses typically
had no previous high school course in a physical science and had not progressed past a
second course in algebra. The prevailing reason for taking the course was to fulfill the
third science requirement for graduation.
Enrollment across the two courses was 71% male, but otherwise mirrored the
demographic composition of the school, including ethnic composition. Across these
classes 42% of students were seniors, and 58% were juniors. During the fall semester,
late entries were common, with five of the 32 students entering after the first week of
instruction, three of those after the first three weeks. A student teacher versed in the
Modeling method of instruction co-taught the class during the spring semester.
Treatment Group Participants for Investigator 2. The students participating in
the treatment group at HS2 consisted of general physics students split between two
classes. A second physics teacher at the same school taught five classes, all of which
were offered for college credit. Data and demographics were collected from the instructor
of these five classes to be used as a comparison group. Half of the students enrolled in the
treatment group were juniors and the other half were seniors. The vast majority of
students were taking physics to fulfill their three years of science. Not one student
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relayed throughout the year that they were interested in a field of work that requires any
more than a class or two of college level physics. Many students in their junior year
expressed that they didn’t care how they performed in class because they have another
year to take a different class. The student population consisted of an ethnically dynamic
47% non-Caucasian population. Overall, the demographics of the experimental classes
consisted of a heterogeneous mix of students due to their differences in gender, ethnicity,
entrance abilities and overall purpose for being enrolled in the class. The one
commonality that the classes used for the treatment group had in common was that all
students were taking the same course and following the same curriculum.
Within Investigator 2’s treatment classes, there was a 12 % student population
that relied on special needs services for accommodations throughout the year. Of these
special needs students: four students fell under the IEP umbrella and were required by
law to receive accommodation on all assignments if requested; two students had a
diagnosis of autism spectrum disorder; one student had severe behavior/opposition
problems and one had decoding of information problems. Two additional students had a
504 accommodation that required more time on assignments or time away from the
classroom at student request. This information was not available for the comparison
groups.
Comparison Groups
Comparison Group 1 was also from HS1. Information for this comparison group
was collected during the school year prior to this study. This comparison group consisted
of two general physics classes, taught by Investigator 1, with a total enrollment of 55
students. As in the treatment groups, these classes were taught using the Modeling
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mechanics curriculum. Comparison Group 1 contributed scores for the Force Concept
Inventory only.
Comparison Group 2 was also from HS2. This group consisted of 5 classes of
dual enrollment, college-level physics, with a total of 150 students, and was instructed by
a colleague of Investigator 2. The Modeling mechanics curriculum was employed in
these classes as well. This comparison group provided overall class average scores for the
Force Concept Inventory only.
Comparison Group 3 was from a suburban high school in Phoenix, Arizona. This
high school had an enrollment of approximately 2,100 students in grades 9-12. This
population was 45% Caucasian, 34% Hispanic, 10% Black, 8% Asian and 1% Native
American. Thirty-five percent of students received free or reduced lunch. Comparison
Group 2 consisted of one Advanced Placement physics course, with a total of 30 students.
This comparison group contributed both Force Concept Inventory and Classroom Test of
Scientific Reasoning scores.
Comparison Group 4 was from another suburban high school in Phoenix. This
high school had an enrollment of approximately 1,800 students in grades 9-12. This
population was 75% Caucasian, 13.7% Hispanic, 4.0% Black, 3.1% Asian and 0.40%
Native American. Eight percent of students received free or reduced lunch. Comparison
Group 3 consisted of one general physics course, with a total enrollment of 22 students.
The Modeling mechanics curriculum and pedagogy were applied in these classes.
Comparison Group 3 contributed data for the Classroom Test of Scientific Reasoning
only.
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Comparison Group 5 was from a rural high school in Louisiana. This high school
had an enrollment of approximately 160 students in grades 9-12. The population of the
school was less than 1% Asian, 76% Black, and 24% Caucasian. This was a public Title
I school, and 90% of the students were eligible for free or reduced lunch. Comparison
Group 4 consisted of one general physics course, with a total enrollment of 8 students.
The Modeling mechanics curriculum and pedagogy were applied in this class. This
comparison group contributed both Force Concept Inventory and Classroom Test of
Scientific Reasoning scores.
Procedure for Treatment
The procedure for the treatment began on the first day of instruction and ended on
the final day of instruction. This included pre-assessments, mechanics instruction using
the Modeling mechanics curriculum for treatment and comparison groups following unit
progression, instruction in concept mapping for all treatment students, color coding of
concept maps , and post-assessments including assessment of concept maps, qualitative
assessment based on student interviews, and quantitative assessment.
Pre-Assessment
Students both in the treatment and comparison groups were given Lawson’s
Classroom Test of Scientific Reasoning (CTSR) and Force Concept Inventory (FCI) pretests during the first week of class. These assessments provide a gauge of prior physics
conceptual knowledge and students’ scientific reasoning abilities.
Unit Progression
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Curriculum units were taught in the order recommended by the Modeling
mechanics curriculum for mechanics as follows:
Unit 1: Scientific Methods
Unit 2: Constant Velocity Particle Model
Unit 3: Uniform Acceleration Particle Model
Unit 4: Free Particle Model
Unit 5: Net Force Particle Model
Unit 6: Two-Dimensional Motion
Unit 7: Central Net Force Particle Model
Unit 8: Energy Model
Unit 9: Momentum
Unit order was flexible at the discretion of the investigator due to classroom concerns and
student need.
Instruction in Concept Mapping
Students from the treatment groups were instructed in the creation of concept
maps to enable their ability to use them effectively throughout the year. Building the
students’ self confidence in designing a usable artifact proved to be important. The
application of concept mapping as a supplement to the learning process was teacher-led
during all nine units, despite investigators’ efforts to switch roles and make the process
student-led. Prior to each lab exercise, a large sheet of butcher paper was rolled out and
hung on one wall of the classroom. To preserve the integrity of the inquiry learning
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process, a central (primary) node was drawn on the paper but remained blank. This was
reserved for the central model of the instructional unit as listed above.
The name of the apparatus or exercise itself was written as a secondary node
connected to the central (primary) node. The apparatus was then demonstrated to the
class, with discussion focusing on possible variables. Two secondary nodes were added
to the butcher paper, with a line drawn to connect these with the central node. The
questions, “What can be changed?” and “What will change?” were added, one to each
new node. Students were asked to brainstorm and record possible answers on their
individual concept maps. After this was completed, volunteers shared ideas with the
class. As students added new ideas, these became new nodes connected to their
respective questions. Depending upon the particular lab exercise, students were then led
to desired independent and dependent variables.
Following data collection and analysis, class discussion included graphical and
mathematical models. As discussion progressed, this additional information was added to
the butcher paper, along with connections to the proper nodes. Following completion of
lab discussion, the central node was filled and nodes representing newly acquired
knowledge were added to the map alongside those representing prior student knowledge.
As the unit progressed, these large class concept maps continued to be modified as
necessary. Students placed discoveries relating to the lab as the main node in the center of
the paper. From this middle node, consecutive linked ideas surrounded this. The overall
look of these early group maps began to resemble a spider web, showing a dynamic
connectivity between ideas.
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This shared, structured concept map creation existed during all units of
instruction, using the same apparatus demonstration, variable brainstorming and
elimination. During the fourth and fifth units, students were expected to create maps
individually and discuss these within their lab teams. This exposed a primary barrier
faced by the investigators during the implementation of concept mapping: our assumption
that students would willingly adapt concept maps into their repertoire of note taking and
study tools proved to be unfounded. The framework for constructing a concept map was
established and repeated throughout the course, led by the teacher, during the first three
consecutive units. After the first three units, the investigators expected the independent
map building process to be completed by students, who would create concept maps on
their own. However, this was not the case. Most students decided not to attempt to make
a map because of the fear of doing it wrong, thereby wasting their time creating a
learning tool that wouldn’t work. Within a week of beginning unit four, the investigators
met and decided to continue with the map building as a teacher-led group process. The
decision to do this was based on the drawings that the students were making, which
showed a disconnect existing between the lesson and their ability to link ideas together on
paper. Concept maps created by the students began to lack not only the dynamic
representations that should be present, but entire ideas (nodes) that allow for a coherence
of physics.
Color Coding
Students were given a sheet of white, 8 ½” by 11” paper for each unit. As the
instructional unit began, students were asked to create an initial map, in pencil, based on
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observations and previous knowledge. Students altered and added to these maps as
activities and discussions provided new understanding, with class time devoted to
summarizing the day’s learning and assimilating this into their concept maps.
To chart the progression of student concept maps, a color-coding system was used
for the first four units. The maps were created using a standard pencil with gray lead. The
first day that the concept maps were altered, a red pencil was used. The second, day,
orange pencils were used. Green pencils were used for the third, blue for the fourth, and
purple for the fifth. Students were encouraged to make their maps rich with diagrams and
drawings rather than just using words, equations, and graphs.
Assessment of Concept Maps
At the end of each unit the concept maps were collected, scored, scanned and
returned to the students to be used as an invaluable tool for studying and reviewing
materials. These scores were added to the grade book as part of the classwork score for
each unit. Scan of these maps were held in secure storage until the end of the data
collection period.
Qualitative Assessment
At the conclusion of the school year, students were interviewed regarding their
opinions with respect to concept mapping and its effects upon learning. Interviewees
were chosen at random from a pool of volunteers, and were asked to participate in
interviews outside of regular instructional time. Interview questions focused on assessing
what student perception was of the difficulties in concept mapping, along with their
perceptions of whether and how concept mapping made retention of certain units and
material easier. Students were also asked to recreate a concept map which had been
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created several months prior, testing the degree to which their memory was or was not
impacted by the concept mapping process. This creation was videotaped, with emphasis
upon verbal prompts designed to encourage the student to explain his or her thinking
process. Prompts included such questions as, “Why did you include that diagram?” and
“What does this show you?”
Quantitative Assessment
At the conclusion of each unit, students were allowed to use their unit concept
maps on the unit test. Following the completion of this test, students submitted their
concept maps which were then scored using a rubric. Scores for these concept maps were
recorded so as to be compared with FCI and CTSR scores.
During the final two weeks of the course, students in both the treatment and
comparison groups were again assessed using the FCI and CTSR. These scores were
compared to both their pre-tests and their concept map scores.
Timeline
During the first week of instruction, FCI and CTSR pre-tests were administered to
establish a baseline. Explicit instruction in constructing concept maps was included in the
first three instructional units. During these units the concept mapping was completely
teacher-guided. We attempted to mandate self-made concept maps for units four and five,
however this proved to be a misguided expectation, as explained in the Treatment section
above. In an effort to mitigate the barriers identified, subsequent unit concept maps
continued to be constructed as a teacher-led group. As each unit concluded, students were
asked to submit their concept maps at which point they were scored. Following the ninth
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and final unit of the Modeling mechanics curriculum, the FCI and CTSR post-tests were
administered and student interviews were conducted.
Data Analysis
Data collection occurred with the use of four primary tools. Completion of the
FCI, CTSR and Concept Map Evaluation Rubric provided quantitative data points which
could be used to measure change over time, while interviews with students provided
qualitative assessment, as outlined below:
Force Concept Inventory
The Force Concept Inventory was administered to students before the first
instructional unit, and again during the last two weeks of instruction. The FCI is designed
to measure introductory physics students’ understanding of mechanics (Coletta &
Phillips, 2005). Pre-instruction and post-instruction test scores were analyzed for each
student with these used to formulate individual Hake gains. The Hake gain G can be
interpreted as the ratio between the actual change in student score from pre- to post-test
compared to the gain the student may have achieved should he have scored a perfect
score on the post-test (Hake, 1998).
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
𝐺=ed on results for all subjects, a majority of students in the treatment group scored within the
first and second quartiles of CTSR scores while a majority of students in the comparison group
placed within the third and fourth quartiles. In other words, the treatment groups’ students
tested at a level of scientific reasoning such that more than half of these students placed lower a
majority of control group students.
Since a positive correlation has been discovered between CTSR scores and normalized
gain on the FCI in previous studies (Coletta & Phillips, 2005), we felt it imperative that
Figure 4: CTSR pre-test score distribution – comparison group
the connection also be made examined in our study. This meant, according to that study,
a lower average FCI Hake gain for the treatment group than for the comparison group
would be possible (Coletta & Phillips, 2005).
Quantitative Pre-Test Results Analysis. Based on results from the FCI and
CTSR pre-tests we concluded that the students in our treatment groups possess a lower
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
scientific reasoning ability than those in the comparison groups yet a statistically similar
level of introductory mechanics knowledge. Although this study did not examine the
causes of this difference, it is important to note two major differences between treatment
and comparison groups: Investigator 2’s classes included a notable percentage of students
receiving Special Education services and comparison group 3 consisted of Advanced
Placement physics students. While we hypothesize that students from the latter group
possess a higher level of scientific reasoning ability that skewed CTSR pre-test scores,
this is a connection that requires further study.
Ongoing Quantitative Results
Concept maps were created and scored throughout the academic year, allowing
the investigators to collect quantitative data that could show improvement in mechanics
comprehension in conjunction with the process of concept mapping over time.
Concept Map Quantitative Results. Student concept maps were constructed
during each instructional unit, collected following unit testing and scored using the
Figure 5: Mean concept map score by unit of Modeling curriculum
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
Concept Map Evaluation Rubric found in Appendix A. Typically 81% of students
submitted concept maps each unit. Of those who failed to submit concept maps,
misplacement of the map was the most common given reason. This percentage was
comparable to the submission of other course assignments. Students submitting concept
maps achieved a mean score of 8.47 of a possible 15 on these maps. This demonstrates
that participating students used the concept maps to record information deemed valuable
by both student and instructor. A drop in scores was found following the second unit.
This can be attributed to the shift in student motivation at this time as will be discussed in
the unexpected discoveries portion of the reflections section. Scores remained, however,
above a score of 56% based on the concept map evaluation rubric.
When examining the relationship between course grade and concept map scores,
we found that a positive relationship exists between these variables. Correlation statistics
suggest that a moderate positive relationship (𝑟=.521) exists between average student
concept map score and the course grade earned for treatment group students. This
correlation is significant at  = .01, leading us to deem this correlation statistically
Figure 6: Overall semester grade versus average concept map score
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
significant. Students who put a greater level of effort into the creation of unit concept
maps also scored higher grades in the course. It is unknown, however, whether concept
map scores increased course grades or if those students who put more effort toward
achieving high grades also did so in regards to concept mapping.
Figure 7: Cumulative exam grade versus average concept map score
Since concept maps were used as a reference for unit tests, we chose to
additionally examine the link between average concept map scores and student score on a
cumulative final exam. Again a moderate positive relationship exists between average
concept map score and student final exam grade. While the correlation between these is
marginally weaker (𝑟 = .424, correlation significant at  = .01) than that between concept
map score and course grade, this nonetheless demonstrates a correlation that can be
deemed statistically significant. It is important to recognize that, for the cumulative exam,
students in Treatment Group 1 were not allowed to use concept maps during this exam
while students in Treatment Group 2 classes did have this resource. A non-directional
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
independent sample t-test showed that, despite this difference in testing procedure, we
fail to reject the null hypothesis that these treatment groups were chosen from the same
population of students.
Post-Test Quantitative Results
The FCI and CTSR were repeated again at the completion of the academic year
for each treatment group. Results were documented and scored, then compared to those
of the comparison groups.
Post-FCI Results. Overall, an increase in FCI scores was observed from pre-test
to post-test, as expected. A Levene’s test of all post-instruction FCI scores showed that
the subsets of treatment and comparison group scores were not of equal variances.
Assuming the variances are not equal, a non-directional t-test assured us that we could
reject the null hypothesis that these two groups are derived from the same population of
students. The treatment group experienced a statistically lower mean FCI post-test score
Figure 8: FCI Hake gain vs. CTSR pre-test score – treatment group
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
of 12.10 when likened to the mean FCI post-test score of 15.44 for the comparison group.
Since both groups began with mean pre-test scores that differed by only 0.07, this posttest difference is notable. Despite beginning the study as a statistically similar group with
the same level of introductory mechanics knowledge, the treatment and comparison
groups had, by the end of mechanics instruction, separated into two distinct groups with
two distinct levels of mechanics knowledge.
The treatment group began with significantly lower CTSR scores and thus lower
scientific reasoning ability than those in our comparison group. We therefore examined
the link between CTSR pre-test score and FCI Hake gain. Correlation statistics for both
treatment and comparison data suggest that a positive correlation exists between CTSR
pre-test scores and FCI Hake gain for both groups. For the treatment group, a moderate
positive relationship with 𝑟 = .342 exists, but with the comparison group a strong positive
relationship of 𝑟 = .612 is present. An ideal 𝑟 value of 1.00 would indicate that all points
lay on the same line and thus a perfect positive correlation could be stated between Hake
gain and CTSR pre-test score. With an 𝑟 value of .612, the comparison group forms a
Figure 9: FCI Hake gain vs. CTSR pre-test score – comparison group
29
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
tighter grouping, but the treatment groups’ 𝑟 value of .342 indicates a positive correlation
nonetheless.
As predicted, the treatment group achieved a lower Hake gain than the
comparison group. The gain achieved, however, demonstrates a significant increase in
introductory mechanics knowledge for both groups. It can be stated that, overall, a
correlation exists between CTSR pre-test score and FCI Hake gain. This gain may be due
to the implementation of the Modeling method of instruction, as this was the tying factor
between both treatment and comparison groups.
When compared within quartiles as defined by CTSR pre-test score, it was found
that a larger increase existed for the first quartile treatment group, who were the lowest
performing on the CTSR, than the first quartile comparison group. Thus, for students
achieving at the lowest level of the group on the CTSR, students who participated in the
concept mapping process achieved higher gains in introductory physics knowledge. For
the second, third and fourth quartiles of scores, students in the treatment groups did not
outperform their comparison counterparts. A gain in Hake score was evident, however,
from one quartile to the next.
Treatment Groups
Students
Hake
Comparison Groups
Students
Hake Gain
Q
26
Gain.155
6
.113
1 Q
21
.184
8
.353
2 Q
14
.261
9
.438
3 Q
10
.346
14
.671
4
Table 1: Hake gains by CTSR quartile
CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
A correlation matrix comparison of average individual concept map scores and
FCI Hake gain revealed that a weak positive relationship (𝑟 = .174) existed between these
two variables. Thus while it can be said that a positive relationship exists between FCI
Hake gain and individual concept map score, this relationship is not significant enough to
state that the gain is due to the creation of concept maps in the classroom.
Figure 10: FCI Hake gain vs. average individual concept map score
Post-CTSR Results. Analysis of CTSR scores obtained for both the treatment
and comparison groups post-instruction demonstrates that a strong correlation exists
between pre-test and post-test scores. It was not surprising that low pre-test scores
corresponded with low post-test scores, and the same relationship with higher pre-test
and post-test scores. A Levene’s test revealed the variability in both subsets, treatment
and comparison, to be similar. A paired samples t-test was conducted for each group of
pre- and post-test scores. For the treatment group t(70) = 5.80, p < , meaning that from
pre-test to post-test the mean CTSR score for all treatment group students increased by a
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
factor of 5.80 times the standard error of these scores. The comparison group mean score,
Figure 11: CTSR post-test-pre-test treatment and comparison groups
t(55) = 4.63, p < , increased as well but by a factor of only 4.63 times the standard error
of that group of scores.
It should also be noted (Figure 12) that as a whole, CTSR scores for the treatment
groups increased while scores in the control groups both increased and decreased. Thus
over the course of the investigation students in the treatment groups experienced an
increase in scientific reasoning ability, but the same cannot be said for the comparison
groups.
As stated previously, the CTSR pre-test scores for the treatment group were found
to be significantly lower than that of the comparison group, thus making necessary the
comparison of scores within each subset rather than as a whole. We are able to reject the
null hypothesis that the scores for both treatment and comparison groups remained the
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
same from pre-instruction to post-instruction. We can furthermore state, based on the tscores for each group, that the treatment group experienced a statistically larger increase
in mean CTSR scores within its sample. This means that despite starting at a level of
reasoning lower than their comparison counterparts, students in the treatment groups
achieved greater personal gains in scientific reasoning ability.
Between average concept map score and CTSR normalized gain, however, it was
found that no relationship, a resulting correlation coefficient of 053, existed. Normalized
gain was computed using the following formula, in the same manner as the FCI Hake
gain:
𝐺=our surprise, however, when we interviewed our case studies, most used colored pencils left
on the counter to create a detailed concept map. This was one of the diagrammatic aspects
of our investigation that seemed to stick with a few students. Coloring the links between
concepts proved to be a moderately effective thought method, used by about half of the
case studies when interviewed.
Personalization and Integration as a Study Tool. The ability to take a teacher-led,
group-developed concept map and customize it to meet the needs of the individual
student seemed to prove incredibly valuable. Students were allowed to use concept maps
to study from and use on quizzes. Many students made the decision to use concept maps
in this way throughout the school year. They wrote all over the empty spaces and back
side with new and helpful information about the unit in progress. Students would place
equations pointing to labs, ideas pointing to equations, and any other combination they
could think of that made sense to them. Many aspects of the concept maps were from a
personal point of view. For some, it was a tool for them to place their collage of ideas on
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
paper, sorted out like a puzzle using arrows, allowing them to give it meaning. When
compared, some maps are visibly much different on the outer portion where additional
nodes were added. This personalized linking varied from student to student. Even though
the class attempted to fill these out as a group, many would write connections on their
own without being prompted as a way to remember and unknowingly make those ideas
more permanent. Evidence for this can be seen in the concept maps created during the
unit of instruction in Case Studies 2-7. Students repeatedly include additional information
on maps, making the personal decision to include information and add detail to each
concept map. This outcome shows that even when students were initially resistant or did
not claim to understand the concepts, they were able to use the process of concept
mapping in an individualized and meaningful manner which helped them to understand
the material.
The students seemed to enjoy constructing concept maps. It was a way to do a
review of the day’s previous material without having to take tedious notes, or fill out a
worksheet. Students showed a favor to concept mapping as a way to take notes or relay
main points of completed labs. Central to the success of this was the allotment of
sufficient time in class during which students could review their concept maps, update as
needed, and prepare to add to them with new information being taught that day. In the
end, concept maps were used by most students as intended: as an alternative to traditional
note-taking, a ‘living document’ that could be added to, changed, and adapted as more
concepts were covered in class.
When adding to a unit concept map, students were asked to get out their personal
maps and write down and connect ideas to each other. For all units, the main ideas were
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
teacher led and connections that should have been listed were showcased. Concepts were
placed from general to more specific giving the appearance of being in a hierarchical list.
Prompting students to get out and use concept maps allowed for a sense of group
learning. The group setting seemed to be the most effective approach because it was a
way to hold everyone accountable. This course- long approach allowed for the
application to be more than just a method to be tossed aside; concept maps became a
permanent part of the course. Integrating mapping into every fabric of the learning
process established concept mapping as a part of the culture in the classroom. Conducting
a teacher led discussion during the construction of the maps assisted students because the
researchers are knowledgeable in the subject matter and were able to help guide the
students to create more useful maps. Many students added to their maps above and
beyond what was discussed, and of course the opposite was true as well.
Student Interviews. As a part of the qualitative assessment, both investigators
conducted interviews with students in the treatment groups. Students were both asked to
participate as volunteers and selected at random with no incentive to participation, and all
interviews were held during the respective last week of school for each student and after
grades had been entered. This allowed for frank correspondence as students knew upfront
that their responses to the survey questions would not in any way be reflected in grades.
Students were asked to respond in three different areas related to their experience with
concept mapping, their perception of its efficacy and any difficulties they faced with the
process, and their ability to use concept mapping to recall memory.
Opinions Regarding Concept Mapping. The student interviews began with
addressing how they felt about concept mapping, asking students, “What did concept
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
mapping help you understand?” Student responses demonstrated a favorable reception to
concept mapping in the classroom. The students freely offered an explanation as to why
concept mapping helped them, stating the following:
Jaden1: “It helped me understand, like the overall, like what we were learning
and it helped with the tests and all that – just helps the bigger picture, in just
reviewing everything we learned in the unit.”
Anna: “Concept mapping, ‘cause then you could keep down what you learned
rather than just memorizing it all. It’s like notes but easier ‘cause it’s in a
picture form.”
Andrew: “It helped me just tie back to the basics of the unit, just, ‘cause
everything got out of hand eventually, trying to remember.”
Henry: “So in the beginning I don’t know, I didn’t really like it that much
because, you know, something new and I — I don’t know, I think as a
teenager you don’t really want to like, get away from, like doing new things I
guess. So in the beginning I didn’t like it but it did help a lot. It’s just like
organizing my stuff into like different sections you know. And then yeah – as
the year went on I really started to like it because like my test scores improved
and all that just, just from the organization itself, you know.”
Ophelia: “It helped me to organize my ideas to see like what falls under what
and to see if there is an idea then like what equation of that, what ideas and all
like that too, so it did help a lot… it did it liked help me with the tests and
stuff.”
1
All students’ names have been changed to protect their privacy.
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
Tyson: “Yeah a little bit, with visualization – placing like what we learned
first in like one area of the paper kind of, and kind of going around so I can
see like in order.”
Jack: “Well yeah – well basically if I didn’t do it I wouldn’t understand – I
wouldn’t understand basic Physics as a whole, the maps really connect a lot of
things that normally students wouldn’t be able to connect, so I think it’s good
conceptually to understand, you know, Physics in this way.”
Jose: “It helped me with the equations… and looking like visually putting
together what the objects are doing.”
Tyler: “Yea, it helped organize equations, and my thoughts, like what graphs
lead to other graphs.”
Daisy: “Yeah they helped me – they helped me understand the concept
obviously and it gave me a better idea of what the unit was about in
comparison to the lab that we did for the unit because it showed the equations
and the equations and different graphs and stuff for those.”
Daniel: “Basic equations and…basic info of the unit we were doing.”
Katherine: “It helped me, uh, kinda remember what I need to do for the test.”
April: “Um, it really helped with the equations, having the equations and stuff
on there, and then seeing the, um, graphs and stuff and how they’re supposed
to go, and which, what’s on each axis and everything really helped. And then
the vocab, that helped, um, because a lot of vocab was in the test so it helped a
lot.”
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
Zane: “Concept mapping has helped me, like, realize the relevancy of, like,
the data that you’re telling to, like, the actual concept or the thing that we’re
doing at the moment like, when we did the concept map and you would have
us, like, show us all the different formulas and what they relate to, that really
helped a lot for me.”
Leanne: “It helped me remember stuff and, like, have things available with the
test and help me put things together ‘cause all the bubbles are connected.”
Cole: “Okay, um, well concept mapping helped with, well I would look at it
and it would help me remember what the equations were, what the vocabulary
were on that certain unit and just pretty much helped with my, if I, with pretty
much most of my tests.”
Difficulties with Concept Mapping. The second question of the interview asked
the same selected students to discuss any difficulties they experienced with concept
mapping throughout the school year. Most students were resoundingly positive about the
concept mapping experience, expressing that they did not face difficulties. Of the
students who expressed difficulties with the process, it was the organization and layout of
the maps themselves that ranked as the primary challenge. Other students seemed to offer
ways they would have done it differently, answering in response to the question, “Did
you face and difficulties facing concept mapping?”
Jaden: “No.”
Anna: “Uh, just categorizing some things.”
Andrew: “Not really.”
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
Henry: “I wouldn’t say that like concept mapping itself, but difficulties like
maybe doing like maybe getting the motivation to do it, because I just, like I
said, I didn’t really want to even learn how to do it because – it just wanted
my style of like learning per se.”
Ophelia: “Sometimes it was hard when it was hard when I was like mapping it
out, I didn’t know right away what equation went to what because I’d arrows
going everywhere but also – and I think for some of them I need to write like
better descriptions of like what was what just like when I looked back at them
after, I remembered what, but that’s all.”
Tyson: “Not really.”
Jack: “In general I thought it was pretty effective, I mean, I don’t know if
have any difficulties.”
Jose: “Only if I missed something and didn’t put it on the map.”
Tyler: “Momentum was very difficult at first, but, still iffy ya know, but that’s
about it.”
Daisy: “Sometimes mine were a little messy and they – I didn’t really have
any other issues with them, they just really helped.”
Katherine: “Um, I guess kinda like organizing it. Interviewer: Okay. How did
you end up organizing? Was that something that you improved upon in the
semester, or was it something you’re still working on? I’m still kinda working
on it.”
Zane: “Um… sometimes it was, um, just figuring out how, how many
equations I should be writing down. For the, as far as when it’s relevant to the
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
test or not because there were, like, two or three times where I just put way
too many formulas.”
Cole: “Yeah, like, I guess whenever we did, like…um…what was it…like,
whenever there was a certain topic we were doing I didn’t know what kind of
vocabulary I should put in or if this was the right equation I need to do this
one, like it was just kind of I didn’t understand which one to put in to make
sure I had it right.”
Demonstration of Retention. The final portion of the student interviews was
included to help the investigators collect evidence supporting the validity of concept
mapping and explored the retention of valuable concepts through the ability of students to
re-create a concept map. This ability would point to the efficacy of concept mapping for
helping students create mental pathways for information that will be held in memory
long-term and can be recalled without being retaught. Specifically, this portion of the
interview asked students to recreate a concept map focused around a topic covered earlier
in instruction. All students from a given treatment group were asked to recreate the same
concept map, integrating their memory of the map created in class months prior with their
understanding of the concepts and their connections to each other.
While we were able to interview a student not present for concept mapping
instruction during the original unit, we did not interview students in comparison groups.
We are therefore unable to, with a large degree of confidence, reject the idea that students
in the treatment and comparison groups possessed the same degree of concept mapping
knowledge. A baseline level of mastery of concepts was relayed by students, who
demonstrated the ability to place connecting ideas next to each other in a logical manner.
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
This trained ability to express natural phenomena visibly through use of a concept map,
which is a diagram, was more beneficial during the recreation process to the student than
if they didn’t possess this ability. The diagramming and connecting of complicated ideas
appeared to be more difficult to pictorialize by a student not present for the application of
the concept mapping method (Case Study 1). The representations drawn on paper during
the interviews stemmed from the cumulative effect of a yearlong process of linking
connected ideas to each other. By practicing the building of concept maps throughout the
year, we placed value on the physical formation of the maps. A byproduct of this was that
it was the student’s mental image of each situation that was being built at the same time.
The goal we as teachers had for students is that concept mapping asked them to create a
picture which, in theory, became a mental image for the student, in the hopes it would
help them learn the concepts in a way that would stay with them long after their high
school physics course had ended. Based on the ability that interview subjects
demonstrated to recreate maps similar to their originals, it appears the images did stick in
their minds. Before and after pictures demonstrate retention and the connectivity of
knowledge students were able to exhibit months after the unit was taught (Case studies 27).
One unexpected result found in this portion of the interview was student use of
color. Students given the option to create their maps in multiple colors, without
prompting to do so, chose to use color as a means of distinguishing between items. This
cements our belief that the concept mapping process used in conjunction with colorcoding developed their mental image like muscle memory is created, through repetition
and patterns and was demonstrated during interviews.
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
One final discovery that points to an increase in student comprehension and
retention was found during the last portion of the interview process. When the students
interviewed were asked to draw the concept map described, they were also asked to
verbalize their process and their reason for approaching it in that manner. The map
chosen, from a unit covered months prior, asked students to explain constant acceleration
as demonstrated through a lab. Students who had integrated this information were
expected to express and verbalize certain key concepts and vocabulary when discussing
their process. Key ideas the investigators were looking to have verbalized by the students
when discussing constant acceleration included: relationships between changing velocity,
velocity’s connection with time, and the meaning of acceleration. Throughout the process
of developing their map during the interview, they were asked to explain what they were
doing and why they did it. The intent of this section of questioning was to focus on the
student and their ability or inability to explain how they organize their perceived mental
model. Through this dialogue process, the students who were in the class for the unit
being discussed demonstrated concept relatedness and proved that a level of
comprehension had been established, pointing to retention of knowledge. Simply drawing
something that had been memorized was not what was taking place in this demonstration;
the students were relaying their concept map both physically and verbally. Of the
students interviewed for this study, one was categorically different than the others. This
student, shown below as Case Study 1, was a transfer into the class, and did not enter the
class until after the unit discussed here was taught. The investigators posited that this
student’s experience with creating the concept map would differ quite significantly from
the experience of all the students who were present when the unit was taught. Her
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
resulting ability to verbalize what she was doing and why were not at the same level,
indicating that she had most likely not retained and integrated the information in the same
manner as her peers.
Following are the transcripts and corresponding re-created maps illustrating the
linking that took place between the concept maps and the learner. Case studies 1-7 are
shown as examples which typify the responses provided by our interview subjects. It
should be noted here that these case studies only account for a portion of the interviewees
who were able to successfully verbalize and diagram a master level of connected ideas by
drawing and explaining a coherent model.
Case study 1 (null result): Jaden. Jaden was a transfer from another class who
came in after the original map was created. In contrast to those students who participated
in recreating their two-dimensional concept map when asked to do the same unit concept
map, she lacked the ability to connect ideas in a logical manner. Instead, this student
listed three unconnected equations on a piece of paper pointing to the word acceleration.
Upon comparing the students who were in class for this unit to the transfer student, it
became obvious that the students present for the creation of the unit concept map during
the time the unit was taught showed the greatest ability to remember the mapping process
and key concepts and to demonstrate the ability to link important concepts to each other.
When taking into account the time gap between when the other students last saw these
maps and when they recreated them, and comparing this to a student who was not in class
when the concept map for the unit was originally introduced, qualitative evidence appears
to point to an understanding of connected ideas possibly not present in a non-concept
mapper. It is apparent below that Jaden has her equations memorized for the unit in
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
question. However, when asked to draw and explain this phenomenon she does not
possess the ability to do so. This can be seen in the example demonstrated below, where
she attempts to draw and explain the motion of an object involved in constant
acceleration, stating that the X-T graph would be straight and the V-T graph would be
curved. It is important to note that Jaden receive an “A” in the course and consistently
had excellent grades and comprehension of the subject matter. In light of this
information, one could reasonably expect that she would have the ability to explain the
subject at hand as well or better than her counterparts, but because she did not have the
memory of prior mapping to call upon, she struggled significantly. Following is an
excerpt of her interview while drawing her concept map.
Jaden: “Okay, so the velocity time graph and you drive the accelerate – you
can derive the acceleration from the slope but that also means that acceleration
equals velocity divided by time in any equations you can get from that too,
and so you can get acceleration like that, and then you have like free fall
acceleration gravity, which is equal to 10 or 9.8 but 10 meters per second
squared, and you can solve stuff with that. I don’t know.”
Interviewer: “It’s okay. Anything else you want to put down? So you have
these two graphs, you have a 9.8 something…”
Jaden: “Yeah gravity.”
Interviewer: “What if I rolled something down a ramp? What will that look
like you think?”
Jaden: “I don’t know how to explain that, I guess…”
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
Interviewer: “If you turn that into a XT and VT what would that look like?”
Jaden: “Your XT will just be a straight line, right? Or like slow climb, but like
that, right? And then your velocity time graph would be curving, so it’s
accelerating something like that. I don’t even know if that’s right.”
Interviewer: “So if you switch those two letters on your side, I think you’d be
right. But yeah I’m following you. I see what you’re saying. Okay.”
Jaden: “And then you have like — so you can tell like your acceleration from
this, it’s going to be a positive…”
Interviewer: “Yeah okay.”
Jaden: “Because it’s a slope.”
Interviewer: “Yeah that’s good.”
Jaden: “I don’t know.”
Case Study 2: Anna. Anna demonstrated a personalization in her concept
mapping, designating topics and categories through the use of shapes. She typically
scored above an 11 out of 15 on her concept maps and achieved a 99% in the course.
Anna’s main concern was including enough equations on her concept maps, as can be
determined from her response to the interview questions.
Interviewer: “I noticed, with you, that you put a little crown around most of
your topic.”
Anna: “Yeah.”
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Interviewer: “Was there a reason for that?”
Anna: “Because that was the, um, the main thing it was about. And then I tried
to keep it organized by putting a circle around, like, the topics and then a
square around the smaller parts of it so I could keep track of all what is the
importance of each thing.”
Interviewer: “Okay. Were there any difficulties that you had in creating the
maps?”
Anna: “Uh, just categorizing some things.”
Interviewer: “Okay. What do you mean by categories?”
Anna: “Like, for example when we did the Newton’s Laws, I didn’t know to
put that under definition or maybe equations.”
Interviewer: “Okay. Um, could you draw a concept map for me for a constant
acceleration unit?”
Anna: “Constant acceleration. So just, like gravity and stuff?”
Interviewer: “Yeah. If you could talk it through, what you’re going to add to
that as you go, that would be fantastic.”
Anna: “Okay, so if constant acceleration is the middle…oh, I spelled it wrong.
So I put this in a crown ‘cause it’s the center. Um…hmmm. I put equations
over here, or formulas. And then a subcategory of that would be that
acceleration due to gravity so you could put g equals 10 meters per second
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
squared. Umm…I could put a definition and then I could put constant
acceleration means constantly speeding up velocity. And then if I put down
here graphs, I could put that if this is time and velocity that if it’s like this,
acceleration equals zero. But, if time, velocity, and it’s like a curve, then
acceleration is greater than zero. That’s basically all you put.”
Interviewer: “Okay. So you’ve put groupings for your definitions, your graphs
and your equations. Is there a reason you chose those particular categories?”
Anna: “Graphs because it’s visual so if you don’t remember exactly what this
stuff means then you can look here. And then the definition to keep track of
maybe what all these are, so maybe if I was going more in depth I could say v
equals velocity, if I didn’t know, if I didn’t memorize that. And then equations
because I use a lot of math all the time so I wanna, like, have a set of the
formulas and stuff.”
Interviewer: “Did you use your concept maps on your tests?”
Anna: “Yeah.”
Interviewer: “Did they help you on your test?”
Anna: “Yeah, they helped me remember stuff.”
Interviewer: “Okay, so mostly remembering. What was it helping you
remember?”
Anna: “Mostly I only used it for the equations. I used it to have equations.”
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Case Study 3: Andrew. Andrew demonstrated that in order to sufficiently map a
concept, students must be willing to include information from multiple instructional
units. When asked to create a concept map covering constant acceleration, Andrew
expressed that he would add centripetal force to this map, as it is a constant acceleration
concept, just learned in a later unit.
Interviewer: “I noticed that you put acceleration in the middle. Is there
anything else tying to acceleration that you would use?”
Andrew: “Um, maybe I would add in centripetal force, and when centripetal
force happens that all the different points, how they have to go towards the
middle and I would connect that to acceleration by talking about how you
need acceleration to change your motion ‘cause in a circle your motion is just
tangent to your line, or the line of the circle so it’s just a tangent so all the net
force would be toward the middle and to get the net force down to the
centripetal force you need acceleration.”
Interviewer: “Okay. Um, would there be any other diagrams that you might
include with that?”
Andrew: “I wouldn’t but I’m pretty sure there’s other ones that maybe other
people would have used if they needed more help with it remembering other
concepts.”
Interviewer: “Did you use your concept maps on your tests?”
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
Andrew: “Uh, I did initially, until my work ethic just got lazy and I didn’t do
it, but it would have helped a lot more on units such as unbalanced forces and
such.”
Interviewer: “Did the color-coding, changing as you went along, did that help
at all?”
Andrew: “Uh, it helped me like remember, like, different ones, like if I were
to go through my backpack and see just like one color it’d be ‘oh, I remember
this one was for velocity,’ or, ‘This one was for position.’”
Case Study 4: Henry. Henry gives importance to the lab within the constant
acceleration unit. Although connections made here were expected within the instructional
unit, it was unusual to see a student remember to include it in the interview concept map.
The connection he makes is to a secondary independent variable in this lab, angle, which
produced a result not instrumental in the formation of the general equation for the unit
but still important. That he makes this connection assures us that the concept map assists
him in remembering valuable information learned in the unit.
Henry: “So basically just your main topic in the middle and then a I’m going
to branch out with what we did from the lab, so what we decided to change
was like the angle it was going, so what – and then what we’ll change – and
then we actually did the, the lab and what we figured out was that the angle of,
how do you say that, just the angle will determine in and then we came up
with a couple of different graphs.”
Interviewer: “What did you write right there?”
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Henry: “The angle would deter– determine the acceleration, like how fast or
like at what rate.”
Henry: “I forgot what angle it was but it was like, we had the XT graph was –
I believe on like that, and the VT, VT was – positive I think, and then the A is
just constant which is constantly increasing.”
Interviewer: “What kind of equations do you think these help us to establish?
So is there anything else you want to add I guess to this.”
Henry: “Here’s an equation for you. So I would say maybe, well first of all,
acceleration equals Delta V over T.”
Interviewer: “And how’d you determine that?”
Henry: “Well over here basically…”
Interviewer: “Do you want to point to that for us, like draw a big arrow all the
way from that to that? Okay, so you’re saying that goes with that?”
Henry: “Yeah, so it’s basically just like finding the V, the V is, you just do,
delta X over T I believe and then to get acceleration, you just do the slope of
that which just gives you a straight line, so acceleration equals Delta V over
T.”
Case Study 5: Ophelia. Ophelia uses the lab as the main node of her concept map,
reinforcing the Modeling curriculum in which the lab exercise is the main hub around
which instruction is centered. She is able to tie all of her learning back to this one
exercise and make connections to all concepts from this exercise.
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Ophelia: “First in the middle I’m going to draw a square and write ramp lab
because we did a lab along with this unit and then so then off the side I’m
going to put graph because with the ramps it shows the different velocities and
so you have this going down and over here you have an equation that I will
think of and then.”
Interviewer: “This went down over here, no it’s okay.”
Ophelia: “Then over here there’s one that’s like, went like this…”
Interviewer: “Okay.”
Ophelia: “… and then over here we have one that there’s one that kind of
looked like this, so it is a curve, and then there’s different equations for them,
and then with the ramp lab you learn – with the ramp lab you learned about
things such as velocity and we learned about things such as acceleration and
then we learned also about what our lab results would mean and so before our
lab we did, what would change, which is – what would change, and then we
like branched off ideas about what we thought would affect the ramp, so it
would be ramp height, then also we have the ramp length, then over here we
have the ramp…”
Ophelia: “…size and size can mean a lot of things, it can mean the length and
the height, but I’m just going to write that because what I am referring to is
just kind of how you have the set up going, and also who it changes, I think
would be like the certain buggy you’re using because some of them don’t
work as well, so it would be the buggy and then from this we can see like the
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different mathematical equations we’ll get from it, that will come from our
data and then so then, what we did with this and we studied for our test and it
helped us a lot.”
Interviewer: “Okay cool. What equations did you get from all that stuff? Did
you get anything? Any math and stuff from all that? I like it all, I love it.”
Ophelia: “V equals D over T and then acceleration …”
Interviewer: “Can you point to where that goes over here?”
Ophelia: “…yeah V equals D over T and when you have a graph like this, the
velocity goes here and the time goes here but then also you derive this graph
from an X T graph and then with this you can make an acceleration graph, and
most of the time those acceleration graphs kind of look like this, but you also
have some negative on the velocity. Also if you want to find your
acceleration its right here, it’s the slope of your line and you can also look at
this and it’ll help you to find like different data points.”
Case Study 6: Tyson. Tyson makes connections between the graphs and equations
of the unit, explaining the connection between these. While at first glance his concept
map may not explain much, he is able to verbally express his thoughts and clarify his
writing. His concept map is truly personal.
Tyson: “…it goes from top probably put some kind of like graphs or
something because if it’s going down a ramp, probably do time with
distance…”
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Interviewer: “Okay.”
Tyson: “So if you start origin from the top it’ll sum and creates faster, looking
like that. So they’re probably be like, I forgot what type of graph it is, but like
it looks like X squared kind of.”
Tyson: “So the slope I think is X squared. I’m not sure. But that’s what you
would get if you had X squared because it’s something like both velocity
versus time, starts off slow then steadily gets faster.”
Tyson: “Then you could start like equations and stuff.”
Tyson: “Okay. I could probably… change of X or just what X would equal at
a certain time since that would be X squared. You would find where on X it’ll
be versus time and so you would probably put time in here – trying to think of
exactly how we did this earlier in the year. Changing the X equals – trying to
think of the exact equation that we had, I’m not sure if this is going to work
out exactly how I thought.”
Tyson: “You want to know the acceleration for the graph of VT. Must be the
final velocity minus initial, initial velocity over T.”
Interviewer: “Okay and that goes with that one?”
Tyson: “Which is the slope I think too.”
Interviewer: “Okay. Was that an important one?”
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Tyson: “Yea, Still trying to think of an equation for X, try to find X. Well the
slope of X will be velocity so no V F equals, I think the initial either plus or
multiply, by something. VF equals VI; I think first times T plus 1½
acceleration T squared. So this will be directly related to the graph of VT and
the velocity, the slope of the X T. So V equals that, I’m trying to think of an
equation for X. I think it’s just times the VT, both velocity of time times the
time, maybe –.”
Interviewer: “Okay. You write that down.”
Tyson: “Yeah.”
Interviewer: “So all these ideas that you’re talking about, what is all this
trying – what’s the big picture here, what is this kind of showing you?”
Tyson: “Showing how everything relates to each other somehow.”
Interviewer: “How everything relates to each other. Yeah, do you feel like
you have a decent understanding of it?”
Tyson: “Yeah, I’m understanding of how it works just hard finding an
equation off the top.”
Interviewer: “Yeah. So what if I asked you some questions about explaining
it? So when that object rolls down the hill what’s happening to that object?”
Tyson: “It starts speeding up because gravity takes hold, which is an
acceleration, so the velocity will speed up, so it’s speeding up and because the
velocity is speeding up, the actual distance for X will go up even faster so it’s
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like X squared because it’ll start off slow and then keep on getting faster and
start increasing exponentially.”
Case Study 7: Jack. Jack demonstrates great retention in his concept map,
including not only graphs and equations but examples to illustrate the concepts. His
writing includes more than he verbally expresses, displaying his preference for visual
learning.
Jack: “Okay. So uniform acceleration is velocity that is constantly increasing.
I guess we’d say that uniform acceleration is the –Okay. … moving objects,
all things accelerate. All things that’s in natural motion, I guess, like in
space.”
Interviewer: “Do you want to use your lab as a reference for your next one
and can you put the lab in there?”
Jack: “Yeah, the ramp lab?”
Interviewer: “Yeah.”
Jack: “Ok the ramp lab, this equation – acceleration.”
Interviewer: “What graph might we get that from? How do we get that
equation?”
Jack: “We get that equation from the velocity graph.”
Interviewer: “Can you draw that?”
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Jack: “Yeah so the velocity graph is like – velocity graph is like this, we could
take the highest velocity, say its 10 – zero, 10 minus zero over the whole total
time which should be 10 seconds, with one meters per second per second
would be –.”
Jack: “Yeah so this is – this is time from the bottom we put the time lapse or
the final time minus initial and then here we put – this is velocity, so velocity
is constantly increasing, as it goes up one meter per second every second.”
Interviewer: “So what’s that line that you made?”
Jack: “This line is the velocity graphically.”
Interviewer: “Okay.”
Jack: “Well the slope is the…”
Jack: “Oh I’m sorry, the slope is the acceleration but the actual – the actual
graph is a velocity graph.”
Interviewer: “All right.”
Jack: “Yeah.”
Interviewer: “So what equation do you get if your slope is your acceleration?
Can you write the equation of that?”
Jack: “The equation of which?”
Jack: “V equals A times T. A times T, no?”
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Interviewer: “Okay.”
Jack: “Yeah.”
Interviewer: “And so what could you do with that now?”
Jack: “With this?”
Interviewer: “Yeah with that equation? What might you do with that?”
Jack: “We take the acceleration times the time to get the velocity.”
Interviewer: “Okay.”
Jack: “So do one times time lapse would be 10 seconds, goes 10 meters per
second.”
Summary of Concept Map Activity. Students actively participating in the formation of
their respective unit concept maps were able to produce a significant artifact. These same
students were able to articulate and defend the formation process of their concept maps.
Students chosen from the treatment groups for our interview section and case study
(approximately 16 students) showcased the ability to demonstrate coherence of
Newtonian concepts. Furthermore, the mental plasticity demonstrated by concept
retention and relatedness shows that students can model their thoughts in a long term
format using a simple yearlong application. The ability demonstrated by students to recall
information they learned months prior and properly express the key concepts, bot
verbally and on paper, reaffirmed the investigators’ belief in the validity of the concept
mapping process. To summarize, “meaningful” learning, then, involves the acquisition of
knowledge in such a way that the concepts become integrated; they can be called upon
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both for recitation purposes and as the stepping stones upon which further concepts may
be added. It results in knowledge that is stored in a way that allows it to be accessed from
many different starting points. That is, it is knowledge that is well integrated with
everything else that you know. Meaningful learning is accompanied by the building of
multiple representations (mental models), models that are connected to models for many
other phenomena (Michael, 2001).
Reflections
Investigator 1
The need to introduce concept mapping into my classroom began as an attempt to
convey the abstract concepts of physics to a population of students for whom abstract
thinking did not come so easily. In the fall of 2012, my school chose to include a group of
nine students with Individualized Education Plans into the physics classroom. For all of
these students, placement in the general education classroom was an exception rather
than the norm. Math skills and communication skills were low across the board and
although this group was accompanied by a certified resource teacher and two one-on-one
aides, none of these adults had experience teaching science much less physics. As the
teacher of record, I was extrinsically motivated to ensure these students learned the
material so as to be reflected in my performance evaluation but, as an educator, I also
wanted to help them grow as scientific thinkers without the worry of grades. This
presented a quandary: how do I present the material necessary to become proficient in
general physics without overwhelming students for whom learning comes with difficulty?
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I tried several strategies to reach my students and increase learning that semester but
concept mapping was by far the most successful.
I had previously used the graphic organizer present in earlier versions of the
Modeling mechanics curriculum but found it to be too structured. For students who, like
me, have larger handwriting the graphic organizer was out of the question. I found that
when we were filling these out, students often just wanted to copy what I would write
down. They treated each box as a list and would check off each equation or graph to
ensure that they had all the information. This led to my belief that the notes students
would take need to be more fluid.
I feel very fortunate that at my school we have a faculty that works together
toward learning goals for our students, sharing common strategies for success. One of
these strategies came in the form of maps. My students already possessed a toolbox of
mapping knowledge they had used in other subjects, I just needed to teach them to apply
this for science.
That first semester I began to introduce mapping for smaller concepts. It became
clear to me that students who struggled with speaking the language of variables and
equations did not experience the same difficulty with drawing and color-coding. I saw
students move from frustration to determination through the use of self-produced
diagrams. Of course, these nine students were not the only ones in the classroom. The
general education students took mapping one step further, producing original works
without teacher prompt. The feedback I was receiving from students was overwhelmingly
positive and I knew that this practice needed to continue.
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During that semester, I taught my students to use several different styles of maps,
each dependent upon the material and desired outcome. I realize now, though, that I
neglected to tie together the ideas these small versions contributed to the instructional
unit as a whole. For our research we chose to focus on one specific style and use this for
an overarching instructional unit note-taking strategy. As I continue the use of concept
mapping in my classroom, I will reintegrate a variety of maps into the curriculum. It is
my opinion that any visual created by students assists in their learning to an extent that
can never be achieved by the instructor alone.
Since I began my teaching career fourteen years ago, I have seen a steady decline
in the mathematical reasoning skills of my students. This poses a conundrum for me as a
teacher. Do I set high standards and encourage only the best and brightest students to
enroll in my course, or do I encourage everyone I can to take Physics knowing that I am
going to encounter a lower mean of mathematical reasoning? I have personally chosen
the latter option in hopes that exposure to such a class will benefit more students and
must therefore adapt to meet the needs of my changing student population.
I am a strong believer in meeting the needs of all types of learners. While
Modeling instruction reaches the visual, auditory and kinesthetic learners through lab
activities and discussion, I know that my students often just want notes. They want
something written down that they can take home and use when they complete homework
or study for a test. I struggled with finding that balance between Modeling instruction and
the lecture so often requested. I will never lecture to my general physics classes as I feel
that this detracts from the student-centered Modeling cycle, but I will continue to
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encourage students to take notes through visual methods such as concept mapping in
order to bridge that gap.
Investigator 2
In my short service to the education of high school students, I have noticed that
intelligence and attainment of more degrees and certifications doesn’t always correlate to
exceptional teaching acumen. I have seen teachers with the highest level of education
collapse under the pressures of teaching and quit well before their contract to serve a year
was fulfilled. Opposite to that, there are teachers with lesser qualifications for teaching
subjects who are beloved by parents and students in spite of their lackluster
qualifications. “Fake it ‘til you make it” is the slogan that many teachers live and teach
by. This is demonstrated by a lack of depth of content knowledge (Gordon, Kane, &
Staiger, 2006): their lessons include skimming through the main ideas or giving equations
to use on problems, thus, teaching with a style that spews out disconnected ideas; they are
fun, energetic, good story tellers and know how to run a classroom. What they lack is the
ability to make one of the most important impacts a teacher can have by showing students
a deeper understanding of the modus operandi of the world we live in, especially
regarding the subject of physics.
In the classroom, I find that confidence and management styles make or break
career longevity. Confidence comes about in various forms with confidence in oneself
and in one's knowledge pertaining to the classroom setting. Sadly, most teachers rely so
heavily on confidence in themselves in their first years of teaching that they don’t have
the time or necessitate the need to really integrate their course material and develop
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confidence in their knowledge. As they progress through their teaching careers, many
teachers never take another core class to promote their content knowledge. These
teachers remain stuck in a learned conceptual stagnation that will most likely continue to
be lacking and/or non-adaptive to learner's’ changing needs. Exceptional science
education in the classroom stems from the ability to effectively communicate and
promote student interest in how natural processes occur and exist in nature. If the
educator ceases to seek and improve upon flaws in their conceptual framework, it is the
future generations that will suffer.
It was upon much self-reflection during my first semester teaching basic physics
that I was led to confront my shortfall in communicating science curriculum in a logical,
cohesive and effective manner. I was “faking it”. My floundering around the subject of
physics over the course of some years was not as obvious to the students because of my
learned false confidence; it was through self-reflection that I began addressing my
learning gaps and recognized the high importance of gaining confidence in my subject
matter knowledge through continued education and professional growth. This reflection
of what type of teacher I was and wanted to be pointed me to the Master of Natural
Science program at Arizona State University, which has helped relieve much of the
uncertainty I felt when discussing physics. My endeavor into a project and program that
would help my students seemed to be of the highest importance. This personal journey to
become a Newtonian thinker will be the main discourse below as it relates to introducing
concept mapping to my classes. The unexpected result that the research had on me was
obvious only after all the applications via concept mapping had manifested a significant
increase in my comprehension of physics. The positive effect of concept mapping was
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undeniable, helping me to process connections between ideas and integrate these
concepts. Physics curricula are now second nature, relayed to the students in a seemingly
effortless manner by a teacher who now possesses confidence in knowledge and not just
in self.
Over time, content teachers will all acquire a set of knowledge that allows them to
explain the main ideas of a subject. As teachers we should strive to not only be able to
explain something and regurgitate it, but go one step further so that students can not only
learn, but be able to explain the material. Through this thought research investigation, I
began to realize that if I am lacking a general understanding of connections between
ideas, there are most likely other educators that have a lack of knowledge to necessitate
proper transmission of ideas. If we are missing a truly deep understanding of how to use
pedagogical knowledge, then we cannot promote critical learning. By using concept
mapping it forcibly made students to be involved in critically analyzing, making
connections of and explaining new information to others in a cohesive manner. Not only
did concept mapping help my students, but myself as well. It is only through the
coherence of Newtonian concepts that allows for the comprehension of basic physics.
All first year teachers are faced with the difficult task of teaching a subject in a
coherent way so that at the end of the day they help more than harm the students
understanding. When faced with teaching a core subject like science there are additional
factors that make this a stressful situation. Luckily for me, I was already a well-seasoned
teacher, having taught earth science, basic physics, basic chemistry and biology. Despite
all of this experience going my way there were some apparent struggles that I had
conflict with throughout the year. The difficulties I faced teaching physics this year
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stemmed from my own misconceptions with physics and how to relate concepts that at
first glance seem disconnected. By concept mapping throughout the year, most of these
inadequacies were alleviated.
Being a novice physics instructor, I feel that concept mapping was as beneficial
for the students as it was for me. I found that my understandings of concepts grew as I
was forced to draw a map that showed a sort of interconnectedness that was not apparent
to me prior to teaching. It was by forcibly looking at these and how they link together that
mandated my core understanding to be established. In order to develop a coherent
thoughtful map it was a struggle and something I wrestled with after school was over. I
say that not only did my comprehension grow through mapping, but so did my thirst for
wanting to know how other connections not covered in class could be drawn.
Going from a novice to a master teacher doesn’t happen in a year, likewise going
from a non- physics thinker to a comprehending physics student also doesn’t happen in
one year. It was however obvious to me that my struggling with this connectivity
between ideas forced a higher level of comprehension that wouldn’t have happened had
concept mapping not been used. As the units were decomposed into their singular ideas,
connecting them in a logical way forced me to critically analyze the arrangement of
ideas.
Our application of concept mapping in the physics classroom was met with
difficulty before the school year had even begun. I asked myself “what should this unit’s
concept map look like”, as if I knew. I had never taught a yearlong physics course or had
to think critically about how ideas relate to each other. I had no idea that by signing off
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on doing research by using mapping that it would mean I would be pushed to learn as
much as I did. There is no doubt that the students learned, I would say that their learning
was only intensified by the application of mapping. There is definitely no doubt as well
that I learned by the same magnitude if not greater by having to help with not only the
typical class work, but by showing connections between the class work. Evidence of my
learning was from my FCI score increasing from a 17 to 26. The constant state of
looking to link ideas to each other really pushed me toward a higher level of
understanding that did not exist prior to applying our method. Having to mentally
research within my own mental model, make changes to and add new connections
allowed a set of connections between subjects that hadn’t existed before.
Unexpected Discoveries
Throughout this action research process, both investigators were tasked with
creating a process that would enable us to test our hypotheses regarding the relevance and
importance of concept mapping while creating as few distractions from the learning
process for students as possible. We began the year-long investigation phase with a plan
for how to move forward and an anticipated timeline. This plan became a living
document by necessity; reality in the classroom and ability of our students sometimes
required that we make adjustments both minor and major. Rather than viewing the
barriers we faced as setbacks, we learned to assess them, address them and implement
changes to our plan as needed. Several unexpected discoveries came out during this
process.
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We anticipated that our students’ pre-test scores would be low, but were unable to
predict the degree of difference between the scores of our students and those in the
comparison groups. This difference in scores persisted even between sister schools of a
unified school district. These lower levels of scientific reasoning led us to focus more
time on those basic skills and placed us in a position to attribute more importance on
fostering thinking skills than we may have otherwise.
Student participation and engagement was an issue for the investigators. We
believed that by giving the students more autonomy over their concept maps, they would
have a larger investment in the process and product. We added the attached concept map
grade to increase motivation and allowed students to use their concept maps on tests. All
of this was decided upon prior to the start of the school year, yet we were not prepared
for the struggle with participation. Students still wanted to create the maps, edit and add
information, and use these on their tests. They did not, however, want to do this on their
own. It was the original intent to have students create concept maps with complete
independence by the sixth unit of instruction, but we found that students fought this
move. We continually have to choose our battles in teaching and decided instead to
modify our technique to the group discussion-fueled concept mapping approach instead.
When students were asked to edit concept maps, altering misconceptions and
adding new information, we persisted in the use of color-coding. When asked about the
color-coding process, students replied positively, stating that the colors assisted in
organization of thoughts and material. This attitude was not, however, evident in the
classroom. Students routinely complained about the use of color-coding yet chose to use
the colors even without prompting. Even after all the complaints the color-coding became
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part of the process for many students who chose to use color as another organizational
tool.
Finally, student attitude was an unexpected factor in our investigation. Although
most students had experience with the visualization of ideas prior to this course, they
fought using them at first. One student, Henry, summarizes this perfectly:
“So in the beginning I don’t know, I didn’t really like it that much because,
you know, something new and I — I don’t know, I think as a teenager you
don’t really want to like, get away from, like doing new things I guess. So in
the beginning I didn’t like it but it did help a lot. It’s just like organizing my
stuff into like different sections you know. And then yeah – as the year went
on I really started to like it because like my test scores improved and all that
just, just from the organization itself, you know.”
Persistence in our belief that concept mapping would be beneficial to our students paid
off in the long run, but we did not anticipate the struggle with the process.
Conclusion
There is no statistical evidence to suggest that concept mapping in addition to
Modeling instruction produces higher gains in introductory mechanics understanding
than the use of Modeling instruction alone. Based on initial levels of scientific reasoning,
the lowest performing students achieved a larger gain in mechanics comprehension than
their comparison counterparts. We were encouraged by the gains in scientific reasoning
by the treatment classes during the investigational period, but believe that this is due
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
more to the process of Modeling rather than the use of concept mapping, as suggested by
the weak correlation between scientific reasoning gains and average concept mapping
score. The moderate positive relationships found between course grade and average
concept map score as well as final exam grade and concept map score highlight the link
between concept mapping and retention. Students who constructed concept maps that
included a larger amount of pertinent information scored higher on a cumulative exam, as
shown in the scores achieved on the cumulative exam versus average concept map score,
than those students whose concept maps included minimal information, highlighting the
benefits of a well-constructed concept map. Qualitative evidence highlights a positive
response to the use of concept mapping as a tool in the classroom. Students and
instructors reported that the use of concept mapping assisted in organizing thoughts in a
clear, concise manner. In addition to helping connect ideas, we suggest that concept
mapping served to increase concept retention when used in conjunction with the
Modeling method of instruction. Evidence for retention was clear during student
interviews conducted months following the instruction by students expressing their maps
in a personal, dynamic model as highlighted in the case study interview section. Students
demonstrated both comprehension of fundamental ideas guiding an important mechanics
principle and ability to link these ideas with understanding gained through subsequent
instructional units. We believe that the construction of concept maps provided an outline
that established core ideas (central nodes) to which students could attach new ideas and
encouraged students to connect new understanding. Students were asked throughout the
year to explore natural phenomena and determine the physical factors that allowed for
changes to happen. Once this discovery had been made and variables identified then they
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
were to be written down in a way that linked them to the discovery. Utilization of these
created concept maps assisted the students in solving problems and creating a
comprehensive understanding of mechanics as a whole.
Implications for Instruction
The scaffolding of information, whether it is teacher-led, or student-generated,
has fueled the research of this project. We (the investigators) observed that a deeper
understanding of mechanics was attained by using concept mapping in the classroom as a
yearlong application. Organizing thoughts on a piece of paper was a tool for our students
to build a framework of collected knowledge to which new information could be added as
it was acquired. Student’s abilities to make connections that may not normally have been
seen were observed in our study, pointing to the importance of class-generated,
individually-built, interconnecting concept maps. Producing a useable concept map did
prove to be difficult for a small percent of the student population. We feel that some of
the frustration that the teachers and students felt by creating concept maps could have
been alleviated by using a pre-made computer generated diagram that includes all nodes
and connections to be filled in throughout the unit. In addition, having a teacher “key” for
what the concept maps should look like would allow for ease of scoring and a better
understanding of what to include for every section. Despite the challenges we faced using
concept mapping, all randomly selected students interviewed felt it was not difficult to
do, offered why they thought it was useful, and demonstrated an average retention
months after the material was taught. It is the investigators’ opinion that concept maps
should be incorporated into the Modeling mechanics curriculum.
Implications for Further Research
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
Overall, we found that the use of concept mapping enhances the student
experience within the Modeling physics classroom. We believe that further research
could examine the use of mapping software rather than the hand-constructed maps used
in our study. In addition, the bubble map structure used in our study was reported to be
restrictive by some students. With more time, we would have used a variety of maps
dependent upon the purpose and content. In addition, our mapping technique focused on
the nodes of the map, not the connectors. We would, if repeating the experience,
emphasize the connectors as well in order to encourage concept connection in a more
detailed manner. Finally, a larger sample size would be preferable, testing students across
multiple Modeling classrooms.
70
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
Appendix A
Concept Map Evaluation Rubric
3
2
1
0
Unit
Concept map
Concept map
Concept map
Concept map
Concepts
includes all new
includes most
includes some
includes no new
concepts learned
new concepts
new concepts
concepts learned
in this unit
learned in this
learned in this
in this unit
unit
unit
Concept map
Concept map
Concept map
Concept map
includes all
includes most
includes some
includes no
graphs discussed
new graphs
graphs discussed
graphs
in this unit
discussed in this
in this unit
Graphs
unit
Equations
Concept map
Concept map
Concept map
Concept map
includes all new
includes most
includes some
includes no new
equations
new equations
new equations
equations
learned in this
learned in this
learned in this
learned in this
unit
unit
unit
unit
Concept map
Concept map
Concept map
includes all new
includes most
includes some
includes no new
physics
new physics
new physics
physics
vocabulary
vocabulary
vocabulary
vocabulary
words and
words and
words and
words and
meanings
meanings
meanings
meanings
Vocabulary Concept map
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CONCEPT MAPPING IN THE MODELING PHYSICS CLASSROOM
Diagrams
Concept map
Concept map
Concept map
Concept map
includes
includes
includes
includes no
examples of all
examples of
examples of
examples of
diagrams used in
most diagrams
some diagrams
diagrams used in
this unit
used in this unit
used in this unit
this unit
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