Radiasi: Jurnal Berkala Pendidikan Fisika
Vol. 18 No. 2 (2025) pp. 75 - 85
http://jurnal.umpwr.ac.id/index.php/radiasi/index
p-ISSN: 2302-6111 e-ISSN: 2549-0826

Profiles of Problem-Solving Strategies in Kinematics: A Comparison Between
High, Average, and Low Achieving Undergraduates
1

Suci Rizkina Tari

, 1Fadiya Haya, 1Musdar

Universitas Syiah Kuala

1

Jl. Tgk. Hasan Krueng Kalee, Kopelma Darussalam, Kec. Syiah Kuala, Kota Banda Aceh, Aceh 24415, Indonesia
|sucirizkinatari@usk.ac.id
| DOI: https://doi.org/10.37729/radiasi.v18i2.6824 |

Abstract
Problem solving is an essential competency in physics learning, particularly in the topic of
kinematics, which requires mastery of concepts, analytical skills, and effective thinking strategies.
Understanding the profiles of students’ problem-solving strategies across different achievement
levels can provide detailed insights into the variety of strategies employed and the areas that require
instructional intervention. This study aims to describe and compare the problem-solving strategies
of Physics Education undergraduate students with high, medium, and low achievement in solving
kinematics problems. A qualitative method was employed, involving six participants representing
the three achievement categories. The primary data were collected through the think-aloud technique,
supported by observations, retrospective interviews, and answer sheet analysis. The comparison of
profiles revealed differences in strategic tendencies and completeness of problem-solving stages
among the three student groups. These findings offer strategic insights for developing adaptive
teaching methods to enhance problem-solving skills across various levels of academic achievement.
Keyword: Problem-solving strategies, Kinematics, Achievement Levels

Article Info:
Recieved:
28/07/2025
Revised:
15/09/2025
Accepted:
26/09/2025

Keywords: Problem solving strategies, Kinematics, Achievement levels

1. Introduction
Problem solving is considered a basic element in learning physics and frequently viewed as the
foundation of students’ conceptual understanding [1]–[3]. Through problem solving, students apply
concepts in practical contexts, which strengthens comprehension and evaluating their knowledge [4].
In physics learning, becoming a proficient problem solver is undeniably one of the ultimate goals, as it
reflects both conceptual understanding and the ability to apply knowledge to novel situations [5], [6].
Despite the recognized importance of problem solving in physics, challenges persist as research shows
that students’ problem-solving skills remain consistently low in physics learning [7]–[9]. One
significant factor contributing to low problem-solving skills in physics is students’ inability to
effectively apply appropriate strategies throughout the problem-solving process [10], [11].
Successful problem solving in physics depends not only on students’ conceptual understanding
but also on their ability to effectively apply strategies throughout the problem-solving process [10],
[12]. The problem-solving process involves multiple steps to reach a solution; however, the sequence
in which these steps are executed is often overlooked in assessments, potentially missing critical
insights into students’ thinking processes and affecting their problem-solving outcomes [13].

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These strategies also vary among students, including those with different levels of academic
performance, while some approach problems with structured reasoning and clear conceptual
understanding, others may rely on superficial cues or rote memorization [11], [13]. Understanding the
problem-solving strategies of students with varying levels of academic performance can provide
valuable guidance for targeted feedback and instructional interventions, enabling learners to refine
their strategies and achieve improved outcomes [14], [15].
Previous studies have explored problem-solving strategies and approaches, with some focusing
only on describing the strategies or approaches used by learners, while others compared novices with
experts or successful with less successful problem solvers. These studies, conducted not only in physics
but also in other fields, aim to provide insights into the cognitive processes involved in problem
solving. According to Gök and Silay [16], the problem-solving process involves four strategies:
understanding the problem, planning the action, constructing a solution, and checking the result, and
teaching these strategies in cooperative groups enhances students’ performance. Hartviksen and
Haavold [17] comparing top-grade students in an advanced mathematics course with participants of a
Norwegian problem-solving contest found that the contest participants demonstrated superior
problem-solving performance. Burkholder [18] examines the problem-solving strategies of
‘transitioning novices’—students who have completed an introductory physics course but are still far
from expert-like reasoning. The results show they mainly rely on intermediate strategies, such as unit
analysis for interpreting mathematical expressions, while only a few uses advanced approaches like
limit checking, which requires mentally simulating system behavior under changing variables. Tóthová
and Rusek [19] conducted comparative study of first year chemistry teacher students and postdoctoral
experts in chemistry education revealed distinct differences in problem-solving approaches: experts
concentrated directly on relevant aspects of the task, whereas novices distributed their attention across
less essential parts and tended to employ limiting strategies that were absent in the expert group.
Although previous studies have addressed this issue, much of the research has focused on
contrasting professional physicists or advanced students with novices, leaving limited understanding
of how problem-solving strategies differ within the general student population particularly across
different achievement levels in a kinematics context. Moreover, many studies consider only high- and
low-achieving students, overlooking the middle group of average performers. This study aims to
examine and compare the problem-solving strategies employed by high, medium, and low achieving
undergraduates while solving kinematics problems. Kinematics was chosen for this study because it is
usually one of the first topics in introductory physics courses. Its basic concepts such as units, position,
velocity, and acceleration are essential and appear in many areas of physics. Strong problem-solving
skills in kinematics are important, as difficulties in this topic can affect students’ overall success in
learning physics. By analyzing differences in how these groups understand problems, plan and monitor
their steps, and execute solutions, this study seeks to provide insights that are vital for developing
personalized instructional strategies, supporting struggling students, and guiding all learners to
enhance their problem-solving skills.

2. Method
This study employed descriptive qualitative research to analyze the problem-solving strategies
of students with low, medium, and high achievement in solving one-dimensional kinematics problems.
The study involved six first-year students from the Physics Education Department at Universitas Syiah
Kuala who had completed the Basic Physics I course, which includes kinematics material. The six
participants consisted of two students with low achievement, two with medium achievement, and two
with high achievement in the Basic Physics I course.

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The participants were selected using purposive sampling. They were categorized into three
achievement groups—high, medium, and low—based on their scores on a kinematics problem-solving
test in a basic physics class, complemented by the lecturer’s evaluation of their problem-solving ability.
High achievers were defined as students scoring in the top range (≥ 75), medium achievers as those
scoring in the middle range (45–74), and low achievers as those scoring in the bottom range (≤ 44) All
participants provided their consent to take part in the study and signed informed consent documents.
Data were collected through four techniques: think-aloud as the primary method, supported by
retrospective interviews, observations, and analysis of written responses to ensure the data were well
validated and to strengthen the credibility of the findings. The think aloud sessions were conducted
separately for each participant at different times. During these sessions, participants were instructed to
verbalize their reasoning while solving the problems. At the same time, the researcher conducted nonparticipant observations to monitor participants’ actions and engagement without direct interference.
Field notes were taken during the observations to assist in formulating interview questions, particularly
to clarify ambiguous expressions used by students during the think-aloud process, such as “this” or
“that,” which cannot be fully interpreted through verbal data alone. Once participants had completed
all the problems, retrospective interviews were conducted. In these interviews, participants were asked
about their reasoning and strategies for example, “Why did you choose a particular method to solve it or to
clarify their actions for example ?”, “Why did you look back at what you had written earlier in the process?” The
interview complemented the think-aloud data and provided deeper insights into students’ thought
processes during problem-solving. Participants’ written responses were also analyzed alongside the
think-aloud recordings to further trace and understand their problem-solving approaches.
Five kinematics problems were used in this research. Prior to the main research, the problems
were piloted with 12 undergraduate students who had completed introductory physics courses
covering kinematics. These students were not included in the main research, were selected to represent
a range of abilities, and were asked not only to solve the test items but also to provide feedback on their
clarity, wording, and level of difficulty. The five problems were adapted from university physics book
[20]–[22]. The problems are shown in Table 1 listed in the order they were used.
The data analysis followed Miles et al.’s framework [23] of data reduction, data display, and
conclusion drawing. In the reduction stage, think-aloud sessions, retrospective interviews, and field
notes were transcribed, then coded using gerunds to capture observable problem-solving strategies
used by participants. Vague or overlapping codes were refined (e.g., distinguishing “Reading” from
“Rereading”), and unclear statements were clarified by cross-checking with observation notes,
interview data, and participants’ written answers. In the display stage, codes were organized into
tables, grouped into broader categories of problem-solving strategies, and compared across low,
medium, and high achievers to highlight differences and similarities. Finally, in the conclusion drawing
stage, the analysis focused on interpreting how each achievement group approached problem solving
and identified key strategies distinguishing low, medium, and high achievers.
Table 1. Kinematics Problem Used in Think-Aloud Session
No
1

Problems
Submarine & Sonar
To avoid detection by an enemy vessel, a submarine must stay deeper than 3000 m. The
vessel uses sonar, which sends a sound pulse into the water and records the echo. If the
echo is received back in 3.6 seconds, will the submarine be detected?
(Speed of sound in water = 1500 m/s)

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2

3

4

5

Emergency Plane Landing
A passenger airplane is flying at 80 m/s when the pilot begins to land on a runway. The
braking
system
provides
a
constant
deceleration
of
−4.0
m/s².
(a) How much time will it take for the plane to come to rest?
(b) Can the plane safely land on a runway of length 1200 m?
Relay Race
In a 4 × 200 m relay the runners have these average speeds:
 Bima: 10 m/s
 Rudi: 8 m/s
 Tika: 5 m/s
The school record for 4 × 200 m is 111 s. If Maya runs last, what minimum average speed
(in m/s) must Maya maintain so the team beats the record by at least 1.0 s?
Two Vehicles Approaching
A bus travels east at 25 m/s, while a car starts 600 m away heading west at 20 m/s. When
they are at this distance, both drivers suddenly notice an obstacle and begin braking. The
bus decelerates at −2.0 m/s², while the car decelerates at −4.0 m/s². Will they collide, or can
they both stop before reaching each other?
Choosing Between Escalator and Stairs
Rina wants to reach her classroom on the 10th floor.
 Stairs: She can run at 4 m/s for the first 5 s, then slows down with a deceleration of 0.2
m/s².
 Escalator: It moves upward at 1 floor per 2 s. Each floor has a height of 4 m. She must
wait 8 s for the escalator to arrive.
Which option will get Rina to the classroom faster?

3. Results and Discussion
The findings revealed thirty distinct strategies observed across participants’ problem-solving
sessions. These strategies were then organized into six strategy categories based on their functions and
roles, providing a clearer view of the strategies used by high, medium, and low achievers. The
identified six categories of problem-solving strategies are understanding, planning, executing,
monitoring, checking, and concluding. Understanding strategies reflect students’ efforts to grasp the
problem context before attempting a solution. They read and reread the statements, underlined or listed
key information, representing the problem using symbols, sketches, or diagrams to make sense of it
and sometimes rephrased the problem in their own word or recalling relevant concepts of the problem.
The typical utterances transcribed were “The question actually ask …” or “So the object starts from rest…”
Planning captures how students emphasized the problem goal, selected formulas, considering
alternatives, making assumptions how to solve the problem, outlined possible steps and creating subgoals. Some carried out this stage confidently, while others made tentative or trial-and-error plans. The
example utterances were “Oh, I need to find the velocity first” or “Maybe I can use that formula here.”
Executing strategies encompass the actual implementation of plans through calculations, applying
formula, constructing equation, algebraic manipulations, or unit conversions to generate results. The
example utterances were “Four times ten is forty, so the distance is 40 meters” or “Then substitute the values
into the formula.”
Monitoring strategies highlight students’ awareness of their ongoing problem-solving process,
such as reflecting on progress, comparing alternatives, reconsidering variables, reasoning obtained
results, recognizing mistakes, making self-correction, and adjusting strategies during the process.

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The participants showed the ability to pause during the process and reflect on their work, occasionally
murmuring, ‘Is this right?’. Checking encompasses strategy where students looked back at their work
to verify accuracy and consistency. This included validating steps, evaluating formulas, verifying the
calculation, evaluating intermediate actions or judging the reasonableness of the result. The typical
utterance transcribed was “Let me check this ….” Finally, Concluding represents students’ strategy in
stating or communicating the answer. The majority of participants stated the answer by directly
mentioning the numerical result, while a few participants explained their answer by relating it back to
the original question, or interpreting the meaning of the answer. The problem-solving strategies used
by low, medium and high achievers presented in Table 2.
Table 2. Problem-Solving Strategies Used by Low, Medium and High Achievers
Categories of
Low
Medium
High
Codes of strategies
strategies
achievers achievers achievers
Understanding Reading the problem
√*
√
√
Rereading the problem
~**
~
√
Extracting given information
√
√
√
Representing the problem (symbols,
~
√
√
sketchs, etc.)
Rephrasing the problem in own
x***
~
~
words
Recalling relevant concept
~
~
√
Planning
Setting the goal
~
√
√
Making assumptions
x
x
√
Selecting the appropriate formula
~
√
√
Considering alternatives
x
~
~
Creating sub-plan
x
~
√
Outlining next step
~
√
√
Executing
Applying formula
√
√
√
Constructing equation
√
√
√
Mathematical Execution
√
√
√
Unit conversion
~
~
√
Checking
Validating steps
x
~
√
Evaluating formulas
~
~
√
Verifying the calculation
x
~
√
Evaluating intermediate actions
x
x
~
Checking with alternative method
x
x
~
Reasoning the result
x
~
~
Monitoring
Reflecting on progress
x
~
√
Comparing alternatives
x
x
~
Reconsidering variables
x
~
√
Adjusting strategies
x
x
√
Realizing mistake
x
~
√
Self-correction
x
~
√
Concluding
Stating the answer (number)
√
√
√
Explaining answer in words
x
x
~
*√ : consistently demonstrated by participants; **~ : demonstrated but inconsistently or with mistakes; ***x : not demonstrated by
participants

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The findings reveal distinct profiles of students’ problem-solving strategies across low, medium,
and high achievers. Low achievers primarily relied on basic procedures such as reading the problem,
extracting given information, and performing straightforward calculations. However, they rarely
engaged in deeper analysis such as rephrased or represented the problem effectively, and almost never
checked or validated their solutions. Their lack of monitoring and reflection often led them to overlook
mistakes, resulting in incorrect answers or incomplete solutions. Medium achievers demonstrated a
wider range of strategies. They were able to organize problem information into physics symbols,
occasionally represent the problem with sketches, select formulas more deliberately, and or creating
sub-plans. They also engaged in checking and monitoring, reconsideration of variables, and selfcorrection, though inconsistently. This partial monitoring allowed them to reach correct solutions in
simpler cases, but their inconsistent checking and evaluation, often led them to rely on trial-and-error
approaches when confronted with more complex tasks.
High achievers employed more systematic and flexible strategies that combined understanding,
planning, executing, monitoring, and concluding strategies. They systematically set goals, selected and
applied formulas, constructed equations, and checked units. Importantly, they frequently monitored
their progress by recognizing mistakes, adjusting strategies, and verifying results. Although some
minor inconsistencies appeared, their frequent reflection and adaptive use of strategies allowed them
to identify and correct errors more effectively than the other groups. Overall, the comparison indicates
that low achievers tended to rely on surface-level procedures, medium achievers showed emerging
strategic awareness but inconsistent checking monitoring strategies, and high achievers demonstrated
integrated and adaptive strategies that enhanced the effectiveness of their problem solving in
kinematics. The comparisons are summarized in Table 3.
Table 3. Comparative Summary of Problem-Solving Strategies Across Achievement Groups
Problemsolving strategy

Understanding

Low achievers
Read the problem
literally, extract given
numbers, but rarely
rephrase or represent the
problem

Medium achievers
Read and record
information, sometimes
represent with symbols
or sketches, but
inconsistently

Planning

Minimal planning; often
jump straight to formula
without setting goals

Executing

Apply formulas
mechanically; rely on
memorization; errors
often uncorrected

Some planning by
identifying goals and
selecting formulas, but
sometimes trial-anderror
Carry out calculations
carefully, sometimes
with hesitation; partial
unit conversion

Checking

Almost no checking or
validation; ignore
inconsistencies

Occasional checking of
results or formulas, but
not systematic

High achievers
Reading carefully,
often reread,
rephrasing,
representing with
symbols/diagrams,
and recalling relevant
concepts
More structured
planning with goals,
formula selection,
sub-plans, and
outlining steps
Perform stepwise
calculations; construct
equations; include
unit checks
Consistent checking
of formulas, units,
results, and alignment
with the problem goal

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Monitoring

No reflect or adjust; no
awareness of mistakes

Occasionally reflect,
reconsider variables,
and attempt selfcorrection, though
inconsistently

Concluding

State final number
without explanation

Often state final
number only; rarely
explain in words

Overall
strategies

Procedural execution
with little reflection or
evaluation

Demonstrate partial
mastery with some
strategic awareness but
inconsistently.

Frequently monitor
progress, realize
mistakes, adjust
strategies, and selfcorrect
State answer and
sometimes explain
meaning or relate
back to problem
Exhibit adaptive and
flexible problemsolving strategies

The problem-solving strategies understanding, planning, executing, monitoring, checking and
concluding observed in this study provide a comprehensive picture of how students navigate
kinematics problem solving. The problem-solving strategies observed align with established models of
problem solving such as Polya’s [24], Schoenfeld’s [25] and previous studies examined problem-solving
strategies [2], [16], [18], [26]. The problem-solving strategies might suggest a linear progress, but the
actual processes observed in students’ sessions were dynamic and recursive, with frequent
backtracking, revisions, and shifts between strategies depending on the challenges encountered. The
findings indicate that high achievers frequently revisited earlier steps when encountering difficulties,
suggesting that flexibility is an essential feature of effective problem solving. This observation aligns
with the studies of Rahayuningsih et al., [27] and Hacatrjana [28] study which propose that the
flexibility to modify a solution strategy contributes to successful problem solving. These results suggest
that teaching instruction should explicitly model and scaffold problem solving strategies, not only
content knowledge, to help students improve their problem-solving performance.
Understanding were the most consistent strategy observed across all levels of achievement. This
aligns with Eryilmaz-Toksoy’s findings [29], which show that the most frequently used problemsolving strategy among students is understanding, and that the understanding phase significantly
influences both the solution process and the time needed to reach a solution. The difference lies in the
duration and variety of understanding strategies used by high, medium, and low achievers: high and
medium achievers employed a wider range of strategies, while low achievers primarily focused on
reading the problem and extracting the given information to understand the problem. This finding
aligns with prior research by Larkin and Reif [30] which emphasized that experts tend to use more
strategies during the understanding stage of problem solving, such as organizing detailed physical
descriptions or retrieving relevant information to guide their solutions.
In the planning category, clear differences emerged among high, medium, and low achieving
participants. Low achievers frequently jumped directly to execution without engaging in planning,
whereas medium achievers demonstrated some planning, though inconsistently. High achievers, in
contrast, exhibited a broader range of planning strategies, which enabled them to reach correct
solutions more effectively than the other two groups. This finding underscores the importance of
planning, consistent with Eichmann et al., [31] who reported that engaging in a planning phase at the
beginning of the problem-solving process leads to higher performance.
The findings suggest that all participants engaged in understanding, executing, and concluding
strategies, whereas planning, checking, and monitoring strategies were primarily observed among high
achievers.

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This reinforces prior research showing that successful problem solvers possess metacognitive
regulation planning, monitoring, and evaluating their learning processes, such as reflecting on progress
and verifying solutions which are key indicators of expertise [25], [32]–[35]. Izzati and Mahmudi [35]
reported that metacognition is essential for successful problem solving, which involves analyzing the
problem, planning a strategy, executing the plan, checking the correctness of each step, and monitoring
progress; students with higher metacognitive skills tend to perform better in problem solving. High
achiever participants demonstrated an ability to pause during execution, reflect on whether their
approach was making sense, and adjust their strategies accordingly. Medium achievers exhibited some
monitoring but did so sporadically, while low achievers showed little evidence of this behaviour. This
uneven distribution suggests that metacognitive monitoring is a distinguishing feature of higher-level
problem solvers. Schoenfeld [25] argued that expert problem solvers constantly regulate their progress
by asking themselves whether their current actions are moving them closer to the solution. Instructional
approaches such as think-aloud model, metacognitive prompts, and reflective questioning can help
foster these skills in novice learners. Checking and monitoring strategies are critical for ensuring the
validity of solutions and for detecting errors. The absence of these strategies among low and medium
achievers often led to incorrect solutions. This echoes findings from previous research showing that
novices frequently terminate problem solving once an answer—any answer—is obtained [36], [37].
Promoting a learning culture that emphasizes verification and reflection may encourage students to
view checking and monitoring as an integral part of the problem-solving process
In summary, the findings indicate that while students at all achievement levels are capable of
understanding and executing problem-solving steps, only high achievers engage consistently in
systematic planning, monitoring, and checking. This imbalance between lower-order strategies
(understanding and executing) and higher-order strategies (planning, monitoring, and checking) likely
contributes to the persistent differences in problem-solving performance among high, medium, and
low achievers. These results underscore the importance of fostering higher-order strategies in
instruction and suggest that explicitly teaching planning, monitoring, and checking may help students
across all achievement levels develop more effective and adaptive problem-solving skills.

4. Conclusion
This study examined students’ problem-solving strategies in kinematics and identified thirty
distinct strategies, which were grouped into six categories: understanding, planning, executing,
checking, monitoring and concluding. The findings indicate that while most students are capable of
understanding and executing, fewer engage in systematic planning, monitoring, and checking. The
imbalance between lower-order strategies (understanding and executing) and higher-order strategies
(planning, monitoring, checking) may explain the persistent gap in problem-solving performance
between high, medium and low achievers. Importantly, the recursive nature of the problem-solving
process observed in this study reinforces that effective problem solving is not a straightforward, stepby-step procedure but a flexible and adaptive process. High achievers demonstrated this adaptability
by moving back and forth between categories as needed, while lower achievers often proceeded
linearly and rigidly, leaving them unable to recover when errors occurred. The study contributes to
physics education research by providing a clearer framework for categorizing students’ strategies
across achievement level. This framework can guide explicit instructional design by modelling expertlike behaviours, encouraging multiple representations, scaffolding planning processes, and embedding
metacognitive prompts- monitoring and checking-into problem-solving tasks. Future research is
recommended to investigate how targeted instructional interventions can foster the use of these
problem-solving strategies across different physics topics and learning contexts.

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Acknowledgement
The authors wish to express their sincere gratitude to the Department of Physics Education, Universitas
Syiah Kuala, for the support and facilities provided during this study. Special thanks are extended to
the students for their time and cooperation, as well as to the lecturers of the Basic Physics I course for
their valuable insights.

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