Prima Magistra: Jurnal Ilmiah Kependidikan ISSN 2721-8112 .
Volume 7 Ae Number 1.
January 2026, pp 64-75 ISSN 2722-4899 .
https://doi.
org/10.
37478/jpm.
Open Access: https://e-journal.
id/index.
php/JPM/article/view/5810 WHEN THINKING FAILS: MISCONCEPTIONS AND THE ROLE
OF COGNITIVE DISSONANCE IN MATHEMATICS TEACHER
EDUCATION
Surya Sari Faradiba1*.
Alifiani2.
Fadhila Kartika Sari3.
Isbadar Nursit4.
Ruhaisa
Deramea5
1,2,3,4
Universitas Islam Malang.
Malang.
Indonesia Yala Rajabhat University.
Yala.
Thailand *Corresponding Author:
Article History Received : 29/05/2025 Revised : 03/09/2025 Accepted : 16/10/2025 Keywords:
Cognitive dissonance.
Conceptual change.
Mathematical Psychological resistance.
suryasarifaradiba@unisma.
Abstract.
Misconceptions in mathematics persist as a problem in teacher education, often rooted in unresolved cognitive conflicts.
This study aims to explore how cognitive dissonance contributes to the formation and persistence of mathematical misconceptions in a prospective mathematics teacher.
Conducted at a private university in Malang.
Indonesia, this research employs a qualitative case study design with one participant, purposefully selected based on prior conceptual errors.
Data were collected through task-based assessments and semi-structured interviews, and were then analyzed thematically.
The findings show that the participant exhibited stable misconceptions in key mathematical areas, particularly when encountering information that challenged prior beliefs.
Rather than adjusting or restructuring incorrect knowledge, the participant displayed psychological resistance through justification, minimization, and selective attention to confirming These mechanisms serve to reduce internal discomfort .
without engaging in conceptual change.
As a result, the erroneous mental model is maintained despite exposure to correct information.
This highlights the critical role of cognitive dissonance in reinforcing misconceptions through defensive cognitive strategies.
How to Cite: Faradiba.
Alifiani.
Sari.
Nursit.
, & Deramea.
WHEN THINKING FAILS:
MISCONCEPTIONS AND THE ROLE OF COGNITIVE DISSONANCE IN MATHEMATICS TEACHER EDUCATION.
Prima Magistra: Jurnal Ilmiah Kependidikan, 7.
, 64-75.
https://doi.
org/10.
37478/jpm.
Correspondence address:
Publisher:
Program Studi PGSD Universitas Flores.
Jln.
Samratulangi.
Jl.
Mayjen Haryono No.
Dinoyo.
Kec.
Lowokwaru.
Kota Kelurahan Paupire.
Ende.
Flores.
Malang.
Jawa Timur.
suryasarifaradiba@unisma.
primagistrauniflor@gmail.
INTRODUCTION
Mathematics education plays a crucial role in developing students' critical thinking and problem-solving skills (Al-Husban, 2020.
Catarino & Vasco, 2021.
Chan, 2022.
GacovskaBarandovska et al.
, 2020.
Hafni et al.
, 2019.
Rauscher & Badenhorst, 2021.
Vachova et al.
, 2023.
Yldz-Feyziolu & Kran, 2022.
Yulianto et al.
, 2.
However, various studies indicate that mathematical misconceptions remain a significant challenge, especially among prospective mathematics teachers.
These misconceptions can hinder the correct understanding of mathematical concepts and adversely affect the quality of future teaching practices (Moosapoor.
Rahaju et al.
, 2023.
Zhang et al.
, 2.
Moreover, previous research has suggested that misconceptions are not only due to a lack of knowledge but also to unresolved cognitive conflicts, known as cognitive dissonance (Harmon-Jones & Mills, 2.
Several studies have examined mathematical misconceptions from different perspectives, including psychological factors and effective instructional strategies to address them (Ancheta & Subia, 2020.
Aygyr & Ozdag, 2012.
Clement, 2.
However, there is still a limited understanding of how cognitive dissonance explicitly influences the persistence of misconceptions among prospective mathematics teachers.
Most existing research focuses primarily on identifying misconceptions without deeply exploring the psychological mechanisms that maintain them.
This gap underscores the need for research examining the role of cognitive dissonance in sustaining these misconceptions.
Addressing this research gap is essential to provide a more holistic understanding of the cognitive processes underlying mathematical misconceptions.
One domain where misconceptions frequently emerge and persist is algebra, a foundational subject in mathematics education that underpins higher-level concepts such as functions, equations, and abstract reasoning.
Algebra is Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea When Thinking Fails: Misconceptions and The Role of Cognitive Dissonance in Mathematics Teacher Education Prima Magistra: Jurnal Ilmiah Kependidikan Volume 7.
Number 1.
January 2026, pp 64-75 particularly important because it acts as a bridge between arithmetic and advanced mathematics, and misconceptions formed in this area can significantly hinder studentsAo long-term mathematical development (Faradiba et al.
, 2024.
Tiew et al.
, 2.
For prospective mathematics teachers, a robust understanding of algebra is critical not only for their own competence but also for ensuring accurate and practical instruction for future students.
Yet, studies have shown that even teacher candidates often struggle with basic algebraic concepts, misapply rules, or retain intuitive but incorrect beliefs from prior learning experiences.
The findings of this study are expected to inform the development of more effective teaching strategies that help prospective mathematics teachers resolve their cognitive conflicts and improve their conceptual understanding.
Therefore, this study aims to examine the role of cognitive dissonance in the formation and persistence of algebraic misconceptions in a prospective mathematics teacher at a private university in Malang.
By focusing on algebra, this research not only highlights a high-stakes area in mathematics learning but also sheds light on the psychological mechanisms, specifically cognitive dissonance and psychological resistance, that influence conceptual stability or change.
The main research question guiding this study is: How does cognitive dissonance contribute to the formation and persistence of algebraic misconceptions in a prospective mathematics teacher? RESEARCH METHODS This study employs a qualitative case study design to explore the cognitive dissonance a prospective mathematics teacher experiences regarding mathematical misconceptions.
The research was conducted at a private university in Malang during the 2024 academic year.
The subject was purposively selected based on prior identification of conceptual errors in mathematics One participant was selected for in-depth investigation, representing the population of prospective mathematics teachers who struggle with persistent misconceptions.
Data collection involved task-based assessments designed to elicit misconceptions and semi-structured interviews to explore cognitive and emotional responses related to conflicting knowledge.
These instruments allowed for an in-depth understanding of the participantAos thought processes, reasoning patterns, and justification strategies (Creswell & Guetterman, 2.
The task was designed to identify and elicit the participant's mathematical misconceptions, particularly in the domain of algebra (Figure .
The tasks were designed to represent common conceptual errors in symbolic manipulation, such as misapplication of the distributive property, incorrect simplification of algebraic expressions, and misuse of negative signs.
These tasks aimed to provoke intuitive but flawed reasoning, thereby triggering cognitive dissonance when participants encountered contradictions between their prior knowledge and formal mathematical The structure and objectives of each task component are shown in Table 1.
Although a total of seven tasks were prepared, the participant was given the flexibility to decide how many tasks to complete during the session.
This approach was adopted to maintain the participantAos emotional stability throughout the assessment process.
Ultimately, the participant chose to work on two tasks, which were sufficient to reveal significant misconceptions and cognitive-emotional responses for in-depth analysis.
Table 1.
Task Blueprint for Algebraic Misconception Assessment Indicator Item Format Purpose Errors symbolic Simplification and To symbolic manipulation misunderstandings in basic algebra Misapplication of Distributive problems To trigger dissonance by confronting distributive property with negative numbers intuitive but incorrect strategies Algebraic Incorrect simplification Combining like terms.
To uncover misconceptions and understanding of algebraic expressions variable substitution Misuse of negative signs Mixed-sign operations To expose intuitive errors and provoke cognitive conflict Aspect Copyright .
2026 Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.
0 International License.
Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea When Thinking Fails: Misconceptions and The Role of Cognitive Dissonance in Mathematics Teacher Education Prima Magistra: Jurnal Ilmiah Kependidikan Volume 7.
Number 1.
January 2026, pp 64-75 Figure 1.
Instructions and Tasks for Identifying Algebraic Misconceptions The semi-structured interview was designed to explore participants' cognitive and emotional responses to the mathematical tasks, with a specific focus on identifying signs of cognitive dissonance, psychological resistance, and the potential for conceptual change.
The interview questions were designed to probe how the participant justified their incorrect answers, whether they experienced discomfort upon recognizing inconsistencies, and how they processed corrective feedback.
By analyzing these responses, the study aimed to reveal internal conflicts and defense mechanisms that may sustain mathematical misconceptions.
The detailed structure of the interview components and their respective purposes is shown in Table 2.
Table 2.
Semi-Structured Interview Blueprint Indicator Sample Questions Purpose Discomfort when AuWhat did you feel when you To realizing the answer realized your answer was psychological conflicts with formal incorrect?Ay experienced by the participant Conceptual Openness to revising AuHas your understanding of To examine potential for after the concept changed after the conceptual change explanation?Ay Psychological Justification, denial, or AuWhy do you still believe your To of original answer is correct?Ay incorrect answer conceptual change Selective Preference for AuDo you trust your previous To detect confirmation bias information confirming method more than the new and prior beliefs explanation?Ay Aspect Cognitive The analysis of interview transcripts and field notes deepened understanding of participantsAo cognitive processes and behavioral responses during the task engagement and interview sessions.
This instrument focused on identifying observable indicators of cognitive dissonance, such as expressions of confusion or frustration, as well as verbal strategies reflecting psychological resistance, like justification or topic avoidance.
Additionally, reflective statements were analyzed to assess the participantAos potential for conceptual change, while repeated patterns across contexts helped evaluate the consistency of misconceptions.
The specific aspects, indicators, and observational purposes of this instrument are shown in Table 3.
The data analysis employed a grounded theory approach, with three coding stages: open coding, axial coding, and selective coding (Table .
In the open coding phase, data were broken down into discrete parts to identify initial codes that emerged directly from the participantsAo responses in task-based assessments, interview transcripts, and field notes.
These codes reflected specific instances of mathematical errors, emotional reactions, and cognitive behaviors.
Examples of open codes include MISC-DIST .
isapplication of distributive propert.
CD-EMODISCOMFORT .
motional discomfort signaling dissonanc.
, and PR-JUSTIFY .
ationalization of incorrect response.
Copyright .
2026 Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.
0 International License.
Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea When Thinking Fails: Misconceptions and The Role of Cognitive Dissonance in Mathematics Teacher Education Prima Magistra: Jurnal Ilmiah Kependidikan Volume 7.
Number 1.
January 2026, pp 64-75 Aspect Expression of Resistance Reflective Conceptual Table 3.
Interview Transcript & Field Notes Blueprint Indicator Data Source Purpose of Observation Signs of confusion.
Transcript excerpts To observe emotional responses frustration, or hesitation & non-verbal cues associated with cognitive dissonance Defensive language.
Interview transcripts To identify verbal manifestations of topic shifting, psychological resistance Attempts to reinterpret Reflective statements To detect moments of conceptual or revise prior concept during interviews reflection and restructuring Repeated errors or Cross-analysis To examine the stability and depth of reasoning across between tasks and misconceptions in varied problem different contexts In the axial coding phase, these open codes were organized into broader conceptual categories based on their relationships, particularly causal, strategic, and consequential ones.
For instance, codes such as PR-JUSTIFY.
PR-SELECTIVE, and PR-MINIMIZE were grouped under psychological resistance, while CD-EMO-DISCOMFORT and CD-AVOIDANCE were clustered under cognitive dissonance.
These categories provided a deeper understanding of the mechanisms by which the participant coped with conflicting information, often leading to the reinforcement rather than the resolution of misconceptions.
The final stage, selective coding, identified a core category that integrates and explains the central phenomenon observed across the data: "The persistence of mathematical misconceptions is sustained by cognitive dissonance and psychological resistance.
" All other themes and codes were interpreted as components that interacted to contribute to this central insight.
The process
revealed that although opportunities for conceptual change existed, they were frequently blocked by internal conflict and defensive reasoning strategies, thereby maintaining erroneous beliefs over Coding Category / Code
Phase
Open
MISC-DIST
Coding MISC-NEG
CD-EMO-DISCOMFORT
Table 4.
Coding Summary Description Source Misapplication the Task-based assessment distributive property Incorrect use of negative signs Task-based assessment Emotional discomfort Interview
indicating cognitive conflict
PR-JUSTIFY
Justification of incorrect answer Interview
OBS-NONVERBAL-CD
Non-verbal signs of confusion Field notes or hesitation CC-REFLECTIVE Attempt reconstruct Interview transcript Axial Cognitive Dissonance Cluster of emotional and From multiple open codes Coding cognitive conflict indicators Psychological Resistance Defense mechanisms against PR-JUSTIFY.
PRconceptual change MINIMIZE.
PRSELECTIVE Mathematical Misconception Conceptual errors shown across MISC-* codes Conceptual Change (Potentia.
Participant's openness to change CC-* codes or reflection Selective Core Category Misconceptions are sustained Integration of all axial Coding by dissonance and resistance RESULTS AND DISCUSSION The analysis of data from the task, semi-structured interviews, and the researcherAos field notes revealed several key findings regarding participants' mathematical misconceptions and the cognitive-emotional processes underlying them.
The results are organized thematically according Copyright .
2026 Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.
0 International License.
Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea When Thinking Fails: Misconceptions and The Role of Cognitive Dissonance in Mathematics Teacher Education Prima Magistra: Jurnal Ilmiah Kependidikan Volume 7.
Number 1.
January 2026, pp 64-75 to the axial codes: Mathematical Misconceptions.
Cognitive Dissonance.
Psychological Resistance, and Potential for Conceptual Change.
Persistent Mathematical Misconceptions Table 1 revealed stable misconceptions in fundamental algebraic operations, such as the distributive property (MISC-DIST) and handling of negative values (MISC-NEG).
The participant consistently expanded expressions like a .
incorrectly as ab c and often failed to apply the sign rules properly when performing algebraic subtraction.
These misconceptions were not momentary errors but persistent patterns across tasks.
"I always thought you could just multiply the first term and leave the rest.
it is what I have always done.
" (Interview transcrip.
This statement indicates the presence of a procedural script, a repeated cognitive routine that has become automatic but is conceptually flawed.
Rather than reflecting a misunderstanding due to a recent error or temporary confusion, this reveals a systematic misconception reinforced over time, possibly through prior uncorrected practice or instructional gaps.
This misconception is also evident in the participantAos written work, as shown in Figure 2.
Figure 2.
ParticipantAos written response showing a distributive property misconception Another consistent error emerged when subtracting negative numbers, particularly in expressions such as Oe5 Oe (Oe.
, where the participant concluded the result was Oe8.
This mistake, labeled MISC-NEG, shows a lack of conceptual understanding of the operation's directionality and sign rules.
The participant explained: "Subtracting a negative just makes the number smaller, doesnAot it? Because negative means less.
" This verbalization illustrates semantic interference: the participant draws on an intuitive but incorrect understanding of negativity as Augetting smaller,Ay without fully integrating the mathematical logic of double negatives.
These kinds of beliefs are often reinforced through everyday language, making them especially resistant to change.
solving this problem, the participant used a number line, interpreting movement to the right as addition and to the left as subtraction.
Starting at Oe5, the participant moved three steps to the left .
ecause of the subtractio.
, arriving at Oe8.
This misconception is visually evident in the participantAos number line representation, as shown in Figure 3.
Figure 3.
ParticipantAos number line showing a misconception with negative subtraction Moreover, the consistency of these misconceptions across different formats .
ymbolic expressions, word problems, and contextual task.
suggests that they are not context-dependent but rather reflect a core cognitive schema.
This schema appears immune to traditional corrective instruction unless cognitive conflict is explicitly triggered and sustained.
From the field notes, the participant was observed expressing confidence in incorrect answers and hesitating only when prompted with conflicting evidence.
This confidence, despite incorrect reasoning, is an important indicator that the misconception has become internalized and normalized, perceived as a AutruthAy within the learnerAos conceptual system.
Overall, this extended analysis suggests that the participantsAo misconceptions are not isolated or accidental but structurally embedded in their mathematical thinking.
As such, addressing them requires more than just error correction.
it necessitates disrupting entrenched mental models through carefully designed cognitive conflict, reflective questioning, and metacognitive scaffolding.
This aligns with theoretical perspectives that view conceptual change not as information replacement but as a reorganization of prior knowledge structures.
A structured summary of these findings, participant responses, and interpretations of their cognitive implications, can be seen in Table 5.
Copyright .
2026 Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.
0 International License.
Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea When Thinking Fails: Misconceptions and The Role of Cognitive Dissonance in Mathematics Teacher Education Prima Magistra: Jurnal Ilmiah Kependidikan Volume 7.
Number 1.
January 2026, pp 64-75 Table 5.
Summary of Persistent Mathematical Misconceptions Type of Participant's Code Task Interpretation Misconception Response MISC-DIST Misuse of a .
= AuI always thought Procedural misconception.
Distributive Property ab c just lacks multiply the first understanding of distribution term and leave the over addition.
MISC-NEG
Misunderstanding of Oe5 Oe (Oe.
AuSubtracting a Conceptual Negative Number = Oe8 negative just makes misunderstanding.
Operations the number smaller, everyday semantics with doesnAot it?Ay mathematical rules.
CONFIDENCE High confidence in Multiple algebra Confident tone and quick incorrect procedures answers despite errors SEMANTICEveryday language AuNegative means Semantic interference leads INT lessAy to resistance to formal mathematical logic mathematical interpretation.
Cognitive Dissonance When Confronted with Conflicting Information When correct solutions were introduced during the interview sessions (Table .
, the participant exhibited visible signs of discomfort and confusionAicoded as CD-EMODISCOMFORT and OBS-NONVERBAL-CD.
Rather than immediately reconciling the error, the participant hesitated, avoided eye contact, and often deflected the issue.
"I feel like IAove seen it done that way, but it just doesnAot make sense to me.
IAom not wrong, am I?".
Exemplifies not only confusion but also an emotional appeal for reassurance, rather than conceptual reconciliation.
This behavior aligns with FestingerAos theory of cognitive dissonance (Harmon-Jones & Mills, 2.
, which posits that individuals experience psychological discomfort when confronted with information that contradicts their current cognitive schema.
Instead of integrating accurate information, the participant exhibited subtle avoidance and began rationalizing the discrepancy, demonstrating cognitive resistance to change.
This reveals a crucial barrier in mathematics education: the resistance is not just a misunderstanding of content, but an emotional and psychological negotiation to preserve oneAos self-consistency.
These findings underscore that effective instructional interventions must address not only content clarity but also learnersAo emotional readiness to confront dissonant information.
A summary of the participantAos dissonance-related behaviors and interpretations is presented in Table 6.
Table 6.
Summary of Cognitive Dissonance Responses and Behavioral Indicators Code Observed Behavior Illustrative Quote Interpretation CD-EMOExpressed anxiety.
AuIt just doesnAot make Emotional DISCOMFORT verbal doubt, and sense to me.
IAom not resulting from conflicting emotional uncertainty wrong, am I?Ay knowledge and self-belief.
OBSAvoided eye contact.
AuNonverbal Nonverbal indicators of NONVERBALhesitated before behaviors responding, visible interview segmentsAy DIS-JUSTIFY Justified AuIAove seen it done Defense mechanism to misconceptions using that way before, vague reasoning maybe it depends on the method.
revising belief.
DIS-DEFLECT
Shifted focus away AuMaybe the question Avoidance strategy to from error.
changed is tricky, or I just protect self-concept and subject or gave vague didnAot read it right.
Ay Psychological Resistance Preventing Conceptual Change Instead of engaging in self-correction, the participant demonstrated resistance mechanisms such as justification (PR-JUSTIFY), minimization (PR-MINIMIZE), and selective attention to Copyright .
2026 Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.
0 International License.
Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea When Thinking Fails: Misconceptions and The Role of Cognitive Dissonance in Mathematics Teacher Education Prima Magistra: Jurnal Ilmiah Kependidikan Volume 7.
Number 1.
January 2026, pp 64-75 confirmatory evidence (PR-SELECTIVE).
These were identified in both the participantAos verbal explanations and reflective responses (Table .
"Maybe it is just a trick question.
In most cases, the way I do it still works.
" This remark exemplifies two resistance mechanisms: minimizing the importance of the contradiction and justifying the continued use of incorrect reasoning.
These behaviors not only reflect emotional self-preservation but also reveal a deeper inertia against conceptual change, as the learner avoids the cognitive effort required to revise faulty schema.
The resistance, therefore, is not rooted solely in misunderstanding but in the perceived psychological cost of acknowledging error.
As such, the participant's learning process is hindered by a desire to preserve cognitive comfort rather than pursue epistemic accuracy.
A summary of the resistance mechanisms and their expressions can be seen in Table 7.
Table 7.
Summary of Psychological Resistance Mechanisms Preventing Conceptual Change Code Observed Behavior Illustrative Quote Interpretation PR-JUSTIFY Rationalizing errors as AuIn most cases, the way I Justification is used to methodical variation or do it still works.
Ay maintain prior belief and avoid legitimate alternatives PRDownplaying the AuMaybe itAos just a trick Cognitive minimization to MINIMIZE relevance or significance question.
Ay reduce the need for mental of mistakes effort and self-correction.
PRFocusing on AuThis is just one Confirmation bias SELECTIVE confirming examples exception, but usually exposure to disconfirming dismissing my answer is accepted.
Ay evidence.
Limited but Observable Signs of Conceptual Change Although psychological resistance remained the dominant response, subtle moments of conceptual openness emerged during the interviews, suggesting the participantAos potential for meaningful change when appropriately supported.
These moments, coded as CC-REFLECTIVE, involved expressions of uncertainty, pauses in reasoning, and genuine self-questioning.
One participant's comment captured this shift: AuWait.
maybe IAom thinking of this wrong.
Is it because the sign is outside the bracket?AyAiindicating a moment of cognitive reflection rather than automatic defense.
Another revealing quote was.
AuNow that you explain it.
I see where I mixed it upA I guess I never really understood why it works that way.
Ay This admission reveals a crack in the cognitive armor, suggesting a realization that the prior understanding was procedural rather than conceptual.
Though brief, such reflective moments offer critical leverage points for instructional intervention.
They suggest that conceptual change is possible, mainly when dissonance is addressed with scaffolding rather than confrontation.
A summary of these findings is shown in Table 8.
Table 8.
Summary of Limited but Observable Signs of Conceptual Change Observed Illustrative Quote Interpretation Behavior CC-REFLECTIVE Engaging in self- AuWait.
maybe IAom thinking of Reflective questioning and this wrong.
Is it because the sign indicates re-evaluating own is outside the bracket?Ay openness to conceptual CC-REFLECTIVE Admitting lack of AuNow that you explain it.
I see Suggests a shift from conceptual where I mixed it upA I guess I procedural to conceptual never really understood why it awareness.
works that way.
Ay CDExpressing AuI hadnAot thought about that.
Emergent awareness of INTELLECTUAL intellectual doubt That could be why it doesnAot conflict between prior belief without emotional work.
Ay and new concept.
OBS-VERBALPausing or Silence or trailing off mid- Non-verbal cue suggesting PAUSE hesitating during sentence Code Copyright .
2026 Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.
0 International License.
Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea When Thinking Fails: Misconceptions and The Role of Cognitive Dissonance in Mathematics Teacher Education Prima Magistra: Jurnal Ilmiah Kependidikan Volume 7.
Number 1.
January 2026, pp 64-75 This study provides a comprehensive insight into how cognitive dissonance influences the formation and persistence of algebraic misconceptions in a prospective mathematics teacher.
Algebra is a critical mathematical domain that demands a solid conceptual foundation to enable learners to handle abstract symbols and operations confidently (Chimoni et al.
, 2023.
Chimoni & Pitta-Pantazi, 2017.
Mathaba et al.
, 2.
The task-based assessment (Table .
revealed that the participant consistently held misconceptions about fundamental algebraic operations, including the distributive property and the manipulation of negative numbers.
These persistent errors are particularly problematic because they reflect entrenched mental models that conflict with formal algebraic rules (Burigana & Vicovaro, 2020.
Fific et al.
, 2010.
Moreton et al.
, 2017.
Tondorf & Prediger, 2022.
VanLehn et al.
, 2.
, thereby negatively impacting future teaching quality.
When confronted with correct solutions during interviews (Table .
, the participant showed clear signs of cognitive dissonance, including emotional discomfort (CD-EMO-DISCOMFORT) and nonverbal avoidance (OBS-NONVERBAL-CD).
This confirms FestingerAos theory that cognitive dissonance arises from the psychological tension created by conflicting knowledge (Harmon-Jones & Mills, 2.
The participantAos hesitation and justifications, such as "IAom not wrong, am I?", illustrate the emotional struggle inherent when established algebraic misconceptions are challenged.
This emotional discomfort serves as a psychological barrier to accepting new, correct information and is closely linked to the persistence of errors.
Further exploration of participantsAo responses revealed strong psychological resistance mechanisms (Table .
, including justification, minimization, and selective attention to confirmatory evidence (PR-JUSTIFY.
PR-MINIMIZE.
PR-SELECTIVE).
Instead of critically examining and restructuring their algebraic understanding, the participant minimized the importance of conflicting information by framing it as an exception or trick question.
Such resistance aligns with previous findings indicating that learners often protect their existing knowledge frameworks by dismissing contradictory evidence, thereby avoiding the cognitive effort needed for conceptual change (Barzilai & Chinn, 2024.
Deng et al.
, 2019.
Elliott et al.
Field et al.
, 2014.
Fific et al.
, 2010.
Liu et al.
, 2024.
Rubenstein-Montano et al.
, 2001.
Shi et al.
, 2020.
Verhagen et al.
, 2014.
Wan et al.
, 2021.
Wu & Jia, 2.
In the context of algebra, this resistance perpetuates misconceptions and limits the learnerAos ability to develop flexible problem-solving strategies.
However, the data also indicated limited but observable signs of conceptual change (CCREFLECTIVE), where the participant engaged in self-questioning and tentative re-evaluation of their algebraic thinking.
For instance, remarks like "Wait.
maybe IAom thinking of this wrong.
it because the sign is outside the bracket?" suggest moments of cognitive openness.
These reflective episodes, though brief, are crucial for conceptual change according to Posner conceptual change theory, which emphasizes that cognitive conflict must be accompanied by motivation and scaffolding to facilitate restructuring of misconceptions (Van Hoof et al.
, 2.
This highlights the potential for cognitive dissonance to act not only as a source of resistance but also as a catalyst for deeper understanding, provided learners receive appropriate support.
Addressing the research question, cognitive dissonance contributes to the formation and persistence of algebraic misconceptions by triggering psychological discomfort that leads to defensive cognitive strategies rather than productive conceptual change.
The participantAos stable misconceptions, despite repeated exposure to correct algebraic methods, exemplify how cognitive dissonance fuels resistance mechanisms that maintain faulty knowledge.
This interplay between cognition and affect illustrates why misconceptions in algebra are remarkably resilient and difficult to overcome without targeted instructional interventions.
Implications for teacher education are clear: effective algebra instruction must extend beyond procedural training to include strategies that help prospective teachers recognize and manage their cognitive and emotional responses to conflicting information.
Techniques such as explicit conceptual explanations, metacognitive reflection, and scaffolded problem-solving can help reduce psychological resistance and promote meaningful conceptual change (Fund & Madjar, 2018.
Gidalevich & Kramarski, 2019.
Metsymuuronen & Rysynen, 2018.
Zheng et al.
By fostering an environment in which cognitive dissonance is constructively addressed.
Copyright .
2026 Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.
0 International License.
Surya Sari Faradiba.
Alifiani.
Fadhila Kartika Sari.
Isbadar Nursit.
Ruhaisa Deramea When Thinking Fails: Misconceptions and The Role of Cognitive Dissonance in Mathematics Teacher Education Prima Magistra: Jurnal Ilmiah Kependidikan Volume 7.
Number 1.
January 2026, pp 64-75 teacher educators can better prepare future mathematics teachers to develop robust, accurate algebraic understanding.
CONCLUSIONS AND SUGGESTIONS
This study reveals that cognitive dissonance plays a pivotal role in the formation and persistence of algebraic misconceptions in a prospective mathematics teacher.
The participantAos emotional discomfort and psychological resistance when confronted with conflicting information demonstrate how entrenched misconceptions are maintained through defensive cognitive strategies such as justification, minimization, and selective attention.
However, limited moments of reflective questioning suggest that conceptual change is possible if supported by appropriate instructional scaffolding.
These findings highlight the complex interplay between cognitive conflict and emotional responses in learning algebra, emphasizing the need for teacher education programs to address both aspects to foster meaningful conceptual understanding.
Despite its contributions, this study has several limitations.
The research was conducted with a single participant, limiting the generalizability of the findings to a broader population of prospective mathematics teachers.
Additionally, the qualitative case study design, while providing rich and in-depth data, relies heavily on subjective interpretation, which may introduce researcher bias.
The study focused solely on misconceptions within algebra, so findings may not extend to other areas of mathematics or educational contexts.
Lastly, the use of task-based assessments and interviews may not capture all cognitive and emotional processes involved in misconception persistence.
Future research should involve larger and more diverse samples of prospective mathematics teachers to examine whether the identified patterns of cognitive dissonance and psychological resistance are consistent across different individuals and contexts.
Longitudinal studies could provide insight into how these processes evolve over time and in response to targeted interventions.
Additionally, investigating the effectiveness of specific instructional strategies designed to manage cognitive dissonance and facilitate conceptual change in algebra would be valuable.
Finally, expanding the scope to include other mathematical domains or comparing pre-service and in-service teachers could enrich understanding and improve teacher preparation programs ACKNOWLEDGMENT The authors gratefully acknowledge the financial support provided by the Faculty of Teacher Training and Education.
Universitas Islam Malang (UNISMA), through an internal research grant awarded under the DeanAos Decree No.
525/G152/U.
07/D/L.
16/I/2025, dated January 15, 2025.
REFERENCES