The research began with a study that utilized a quasi-experimental approach to in- vestigate the impact of a technology-assisted learning model on the mathematical problem- solving ability (MPSA) of class XI students at a high school in Bintan, Indonesia. The find- ings indicated a significant improvement in the students’ MPSA due to the use of the tech- nology-assisted model. However, none of the students fell into the high or very high MPSA category (Table 1). This finding suggested that the students may have faced challenges, leading to errors in their response to the non- story mathematics problems provided.

The participants were selected based on purposive sampling criteria, which included their readiness to participate (evidenced by re- taining their answer sheets and active partici- pation in the classroom), willingness to be in- terviewed, and the potential value of the infor- mation they could provide (Etikan, 2016). Four female participants who met these crite- ria were selected. There is no correlation be- tween sample size and study quality in phe- nomenological research (Bartholomew et al., 2021). The participants were categorized based on their MPSA levels (Table 1).

Table 1 shows that most students fall into the low MPSA category. However, from the initial participant selection, only four partici- pants met the criteria. Table 2 describes the four participants’ MPSA level.

The instrument in qualitative research is the researchers themselves (Wa-Mbaleka, 2020). However, other instruments were used to collect research data, such as the non-story MPS test. This test presents open-ended problems to the students. Table 3 shows the non-story MPS test problems provided to the students.

The validity of this test was confirmed through the expert judgment of three experi- enced mathematics teachers with over 10 years of teaching experience each. The esti- mation of Aiken’s V was 0.75 for every item, indicating moderate validity (Retnawati, 2016). Additionally, the test’s validity was supported by estimating reliability (α and ω coefficients) and conducting item analysis. In item analysis, discriminatory power (Pearson correlation/p) and level of difficulty (T) were estimated. Table 4 presents the item anlysis results, reliability estimation, and the decision for the MPS test instrument.

The research procedure followed qualita-tive research protocols, which included the following steps: (1) ensuring all research-re-lated legalities are addressed, ( 2) developing a non-story MPS test and listing opening questions for the interview, (3) validating the test instrument, (4) analyzing test items, ( 5) revising the test, (6) collecting data, (7) ana-lyzing the data, (8) presenting the findings, and ( 9) drawing conclusions.

In this research, the data collection techniques employed included tests and nontests. The test technique has been previously ex-plained. Non-test techniques involved obser-vation, documentation, and unstructured in-terviews. The researchers also used the trian-gulation method to ensure the truth value of the data (Carter et al., 2014)(Lopez & Whitehead, 2014).

The observations were conducted by ob- serving students during a mathematics class. The documents collected comprised student answer sheets, a list of attendees, and students’ score lists. Observations and docu- ment collections were conducted to gather background information and assess the stu- dent’s potential data value contribution for in- terviews. Additionally, unstructured, in-depth phenomenological interviews were conducted to gather information on the participants’ ex- periences, feelings, and beliefs (Groenewald, 2004).

Phenomenological interviews offer a glimpse into universal essences and eidetic structures (Aguas, 2022). In this study, the in-terviews were conducted through the Zoom meeting application. The participants permit-ted the interviews to be recorded, and the con-versations were transcribed verbatim (Aagaard, 2017).

The data analysis phase followed (Aguas, 2022) analysis steps, which combine Moustaka’s transcendental phenomenological data analysis and Van Manen’s hermeneutic approach. The researchers used the NVIVO 12 (trial version) software for the data analy- sis. The data analysis procedure by (Aguas, 2022) is outlined in Table 5.

The descriptive MPS model by Rott- Specht-Knipping consists of an understanding (analysis) phase, an exploration phase, a plan- ning phase, an implementing phase (some- times combined with planning), and a verifi- cation phase. This model captures the full range of possible processes in students’ MPS in a non-linear way, making it more flexible than the normative MPS model. Table 6 pre- sents indicators for each MPS phase based on Rott-Specht-Knipping’s framework.

Next, after identifying the indicators for each MPS phase, the students' answer sheets were analyzed based on these indicators to determine the MPS process followed. Table 7 presents the sequence of participants’ MPS process in answering mathematics prob- lems as reflected in their answer sheets.

Table 7 shows that only RS1 provided complete answers to all the problems. RS1 also utilized validation methods to confirm her answers, except for item 2 (problem 2). Meanwhile, RS2 and RS3 did not find a solution for problem 4, while RS4 only succeeded in solving problem 1.

Moreover, RS1 demonstrates greater consistency in executing the MPS process than RS2, RS3, and RS4 by following the A→P→I→V process, except for problem 2. RS1 and RS3 also engaged in the exploration phase at problem 1, while RS2 and RS4 did not. Additionally, RS2 and RS3 are more prominent in the MPS A→P→I process, whereas RS4 excels in the analysis phase.

Furthermore, RS1 exhibits the most tran-sitions between phases, namely A→P→E→I→E→V for addressing problems 1 and 2. These processes align with the flow and transitions outlined in Rott-Specht-Knipping's descriptive MPS model (Rott et al., 2021). Students need to know that solving a math problem involves a flexible and adap-tive approach, where they can navigate back and forth to determine the most effective solution (García et al., 2019).

The online interviews were conducted at the end of June 2024. Once all participants joined the Zoom call, they were placed in breakout rooms for individual interviews. The participants were enthusiastic when asked about their well-being, demonstrating their willingness and readiness for the interviews. On average, the interviews lasted approxi-mately 22 minutes.

All participants were highly active students in the classroom and had good communication skills. They also remembered the top-ics tested in the Mathematics Specialization subject, including circle formulas, positions of lines, and the tangents to a circle equation. They found the instructions on the question sheet, particularly in the recommended an-swer format section, to help answer non-story mathematics problems. RS3 provided the following statement:

“It was useful, sir. For example, if we don’t have enough information, we won’t know what to ask about, and what plans to make. So, we also can’t answer the question. Of course, the first thing we need to do is understand the provided information first, then we can figure out what the question is asking about. After we know what is being asked, we can determine which formula we can use.”

However, as shown in Table 7, it is evi- dent that not everyone adheres to the recom- mended answer format, including RS3. This finding suggests that the students faced obsta- cles that prevented them from presenting an- swers in the recommended format.

Nevertheless, all participants clearly understood the questions posed in each problem. RS1, RS2, and RS3 confidently stated they had no issues and answered problem 1 cor-rectly. RS4 also claimed the same but strug-gled with problem 1.

RS1, RS2, and RS4 encountered difficul- ties in problems 2, 3, and 4, while RS3 faced challenges in points 3 and 4. These initial findings shed light on potential obstacles, prompting a deeper investigation. The results of the analysis of students’ errors in solving mathematics problems are presented in Table 8

Table 8 shows that the initial error oc- curred because the participant made an analy- sis error. Lester’s research indicates that an individual’s analysis or understanding phase significantly impacts their MPS performance (Pugalee, 2001) The analysis phase, which involves understanding and defining the prob- lem, is crucial in the MPS process and en- gages various parts of the brain (Anderson et al., 2014). Therefore, if this phase is flawed, students may encounter errors when progress- ing to the next phase. The relationship be- tween all types of errors is shown inFigure 1.

Figure 1 shows that no exploration errors were detected because the exploration phase was exclusively conducted on problem 1 by RS1 and RS3 (Table 7). Additionally, there were planning errors stemming from carelessness. This finding aligns with the definition of carelessness provided by (Clements, 1982), where RS1 responded accurately during the planning phase in the interview but presented the work incorrectly on the answer sheet.

(White, 2005) also categorizes careless- ness as a common error in solving mathemat- ics problems. In addition,(Ken) Clements, 1980) discovered that carelessness can lead to other errors. A hierarchy of participant er- ror types was established for answering non- story mathematics problems, as shown inFigure 2.

In Figure 2, the percentage of verification errors was the lowest, as some participants did not complete the verification phase for certain problems. Some students dislike using verifi- cation methods to check their answers (García et al., 2019). This sentiment has been sup- ported by previous studies, such as those con- ducted by (Cleary & Chen, 2009) and (García et al., 2016).

After identifying the types of errors in re-sponding to non-story mathematics problems, the participants were interviewed about the factors that led to these errors. Before the in-terview, RS1 acknowledged some of her er-rors by promptly stating, "That was incorrect [in point 2, implementation error]." The other three participants did not exhibit the same behavior. Consequently, the participants were categorized into two themes: those conscious of their errors and those who were not. This finding was also found in previous studies, such as the study by (Adinda et al., 2021).

The students' ability to realize errors can be trained by giving them self-reflective activities. Engaging students in self-reflective activities can enhance their ability to recognize errors, improving focus, motivation, and learning engagement (Karaali, 2015). This ac-tivity can also improve the students' MPS per-formance (Kwon & Jonassen, 2011).

Next, the interview transcripts were ana- lyzed using the Aguas steps, and all previous types of coding were incorporated. Following the analysis, the relationship between the fac- tors was derived from the identified themes, categories, and sub-categories. The results of this analysis are presented in Figure 3.

Figure 3 shows five themes affecting the students’ errors in solving non-story MPS problems: MPS abilities, cognitive condi- tions, affective conditions, motivation, and self-awareness. Research has shown a recip- rocal relationship between cognitive and af- fective conditions (Trezise & Reeve, 2014) This finding is supported by case studies conducted by (Furinghetti & Morselli, 2009), which validate Schoenfeld’s assertion that cognition and affect in MPS are intercon- nected. In addition to these two themes, other themes may also be interrelated.

1) MPS Ability (MPSA) Domain

For the error factor based on MPS ability (MPSA), almost all participants did not ex- plore the mathematical problems (Table 7). The exploration phase in solving mathematics problems typically involves visual represen- tions of crucial information. Skipping this phase can reflect students’ MPS abilities, as stated by (Krawec, 2014).

The lack of exploration is considered an error factor because, according to Schoenfeld, exploration is the heuristic core of MPS (Rott et al., 2021). (Rott et al., 2021) also indicated that the exploration phase was observed at least once in non-routine problems. These studies highlight the significance of the explo-ration phase in addressing mathematics problems.

Furthermore, it was observed that in several instances, participants completed only the planning phase of the problem-solving process without progressing to the exploration phase, which is crucial for thoroughly analyzing and testing potential solutions. This incomplete approach significantly impacted their ability to arrive at correct solutions for the non-story mathematics problems. Specifically, all problems attempted without the exploration phase resulted in incorrect or incomplete solutions, highlighting the importance of engaging with the exploration phase to verify and refine initial ideas ((Hardini et al., 2021); (Darmawan & Suparman, 2019)). Moreover, a pattern of errors was evident in those problems that had not undergone the exploration phase, suggesting that skipping this step led to fundamental misunderstandings or overlooked aspects of the problems ((Khusnani et al., 2023); (Kurniawan et al., 2022)). The only exception to this trend was observed in RS2 in Problem 1 (refer to Table 8), where the participant's planning alone appeared sufficient to generate the correct solution. These findings underscore the critical role of the exploration phase in the problem-solving process, as it allows for the testing and modification of initial plans, ensuring a more robust and accurate solution.

2) Cognition Domain

For the cognition domain, the following factors contributed to the students' errors: lack of understanding, confusion, dead mind, and misinterpretation. The issue of confusion was also identified in a study conducted by Ruzlan, Rosalinda, and Arsaythamby in 2013 (Veloo et al., 2015). These factors can hinder comprehension of concepts or schema. Sub-stantial evidence indicates that domain-spe-cific knowledge, in the form of schemas or concepts, is the key factor that sets experts apart from novices in MPSA (Sweller, 1988)(Veloo et al., 2015).

Furthermore, evidence was found of the influence of other cognitions in terms of students’ cognitive styles (field-dependent, intermediate, and independent) influencing MPSA linearly (Ulya, 2015). If there are is- sues with understanding the concepts or sche- mas, students may struggle to grasp the prob- lems and may even be unable to attempt to solve them (Rhodes, 1987). For instance, RS4 faced challenges in comprehending concepts related to points 2, 3, and 4, limiting progress to the analysis phase (refer to Table 7 and Table 8).

3) Affective Domain

The identified factors related to affective conditions include feeling tense, the demand to answer, ambition, and nervousness. This domain has been extensively studied in con-nection with MPS, as demonstrated in re-search by (DeBellis & Goldin, 2006), which categorizes affection into beliefs, attitudes, emotional states, and ethics/morals/norms. Based on the interview results, only RS3 did not exhibit any affective conditions, while RS1, RS2, and RS4 were nervous.

4) Motivation Domain

RS1 felt nervous because she felt she was demanded to answer the question, she said; "I was just nervous because it was like I was be-ing forced [pressured]. It seems like the ques-tion is difficult," and "The important thing is to answer." RS2 felt tense, nervous, and am-bitious, she said; "Nervous and afraid of mak-ing errors. I used the wrong formula, sir," and "I want to try to get good grades, sir." Mean-while, RS3 did not feel any affection, and RS4 felt nervous. Apart from RS3, the other par-ticipants expressed epistemic emotional states, namely emotions whose object is fo-cused on knowledge and meaning (Muis et al., 2015).

Motivation plays a significant role in students' MPSA and performance. (Irhamna et al., 2020) found that motivation accounted for 15.8% of students' MPSA. Similarly, (Fatimah et al., 2019) reported that motivation signifi-cantly impacted students' MPSA. Research has shown that motivation, mediated by self-efficacy, impacts students' MPS performance (Özcan & Eren Gümüş, 2019).

In contrast to the research by (Ken) Clements, 1980), which considered motivation as a type of error, this study identified motivation as a contributing factor to errors, and is divided into two parts: laziness and cheating intention. Laziness was found in RS1 as she said she was "Lazy to re-read [questions]" in point 2. Thus, the student was careless, which led to planning errors.

Moreover, (Pavlin-Bernardić et al., 2017) found that motivation is closely linked to active cheating. Cheating intention is key in actively seeking to cheat to enhance one’s success. Cheating intentions were found in RS2, RS3, and RS4, who admitted they had such intentions. The three participants stated that they failed to act on their intentions. RS2 said this was due to the lack of time; she said:

“Maybe, yesterday it was number four, because it wasn’t filled, right. [Whispering to friend] Help! But [in the end] it wasn’t filled either. Because the time is up”.

RS3 and RS4 stated that they failed to act on their cheating intention because their friends also did not find a solution, as RS3 said

“There are a few codes [or whispering to friends]. In the end, he/she didn’t know either, so we just had to answer it ourselves”.

5) Self-Awareness Domain

For the self-awareness domain, two factors were identified: time management and lack of preparation. According to (Blakemore & Frith, 2003), self-awareness of certain actions is influenced by various aspects, such as awareness of intention and a sense of agency. Self-awareness accuracy is also expected to improve with age (Demetriou & Kazi, 2006). Therefore, time management and lack of preparation fall under these two overlooked aspects and that there is an element of intentionality carried out by students.

Other than RS4, the other three participants complained that they ran out of time to solve the problems. RS2 mentioned, “Yeah, there was not enough time, sir. Because I was thinking about the previous question, sir. So, I didn’t get to fill in number 4.” Additionally, RS1 and RS4 felt that they had not prepared themselves enough to face these non-story mathematics problems. RS4 stated, “Yes, I didn’t prepare myself well for this test, sir.”