The Relationship between Mathematics Teachers’ TPACK and Students' Mathematical Resilience

. Previous research shows that teachers play a role in determining students' math resilience. However, there is still little research on the type of teacher competencies that support students' mathematical resilience. This study examines the effect of mathematics teachers’ Technological Pedagogical Content Knowledge (TPACK) on students' math resilience. This quantitative study involved 163 students from a junior high school and four senior high schools in the East Kalimantan region. Data was collected through questionnaires that measured mathematics teachers' TPACK from the student perspective and students’ math resilience. Information about the gender of respondents is also collected. Data were analyzed using multiple linear regression and moderated regression. The results exposed that the mathematics teachers’ TPACK significantly affected students' math resilience. The components of Pedagogical Knowledge and Technological Pedagogical Content Knowledge partially affect students' math resilience. However, the study found no moderation by student gender on the relationship between mathematics teachers' TPACK and students' math resilience. This study contributes significantly to understanding the role of mathematics teachers' TPACK in improving students' math resilience. The results can be a reference for related parties, especially in developing more effective mathematics teacher training and competency development programs.


Introduction
One of the negative impacts of the abrupt implementation of online learning during the Covid-19 pandemic is that students' mathematics achievement tends to be low (Ariyanti & Santoso, 2020;Mahfud, Mardiyana, & Fitriana, 2021;Tambunan, 2021).Since math achievement commonly represents students' competency in mathematics, low math achievement during online learning indicates that mathematical knowledge and skills were not well grasped.Moreover, the range of knowledge and skills that should be achieved also become narrower as the policy of the Indonesian government to simplify the curriculum during the pandemic (Pedoman Pelaksanaan Kurikulum pada Satuan Pendidikan dalam Kondisi Khusus, 2020) so that schools only focus on essential mathematics competencies and content for students (Zhao, 2022).It is feared that once offline learning resumes, the focus will shift back to a normal curriculum with an emphasis on more math skills (Pusat Penelitian Kebijakan Badan Penelitian dan Pengembangan dan Perbukuan Kemdikbudristek, 2021).Since the mathematics curriculum is arranged hierarchically and structurally from the simplest to the most complex (Maharani & Retnowati, 2020), the loss of several competencies during the pandemic can be a challenge for students when entering post-pandemic learning, that is, difficulties in succeeding to the next level of learning mathematics.
Apart from the need to review previous knowledge and skills, facing challenges in learning mathematics also demands a constructive mindset, exemplified by math resilience.
One factor that affects students' mathematical resilience is their teachers.Several qualitative studies described the role of math teachers in students' math resilience.A study by Khumalo, Van Staden, and Graham (2022) explained that a caring teacher is a teacher who understands students' difficulties and motivates them so that they become resilient.Moreover, a study by Pulungan, Retnawati, & Jaedun (2022) showed that teachers are essential in overcoming students' difficulties in learning mathematics through the teachers' openness to questions.The findings of Jameson (2020) also indicated that one source of maths anxietyrelated to math resilience-is the teachers' teaching style.Hence, the mathematics teachers' competency affects students' math resilience levels.
Quantitatively, a study by Pitzer and Skinner (2017) showed that teacher support is crucial in building students' motivational resilience.In addition, the findings of Bykova and Chirkina (2020) indicated that positive teacher-student relationships, including listening, appropriate treatment, and helpfulness, are positively related to students' resilience.These qualitative and quantitative researches show that many teachers' attributes may related to students' math resilience.Identifying significant teacher competencies for students' math resilience is ongoing.
However, an adequate framework of teacher competency is needed to provide more clarity and confidence in identifying these competencies.
The teacher competency framework that researchers consider relevant to the current learning situation is the Technological Pedagogical Content Knowledge (TPACK) framework.
The TPACK framework was developed from the Pedagogical Content Knowledge (PCK) competencies.Competence in the TPACK framework is the knowledge of teachers based on three domains of knowledge that influence each other and intersect technological, pedagogical, and content knowledge (Voogt, Fisser, Pareja Roblin, Tondeur, & Van Braak, 2013).
A study by Moore-Adams, Jones, and Cohen (2016) suggested that mastering technology is vital in delivering material and supporting students.A study by Lyakhova and Joubert (2022) also proved that teachers' skills in implementing blended learning determine students' math resilience.Regarding mathematics content knowledge, many students struggle with learning mathematics because they have difficulty comprehending its content., so teachers' content knowledge should be able to help students overcome it (Zhu & Kaiser, 2022).Regarding pedagogy, the teachers' capacity to motivate and build students' confidence plays a role in addressing negative attitudes toward mathematics, such as anxiety, fear, and lack of selfconfidence (Pajares, 2003).These previous studies indicate that the TPACK framework is related to students' math resilience.
Besides being influenced by external factors, students' math resilience levels can also stem from personal characteristics like gender.Several studies showed the inconsistency of the students' math resilience differences based on gender (Az Zahra & Hadi, 2022;Rahmawati & Kismiantini, 2022;Ricketts, Engelhard, & Chang, 2017), while some math anxiety as an antithesis of math resilience-studies show that girls have higher math anxiety than boys (Devine, Fawcett, Szucs, & Dowker, 2012;Dowker, Sarkar, & Looi, 2016;Luttenberger, Wimmer, & Paechter, 2018).Also, several studies showed that gender stereotypes can influence how teachers treat their students (Gilchrist & Zhang, 2022;Mwamwenda, 2011).Thus, gender must be examined as a moderator in the relationship between mathematics teachers' TPACK and students' math resilience.Nevertheless, the relationship also has not been investigated.By using the TPACK framework, this study aims to fill the gap of the unspecific teacher competency framework from the previous studies.This study also investigates the contribution of gender as a moderator in the relationship.Concordantly, this study has contributed in three ways.First, it confirms the vital role of teachers in establishing math resilience.Second, it identifies mathematics teachers' competencies significant to math resilience.Third, it enriches insight into the contribution of gender to mathematics attitude.

Method
This study is correlational research (Creswell, 2012).This study used a multiple linear regression model to investigate the relationship between mathematics teachers' TPACK and students' math resilience (Figure 1a).The study suggests that math teachers' TPACK components, including Technological Knowledge, Pedagogical Knowledge, Content Knowledge, Technological Pedagogical Knowledge, Technological Content Knowledge, and Technological Pedagogical Content Knowledge, impact students' math resilience.Additionally, a moderated regression analysis was used to examine the significant contribution of gender to the relationship (Figure 1b).Math resilience was measured by a questionnaire from Wibowo, Slamet, and Sudjadi (2018), which was adapted from Sumarmo ( 2016) and Lee and Johnston-Wilder (2017).The questionnaire consists of 33 items on a Likert scale (1-5), including six indicators: good aid givers; easy to socialize; adaptive to their environment and willing to discuss with their peers; confident, hard-working, persevering, and not giving up when faced with failure, obstacles, and uncertainty; strive to come up with creative solutions and fresh ideas to challenges; good self-control and being aware of his feelings; self-motivation from the experience of failure; high curiosity, reflective spirit, researcher, and skilled in using various learning resources.Based on the validity and reliability test, this instrument was valid (sig < 5%) and reliable (ɑ = 0.884).
Google Forms were used to design and distribute both instruments via math teachers to junior and senior high school students in East Kalimantan.One hundred seventy responses filled out the questionnaire, but only 163 responses were used for analysis as seven did not clearly state their gender on the questionnaire.The description of respondents based on gender, district/city origin, school status, and school level is presented in Table 1.The data were analyzed in three steps.The first step is analyzing data descriptively and categorizing the mathematics teacher competence and student math resilience level based on Table 2 (Ebel & Frisbie, 1991).Then, multiple linear regression analysis examined the relationship between mathematics teachers' TPACK and students' math resilience.Finally, moderated regression analysis examined the significance of students' gender in moderating the relationship.
Which X is the respondent' score,  ̅ is the mean of the respondents' score, and s is the standard deviation.

Results and Discussion
This study examined the relationship between mathematics teachers' TPACK and students' math resilience and whether gender moderates the relationship.The descriptive analysis of mathematics teachers' TPACK and students' math resilience are presented in Table 3 and Figure   2. The results of multiple linear regression analysis and moderated regression analysis are presented in Table 4 and Table 5.
The results of the descriptive analysis (Table 3) show that respondents appraised their mathematics teacher competence as very high, both overall and by gender.Most respondents appraised their math teachers as having excellent teaching skills within the TPACK framework, according to the distribution of respondents by the level of mathematics teacher competency assessment depicted in Figure 2a.This finding is similar to several studies from various subjects and levels of education (Nisa, Ramadhan, & Thahar, 2023;Quyen, 2022).Table 3 illustrates that, despite varying student levels, respondents generally perceive teacher competencies similarly (mean > standard deviation).The t-test concludes that there was no significant difference between male and female respondents' perceptions of mathematics teachers' TPACK either in general or The insignificant difference was also found in a study by (Efilti & Çoklar, 2013), which indicated that teachers treat their students the same way without gender discrimination.Table 3 indicates that respondents had high math resilience overall and by gender.In addition, Figure 2b shows that around 60% of respondents have high or very high levels of mathematical resilience.The results suggest that respondents have a positive attitude toward learning mathematics when encountering challenges.Since the data was collected after the pandemic, it was surprising that students did not struggle with math.This level of math resilience is higher than that of students in Zanthy, Kusuma, and Soemarmo (2019).In addition, as perceived teacher competencies, respondents' assessment of their math resilience also tends to be the same (mean > standard deviation).The t-test concludes that there was no significant difference in math resilience levels between male and female respondents (p-value = 0,52).The multiple linear regression analysis (Table 4) showed that the mathematics teachers' TPACK simultaneously affects students' mathematical resilience, while only the components of Pedagogical Knowledge (p-value = 0.01) and Technological Pedagogical Content Knowledge (pvalue = 0.04) had a partial effect.The regression coefficient indicates a positive relationship between two significant TPACK components and math resilience.This means that teachers' instructional capabilities, integration of pedagogical, mathematical content knowledge, and technological competency are essential for building students' resilience in mathematics.
While previous studies have indicated the important role of mathematics teachers in building students' math resilience (Bykova & Chirkina, 2020;Jameson, 2020;Khumalo et al., 2022;Pitzer & Skinner, 2017;Pulungan et al., 2022), this study emphasizes which teachers' competencies are influential: pedagogical competence and technological competence that integrated to pedagogical and content knowledge.Theoretically, these findings support the construct developed by Lee and Johnston-Wilder (2017) that one of the key components of math resilience is the ability of students to recognize when they are struggling and to seek appropriate support or assistance.When learning in the classroom, teachers represent a crucial resource for students.The teacher's instructional approach significantly influences students' perception of the support they receive (Wentzel, Battle, Russell, & Looney, 2010).Therefore, competent teachers create positive perceptions and resilience in math.Moreover, this finding aligns with previous studies that support the idea that the level of pedagogical competence of teachers not only affects students' negative attitudes towards mathematics (Jameson, 2020;Pakarinen, Kiuru, Lerkkanen, Poikkeus, Ahonen, & Nurmi, 2011;Patrick, Turner, Meyer, & Midgley, 2003), but also their positive attitudes towards the subject (Ekmekci & Serrano, 2022;Siegle, 2007;Wentzel, 2002), including math resilience.
Although previous research has shown that mastery of mathematics content and technology is related to students' attitudes toward mathematics (Moore-Adams et al., 2016;Zhu & Kaiser, 2022), this study surprisingly did not find the same result.This relates to the characteristics of the Z and Alpha generations.These two generations grew up in the technological advancement era and are adept at using technology for learning (Tafonao, Saputra, & Suryaningwidi, 2020).Hence, teachers' mastery of technology is irrelevant to student resilience in learning because of their technology-native status.Furthermore, a study by Fessakis, Gouli, and Mavroudi (2013) explained that students are more likely to use technology in learning and solving math problems.
This relates to the concept of the teacher as a facilitator rather than the primary source of knowledge.As a result, teachers' mathematics content knowledge becomes irrelevant to students' math resilience.
While content knowledge and technological knowledge are not partially significant, it was found that the teacher's competence to combine technology, pedagogy, and content has a significant effect on math resilience.This shows that these three competencies must stand together.Teachers need to combine pedagogical, mathematics content, and technological knowledge to provide exciting and relevant learning and support the development of students' math resilience.This finding is relevant to a study by Sampaio and Coutinho (2015) that teachers should use technology aligned with their learning objectives and pedagogies to optimize student learning outcomes.This statement highlights the TPACK framework's impact on teacher professionalism development.
Although this study shows that mathematics teachers' TPACK is significant to students' math resilience, those competencies are not the primary determinant of math resilience.This can be seen from the value of the coefficient of determination (Table 4), which is relatively small (23.8%).However, it contradicts a study by Khumalo et al. (2022), which stated that the teacher has an essential role in building students' resilience.The inconsistency may be explained by the participants' characteristics from each study.The previous study concerned students in a disadvantaged environment, while this study was conducted in urban schools.Therefore, further study is needed to reveal other factors that play an essential role in the formation of students' math resilience, especially related to the socioeconomic context (Borman & Overman, 2004;García-Crespo, Suárez-Álvarez, Fernández-Alonso, & Muñiz, 2022).Furthermore, moderated regression analysis was carried out to examine the effect of PK and TPACK on math resilience with gender as a moderation variable (Table 5).The analysis revealed no significant interaction between gender and either TPACK (p-value = 0.31) or PK (pvalue = 0.87).Based on the findings, it can be concluded that gender does not affect the relationship between TPACK and PK with students' math resilience.This implies a significant correlation between TPACK, PK, and students' math resilience, and this relationship is not influenced by gender.Therefore, the teachers' competence in PK and TPACK can enhance students' math resilience, irrespective of gender.
This finding is supported by the previous different tests that showed no difference between male and female respondents in the mathematics teacher competence rating and the math resilience level.The insignificant differences in the level of math resilience between male and female respondents are thought of as a result of gender having no significant contribution to the relationship between mathematics teacher competence and student math resilience.So, it is assumed that male and female students are taught mathematics equally by professional teachers.
That is, it was not found that teachers in the observed school held gender-stereotyped beliefs and practices, in contrast to previous studies that confirmed them (Gilchrist & Zhang, 2022;Mwamwenda, 2011;Osaďan, 2012;Tahseldar, 2018).Therefore, this finding contributes to the research on gender in education.

Conclusion
The results show a significant relationship between mathematics teachers' TPACK and students' math resilience.Partially, the components of Pedagogical Knowledge (PK) and Technological Pedagogical Content Knowledge (TPACK) significantly affect students' math resilience.The ability to effectively integrate pedagogical knowledge, content knowledge, and technology in mathematics teaching is crucial in developing students' math resilience.However, the study found no moderation effect from gender on the relationship between mathematics teachers' TPACK and students' math resilience.
The results emphasize the vital role of mathematics teachers in building students' math resilience.Developing the competence of TPACK and PK through professional development programs that focus on teaching skills, content mastery, and the use of technology could be an effective strategy for building student resilience in facing complex mathematics learning challenges.However, an important note in interpreting these results is the need for further studies with more extensive and representative samples to strengthen these findings.Also, other variables such as motivation, emotional intelligence, or environmental factors should be considered in future studies to deepen understanding of the factors that affect students' mathematical resilience.
Since gender does not play a significant role in the relationship between math teachers' TPACK and students' math resilience, it is crucial to address gender-based disparities in math education separately.This could involve examining differences in math self-efficacy, confidence, and interest between male and female students and how these factors influence their resilience.Future studies should also explore additional variables and delve into qualitative investigations to provide a more comprehensive understanding of the relationship between TPACK and math resilience in the classroom.
Figure 1.Regression models Mathematics teachers' TPACK was measured by a modified questionnaire from Çetin and Erdogan (2018).The questionnaire developed by Cetin & Erdogan measured the competence of math teachers as a self-appraisal.Meanwhile, this study measured mathematics teachers' TPACK from the students' perspective, so it needs adjustments to improve the readability of respondents.The modified questionnaire contains 33 items on a Likert scale (1-5) consisting of six components: Technological Knowledge (TK), Pedagogical Knowledge (PK), Content Knowledge (CK), Technological Content Knowledge (TCK), Technological Pedagogical Knowledge (TPK), and Technological Pedagogical Content Knowledge (TPACK).Based on the validity and reliability tests, this instrument was valid (sig < 5%) and reliable (ɑ = 0.946).

Figure 2 .
Figure 2. The distribution of respondents based on their TPACK (a) and math resilience (b) criteria

Table 1 .
Respondents description

Table 2 .
TPACK and math resilience level

Table 3 .
Descriptive statistics of TPACK and math resilience

Table 4 .
Results of multiple regression analysis

Table 5 .
Results of moderated regression analysis