In-service mathematics teachers’ preparedness, knowledge, skills, and self-efficacy beliefs of using technology in lesson delivery

Abstract

This research examined the competencies (preparedness, skills, knowledge and self-efficacy beliefs) of High School teachers in teaching mathematics with technology. The study employed the explanatory sequential mixed-methods design where a questionnaire, observation guide and semi-structured interview guide were used to collect data. A stratified sampling technique was used to select 202 mathematics teachers for the study. Descriptive statistics and multiple regression were employed to analyse the quantitative data. Thematic analysis was used for the qualitative data. The findings indicated that mathematics teachers possessed high technology knowledge and self-efficacy, but they had relatively low preparedness and ICT skills in using technology in their lessons. In addition, ICT skills and teacher preparedness emerged as the best predictors for technology usage in mathematics lesson delivery. This implies that mathematics teacher education programmes should consider making ICT a core component of their curriculum to prepare prospective teachers to teach mathematics with technology.

Keywords:

• Teacher preparedness
• ICT skills
• technology knowledge
• self-efficacy beliefs
• competencies
• lesson delivery

PUBLIC INTEREST STATEMENT

The use of technology in enhancing the teaching and learning of mathematics has been advocated by several researchers, curriculum developers and mathematics educators. Nonetheless, the role of mathematics teachers’ competencies in realising this objective is very crucial. Hence this paper researches the competencies (preparedness, skills, knowledge and self-efficacy beliefs) of Senior High School mathematics teachers in incorporating technology in their lesson delivery. The findings indicated that mathematics teachers possessed high technology knowledge and self-efficacy, but they had relatively low preparedness and ICT skills in using technology in their lessons. In addition, ICT skills and teacher preparedness emerged as the best predictors for technology usage in mathematics lesson delivery. This calls for the need for teacher professional programmes in technology integration in mathematics lesson delivery to augment the preparedness and skills of teachers to realise the full potential of technology in teaching mathematics.

1. Introduction

The role of teachers in integrating technology into classroom lesson delivery is very vital. Teachers’ competencies encompass knowledge, skills and abilities that result in essential behaviours expected from them (United Nations Educational, Scientific and Cultural Organization [UNESCO], 2016). Mathematics teachers are expected to possess adequate technology knowledge, ICT skills and self-efficacy beliefs to incorporate technology in their lesson delivery. S. K. Wang et al. (2014) reiterated the viewpoint of Raob et al. (2012) that teachers need to possess the requisite technology knowledge, ICT skills and self-efficacy beliefs in using technology in classroom instruction.

Keong et al. (2005) reiterated the importance of mathematics teachers possessing effective skills and knowledge to incorporate technology into mathematics lessons. As a result, mathematics teachers need to be knowledgeable about the difficulties and possibilities of technology in teaching mathematics. The introduction of technology on its own does not enhance teaching and learning (Bransford et al., 2000), but effective and efficient integration of technology into the classroom environment has the potential of improving academic achievement (Jhurree, 2005). This could mainly be achieved by teachers who possess competencies in technology and its usage. Agyei (2012) further established that integrating technological innovations into mathematics education depends on how teachers are prepared to integrate technology into their lesson delivery. As technology evolves, teachers need to be equipped with adequate technology knowledge and ICT skills to adopt new technology tools and resources in their lesson delivery. However, some existing frameworks for technology integration such as the TPACK framework focuses on the integrated knowledge of subject-matter, pedagogy and technology of teachers in teaching with digital tools (Graham, 2011). On the other hand, technology competence framework proposed in this study goes beyond knowledge to comprise skills, preparedness and self-efficacy beliefs that enables teachers to incorporate technology into their lesson delivery.

Considering the opportunities technology presents in the classroom, governments of many nations have invested massively in incorporating technology in their school systems. Khambari et al. (2009) carried out a matrix of ICT initiatives in many countries worldwide in the last decade and discovered that governments of numerous countries had made significant investments to incorporate ICT into their various education systems. A report presented to the MasterCard Foundation on Secondary Education in Africa by Burns et al. (2019) revealed that four countries in Sub-Saharan Africa (Cape Verde, South Africa, Botswana and Mauritius) had developed their education systems massively to integrate ICT into their secondary school education. This report buttresses the enormous investments of governments of various African countries to incorporate technology into their education. For example, in Ghana, 87% of Senior High Schools (SHS) have been furnished with technology infrastructure (Ministry of Education [MoE], 2009). To increase the quality of ICT integration in the classroom at the SHS level in the country, 555 schools have received ICT infrastructure support (Ministry of Education [MoE], 2016). Also, the 2021 one-teacher-one laptop computer project is ongoing (Yalley & Chapman, 2022). This project is to ensure that every teacher at the pre-tertiary level receives a TM1 laptop computer. Despite these infrastructural developments made by the government, research (Agyei, 2012; Mensah, 2017; Mensah & Agyei, 2021) have revealed that a substantial number of SHS mathematics teachers do not incorporate technology in their lesson delivery.

Nevertheless, the Ghanaian SHS mathematics curriculum requires mathematics teachers to incorporate technology into their mathematics instruction (Asiedu-Addo et al., 2016). For instance, teachers are expected to use technological resources such as spreadsheets, calculators and computers to teach content such as statistics, functions and geometry at the SHS level (CRDD, (2010).). This demand has led teacher education institutions in Ghana to include technology-related courses in their curriculum to equip mathematics teachers with competencies (technology knowledge, ICT skills and self-efficacy beliefs) to integrate technology in their teaching (Asiedu-Addo et al., 2016). However, mathematics teachers who have graduated from teacher education institutions ten years ago did not have the opportunity to be equipped with the required competencies for using technology to teach. Joshi (2016) speculated that mathematics teachers may be less aware of specific mathematics software such as Geometer’s Sketchpad, Graphmatica and GeoGebra. If teachers are less aware of these digital resources, then it is likely that they would not include such tools in their pedagogical decisions.

Difficulties associated with using technology in Ghana’s education system are not exclusively due to lack of technological resources, but also due to an insufficient supply of trained human resources (Agyei, 2013). This presupposes that teacher preparedness, skills, knowledge and self-efficacy beliefs play a vital role in incorporating technology in teaching mathematics (National Council of Teachers of Mathematics [NCTM], 2011). Research on the predictors of technology usage in teaching mathematics has mainly focused on the availability of technology resources, demographic factors, student-related factors and school environment factors (Agyemang & Mereku, 2015; McCulloch et al., 2018). Thus, there is a minimal consensus on in-service mathematics teachers’ preparedness, knowledge, skills and self-efficacy in using technology in lesson delivery. Consequently, questions like “to what extent are teachers prepared to teach with these technologies” and “what competencies do mathematics teachers possess in teaching with specific mathematics technologies” remain. Also, the key competencies that influence mathematics teachers’ ability to incorporate technology in their lesson delivery are yet to be determined. To this end, the study sought to explore mathematics teachers’ competencies (technology knowledge, preparedness, ICT skills, self-efficacy beliefs) in incorporating technology in their lesson delivery.

1.1. Research questions

The following research questions, therefore, guided the study.

1. What are mathematics teachers’ competencies (knowledge, preparedness, skills, self-efficacy beliefs) in incorporating technology in teaching mathematics?

2. To what extent do in-service teachers’ knowledge, skills, self-efficacy beliefs and preparedness influence technology usage in teaching mathematics?

1.2. Theoretical underpinnings

The study was underpinned by the Social Cognitive Theory. Albert Bandura propounded the Social Cognitive Theory in 1986. The Social Cognitive Theory (SCT) has helped gain insights into the intrapersonal attributes and environmental factors that change human behaviour towards the implementation of curriculum innovation. While developing the SCT, Bandura (1997) acknowledged that vicarious experience and observation play a significant role in human behaviour and learning. Parajes (2002) reported that, people are proactive, self-regulatory and self-reflective entities instead of merely reactive organisms responding to external factors. Bandura (1997) considered human development to be the outcome of complex interactions of personal, behavioural and environmental factors. Thus, the results of a person’s behaviour inform and alter their intrapersonal and environmental factors, adjusting and informing subsequent behaviour. The resulting reciprocal determinism is hinged on the premise that; intrapersonal factors in the form of affective, biological and cognitive events; human behaviour and environmental factors create interconnections that lead to triadic reciprocality, as illustrated in Figure 1.

Figure 1. Social Cognitive Theory (Parajes, 2002)

With the proliferation of technology resources in schools (environment), intrapersonal factors have gained much attention as influential in teachers’ quest to incorporate technology in their lesson delivery (behaviour). In the phase of technology integration, environmental factors such as availability of technology resources, classroom environment among others have a role to play. In spite of the aforementioned, teachers’ competencies in technology form and shape their decisions to use technology in classroom lesson delivery (Niederhauser & Lindstrom, 2018). This assertion presupposes that teachers’ intrapersonal factors, such as technology knowledge, ICT skills, teacher preparedness and self-efficacy beliefs, could play a decisive role in determining teachers’ use of technology in teaching mathematics. This study pays particular attention to how intrapersonal factors (competencies) influence the use of technology in teaching mathematics (behaviour). Hence, intrapersonal factors are discussed in detail in the subsequent section.

1.3. Intrapersonal factors

Some studies (Asiedu-Addo et al., 2016; Powers & Blubaugh, 2005) have revealed that teachers are primarily prepared to use technology in lesson delivery through their teacher education programmes. On the contrary, Hudson and Porter (2010) agreed with Kafyulilo et al. (2015) that teachers’ preparedness to use technology in teaching mathematics could be enhanced through teacher professional development training programmes. As agents of change and the principal actors in the teaching process, teachers must be prepared to accept the paradigm shift of incorporating technology into lesson delivery. Teacher preparedness is critical in developing teachers’ competencies in integrating technology in lesson delivery (Cheal et al., 2012; Hero, 2020). Research has emphasised the value of teacher education programmes that help teachers increase their technology abilities to use a range of instructional methods to effectively incorporate technology into the curriculum (Lock & Redmond, 2010).

Technology knowledge comprises understanding educational technologies, bearing in mind their potential for a particular subject area. Hughes (2005) reiterated that for teachers to develop appropriate technology knowledge, it is necessary to learn and acclimatise to current development in technology since new technologies evolve with time. Limited use of technology in teaching has been attributed to low levels of technology knowledge (Mailizar & Fan, 2019; Tezci, 2009). Survey results by (Mailizar & Fan, 2019; Spangenberg & De Freitas, 2019) have indicated that mathematics teachers have virtually inadequate knowledge of ICT and its usage in the teaching of mathematics. Although the teachers reported considerable knowledge levels in general technology software (MS Word), they exhibited lower knowledge levels in specific mathematics software such as Computer Algebra System, Dynamic Geometry Software and Dynamic Mathematics Software (Mailizar & Fan, 2019). However, further analysis showed that the teachers had higher knowledge levels for GeoGebra—one of the Dynamic Geometry Software. In the same vein, Tella et al. (2007) explored the teachers’ perceived usefulness and ease of use of technology in their lesson delivery in Nigeria. Tella et al. (2007) reported that 33.8% of the teachers lacked the expertise for technology adoption, 21.5% of the teachers did not have sufficient technology knowledge of appropriate technology tools in education and 25.8% of the teachers lacked the knowledge needed to evaluate the use of technology in classroom instruction.

Mathematics teachers’ ICT skills have been widely reported as one of the significant determinants of technology usage in teaching by numerous scholars across the globe (e.g., Agyei & Voogt, 2011; Das, 2019; Kamau, 2014). A qualitative study by Rouf and Mohamed (2018) revealed that although teachers in Bangladesh possess basic technology skills, they cannot effectively use technology in teaching the subject. Unlike Rouf and Mohamed (2018), Agyei and Voogt (2011) found ICT skill as the predominant predictor of teachers’ technology integration in teaching and learning mathematics. Conversely, using an exploratory sequential mixed method design, Ashiono et al. (2018) acknowledged that training teachers on basic ICT skills had no significant effect on the use of technology in mathematics lesson delivery. Nonetheless, enhancing teacher ICT skills through continuous professional development can enhance the use of technology in teaching (Perienen, 2020).

Lemon and Garvis (2016) revealed different levels of self-efficacy beliefs in adopting technology in classroom lesson delivery between two cohorts of respondents. One cohort reported high levels of self-efficacy beliefs while the other cohort of pre-service teachers did not feel confident in all areas of technology engagement. Conversely, Giles and Kent (2016) reported high self-efficacy beliefs for teachers in teaching with technology. Both studies concluded that self-efficacy belief is one of the motivational variables that can influence the confidence and competence of teachers in teaching with technology. Njiku et al. (2020) indicated that although mathematics teachers possessed moderate self-efficacy beliefs, a significant correlation was realised between self-efficacy beliefs and technology usage. Njiku, et al’s study did not investigate how other intrapersonal factors related to teachers such as technology knowledge, teacher preparedness and ICT skills also influence technology usage. Similarly, Caner and Aydin (2021) agreed with Abbitt (2011) that teachers’ self-efficacy beliefs could predict technology usage in lesson delivery.

From the extant literature and the Social Cognitive Theory, teachers’ competencies for incorporating technology in mathematics teaching are influenced by attributes related to teachers. These attributes include technology knowledge, teachers’ self-efficacy beliefs, ICT skills and teacher preparedness. While Social Cognitive Theory has several dimensions, this study is mainly concerned with the role of intrapersonal factors, including technology knowledge, ICT skills, teacher preparedness and self-efficacy beliefs about technology in determining behaviour (use of technology in mathematics lesson delivery). Based on these assertions from the Social Cognitive Theory, a conceptual framework named “Teacher technology competency framework” was developed for the study. As illustrated in Figure 2, the conceptual framework portrays the linkage between teachers’ competencies in technology (teacher preparedness, technology knowledge, ICT skills and self-efficacy beliefs about technology) and the use of technology in mathematics lesson delivery.

Figure 2. Teacher technology competency framework

In this study, teachers’ competencies were conceptualised as a set of teacher preparedness in using technology tools, teachers’ self-efficacy beliefs about technology tools, ICT skills in technology tools and teachers’ technology knowledge about basic technology tools that enable teachers to teach mathematics with technology. Teachers’ preparedness was described as teachers’ exposure to basic technology tools and the training received on using technology tools and resources in their mathematics lesson delivery. Also, technology knowledge was referred to as teachers’ knowledge concerning the various basic technology tools used in teaching mathematics. In a nutshell, teachers’ knowledge of scientific calculators, educational software such as GeoGebra, spreadsheets and multimedia in teaching mathematics characterised teachers’ technology knowledge in this study. Multimedia is referred to as the use of audios, videos and images in teaching concepts in mathematics. In this study, ICT skills were described by applying the knowledge acquired from training or experience in using basic technology tools in lesson delivery. Again, self-efficacy belief was conceptualised in this study as teachers’ beliefs about their abilities to use basic technology tools in the teaching of mathematics. Behaviour is also conceptualised as the use of technology resources in mathematics lesson delivery.

1.4. Research design

The study employed the explanatory sequential mixed-methods design involving questionnaire, lesson observation and interviews. Quantitative data was collected first using a questionnaire. The qualitative data was then collected using observation guide and semi-structured interviews guide. The findings from these data were integrated by comparing or connecting quantitative and qualitative data (Creswell & Tashakkori, 2007). The qualitative data supported the quantitative data through triangulation and accounted for meanings and deeper understanding of participants’ competencies in teaching mathematics with technology. Specific details regarding mathematics teachers’ competencies were ascertained from the qualitative data after they had shared their general views in the quantitative phase. In an explanatory sequential mixed-methods design, qualitative data is useful in elaborating the quantitative findings (Gray, 2013).

1.5. Sample and participants

The population for the study was 325 mathematics teachers Kumasi Metropolis in Ghana. The study employed a stratified sampling technique to draw a sample of mathematics teachers from public SHS in the Metropolis. Teachers with diverse cultural backgrounds from several parts of the country are found in the Kumasi Metropolis, making the metropolis an ideal location for the study. The Computerised School Selection and Placement System [CSSPS] (2019) guided the grouping of SHS into three strata (Category A, B and C). This is because CSSPS group schools in each category are homogeneous with regards to several characteristics such as quality and quantity of infrastructure (school buildings, ICT labs, libraries etc.), learning facilities, staffing (quality and quantity of teachers) and academic performance (Nsiah-Peprah, 2004). Using Slovin’s sample size determination formula at 5% sampling error (Stephanie, 2003), a sample size of 220 mathematics teachers was selected. Demographic details of the respondents revealed that male mathematics teachers (84.2%) dominated the study.

For the qualitative phase, mathematics teachers were selected purposively based on their teaching experience, preparedness to incorporate technology in lesson delivery and willingness to partake in the qualitative phase of the study. The sample size in the qualitative phase was determined when the data saturation point (a point where you are not getting any new information) was attained (Fugard & Potts, 2015). In line with this, the authors realised from the engagements with participants that saturation point was attained after observing lessons and interviewing two respondents from each stratum. Thus, six participants were engaged in the qualitative phase of the study. The six participants from the classroom observations and interviews were identified with pseudonyms with respect to the category of their schools. The teachers from category A schools were identified with CATA_T1, CATA_T2 and those in category B schools were identified with CATB_T3 and CATB_T4. Also, those in category C schools were identified with CATC_T5 and CATC_T6. This was done to attribute the comments to the particular teachers who made them.

1.6. Instruments

Validated scales were used to measure teachers’ preparedness, ICT Skills, self-efficacy beliefs and technology knowledge for teaching mathematics with technology. Teachers’ technology knowledge was measured using the TPACK survey (Schmidt et al., 2009). Teachers’ self-efficacy beliefs were measured using Computer Technology Integration Survey by L. Wang et al. (2004). The items for technology knowledge and self-efficacy beliefs were measured on a five-point Likert scale (1 = Strongly Disagree, 2 = Disagree, 3 = Undecided, 4 = Agree, 5 = Strongly Agree). Disagreement to the items meant that teachers possessed low self-efficacy about teaching mathematics with technology and vice versa. Teachers were required to indicate their level of effectiveness using a five-point Likert scale (1 = Not effective, 2 = Not very effective, 3 = Effective, 4 = Very effective, 5 = Highly effective) in exhibiting the ICT skills adapted from the Basic Technology Competencies for Educators Inventory [BTCEI] (Flowers & Algozzine, 2000). ICT skills were measured under four main domains: calculator skills, GeoGebra skills, spreadsheet skills and multimedia skills. The authors developed eight items to measure how pre-service preparation programmes introduced mathematics teachers to the use of technology in teaching and learning mathematics. The items were measured on a four-point Likert scale (1 = Not at all, 2 = A little, 3 = Somewhat, 4 = A lot).

The instruments were also pilot tested to ascertain their validity and reliability. The Cronbach Alpha coefficients obtained were all above .85, indicating that the questionnaire was highly reliable for the study. Kline (2005) reported that an alpha coefficient of .70 is acceptable, .80 is very good and .90 is considered excellent when measuring the reliability of a research instrument. According to Creswell (2014), eight approaches can improve the quality of qualitative research. These include prolonging the engagement, external audits, member checks, triangulation, peer debriefing and examination of bad cases and clarifying the researcher’s bias. However, the qualitative researcher needs to engage in at least two of these methods throughout a particular study, according to Creswell (2014). Achieving the trustworthiness of qualitative data was done using member checks, external audits and triangulation (Creswell, 2014), which are the most common and cost-effective techniques for doing so (Frey, 2018).

1.7. Data analysis

Means and standard deviations were used to analyse the first research question. The mean benchmarks proposed by Alston and Miller (2002) and Yidana and Asare (2021) was employed to interpret the Likert scale. A mean score less than 2.5 was considered as teachers having low levels of technology knowledge, teacher preparedness, ICT skills and self-efficacy beliefs, while a mean score ranging from 3.5 to 5.0 was regarded as teachers having high levels of technology knowledge, ICT skills and self-efficacy beliefs. Standard multiple regression was used to analyse the second research question.

Preliminary analysis of the data was conducted to ascertain the assumptions of standard multiple regression. The sample size of 202 for the study was enough for multiple regression to be carried out (Tabachnick & Fidell, 2013). There were no outliers in the data as the standardised residuals were found between −3.3 to 3.3 in a scatter plot (Pallant, 2016). Collinearity diagnostics using Variance Inflation Factor (VIF) and Tolerance was conducted. The Tolerance and VIF coefficients of the variables comprised: teacher preparedness (Tolerance = 0.834, VIF = 1.199); technology knowledge (Tolerance = 0.532, VIF = 1.879); ICT skills (Tolerance = 0.773, VIF = 1.294) and self-efficacy beliefs (Tolerance = 0.603, VIF = 1.199). Tolerance coefficients higher than 0.10 and VIF coefficients less than 10 recorded showed that there was no possible multicollinearity in the data (Pallant, 2016).

Braun and Clarke’s (2013) thematic analysis approach was used to analyse the qualitative data. In this study, the authors repeatedly listened to the interview sessions’ recordings to familiarise themselves with the incipient patterns in the data. Later on, the qualitative data was transcribed and colour coded in MS Word to identify emerging themes from the data. After gaining a fair idea of the emerging patterns, the transcribed interview data was then imported into a qualitative data analysis software (HyperRESEARCH 4.5.3) for further coding and analysis. The codes were later refined and organised under themes using research questions and the intrapersonal factors described in this study. The authors identified, organised and interpreted the themes in the textual data in relation to the research questions. Participants’ comments and phrases were used to produce reports for the qualitative findings to support and explain the results from the quantitative phase (Creswell, 2014).

2. Results

Research question one was “what are mathematics teachers’ competencies (technology knowledge, preparedness, ICT skills, self-efficacy beliefs) in incorporating technology in teaching mathematics?” This research question sought to explore the technology knowledge, teacher preparedness, ICT skills and self-efficacy beliefs that SHS teachers possessed in incorporating basic technology tools in the teaching of mathematics. The results are presented in Tables 1–4.

Table 1. Technology knowledge of teachers

Technology Knowledge	M	SD
I know how to solve my own technical problems	3.67	.916
I can learn about technology easily	4.15	.747
I have the technical skills I need to use technology	3.95	.821
I know about a lot of different technologies	3.55	1.046
I frequently play around the technology	3.72	.990
I keep up with important new technologies	3.66	.906
I have had sufficient opportunities to work with different technologies	3.42	1.118
Overall	3.73	0.935

Table 2. Teacher preparedness for incorporating technology in mathematics lesson delivery

Teacher Preparedness	M	SD
My teacher preparation programme introduced me to technology tools for teaching mathematics	2.55	.951
My pre-service training introduced me to how to teach mathematics with technology tools	2.49	1.043
My pre-service teacher education programme included courses that are related to technology integration in teaching mathematics	2.52	.998
My teacher education programme introduced me to designing lessons using technology to meet the needs of diverse learners	2.41	.969
My lecturers appropriately modelled combining content, technologies and teaching approaches in their teaching	2.55	.967
My teacher education program gave me opportunities to practice teaching mathematics with technology	2.56	1.021
My teacher preparation programme introduced me to select appropriate technology tools to specific content areas in mathematics	2.41	.922
My teacher preparation programme introduced me to designing lessons using online tools	2.35	1.046
Overall	2.48	0.990

Table 3. Self-efficacy beliefs of teachers

Self-efficacy beliefs	M	SD
I feel confident that I can successfully teach relevant mathematics content with the appropriate use of technology.	4.08	.932
I feel confident that I have the skills necessary to use the computer for mathematics instruction.	3.96	.979
I feel confident in my ability to evaluate software for teaching and learning.	3.67	.942
I feel confident I can regularly incorporate technology into my lessons when appropriate to student learning.	3.92	.854
I feel confident about selecting the appropriate technology for instruction based on curriculum standards.	3.91	.848
I feel confident that I will be comfortable using technology in my teaching.	4.12	.867
I feel confident I can consistently use educational technology in effective ways.	3.98	.864
I feel confident I can provide individual feedback to students during technology use.	3.90	1.014
I feel confident that I can motivate my students to participate in technology-based lessons.	4.14	.893
I feel confident that I understand computer capabilities well enough to maximise them in my classroom.	3.88	.890
Overall	3.96	0.908

Table 4. ICT skills for teaching mathematics

ICT Skills		M	SD
Spreadsheet Skills		2.99	1.260
Calculator Skills		3.91	1.114
Multimedia Skills		2.63	1.269
GeoGebra Skills		2.50	1.241
Overall		3.01	1.221

2.1. Technology knowledge of teachers

To ascertain the technology knowledge levels of the SHS mathematics teachers, they completed a self-reported scale. A summary of the results is presented in Table 1.

From Table 1, the mathematics teachers reported high levels of technology knowledge (M = 3.73, SD = 0.935). To demonstrate their technology knowledge, the mathematics teachers indicated that they could learn about technology easily (M = 4.15, SD = 0.747). This was confirmed in an interview with CATC_T5, who asserted that “the rapid increase in technology tools and resources has aided him to know a lot about several technology tools and resources”. In general, the mean values reported by the mathematics teachers indicated high levels of technology knowledge.

In addition, evidence from the qualitative data presupposed that the mathematics teachers involved in this study were familiar with a couple of basic technology tools used in teaching mathematics (M = 3.55, SD = 1.046). When the authors inquired about the participants’ familiarity with specific basic technology tools during the interview, CATA_T1 mentioned that “I am familiar with Calculator, Microsoft Mathematics, GeoGebra, Excel and others”. All the participants interviewed reported that they were familiar with calculator, but CATB_T4 and CATC_T6 added that apart from the calculator, they were familiar with GeoGebra and multimedia resources such as video lessons from the YouTube respectively. To help ascertain the reasons for the high levels of technology knowledge reported by the teachers, CATC_T6 recalled from his teacher education programme that “ … one lecturer prepared a manual for us on how to use the calculator and took us through the basics of using the various functions on the calculator”. Furthermore, CATA_T1 also specified that “I used the internet to learn about these technologies during my national service period as a teaching assistant.” Hence, the results from the questionnaire data and interview data suggested that the mathematics teachers possessed, to some extent, high knowledge of technology integration. The results indicated that the mathematics teachers were familiar with basic technology tools such as calculator, GeoGebra, Multimedia and Spreadsheet for teaching and learning mathematics

2.2. Teachers’ technology preparedness

The teachers completed a self-reported scale on their level of preparedness towards the use of technology for pedagogical practices. The results are presented in Table 2.

From Table 2, the mathematics teachers reported low level (M = 2.48, SD = 0.990) of teacher preparedness in incorporating technology in their lesson delivery. The result was suggestive that the mathematics teachers were not introduced to designing mathematics lessons using online tools (M = 2.35, SD = 1.046) in their teacher education programmes. Also, the mathematics teachers reported that their teacher education programmes gave them less exposure to; selecting appropriate technology tools to specific content areas in mathematics (M = 2.41, SD = 0.922) and designing lessons using technology to meet the needs of diverse learners (M = 2.41, SD = 0.969). Thus, generally, the mathematics teachers reported lower levels of preparedness in using technology in mathematics lesson delivery.

Evidence from the qualitative data also revealed that the participants were less prepared to incorporate technology in the teaching of mathematics. When they were asked about how they used technologies in teaching mathematics, CATB_T3 agreed with CATA_T1, who recounted, “ … at the tertiary level and during my national service but it wasn’t adequate, just some brief introduction to some software was made. The mathematics education programme rarely exposed us to designing mathematics lessons with the available technology tools”. On the contrary, CATA_T2 commented that “back in school, I read mathematics education and minored in ICT, so we read several courses in ICT from level 100 to level 300 which introduced us to several technologies such as GeoGebra, Java and Excel”. This presupposed that not all the mathematics education programmes offered to prepare teachers adequately for technology integration. Moreover, CATB_T4 lamented that “I have not had the opportunity to attend any professional development workshop on teaching mathematics with technology”. CATB_T4ʹs comment implies that there is limited or no in-service training for mathematics teachers on using technology resources in mathematics lesson delivery.

2.3. Teachers’ technology self-efficacy beliefs

Also, in answering Research Question One, the mathematics teachers were required to rate their level of self-efficacy beliefs for incorporating technology in their mathematics lesson delivery. The results are presented in Table 3.

With regards to the self-efficacy beliefs reported by the mathematics teachers, the overall mean (M = 3.96, SD = 0.908) presented in Table 3 showed that the mathematics teachers had high level of self-efficacy beliefs in incorporating basic technology tools such as calculators, spreadsheets, multimedia and GeoGebra in their mathematics lesson delivery. It is apparent from the results in Table 3 that the teachers reported high self-efficacy beliefs in areas such as; “I feel confident that I can motivate my students to participate in technology-based lessons” (M = 4.14, SD = 0.893), “I feel confident that I will be comfortable using technology in my teaching” (M = 4.12, SD = 0.867) and “I feel confident that I can successfully teach relevant mathematics content with appropriate use of technology” (M = 4.08, SD = 0.932).

Remarkably, all the items measuring self-efficacy beliefs of the mathematics teachers recorded mean values greater than 3.5, which indicates high level of self-efficacy beliefs about incorporating basic technology tools in mathematics lesson delivery. CATC_T5 accentuated his self-efficacy beliefs during the interview that “ … in the process of teaching, one thing is I know how to use the technology, so I always calm my nerves down and allow the technology to take its role”. CATA_T1 and CATB_T4 shared similar belief that “they are confident that they can teach mathematics with technology when the necessary technology resources are provided in the classroom.” In brief, the mathematics teachers asserted that they possessed high self-efficacy beliefs about teaching mathematics with technology. Thus, the results indicated that the mathematics teachers are confident in teaching mathematics with technology.

2.4. ICT Skills of mathematics teachers

With respect to ICT skills, the teachers were asked to rate their skills in using basic technology tools such as spreadsheets, calculators, multimedia and GeoGebra in mathematics lesson delivery. The results are presented in Table 4.

The overall mean score of the construct of ICT skills, as indicated in Table 4, was relatively moderate (M = 3.01, SD = 1.221) of ICT skills. It was evident from the results that the teachers reported high skills in using calculators in teaching mathematics (M = 3.91, SD = 1.114). On the other hand, the mathematics teachers reported relatively low skill level (M = 2.50, SD = 1.241) in using GeoGebra in teaching mathematics. The high calculator skills reported in the quantitative results were reiterated by CATB_T4 while commenting on his ICT skills during the interview session. He mentioned that “I am able to guide students to use a calculator to calculate means, standard deviations and variance”. CATB_T4 further explained that “I have been using the calculator to do mathematics right from SHS days through to the University, so I am able to use it efficiently.” Also, CATC_T5, as well as CATA_T2, shared similar viewpoints that “they possess the skill of using calculators to solve simultaneous equations.” On the other hand, CATB_T3 lamented that “I don’t use GeoGebra and spreadsheet here because I have not been trained to acquire the skills to use them”. The participants’ comments in the qualitative data affirmed the results attained from the quantitative analysis. From the preceding analysis, the mathematics teachers reported a high level of calculator skills. Nonetheless, they indicated in the interview that they possessed low skills in using a spreadsheet, GeoGebra and multimedia to teach mathematics.

Apart from the four technologies: spreadsheets, calculators, multimedia and GeoGebra considered in the study, CATA_T1 mentioned during the interview that, “personally I possess the skills of using Microsoft mathematics to solve mathematics questions, but I mostly use it in the house while preparing for lessons”. This presupposed that the technology tools considered in this study were not exhaustive. Overall, analysis regarding the first research question showed that the mathematics teachers possessed high level of technology knowledge and self-efficacy beliefs; notwithstanding, they reported low levels of teacher preparedness in teaching mathematics with technology. The results also pointed out that mathematics teachers generally had fairly moderate levels of ICT skills, although they reported high levels of calculator skills. Again, the teachers indicated that they were familiar with basic technology tools such as calculator, GeoGebra, Multimedia and Spreadsheet used in teaching mathematics.

The second research question (to what extent do knowledge, skills, self-efficacy beliefs and preparedness of in-service teachers influence technology usage in teaching mathematics?) sought to ascertain the influence of the various subscales of teachers’ competencies on the use of technology in teaching mathematics. Standard multiple regression was employed to measure the impact of technology knowledge, ICT skills, self-efficacy beliefs and teachers’ preparedness on technology use in teaching mathematics. Descriptive analysis of the data revealed relatively low use of technology among the mathematics teachers (M = 2.32, SD = 1.091). For example, mathematics teachers reported low levels of using dynamic geometry software such as GeoGebra in mathematics lesson delivery (M = 1.86, SD = 1.042). Similarly, the mathematics teachers reported low levels of using electronic spreadsheets in designing lessons and teaching mathematics concepts (M = 2.46, SD = 1.120). Furthermore, the results from the regression analysis are presented in Tables 5 and 6. The statistical significance of the model was examined using ANOVA Table and a summary of the results is shown in Table 2.

Table 5. Model summary and ANOVA table (teacher preparedness, technology knowledge, self-efficacy beliefs and ICT skills)

	df	Sum of Squares	Mean Square	F(Sig)	R	R-Square
Regression	4	4659.253	1164.813	26.299(.000^a)
Residual	197	8725.227	44.290
Model					.590^b	.348
Total	201	13,384.480

Note: ^a p < 0.05; ^b Predictors: (Constant), teacher preparedness, technology knowledge, self-efficacy beliefs and ICT skills; Dependent Variable: Use of technology in teaching mathematics; Adjusted R-squared = .335; Std. error of the Estimate = 6.655

Table 6. Estimated coefficients of predictors (ICT skills and teacher preparedness)

Variable	R	R-Square	F(Sig)	Standardised Coefficients	t	Sig
Impact of Teacher preparedness	.442	.195	48.491(.000^a)	.442	6.964	.000^a
Impact of ICT skills	.517	.268	73.059(.000^a)	.517	8.547	0.000^a
Impact of ICT skills and Teacher preparedness	.588	.346	52.706(.000^a)	0.414 (S) 0.299 (P)	6.783 4.895	0.000^a 0.000^a

Note: ^A p < 0.05; S = ICT skills, P = Teacher preparedness; Constant = 4.993; Adjusted R-squared = .340

Table 5 presents the model summary with R Square, indicating how much of the variance of the use of technology in teaching mathematics was explained by teachers’ preparedness, knowledge, self-efficacy beliefs and ICT skills. When the R Square (.348) is expressed as a percentage, the regression model (teachers’ preparedness, ICT skills, knowledge and self-efficacy beliefs) explained 34.8% of the variance in using technology to teach mathematics. The results from the ANOVA Table revealed that the model reached statistical significance [F (4, 197) = 26.299, p< 0.001] in predicting the use of technology in the teaching of mathematics. Each of the independent variables included in the model was evaluated to ascertain their contribution to the prediction of using technology in teaching mathematics. The results showed that self-efficacy beliefs (p = 0.512) and technology knowledge (p = 0.933) were not significant predictors of using technology to teach mathematics. This result appeared to contradict the expectation that an increase in self-efficacy beliefs and technology knowledge would lead to a corresponding increase in the use of technology in teaching mathematics. Further analysis was conducted to improve the regression model by exploring the impact of ICT skills and teacher preparedness on using technology to teach mathematics.

The R-Square (.195) reported for using technology in teaching mathematics indicates that the mathematics teachers’ preparedness explained approximately 20% of the variance in using technology in teaching mathematics. The p-value indicated that teacher preparedness was a significant predictor of using technology to teach mathematics (p < 0.001). Again, approximately 27% of the variance in using technology to teach mathematics was explained by the ICT skills of the mathematics teachers. The p-value affirmed that ICT skills were a significant predictor of using technology to teach mathematics (p < 0.001). Putting ICT skills and teacher preparedness together, the R-Square for using technology to teach mathematics increased to 0.346. This indicates that the predictability of using technology in teaching mathematics increased to approximately 35% when ICT skills and teacher preparedness were combined. The F- test highlighted that the resulting model is significant [F (2, 199) = 52.706, p < 0.001]. As a result, the standardised coefficients of the independent variables yielded the regression model as follows:

Use of Technology in teaching mathematics = 4.993 + 0.414 ICT skills + 0.299 Teacher preparedness.

From the regression model, the coefficient of teacher preparedness (β = 0.299) suggests that a unit increase in teacher preparedness would increase technology usage in teaching mathematics by 0.299 units. ICT skills (β = 0.414) depicts that if there is a unit increase in teachers’ ICT skills, technology usage in teaching mathematics will increase by 0.414 units. The regression model is suggestive that technology usage in teaching mathematics is best predicted by ICT skills, followed by teacher preparedness.

It can be speculated from the results that if SHS mathematics teachers’ ICT skills and technology preparedness are enhanced, it can improve their adoption of technology in teaching mathematics. This implies that mathematics teachers should be adequately prepared to equip them with the needed ICT skills to incorporate technology in their lessons. In the interviews, the teachers expressed their views on the intrapersonal factors that influence their ability to use technology in teaching mathematics. CATC_T6 mentioned that:

As a mathematics teacher, I cannot employ technology in the teaching of mathematics if I do not have the knowledge and the skills required to use them. But to acquire the requisite knowledge and skills, I have to be trained on how to teach mathematics with technology.

From the above comment, ICT skills and preparing teachers adequately are crucial factors in predicting an individual’s competence to teach mathematics with technology. Similarly, CATA_T1 emphasised that “I believe if my skills in using technology tools are improved, it will enable me to prepare and teach mathematics lessons with technology.” Also, CATA_T2 affirmed one of the significant predictors of technology usage in teaching mathematics identified in the quantitative findings. When he was asked about the intrapersonal factors that influence his ability to teach mathematics with technology, he emphasised that:

I think it is my preparedness because first of all during my teacher preparation programme back in school I learnt almost everything on how to use a calculator to solve basic mathematics problems and while on the job this has helped me to guide my students to use the calculator to solve simultaneous equations, quadratic functions among others in my classroom lesson delivery.

The qualitative findings corroborate the quantitative findings, highlighting that teachers’ ICT skills and preparedness were the best predictors of technology usage in teaching mathematics. Altogether the results revealed that teachers’ competencies significantly predicted technology integration in teaching mathematics, technology knowledge and self-efficacy beliefs were not significant predictors of using technology to teach mathematics. Among the four sub-constructs of competencies explored in this study, ICT skills best-predicted technology usage in teaching mathematics, followed by teacher preparedness. Also, ICT skills and teacher preparedness explained only 34.6% of the variance in using technology to teach mathematics, which presupposes that other factors that influence the use of technology in teaching mathematics exist.

2.5. Discussion of results

The literature has established that incorporating technology in mathematics lessons enhances the teaching and learning process of mathematics concepts (Das, 2019; Joshi, 2016). Nonetheless, effective integration of technology in classroom lesson delivery requires teachers who possess the requisite competencies to do so. This study was set out to investigate the competencies of SHS mathematics teachers in incorporating technology in their lesson delivery. To ascertain the competencies of the mathematics teachers in teaching mathematics with technology, their technology knowledge, teacher preparedness, self-efficacy beliefs and ICT skills were explored.

The results indicated that mathematics teachers had high levels of technology knowledge. This result contradicts findings reported by Mailizar and Fan (2019) which indicated that mathematics teachers have virtually inadequate knowledge of ICT and its usage in the teaching of mathematics. The mathematics teachers in this study affirmed that they are familiar with basic technology tools such as calculator, Microsoft Mathematics, GeoGebra, Excel and Multimedia (specifically video lessons from YouTube) used in teaching mathematics. SHS mathematics teachers were familiar with these technology resources used in teaching mathematics because some of these technologies are recommended in the Ghanaian mathematics curriculum for teachers use (CRDD, 2010). The teachers also reported the use of internet to learn about these technology tools, hence their familiarity with these technology tools.

Also, it could be attributed to the fact that the study participants were youthful (less than 40 years), which presupposes that they were birthed in the digital era hence their familiarity with basic technology tools used for teaching mathematics. This result builds on evidence by Mailizar and Fan (2019), who reported that mathematics teachers exhibited higher levels of technology knowledge specifically for GeoGebra. A teacher who is well-versed in technology can adopt new technologies to the classroom setting and comprehend how technology can enrich the delivery of a specific concept. Contrary to this finding, Joshi (2016) stated that mathematics teachers are less aware of particular mathematics software such as GeoGebra, Geometer’s Sketchpad and Graphmatica.

This study revealed that mathematics teachers have low level of preparedness in incorporating technology in mathematics lesson delivery. This finding suggested that mathematics teachers have little exposure to technology tools and how to design mathematics lessons with technology during their teacher preparation programmes. As a result, teachers do not feel well prepared to incorporate technology in their lesson delivery. The results contradict the findings of (Asiedu-Addo et al., 2016; Powers & Blubaugh, 2005) that teachers were well prepared to use technology in lesson delivery through their teacher education programmes. The findings support earlier findings by (Chigona & Chigona, 2013; Garba et al., 2013), who reported that instructional courses offered in pre-service teachers’ education programmes do not adequately expose future teachers to teaching mathematics with technology. This finding implies that if mathematics teachers are less prepared to teach mathematics using technology, it could result in low use of technology in teaching mathematics. This means that there is a need for teacher education programmes to consider adding technology-related courses in their curriculum to prepare teachers adequately on how to teach mathematics with technology. A possible explanation for this finding might be that, while these in-service teachers were pursuing their teacher preparation programmes technology related courses that prepares teachers on designing mathematics lessons with technology were few or non-existent. It is also possible that few or no professional development programmes on technology integration in mathematics lesson delivery was organised for in-service mathematics teachers to prepare them adequately for teaching mathematics with technology.

With respect to self-efficacy beliefs, the analysis pointed out that mathematics teachers possessed high self-efficacy beliefs in incorporating technology in mathematics teaching. This suggests that the mathematics teachers were confident in their ability to use basic technology tools in their lesson delivery. This is very vital because previous studies (Abbitt, 2011; Schrum et al., 2008) support the influence of teachers’ self-efficacy beliefs on technology integration in classroom lesson delivery. The mathematics teachers believed they possess high self-efficacy in teaching mathematics with technology. Similar to this finding, Giles and Kent (2016) disclosed that teachers have high self-efficacy to use technology for lesson delivery. Nonetheless, Lemon and Garvis (2016) reported that teachers did not feel confident in all areas of technology engagement in classroom lesson delivery, while Njiku et al. (2020) reported that mathematics teachers possessed moderate levels of self-efficacy beliefs for teaching mathematics with technology. The finding suggests that once teachers have high confidence in their technology capabilities, it could directly or indirectly influence their technology integration in mathematics lessons.

Again, the results showed that the mathematics teachers have relatively low ICT skills in using basic technology tools such as spreadsheets, multimedia and GeoGebra in teaching mathematics. In line with the literature reviewed, most mathematics teachers do not possess sufficient technology skills to design technology-rich mathematics lessons (Das, 2019; Kamau, 2014). On the other hand, the study indicated that the mathematics teachers have high ICT skills in using calculators for teaching mathematics. This could be attributed to the easy accessibility of the calculator to both teachers and students in the Ghanaian classroom. Also, the teachers have had opportunity to use calculators both as a student and as a teacher enhanced it is not surprised, they rated themselves high regarding the skills required for using calculators in teaching mathematics to students.

Our finding contrast that of Rouf and Mohamed (2018). They reported that most school teachers have high proficiency in ICT skills, particularly in multimedia presentations, spreadsheets and the internet. Our findings differ from these authors because technology integration is context specific. Most Ghanaian high schools are not endowed with technology facilities such as ICT laboratory (where the computers are installed with mathematics application software), uninterrupted power and internet supply; and hence many teachers may be less motivated in committing resources into developing ICT skills. The relatively low ICT skills reported in the use of GeoGebra, spreadsheet and multimedia calls for the need to train mathematics teachers to equip them with the requisite ICT skills for effective implementation of technology integration in mathematics lessons.

In addition, the findings highlighted that teachers’ competencies (teacher preparedness and ICT skills) significantly predict the use of technology in mathematics lesson delivery. The results shed more light on the evidence established by the Social Cognitive Theory that intrapersonal factors (competencies) significantly predict an individual’s behaviour. However, technology knowledge and self-efficacy beliefs did not significantly predict the use of technology in teaching mathematics as reported in the current study. The finding contradicts the report by Lent et al. (2002) that the prevalent intrapersonal factor influencing behaviour is an individual’s self-efficacy beliefs. It has been emphasised in the literature that increasing the self-efficacy beliefs of teachers will lead to successful technology integration in lesson delivery (Abbitt, 2011; Caner & Aydin, 2021). Contrary to expectations, this study did not find a significant effect of self-efficacy beliefs on technology usage in mathematics lesson delivery. This finding is somewhat surprising given the fact that researchers such as Voogt et al. (2013) reported that technology knowledge, pedagogical beliefs and technology use are intertwined. Thus, the decision to use technology in teaching is dependent on teachers’ level of technology knowledge and pedagogical beliefs. One observation that could explain this outcome is the fact that technology use levels among the teachers were relatively low in the current study. Hence, the low levels of technology use in mathematics lesson delivery in this research could not be attributed to teachers’ high levels of technology knowledge and self-efficacy beliefs hence the two constructs not predicting technology use in the current research significantly.

Among the predictors explored in this study, ICT skills emerged as the best predictor of technology usage in mathematics lesson delivery, followed by teacher preparedness. This finding is consistent with the result of Agyei and Voogt (2011), who identified ICT skills as the best predictor of technology usage in the teaching mathematics. Conversely, Ashiono et al. (2018) indicated that training teachers on ICT skills had no significant effect on technology usage in teaching mathematics. Although teachers reported high technology knowledge and self-efficacy beliefs in this study, technology knowledge and self-efficacy beliefs did not significantly predict the use of technology in mathematics lesson delivery. It could be attributed to the fact that knowing about the available technologies that can be used to teach mathematics alone is not enough for effective integration of technology mathematics lesson delivery. Teachers need to be equipped with skills for selecting the appropriate technology tools for specific mathematics concepts and be prepared on how to design lessons with these technology tools. Cheal et al. (2012) affirmed that teacher education courses need to be more contextualised to equip teachers with requisite ICT skills and technology knowledge to promote ICT integration in the classroom.

National Council of Teachers of Mathematics [NCTM] (2011) emphasised this finding in a report that it takes competent teachers to make fair use of technology to enhance students’ aptitude in mathematics. In a nutshell, the result highlighted that although mathematics teachers may possess high levels of self-efficacy beliefs and technology knowledge, they require ICT skills and appropriate preparedness to incorporate technology in their classroom lesson delivery. The finding implies that the use of technology in teaching mathematics would increase if mathematics teachers were adequately prepared and equipped with high ICT skills.

3. Conclusions and implications

It can be concluded from the findings that mathematics teachers possessed adequate technology knowledge and self-efficacy beliefs needed to teach mathematics with technology. Mathematics teachers are familiar with basic technology tools such as calculators, GeoGebra, Multimedia and Spreadsheet used in teaching mathematics. The teachers less use GeoGebra, Multimedia, Spreadsheet in their pedagogical decision as compared with that of calculators.

Consistent with the Social Cognitive Theory, the study established that intrapersonal factors (technology knowledge, self-efficacy beliefs, ICT skills and teacher preparedness) are significant predictors of human behaviour (teaching mathematics with technology). Teachers who have limited levels of preparedness and ICT skills would rarely incorporate technology in their lesson delivery. Technology knowledge and self-efficacy beliefs alone do not automatically guarantee technology integration in classroom lesson delivery, but teachers need requisite ICT skills and preparedness to use technology to teach mathematics. The technology knowledge level and self-efficacy beliefs reported by the mathematics teachers imply they would welcome the use of basic technology tools such as GeoGebra, spreadsheet and multimedia in their lesson delivery. Therefore, with the requisite training and preparation, the teachers may embrace the demand of using technology in teaching mathematics.

With the low levels of preparedness and relatively moderate levels in ICT skills, the curriculum for mathematics teacher education programmes should be reconsidered to include ICT-related courses that would furnish future teachers with ICT skills and give them hands-on experience in designing and teaching mathematics lessons with technology. This also implies the need for professional development programmes for in-service mathematics teachers to supplement their preparedness and ICT skills to incorporate technology in mathematics lesson delivery. Thus, to achieve the affordances of technology in mathematics lesson delivery, it behoves on mathematics teachers to make efforts to augment their ICT skills and preparedness for teaching mathematics with technology.

4. Limitations and further research

Only teachers from public high schools in the Kumasi Metropolis were included in this study’s sample. This may affect the generalisation of the research findings over all SHS, which comprise private, vocational and technical schools. The study revealed that ICT skills and teacher preparedness accounted for 34.6% of the variance in using technology in teaching mathematics. It is recommended that research be conducted to explore other factors that affect the use of technology in teaching mathematics to enable mathematics teachers to tackle the challenge of teaching mathematics with technology.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors received no direct funding for this research.

Notes on contributors

Emmanuel Agyei

Emmanuel Agyei holds a Master of Philosophy degree in Mathematics Education. He is a mathematics tutor who is passionate about research on issues concerning teaching and learning of mathematics with much interest in emerging issues in technology integration in mathematics lesson delivery.

Douglas Darko Agyei

Douglas Darko Agyei (PhD) is a Professor of Mathematics Education in the Department of Mathematics and ICT Education at the University of Cape Coast. His research interest includes Mathematics Education, Educational Technology, TPACK and his research has resulted in over 60 publications in several refereed journals. He has over 12 years of professional experience in managing projects relating to ICT Education.

Isaac Benning

Isaac Benning (PhD) is a lecturer in the Department of Mathematics and ICT Education at the University of Cape Coast. His areas of expertise include: Interactive teaching; Education research on professional development towards technology integration in teaching and learning; using HyperRESEARCH for qualitative data analysis.