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Humanities and Social Sciences Communications volume 11, Article number: 1094 (2024)
833
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Given the substantial body of educational research highlighting the significant influence of student attitudes on academic performance, particularly in disciplines like statistics where anxiety is prevalent, there is a need to investigate how innovative methodologies could reshape these attitudes. This paper will capitalize on the advancements from previously uncombined innovative methodologies of teaching statistics, such as project-based learning, data analytics, collaborative work, or the use of technology. Specifically, this paper reports on the design, implementation, and evaluation of innovative technology-enhanced, collaborative, and data-driven project-based learning, aiming to positively impact students’ attitudes towards statistics as a cornerstone to improve statistical knowledge. To achieve this, a quasi-experimental research study involving 174 secondary students was undertaken, with participants divided into an experimental group (EG) and a control group (CG). Results indicate a notable positive shift in attitudes among EG students following the intervention. The EG students decreased their anxiety after the intervention and, increased their affect and positive attitude toward using technology for learning statistics. By contrast, the CG students do not show any positive effect on their attitudes. These findings underscore the potential of the innovative instructional design implemented in this project to not only foster practical statistical problem-solving skills but also cultivate positive attitudes crucial for statistical competence. Educational implications are discussed.
In our increasingly digital world, technology generates vast quantities of data, and with the rise of artificial intelligence, this influx is set to skyrocket. To effectively harness and make sense of this data, citizens need to be equipped with robust data analytic skills. As evidence-based decision-making becomes increasingly imperative, advanced data analytic abilities will be indispensable. However, a significant challenge lies in the fact that many secondary students lack the positive attitudes necessary to engage with and learn data analytics skills and statistics (Garfield and Ben‐Zvi, 2007; Szczygieł and Pieronkiewicz, 2021).
Previous educational research has confirmed the role of developing positive attitudes to obtaining better results and meaningful learning of mathematics and statistics (e.g., Albelbisi and Yusop, 2018; Dowker et al., 2019; Muñoz et al., 2018; Silva and Sousa, 2020).
In the same vein, Emmioğlu and Capa-Aydin (2012) point out that positive attitudes towards statistics correlate positively with higher students’ results in statistics courses. Furthermore, several studies indicate that most students and adults do not statistically reason about important issues that affect their lives because they have not acquired the necessary skills (Domu et al., 2023; Garfield and Ben‐Zvi, 2007; Haddar et al., 2023; Özmen and Baki, 2021). Therefore, many students do not understand the usefulness or application of statistics in real and daily life and develop negative attitudes, e.g., anxiety, towards statistical content (Gal and Ginsburg, 1994; Williams, 2015). Rejection towards this subject is also accounted for by the widespread and well-known mathematical anxiety (Szczygieł and Pieronkiewicz, 2021) due to the student’s perception that statistics posits a great deal of mathematical content, without a real application and is difficult to understand (Gal and Ginsburg, 1994).
This paper capitalizes on the advancements from previously uncombined innovative methodologies of teaching statistics, such as project-based learning, data analytics, collaborative work, or the use of technology; and it designs an innovative instructional design to promote positive students’ attitudes towards statistics. Moreover, the paper reports on the implementation, and evaluation of technology-enhanced, collaborative, and data-driven project-based learning and its impact on students’ attitudes towards statistics via a quasi-experimental study. The paper contributes with an innovative pedagogy that combines and integrates the advancements of already testing teaching methods for engaging students in big data analysis, increasing their positive attitudes towards statistics, a cornerstone to improve students’ statistics skills and learning.
Attitudes have been broadly defined as not directly observable, inferred aspects consisting of beliefs, feelings, and behavioural predispositions towards the object to which they are directed (Nolan et al., 2012). Although the attitude definition is not consistent in the literature, in accordance with the most frequent definitions in research, an attitude is a psychological tendency that is expressed by evaluating a particular entity with some degree of favour or disfavour (Savelsbergh et al., 2016). Hence, this psychological tendency is shaped through experience and determines future behaviours. In this line of argument, an attitude can be seen as a personal characteristic that has an influence on subject’s behaviour (Di Martino and Zan, 2015).
In the context of learning, attitudes towards mathematics, and statistics in particular, are profound feelings and emotional reactions shaped by students’ experience in solving statistics tasks and throughout time (Tuohilampi, 2016). In other words, attitudes toward statistics can be seen as students’ expectations towards this subject, and according to them, the student will have one reaction or another in statistics class (Batanero and Díaz, 2011). Math anxiety is the sensation of concern and worry felt when thinking about mathematics or while doing a mathematics task (Abín et al., 2020).
Educational research claims that positive attitudes towards mathematics and statistics can be promoted by implementing innovative teaching methods that include, among others, the following five educational variables: (a) student-centred learning; (b) project-based learning and solving real problems or challenges familiar to students; (c) data analytics (henceforth DA) skills; (d) collaborative learning and e) use of interactive technologies (Chew and Dillon, 2014; Savelsbergh et al., 2016).
In this line of argument, recently, the growth in the everyday use of digital technologies is creating vast reservoirs of data. These data have huge but largely untapped potential. The economic sector has already considered the necessity to understand the “big data” generated in each sector and turn it into insight and action. Therefore, there is an increasing demand for citizens with the skills and creativity capable to perform data-driven decision making (Frischemeier et al., 2022). For example, the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report (Bargagliotti et al., 2020) for the pre-K-12 classroom explicitly emphasize the need for innovative instructional programmes about data analytics to teach students to: formulate questions that can be answered using data, learn to collect data, organize data, create graphs and charts with data to answer their questions. In this context, there is a need for studies that innovate and extend best practices in teaching statistics in schools using data analysis and technology-enhancement through a project-based learning approach (Chew and Dillon, 2014; Koparan and Güven, 2014). Countless investigations point to the positive impact of technology on students’ attitudes, and so technology-driven teaching becomes a useful pedagogical tool for teaching and learning statistics (Emmioğlu and Capa-Aydin, 2012; Ramirez et al., 2012).
In this line of research, this paper aims to design, implement, and evaluate a technology-enhanced, project-based intervention that could offer secondary students the statistical and digital skills needed to use data to address real-life problems. Specifically, in this paper, we analyse the effects that this technology-enhanced project-based intervention could have on students’ attitudes toward statistics. Our working hypothesis is that students will improve their positive attitudes towards statistics because the technology-enhanced project-based intervention will create a meaningful and positive learning environment that will raise the student’s awareness of the role of data, statistics, and technology in many everyday problems.
In the next sections, we revise previous research on the effects of the four uncombined, innovative educational variables in statistics education, namely: (i) project-based learning, (ii) data analytics approach, (iii) use of technology, and (iv) collaborative work. This will be followed by our research study, the results and discussion of our findings and, finally, the educational implications for statistics education.
The use of project-based Learning (henceforth PBL) has been increasingly practised globally in schools. This methodology is characterized by the introduction of the following four educational variables: student-centred learning, problem-solving structured in different research phases, contextualized learning contents in real and open-ended challenges and collaborative work (Haatainen and Aksela, 2021). In this line, Batanero and Díaz (2011) claim the importance of contextualizing the data used in real-life problems when designing PBL in statistics. This aspect encourages, firstly, the student’s interest and motivation, even more so if they can choose to tackle the problems they are interested in; secondly, students value the relevance of statistics since it can solve real-life problems and facilitate scientific and economic development. Overall, they adhere to the theory that PBL can improve the students’ attitudes toward statistics. In this same line of argument, Santos (2016) adds to the equation the influential role of digital technologies in solving collaboratively real-life problems and increasing the positive attitudes towards learning statistics to solve a problem in small groups.
Different quasi-experimental studies have reported the benefits of this innovative methodology on students learning and on students’ attitudes and affect towards statistics (Bateiha et al., 2020; Chong et al., 2019; Özdemir et al., 2015; Markulin et al., 2021). In these studies, it is reported that PBL methodology promotes the creation of a creative environment, as most students perceived the project to be an easy and enjoyable activity that favours the learning of mathematical concepts as well as the development of key soft skills such as sense of responsibility, communication skills and ability to work in small groups (Özdemir et al., 2015). Besides, PBL encourages students to take a more active role by allowing them to take responsibility for and decisions on their own learning process while the teacher guides them through their learning processes, by taking into account their interests (Moreno-Guerrero et al., 2020). These PBL characteristics could have a positive impact on students’ attitudes towards statistics (Özdemir et al., 2015), and on students’ affect towards learning statistics (Chong et al., 2019).
Recently, along with the appearance of interactive technologies, new ways of engaging with real-life data—notably via interactive data visualizations—have emerged and new ways of thinking and learning from complex data have evolved (Engel, 2017; Sutherland and Ridgway, 2017, Rao et al., 2023). In this context, various authors have seen the need to develop studies that introduce the perspective of data analytics when designing PBL in teaching statistics (Kazak et al., 2021; Zotou et al., 2020). From this perspective, data analytics is seen as a process of engaging students creatively in exploring data to understand our world better, draw conclusions, make decisions and predictions, and critically evaluate present/future courses of action (Fujita et al., 2018). Data analytics does not focus on learning mathematical procedures but on understanding and interpreting data to solve a real-life problem (Chew and Dillon, 2014). Furthermore, data analytics reinforces the active role of students in learning statistics as they must make the effort to focus on the process of understanding and interpreting data to address a real-life problem. The students are encouraged to solve the problem since the teacher acts only as a guide and will not provide them with a solution.
Interactive technologies have been essential in teaching and learning statistics and data analytics. Technologies can provide a creative and interactive environment to represent, visualize and manipulate data in a way that encourages students to think and learn from complex data. In this respect, our educative intervention has designed a technology-enhanced, project-based learning environment that promotes the use of a variety of technological tools for learning key statistical concepts and developing key skills, e.g., explore, understand and interpret data to solve a real problem. In the next section, we will present key studies that have used technology affordances to promote better statistical literacy and positive attitudes toward statistics.
In the use of technology for teaching mathematics, there is a trend towards constructivist tasks based on research, which supports collaborative approaches, resolution of problems, and the practice of learning by doing. Bray and Tangney (2017) point this out through a systematic analysis of 139 studies and, in view of the results, conclude that contemporary technologies increase collaboration and allow a practical application of mathematics through visualization, modelling and manipulation. They claim that technologies provide an interactive, dynamic, and contextualized learning of the subject. These technological affordances facilitate experimentation and testing of ideas and manage to change classroom dynamics from the teacher leading the session and transmitting knowledge to more dynamic student-centred research.
Technological tools are also increasingly used in teaching statistics as the means to mediate and promote learning of problem-solving strategies and statistical challenges. Among the affordances of technologies to promote statistical education, Ridgway et al. (2017) highlight data visualizations as they facilitate interaction with data in a more intuitive, dynamic, and exploratory way. Such software programmes as TinkerPlots (dynamic data exploration, available at https://www.tinkerplots.com/) or common online data analysis platform (CODAP, available on http://codap.concord.org) are widely used to promote statistical literacy and positive attitudes toward statistics. Among the main characteristics of these software programmes, the more salient are the next four: (a) they facilitate modelling activities, in which students can deeply analyse real-world situations through mathematical representations and asking questions, (b) they mediate between conceptual thinking and investigate probability events and identify patterns, (c) they improve intuition about data representation and analysis, and (d) they facilitate the creation of graphs (Gonzalez and Trelles, 2019; Kazak et al., 2014).
Various authors provide evidence of how the characteristics of technologies such as TinkerPlots, CODAP, and Fathom improve the students’ learning and attitudes. Gonzalez and Trelles (2019) investigated how a group of 15-year-old students increased their motivation through modelling activities in mathematics through TinkerPlots. In this study, modelling is defined as a learning system that encourages students to ask questions and analyse situations that could be real through mathematics. Other authors agree that the use of technological tools, such as CODAP is essential to develop students’ statistical reasoning (Casey et al., 2020; Mojica et al., 2019). The ability of CODAP to facilitate working with large data sets makes it easier for students to focus on making decisions about data analysis and reasoning about different forms of data representation, rather than on struggling with computational work, since no programming knowledge is required (Casey et al., 2020; Frischemeier et al., 2021). In this line, Kazak et al. (2014) showed how 11-year-olds improved their understanding of statistics with the help of TinkerPlots through collaborative work in small groups. The authors used TinkerPlots as a technology that mediated conceptual thinking to investigate various probability events in statistics and identify patterns. They argued that this software favoured the improvement of the students’ intuition about data representation and analysis and facilitated the creation of graphs.
Many other studies amplify the potential of technology in favouring positive attitudes and learning of mathematics by integrating technology in the classroom along with other teaching and learning strategies that have also proved relevant for improving mathematics learning. Attard and Holmes (2020) show that new technologies manage to place the student at the centre of the teaching–learning process: technology captures the attention and interest of students by means of immediate instructions and feedback. In addition, technology offers students an additional and different space for communication, beyond the classroom (Attard and Holmes, 2020).
The technology-enhanced, project-based study presented in this paper explicitly implements the findings of recent educational research based on supporting classroom dialogue, thinking and collaborative learning. In the next section, we will present these key findings.
Collaborative work has been embedded in PBL (Fredriksen, 2021; Lyons et al., 2021; Ozdamli et al., 2013; Özdemir et al., 2015) and its impact on students’ development of positive attitudes towards mathematical learning is highly reported (Kazak et al., 2014; Moreno-Guerrero et al., 2020; Özdemir et al., 2015). Furthermore, educational research claims that interactive technologies can afford group work and communication and enrich the development of key problem-solving strategies (Kazak et al., 2014; Major et al., 2018; Noll et al., 2018).
Promotion of collaborative learning involves working explicitly on ground rules, interactional processes, and exploratory talk (Mercer, 2019). Exploratory talk improves attitudes toward learning as it facilitates the exploration and understanding of content and promotes intersubjectivity between group members when creating jointly new knowledge and understandings (Gómez, 2016; Knight and Mercer, 2015; Mercer et al., 2019). Dialogue is also very important for better organization and management of the group. This aspect is verified by Kazak et al. (2014) through an intervention based on collaborative work with technology. In this experiment, students were instructed to communicate with their classmates in a dialogical way, following five ground rules: (1) ensuring that all members of the group contribute with ideas; (2) asking classmates for arguments, listening to explanations and making an effort to understand; (3) being interested in what the others think; (4) taking into account different points of view or alternative methods, and (5) trying to reach a consensus before carrying out an action with the computer. This study, whose main objective was to teach key concepts of statistics and probability to 11-year-old students, through qualitative analysis of the dialogues from the groups, concluded that the students improved their communication with and opinions about their classmates. It also proved that their contributions were incorporated and integrated, thus facilitating the consensus of ideas.
Our study aims to contribute to research on the design and application of innovative methods in teaching statistics. To this end, our research took a quasi-experimental approach toward answering the following research question: what are the effects of a collaborative, technology-enhanced and data-driven project-based intervention on students’ attitudes towards statistics? Our general working hypothesis was that the design and implementation of a long-term real-classroom intervention that embeds and combines the three key educative variables for the promotion of statistics education, i.e., collaborative learning, technology-enhanced learning, and project-based learning, would have a positive impact on the students’ attitudes towards statistics. Furthermore, our expectations were that those students who received a collaborative, technology-enhanced project-based intervention would improve their attitudes towards statistics unlike their counterparts who followed a regular standard curriculum.
Our research aims to confirm or reject the next four hypotheses:
H1. Students following the collaborative, technology-enhanced, data-driven project-based intervention (henceforth SPIDAS) will improve their global attitude towards statistics. This increment will be higher than their counterparts who follow a traditional intervention.
H2. Students following the SPIDAS intervention will decrease their anxiety towards statistics, unlike their counterparts who follow a traditional intervention.
H3. Students following the SPIDAS intervention will increase their affect towards statistics more than their counterparts who follow a traditional intervention.
H4. Students following the SPIDAS intervention will improve their attitude towards learning statistics with technology more than their counterparts who follow a traditional intervention.
This research is part of a larger EU ERASMUS+ project called International Strategic Partnership for Innovative in Data Analytics in Schools (SPIDAS henceforth) aiming to innovate and extend best practices in data analytics in schools. In this paper, we will report only on one aspect of the ERASMUS+ project; with an eye on analysing the impact of a SPIDAS educational intervention on students’ attitudes towards learning statistics, a quasi-experimental design was planned in which an experimental group (henceforth EG) followed the SPIDAS instruction, and a control group (henceforth CG) followed the traditional education method.
Readers can learn more about the design, implementation, and multi-method evaluation of the statistics innovative instructional carried out in this Erasmus+ project in Cujba and Pifarré (2023, 2024) and in https://spidasproject.org.uk/ web site.
A total of 174 students from two Spanish private publicly funded schools in the 8th grade (13–14 years old) participated, either as part of the experimental group (EG) or the control group (CG). 110 students belonging to the EG and had a homogeneous gender distribution: 52.7% (58) of them were girls and 47.3% (52) of them were boys. In the CG participated 64 students and the gender distribution was also homogeneous: 53.12% (34) of them were girls, and 46.88% (30) of them were boys. Additionally, both schools had similar medium socioeconomic characteristics, and the sample demonstrated a comparable level of general academic achievement, as evidenced by the results of the National Test of Basic Skills. Several studies showed a significant correlation between socioeconomic status and academic achievement, being negative in schools with lower socioeconomic status backgrounds (Berkowitz et al., 2017).
Additionally, the study assessed participants’ prior statistical knowledge, uncovering a notable deficiency in this area (Cujba and Pifarré, 2023). For further insights into the beneficial effects of the innovative instructional design detailed in this paper on enhancing students’ statistical knowledge, readers are encouraged to explore the Cujba and Pifarré (2023) findings.
Following previous research in the area (e.g., Nolan et al., 2012), this study evaluates the students’ attitudes towards statistics with technology using a questionnaire developed and validated exploratory into Spanish (Cujba and Pifarré, 2024). In synthesis, the validation process consisted of three steps: firstly, the questionnaire development was based on a thorough revision of previous international questionnaires. Secondly, a double back-translation of the original items was carried out and followed a consensus process among expert judges’ methodology (content validity). Thirdly, the questionnaire developed was applied and tested to a sample of 254 13/14-year-old Spanish Secondary Education students. As a result of this process, a three-factor structure (namely anxiety, learning statistics with technology and effect) was found through exploratory factor analysis using the varimax rotation with the SPSS programme. Evidence of internal consistency was provided with an α = 0.83 (“anxiety” factor α = 0.83; “learning statistics with technology” factor α = 0.76; “affect” factor α = 0.77). The results showed suitable psychometric properties to use the questionnaire to evaluate secondary education students’ attitudes toward statistics with technology in the Spanish language.
The final version of the questionnaire contains 16 items structured along three factors: anxiety, learning statistics with technology, and affect. The questionnaire was applied to the 174 students who participated in this study at two different moments: before and after the educational intervention. The students were tested individually, and their attitudes were evaluated using a Likert scale of 4 options: 1 = Totally disagree, 2 = Disagree, 3 = Agree, and 4 = Totally agree. Scores on all negatively worded items (i.e., anxiety factor items) were reversed prior to data analysis.
The EG educational intervention lasted 30 h, distributed over 2 months. Students completed a real-life statistical project on how the weather influences daily activities, a topic of great current interest that requires well-argued, data-based answers. Students worked in small groups of 3–4, combining on-site classroom activities with work outside the classroom. For the outside work, the groups collaborated synchronously on shared documents using the Google Drive platform.
SPIDAS project incorporates and combines innovatively the three key pedagogical axes considered by the literature review as relevant in promoting data analysis skills in students, namely: (1) data-driven project-based learning, (2) collaborative learning and (3) the use of technology to help to learn statistics through visual learning (Frischemeier et al., 2021). In our project, we used the open-source software CODAP. This software has the same attributes as TinkerPlots. Both software are easy to use by inexperienced users, allow flexible plot creation, deal with data as a first-order persistent object, support an exploratory and confirmatory analysis, and are very interactive (McNamara, 2018). As a disadvantage, TinkerPlots needs previous installation and a payment license per computer.
Next, we describe how the three pedagogical axes were incorporated into the SPIDAS educational intervention. Fig. 1 graphically illustrates how the SPIDAS intervention leverages and combines the advancements of these three innovative methods for teaching statistics. Readers can learn more about the SPIDAS educational intervention in: https://spidasproject.org.uk.
SPIDAS intervention.
Data-driven project-based learning: The SPIDAS intervention explicitly incorporates the four educational variables highlighted in the PBL literature review (e.g., Batanero and Díaz, 2011; Bateiha et al., 2020; Haatainen and Aksela, 2021): (a) structure of students’ learning process in enquiry phases; (b) statistical literacy contextualized in real and daily life; (c) active role of the students and guidance role of the teacher and (d) development of ‘data analytics (DA) cycle’ drawn on PPDAC statistical enquiry cycle (Wild and Pfannkuch, 1999), statistical thinking process (Wild et al., 2011) and informal statistical inference (Makar and Rubin, 2018). In synthesis, the main tasks of the data-driven project are presented in Table 1. To give more information about the instructional design, Table 1 and Figs. 2–5 present examples of activities of one group of students.
Example of Define the problem activity.
Example of students’ graph for Explore data.
Example of Draw conclusions activity.
Example of Make decisions activity. It is presented students’ infographic to communicate their project decisions and conclusions.
Collaborative learning: Students worked in small groups during the whole project and were encouraged to actively create, reflect and evaluate ideas by using effective communication skills and ground-rules. Three specific strategies from “Thinking Together” programme (Mercer et al., 2019) for promoting good small-group work and exploratory talk were explicitly taught and these are (a) reflection on group roles, (b) reflection on attitudes and behaviours that promote collaborative learning, and (c) development of effective ground rules.
Technology: The SPIDAS project used two types of technologies: CODAP data analysis software and different applications linked to Google Drive. CODAP software allows graphical visualization of data and supports students understanding and interpretation of their data. Due to the CODAP interactive and manipulative design, students can actively explore their own data and obtain meaningful graphical representations that could help draw data-based conclusions (e.g., Fig. 3). Considering the extensive research about the role of interactive technologies (Major et al., 2017; Pifarré, 2019) to enhance collaborative work and dialogic discussions, some Google Drive applications (such as Docs, Slides) were used. These applications allow the creation of synchronic and multi-user workspaces that in our project fostered four key processes of collaborative work with technology: (a) discussion of shared ideas; (b) co-construction of new ideas, planning and reflection on joint work; (c) support to the development of statistics literacy and (d) enrichment of data analytics strategies such as organization of data, manipulation of data, creation of graphs, analysis of data and making decisions based on data.
The innovative instructional design advocated for student-centred methodologies, wherein teachers adopted a dual role: part lecturer, part coach, fostering collaborative learning within student groups. They facilitated the data analytics projects undertaken by each group, providing guidance throughout the process and supporting them in drawing conclusions and making informed decisions based on their analyses.
The CG followed a traditional intervention. It also lasted 2 months. It was a teacher-centred intervention and the teacher mainly used lectures to teach the same statistical concepts taught in the EG. The statistical literacy taught integrates the next concepts: mean, median, mode, range, variability, qualitative and quantitative variables, frequency, proportional reasoning, count, reading graphs, sample, and population. CG students followed the lectures, had a passive role, paid attention to the explanations of the teachers and applied what they had learned by carrying out a series of individual and routine exercises. Unlike the EG, in the CG all the students worked with the same data provided by the teacher. Some of these exercises were carried out outside the classroom, as homework and these exercises were solved individually.
Regarding the use of technology, Excel software was used. This technological tool consists of a spreadsheet that allows calculations and graph creation. Working with this software requires being knowledgeable about the mathematical operations necessary to execute the desired parameters. We believe that with Excel, students should invest more time in understanding which calculations and formulas they need to apply and how, rather than lesson analysing and interpreting data. The teachers explained in class the operations that were to be carried out with Excel, so that, at home, the students could carry out most of the activities. These activities contained real-life data, yet lacked contextualization of the problem or daily life situation.
In order to analyse the sample normality a Shapiro–Wilk statistical test was run with SPSS. Due to the sample is not normally distributed, non-parametric tests were used. On one hand, for comparing the intragroup differences between the pre-test and post-test results, the Wilcoxon test was established. On the other hand, Mann–Whitney U test was used to analyse the intergroup differences between the post-test results in both groups (experimental vs. control).
This section will analyse the effects of the technology-enhanced, collaborative and data-driven project-based learning on four variables (or factors) included in the questionnaire on the students’ attitudes towards statistics, namely: (a) global attitude towards statistics learning; (b) anxiety towards statistics; (c) affection towards statistics; and (d) attitude towards statistics with technology. The global attitude score resulted from the sum of the 16 items included in the questionnaire (Annex). Similarly, the score for each factor was calculated by adding the ratings of all the items that composed each factor. Therefore, the factors of anxiety (i5, i7, i10, i11, i12) and affection (i1, i3, i8, i14, i15) contained five items each and the statistics learning with the technology factor contained six items (i2, i4, i6, i9, i13, i16). The Likert scale was a four-point scale: 1 (strongly disagree), 2 (disagree), 3 (agree), or 4 (strongly agree).
Wilcoxon analyses were carried out to study the effect of the educational interventions on each experimental (EG and CG) group of students’ attitudes toward statistics. The effect size was checked with Cohen’s d statistic. Table 2 summarizes these results. Experimental group students showed significant differences (α = 0.05) in their global attitude score. Besides, experimental group students displayed significant scoring differences in the anxiety and technology factors. Although there was a positive trend in the affection factor, no statistical significance was found.
The control group students did not show significant differences neither in global attitude scores nor in any of the three factors analysed.
A Mann–Whitney U test analysis was carried out to investigate the differences between the two groups, before and after students’ participation in the SPIDAS intervention. The effect size was checked with Cohen’s d statistic. Table 3 summarizes these results. These analyses display significant differences (α = 0.05) between EG and CG students as regards their global attitude score and in three factors of the questionnaire: namely Anxiety, Affection, and use of Technology. Figure 6 displays the mean scores obtained by the two groups in pre- and post-measurements of the different factors of the questionnaire and the significant statistical differences observed in the analysis.
Pretest and posttest results and statistical differences between EG and CG students.
Furthermore, these results firstly show that the experimental group obtained higher mean post-test scores than the control group regarding the overall attitude questionnaire towards statistics (see Fig. 6). The experimental group presented a higher global attitude score in the questionnaire both before and after the intervention. Although before the intervention the global attitude of the EG students was already higher than that obtained by the CG, the post-intervention improvement was greater and statistically significant in the EG and not in the CG, whose improvement was hardly perceived. This result allows us to conclude that the SPIDAS intervention had a positive impact on the student’s attitudes toward learning statistics with technology.
Secondly, EG students significantly decreased their levels of anxiety toward learning statistics after their participation in the SPIDAS intervention, unlike the CG students, who showed a statistically low decrease in this variable. The difference in the post-measure between both groups was statistically significant, being the EG score higher than that of CG students (Fig. 6).
Thirdly, regarding the affection factor, in EG students there was a tendency to improve this factor after the SPIDAS intervention. The post-test value was higher than that of the pre-test in this group. On the other hand, in the CG the post score in the affection factor decreased. Therefore, the impact of the traditional intervention had a negative impact on the student’s perception of their abilities to learn and solve statistical problems. The comparison between the two groups (see Fig. 6) yielded statistically significant differences between the EG and the CG, in the pre- and post-measures. In addition, the EG showed a higher score in the post-measure while the CG decreased its post-score. This result increased the differences between the two groups in this variable. These data allow us to conclude that the impact of the SPIDAS intervention also had a positive impact on the affection variable towards learning statistics.
Finally, with respect to technology, EG students significantly improved their attitude toward learning statistics with technology after the SPIDAS intervention, unlike the CG students who hardly showed any improvement. The comparison of post-intervention scores between both groups (see Fig. 6) as regards the technology factor shows statistical differences between both groups, namely, EG students obtained higher scores in this factor compared to CG students. Thus, the technology-enhanced intervention positively influenced the students’ attitude towards learning statistics.
The main objective of this study was to investigate the effects of technology-enhanced, collaborative, and data-driven project-based learning on the students’ attitudes towards statistics. This study distinguishes itself from other PBL studies on statistics because we investigated a long-term intervention in real classrooms and integrated into one intervention the three pedagogical variables that previous research highlighted as relevant in statistics education: (a) the use of technological tools and affordances for analysing and visualizing data, (b) enrichment of collaborative strategies and (c) project-based learning with a data analysis approach.
Results show that the designed SPIDAS intervention had a highly positive impact on the students’ attitudes toward statistics (Hypothesis 1) and on student’s affect towards learning statistics (Hypothesis 3). Our results support those obtained by other authors that indicate that the PBL is an innovative methodology that meets the necessary characteristics to improve students’ attitudes and increase their interest and motivation towards statistics, as the active role of students in investigating real-life questions is notable (Koparan and Güven, 2014; Siswono et al., 2018). The EG intervention granted students an active role in investigating a problem that both captured their interest and was related to a daily problem, with the added use of technology. According to Siswono et al. (2018), improvement in learning statistics is greater if the PBL is combined with technology.
Furthermore, our SPIDAS intervention explicitly taught students a series of collaborative strategies, such as the assumption of different roles, drawing up a joint work plan, managing time for solving problems, distributing responsibilities and co-evaluating group work. Previous educational research highlights that the improvement of the organization and management strategies of group work has a positive impact on the better functioning of small group work and on the creation of positive synergy between group members, which in turn has a positive impact on the all-students’ attitudes towards learning (Chang and Brickman, 2018; Pai et al., 2015). In this respect, our study confirms these results.
Unlike the results obtained by the EG students, the traditional intervention followed by the CG did not improve the students’ attitudes towards statistics. Previous research points out that one of the limitations of traditional teaching is that it does not contextualize statistical concepts with real-life situations and thus, students cannot establish meaningful links with daily life problems. This has a negative impact on the students’ attitudes towards learning statistics (Bateiha et al., 2020; Hwa, 2018; Özdemir et al., 2015). Our CG students learned statistical concepts focusing on mathematical procedures and calculations of sets of data that bore no relation with their real-life context. This makes it difficult for students to build meaningful learning and feel that statistical concepts could be useful for them outside the school context and for solving daily problems (Lalayants, 2012). Different studies highlight that the practical use of curricular content in collaboration with peers and with the teacher’s guidance is one of the key elements that can explain students’ learning (Andrade and Chacón, 2018; Torrecilla, 2018). These elements are emphasized in the experimental intervention and, on the contrary, are not usually part of a more traditional teaching.
Despite the positive results obtained by EG in all the factors of the questionnaire, it was revealed that for both groups—EG and CG—there was a certain lack of interest of the students towards statistics (item 3 → EG p = 0.007; CG p = 0.047) and they did not get to enjoy learning statistics (item 1 → EG p = 0.081; CG p = 0.104), since these items present lower scores in post-intervention measure than the pre-test measure. Also, technology did not make the learning of statistics more interesting (item 16 → EG p = 0.976; CG p = 0.50). Despite this negative perception of learning statistics, the actual improvement in EG compared to CG is remarkable as it is supported by statistically significant differences.
One possible explanation for the slight improvement in the EG students’ affection may be accounted for in that the PBL involves more complex procedures, more effort, and more time in fulfilling the tasks than traditional teaching to learn the content (Koparan and Güven, 2014). Being the first experience of the students with a PBL, they may need being involved in further and longer-term PBL experiences to present better and more positive perceptions about learning statistics. Therefore, more long-term studies using innovative methodologies are needed to investigate more about the impact of these methodologies on students’ attitudes and affection in learning statistics (Siswono et al., 2018).
Our results also reveal that the SPIDAS instruction had a positive impact on the decrease of the students’ anxiety towards learning statistics (H2). In addition, our results show that the educational intervention followed by the EG had a greater impact than the traditional intervention followed by the control group in reducing students’ anxiety towards learning statistics. These findings are consistent with those found in previous research studies, which claimed a strong relationship between mathematical anxiety, motivation and mathematical achievement (Abín et al., 2020; Henschel and Roick, 2017; Passolunghi et al., 2016).
On the other hand, unlike the results obtained with EG students, the CG students’ anxiety may not have decreased because they learned statistical contents with insufficient context and application to real life. In this line of argument, Lalayants (2012) claimed in his study that the fear felt by a group of university students towards learning statistics was caused mainly by the lack of connection between their studies and statistics. Basically, they did not understand how to apply the content to real-life situations. The same group of university students declared in the questionnaire that it would have helped them reduce anxiety if they had found any of the following aspects in their statistics classes, i.e., practical real-life problem-solving related to their future profession, teachers who cared about their negative feelings, working sessions with technology, and collaborative work in small groups, as opposed to individual work.
Although students decreased their anxiety towards statistics after their participation in the SPIDAS intervention, students still expressed certain levels of anxiety when doing statistics (item 11 of the questionnaire → EG p = 0.069; CG p = 0.661). On this issue, some authors defend that a low level of anxiety toward statistics is not necessarily totally negative. In some cases, a low level of anxiety can motivate students not to give up and continue working to understand the content (Çiftçi, 2015).
These results coincide with those found in previous studies that indicate the benefits of implementing a collaborative and student-centred learning methodology (Bateiha et al., 2020) and carrying out contextualized activities involving real-life problems (Chong et al., 2019) contributed to the students’ increased affection. These characteristics were included in the SPIDAS intervention and, therefore, helped to improve the EG students’ value judgments and motivation in the present study.
Regarding the intensive use of a variety of technological tools to learn key statistical concepts and data analysis skills (Hypothesis 4), our study indicates a statistically significant improvement in the EG students’ attitude towards learning statistics with technology. CG students do not show any progress on this variable. Therefore, the designed SPIDAS intervention confirms that the combination of the use of technology and collaborative work in small groups are powerful pedagogical tools to improve students’ attitudes towards statistics.
These results are consistent with those found by various authors, such as Kazak et al. (2014), who present the use of the TinkerPlots software as an enabling technology for understanding statistical concepts. Other authors conclude that new technologies encourage collaboration, motivation and facilitate the performance of student-centred activities, a combination that improves students’ attitudes toward learning statistics (Attard and Holmes, 2020; Bray and Tangney, 2017; Gonzalez and Trelles, 2019; Moreno-Guerrero et al., 2020).
It is worth noting the higher increase shown by EG in comparison with CG in Item 6 (EG p = 0.000; CG p = 0.031). In our view, this result suggests that the use of CODAP throughout the SPIDAS intervention supported the students’ creation of useful data visualizations and students’ learning of data analytics skills. CODAP software facilitates learning, and this has a noticeable positive impact on student attitudes (Woodard et al., 2020).
As a final conclusion, this study suggests that implementing technology-enhanced, collaborative, and data-driven project-based learning can provide the basis for an appropriate teaching approach to improve secondary students’ attitudes toward statistics, to have a positive impact on the student’s motivation to learn statistics and on the reduction of anxiety in solving problems about this subject. In light of the results of this study, these three educative variables should be considered and included in the design of educative interventions that have the objective to engage students in data analytics in which students are able to select a real problem to investigate, collect and explore appropriate data, make inferences and discuss their conclusions using a data-based approach.
The study shows some limitations that call for further research. Firstly, it was the first interaction of students with statistics, the use of CODAP software in PBL and this learning approach requires a high cognitive implication from students during the learning process (Ge and Chua, 2019). This novelty may cause a cognitive overload that could reduce the impact of the innovative intervention on the students’ attitudes toward statistics. Therefore, the design of longer interventions with a longitudinal research approach capable of improving the students’ attitudes over a longer period of time would probably soften the impact of cognitive overload.
Secondly, our study has revealed that despite the innovative intervention, some EG students still feel anxiety towards learning statistics. Despite this, some research claims that a certain level of anxiety can boost students’ positive actions to not give up and, as a result, successfully fulfil a task (Çiftçi, 2015). Therefore, it would be interesting to design more qualitative research methods capable of capturing and measuring positive levels of anxiety for learning statistics.
Thirdly, as previous studies noted the relevance of socioeconomic status in academic achievement (Berkowitz et al., 2017), for future research, the socioeconomic level of the students will be considered as an independent variable.
Fourthly, the questionnaire used in the study has been useful for evaluating students’ attitudes toward statistics using technology. However, the questionnaire needs further validation to extend the results to other contexts. To this end, as a future research action, we plan to expand the sample, analyse its external validity, and compare the results of the confirmatory factor analysis obtained in this study against other samples (such as students from other courses of Secondary Education, Upper Secondary Education and even university students).
The overall results found in this study are promising for improving students’ data analysis competences with technology and they can be seen as a contribution to the United Nations Education 2030 Agenda which emphasises the need to equip all students with technological and mathematical knowledge. By following this agenda, it is expected that a greater number of students will reach the minimum levels of knowledge in mathematics.
The data supporting this study’s findings are available from the corresponding author (manoli.pifarre@udl.cat), upon reasonable request. The data are not publicly available because they contain information that could compromise the privacy of research participants.
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This paper has been funded by the Strategic Partnership for the Innovative Application of Data Analytics in Schools (SPIDAS) project, European Union’s Erasmus+, under Grant 2017-1-UK01-KA201-036520. Furthermore, the paper has been partially funded by the Spanish Ministry of Science and Innovation under Grant PDC2022-133203-I00. All views expressed are those of the authors, not the European Commission or the Spanish Ministry. Finally, the authors would like to thank the teachers and the pupils of the schools Claver Raïmat Jesuïtes-Lleida and Maristes Montserrat-Lleida for their participation in the study reported in this paper.
Department of Psychology, Faculty of Education, Universitat de Lleida, Lleida, Spain
Andreea Cujba & Manoli Pifarré
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Manoli Pifarré, as the project’s principal investigator, led the conceptual background and the methodology of the paper. Both authors were equally involved in data collection, analysis, and manuscript writing.
Correspondence to Manoli Pifarré.
The authors declare no competing interests.
Approval was obtained from the University of Lleida ethics committee. The vice-rector of research and transfer signed the International Strategic Partnership for Innovative in Data Analytics in Schools (SPIDAS) ERASMUS+ project implementation in the schools that were partners of the project. The procedures used in this study adhere to the tenets of the Declaration of Helsinki.
The schools and teachers participating in this study were also partners in the SPIDAS ERASMUS+ project. The headteachers and the participating teachers were responsible for collecting signed informed consent forms from the parents of all students involved in the study. The signed informed consents were collected previously to the educative intervention. These forms explicitly requested permission from the families to use the data for research purposes.
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Cujba, A., Pifarré, M. Enhancing students’ attitudes towards statistics through innovative technology-enhanced, collaborative, and data-driven project-based learning. Humanit Soc Sci Commun 11, 1094 (2024). https://doi.org/10.1057/s41599-024-03469-5
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