1 Introduction

Geometry, an essential branch of mathematics, plays a significant role in the development of students’ thinking. The National Council of Teachers of Mathematics (NCTM, 2000) elaborated the importance of developing the geometric thinking of middle school students in Principles and Standards for School Mathematics. NCTM pointed out that geometry and spatial skills can help students solve problems and show their mathematical understanding in the classroom and the real world. In addition, geometry has an important role in critical thinking, visualization skills, and reasoning skills (Jones, 2002). Clements (2004) emphasized that in early childhood, geometry and spatial reasoning are the basis of most mathematics learning. Geometric materials are widely studied in school mathematics (Widyasari & Mastura, 2020). Nevertheless, according to the survey results of the Programme for International Student Assessment (PISA), student competence with geometric materials is very low, especially in understanding graphics and forms (Suwaji, 2008). Many students have difficulties in learning geometry (Connolly, 2010; Škrbec & Čadež, 2015), and some students have no confidence in geometry classes (Le & Kim, 2017). The low geometric thinking ability of students is caused by many factors, including teaching quality, learning skills and media used by teachers, but it is mainly caused by media (Widyasari & Mastura, 2020). Ibili et al. (2019) argued that difficulties in learning geometry arise because geometry teaching methods are limited to the use of teacher drawings, oral explanations and textbook pictures.

Liu (2001) suggest that the use of technology in the form of the latest software in developing children’s thinking about geometry is necessary. The collaboration between augmented reality (AR) technology and learning media is one of the creative and innovative efforts offered to students. Previous studies (Bernard, 2015; Maarif, 2013; Noviana & Rahman, 2013) have shown that using technology-based instructional media can improve learning quality and develop mathematical ability. The pictures in picture books play an essential role in communicating and understanding the concepts presented in the text (Nikolajeva & Scott, 2000). Mathematical picture books, which present mathematical content in the form of text and images (Marston, 2010), can improve children’s mathematical communication skills, help them understand mathematical concepts and improve their self-confidence in solving problems (Martinez & Martinez, 2001). With the rapid development of new technologies, picture books have transitioned from paper books to various types of e-books (Damayanti & Febrianti, 2020; Furenes et al., 2021; Yeari et al., 2023). In recent years, AR picture books have gained popularity as an innovative form of digital picture books (ChanLin, 2018; Suryani et al., 2021). In the field of mathematics, AR can replace or complement textbooks and other printed resources that allow only 2D visualization by visualizing mathematical objects in 3D (Özçakır & Çakıroğlu, 2022). Widyasari and Mastura (2020) believe that AR technology has a combination of three-dimensional, interactive and interesting comprehensive technical characteristics, that create space for geometry learning and can improve geometric thinking. Some studies (Corrêa et al., 2013; Kirner et al., 2012) have suggested that reading AR-based interactive books can promote geometry learning. For example, Kirner et al. (2012) revealed that interactive books combined with AR technology can support the teaching and learning of geometric topics, including stereoscopic graphics. However, some studies have shown that AR may have a negative impact on students’ learning (Dunleavy et al., 2008; Morrison et al., 2009). Goff et al. (2018), and Santos et al., (2013, 2016) provided evidence that AR can maintain a low cognitive load or even reduce cognitive load, but some researchers argued that AR technology may impose additional cognitive load on students (Akçayır & Akçayır, 2017; Antonioli et al., 2014; Cheng & Tsai, 2013). Both sides argue in terms of empirically validated principles from cognitive load theory (CLT; Sweller, 1988, 2011) and the theory of multimedia learning (Mayer, 2019). In recent decades, there has been an increasing amount of research on AR technology in educational settings, but the number of studies dedicated to investigating the effects of AR picture book reading is still quite limited (Ahmadi et al., 2015; Stanica et al., 2019; Strouse & Ganea, 2017), and research on the specific effects of technology on geometry learning is also limited (Gutiérrez, 1996). According to Cevikbas et al. (2023) analysis, the learning effects of AR technology in various basic areas of mathematics have not been adequately studied. Previous studies have been limited to examining the effects of AR-assisted geometry instruction on geometry achievement, spatial ability, or student motivation (Billinghurst & Duenser, 2012; Gün & Atasoy, 2017; İbili & Şahin, 2015), but less research has been conducted on the outcomes of affective learning with AR (Akçayır & Akçayır, 2017). In addition, several mathematics educators have studied students' geometric thinking (Abdul Halim & Effandi, 2013; Škrbec & Čadež, 2015; Wu & Ma, 2005). However, most of their studies have been conducted on secondary school students, and there is a lack of research on the geometric thinking of learners at the elementary school level (MdYunus et al., 2019). Therefore, the effectiveness of AR mathematical picture books to enhance elementary school students' geometric thinking deserves further research.

This study aims to further explore the effectiveness of AR mathematical picture books in improving students' geometric thinking, and explores the effects of AR mathematical picture books on students' cognitive load and flow experience. By exploring the effectiveness of AR mathematical picture books in the elementary school mathematics curriculum, this study contributes to the current efforts to incorporate AR picture books into the classroom environment. The study provides a new path for the cultivation of elementary school students' geometric thinking and a new perspective for interactive teaching between teachers and students. Moreover, the collaboration between AR technology and picture books in this study will provide some empirical references for future researchers, educational AR software developers and teachers. This study could be useful for future research focusing on the benefits of AR-based instructional environments, particularly AR tools for geometry education.

Specifically, this study used quantitative and qualitative methods to explore the differences between three groups of students: reading AR mathematical picture books, reading mathematical picture books, and reading mathematical texts. We developed mathematical picture books based on AR technology and conducted geometric history reading activities based on three different reading media. Through a quasi-experimental setting, the effects of three different reading media on primary school students’ geometric thinking, cognitive load and flow experience were compared, and the following hypotheses were proposed:

  • H1: Reading AR mathematical picture books can improve the level of geometric thinking of primary school students.

  • H2: AR mathematical picture books can reduce the cognitive load of primary school students in the reading process.

  • H3: AR mathematical picture books can enhance the flow experience of primary school students in the reading process.

The study is organized as follows: Following the introduction, the literature review is conducted in Sect. 2. The methodology of the work is explained in Sect. 3. The results are presented in Sect. 4. In Sect. 5, the implications of our study are highlighted, and limitations and future research directions are provided. Lastly, Sect. 6 is a general conclusion.

2 Literature review

2.1 AR mathematical picture book

Picture books are characterized by simple words, vivid illustrations and rich and easy-to-understand scenes (Zhang et al., 2023), which provide readers with an easy-to-perceive learning experience. In the 1990s, the NCTM advocated the integration of picture books into junior students' mathematics learning (NCTM, 1989, p.27), and mathematics picture books came into being. Mathematical picture books present mathematical content in the form of text and images (Marston, 2010), help students have mathematical dialogues and communication (Nesmith & Cooper, 2010, p.280), and stimulate students to learn mathematics (Zhang et al., 2023). AR is a fusion technology that adds virtual objects to the real world (Dan & Park, 2019) and allows users to view and interact with virtual content in the real environment. The earliest example of applying AR to picture books is MagicBook (Billinghurst et al., 2001). In AR picture books, characters and objects are presented as 3D animations accompanied by various technical effects (e.g., video and audio) and interactive features (e.g., touch, zoom, and rotate) (Alhumaidan et al., 2018). The virtual content in the AR picture book overlaps with the printed images in the physical picture book and appears on the screen at the same time, forming a unified hybrid space (Liu et al., 2019). Readers can see the virtual content superimposed on real books on the AR display and obtain a brand-new reading experience. In summary, AR mathematical picture books are a kind of picture book that combines AR technology and presents math content in various ways in the virtual and real worlds.

2.2 Influence of AR mathematics picture book reading on geometric thinking

Thinking refers to the process by which the brain searches for answers, ideas or questions (Ananda et al., 2018). Geometry is a visual model presented by nonphysical phenomena, which are related to the real world and include the mathematical part studied (Hanafi, 2018). In the 1950s, Dina Van Hiele-Geldof & Pierre Van Hiele, inspired by Piaget’s theory of stages of cognitive development, proposed Van Hiele's geometric thinking model, which divided the development of geometric thinking into five levels: visualization, analysis, informal deduction, formal deduction and rigor. The development of each level is continuous, and it is possible to jump to the latter level only after reaching the previous level (Usiskin, 1982; Burger & Shaughnessy, 1986). Van Hiele’s geometric thinking model describes how people perceive geometry, which has been successfully applied to the measurement of students’ geometric thinking levels. The Van Hiele Geometry Test (VHGT) of the Cognitive Development and Achievement in Secondary School Geometry (CDASSG) Project was designed by Usiskin et al. (1982) based on Van Hiele’s geometric thinking level theory (Şefik et al., 2018). It consists of 25 multiple-choice questions, grouped into sets of five questions representing five hierarchical types of Van Hiele’s geometric thinking. Scholars from different regions have translated and adapted it, such as Astuti et al. (2018) and İlhan and Oral (2012), who localized the topic and found that all versions performed well after validation testing and reliability research. Therefore, the geometric thinking assessment test in this study is also based on the VHGT.

Mathematical picture books and AR have a positive influence on the level of geometric thinking (Widyasari & Mastura, 2020; Kirner et al., 2012; De Ravé et al., 2016; Song et al., 2019), which means that these are favorable forms for improving geometric thinking. Geometry is a subfield in early mathematics involving measurement, calculation, reasoning, visualization and other aspects (Jones, 2002), and it is one of the important areas of mastery in mathematics learning. The stories, pictures and situations provided by math picture books create a meaningful math learning environment for students (Elia et al., 2010), which is helpful for students to learn geometry. Previous studies have shown that reading picture books can arouse children’s mathematical thinking and promote early mathematical development (Splinter et al., 2022), especially in the field of computing ability (Gibson et al., 2020; Mix et al., 2012). They also have a positive influence on students’ mathematical attitudes, academic performance and mathematical representations (Zhang et al., 2023).

Previous studies have shown that it is difficult to learn solid geometry by relying only on traditional two-dimensional graphics (Battista, 2003; Gülkilik et al., 2015), and when used as a learning tool, AR technology can help students understand geometry and mathematics (Tomaschko & Hohenwarter, 2019), creating more possibilities for the presentation of geometric objects. Developed by Chang et al. (2007), GeoCAL provides an AR interactive operation mode for primary school students, who can learn geometric concepts and shapes in the process of interacting with virtual objects. Olkun et al. (2005) asked students to explore geometry in the AR dynamic environment in Geometers’ Sketchpad. Ibili et al. (2019) carried out geometry teaching based on an AR geometry tutorial system. De Ravé et al. (2016) used mobile AR systems in geometry to improve students’ spatial skills and ability to understand and describe geometrical terms. Song et al. (2019) let children use virtual turtles to experience and identify the same or mirror images in TurtleGO based on AR technology to develop their spatial ability. Zhu et al. (2017) made an educational game based on AR technology, teaching abstract concepts such as color mixing, mathematics, and 2D and 3D shape recognition to preschool children. Obviously, AR has been widely used in geometry teaching, and some researchers have also found that AR has a positive effect on students learning geometry and related mathematics content (Dünser et al., 2006; Khalil et al., 2018). In an environment supported by AR technology, students can visualize complex spatial relationships and abstract concepts. While developing geometric concepts, they can also analyze and describe two-dimensional and three-dimensional shapes more clearly (Chang et al., 2007), further understand spatial transformation (Shaghaghian et al., 2022), and improve their spatial skills and abilities (De Ravé et al., 2016; Song et al., 2019).

However, studies dedicated to investigating the effects of AR picture book reading are still limited (Ahmadi et al., 2015; Stanica et al., 2019). İbili and Şahin (2015) and Gün and Atasoy (2017) point out that previous studies have been limited to examining the effects of AR-assisted geometry instruction on geometry achievement, spatial ability, or student motivation. Therefore, this study aims to explore the effects of AR mathematical picture book-assisted geometry instruction on geometric thinking.

2.3 Cognitive load and flow experience in AR mathematics picture book reading

Cognitive load is a multidimensional structure of the effort that learners add to their cognitive system when dealing with specific tasks, and its theory focuses on the difficulty of processing information in working memory (Sweller et al., 2019). In the process of learning and problem-solving, most learners have limited working memory resources that are devoted to dealing with the complexity of practical learning tasks, teaching materials and the learning process itself. By managing and controlling the cognitive load in the learning system, the best learning effect can be achieved. Cognitive load theory divides cognitive load into three types: internal cognitive load, external cognitive load and related cognitive load (Sweller, 2011). Intrinsic cognitive load is determined by the complexity of current tasks, the number of elements that must be processed at the same time (Sweller et al., 2011) and prior knowledge (Sweller et al., 2019). External cognitive load is unnecessary cognitive load, which prevents learners from forming mental models of knowledge, skills and abilities in specific fields. The related cognitive load will be reflected when learners make cognitive and mental efforts to organize new knowledge; it is thus positively correlated with learning achievement (Choi & Kim, 2021). To promote effective learning, the external cognitive load should be reduced as much as possible in the teaching process, the related cognitive load should be increased, and the total cognitive load should not exceed the cognitive load that learners can bear. Research shows that picture books help students develop more complete communication and understanding (Van den Heuvel-Panhuizen & Elia, 2011) and increase their attention and memory of what they have learned (Biemiller & Boote, 2006). In addition, Buchner et al. (2022) showed in a systematic review of the cognitive load and performance affected by AR that most studies reported that AR-based teaching induced a lower or equal cognitive load to more traditional conditions. However, some researchers (Akçayır & Akçayır, 2017; Antonioli et al., 2014; Cheng & Tsai, 2013) have shown that AR technology can provide too much information at once in a learning task, increasing the cognitive load.

The concept of flow experience was first put forward by American psychologist Csikszentmihalyi (1975), who believed that flow was a positive psychological state with challenges, internal rewards and pleasure. In addition, Csikszentmihalyi (1997) believed that when a person’s skills are balanced with the difficulty of a task or activity, the experience of flow and a corresponding sense of high enjoyment are more likely to occur. Zhang et al. (2023) systematically summarized the teaching effect of picture books in mathematics and showed that integrating picture books into mathematics teaching would help students have a more positive attitude toward mathematics and reduce mathematics anxiety. The research of Luedtke and Sorvaag (2018) also shows that picture books can reduce students’ anxiety or math phobia, and the use of interesting plot narratives and characters in picture books will cause the content to be more memorable, which will enhance students’ learning motivation. In addition, math picture books can improve enthusiasm for understanding math problems and finding solutions, as students become engaged and guess what will happen next (Billings & Beckmann, 2005), thus generating a high degree of participation. AR technology has shown extremely obvious advantages in improving the flow experience. In the user experience, the information, aesthetics, novelty and supersocial relationship brought by AR have a positive impact on the user’s flow experience. In the comparison of different media, Yuan et al. (2021) argued that AR brings a heightened flow experience to students compared to the web.

In summary, it can be seen that there is a controversy in previous studies regarding the effect of AR technology on cognitive load in learning. Akçayır and Akçayır (2017) stated that previous studies have mainly focused on examining the effect of AR technology on academic performance, while there are fewer studies on affective learning outcomes. Therefore, in this study, cognitive load and flow experience were included as dependent variables and the effects of AR mathematical picture books on the cognitive load and flow experience of elementary school students were investigated.

2.4 Conceptual framework

Across the different fields of knowledge, researchers have focused on two distinct orientations to educational research, the acquisitionist and the participationist approaches, which have influenced our understanding of learning and the practices of teaching in all content areas (Sfard & Cobb, 2022). Acquisitionism holds that mathematics is discovered or constructed by mathematicians and acquired or reconstructed by learners. Participationism views mathematics as a form of human activity rather than something acquired and sees learning mathematics as a process of becoming a formal participant in this unique activity. To answer some key questions in the research of mathematics education, we have to completely modify some default assumptions as the basis of the research (Sfard & Cobb, 2022). Therefore, the math area has developed the second orientation of participationist approaches, and the research foundation has developed from “learning is the acquisition of concepts” to “learning is the continuous development of participation in activities”. Thus, students’ participation is a very important part of mathematics learning, and how to improve students’ participation in mathematics learning deserves more attention. Interacting with technology can improve the learning experience and is an effective measure to enhance students’ learning participation. Many studies have confirmed that AR technology can promote students’ participation and enhance the learning experience (Ibáñez et al., 2014; Liu & Tsai, 2012; Yuan et al., 2021), but some studies have shown that AR may have a negative impact on students’ learning (Morrison et al., 2009; Chiang et al., 2014; Radu, 2012). Richardson (2016) points out that unfamiliarity with AR applications can lead to cognitive overload or spending too much time in learning activities. One of the explanations for these findings is the replacement hypothesis, according to which the negative effects of using technology are directly proportional to the time people spend on equipment (Rozgonjuk et al., 2021). The current research can supplement this theoretical framework by providing empirical evidence, which can further help the discussion on the relationship between the use of technology and academic achievements.

3 Method

This study used quantitative and qualitative methods to explore the differences between groups reading math picture books based on AR technology and reading math picture books and math texts. A quasi-experimental research design was used to compare the effects of three different reading media on primary school students’ geometric thinking, cognitive load and flow experience. Quantitative data were taken from the students’ pre-and post-test data. Qualitative data collected through semi-structured interviews were analyzed to support quantitative findings. In this section, participants, materials, research procedure and data collection instruments are presented.

3.1 Participants

Eighty-three fourth-grade students at an elementary school in China were divided into three groups to participate in the experiment. The circle is a geometric concept in the curricular content for the first volume of grade 6. Students had not learned about circles in class before the experiment, and their prior knowledge related to circles was basically the same. A pre-test of the geometric thinking level of all the students was conducted before the experiment, and the results showed that there was no significant difference in the initial geometric thinking level of the three classes of students. All participants participated voluntarily, and they all had normal vision and no reading or mental disorders. Before the experiment began, participants were informed that they could choose to quit at any time, and we promised that all personal information would be kept strictly confidential.

3.2 Materials

The reading materials for all participants are on the topic of the historical story of the circle. By reading the historical story of the circle, we can understand the basics of the circle and determine the circumference and area of the circle. The History of Circles is a picture book independently developed and compiled by this study, with the historical story of the circle as the main content. The content of the picture book is reasonable after the teacher's examination. The design of the picture book is shown in Fig. 1. Additionally, we independently developed AR software that can be used with mathematical picture books. Students can use electronic mobile devices with cameras (such as smartphones and tablets) to view virtual content in the software and interact with it. For example, when students use a tablet computer to scan the picture book, the virtual content overlaps with the printed image in the physical picture book and appears on the tablet computer screen at the same time. This virtual content includes rendered 2D and 3D objects and scenes, which are both static and dynamic. Students can interact with virtual objects by touching the screen with gestures, such as clicking on circular objects, measuring the circumference of a circle, talking to people and cutting around barrels. Some software interfaces are shown in Fig. 2.

Fig. 1
figure 1

Pictures of mathematics picture books

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Fig. 2
figure 2

AR-supporting software interface

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3.3 Procedure

We chose a quasi-experimental research method and set up two experimental groups and one control group. In the experiment, three different reading media (AR mathematical picture book, mathematical picture book and mathematical text) were taken as independent variables to explore the effects of these three reading media on pupils’ geometric thinking level, cognitive load and flow experience. Three classes were randomly assigned: experimental group 1 (EG1) students (n = 27) used AR mathematics picture books; experimental group 2 (EG2) students (n = 27) used math picture books; and the control group (CG) students (n = 29) used traditional mathematical texts.

The research process is shown in Fig. 3. The experimental environment is the classroom of this school. Throughout the activity, students mainly read independently based on the distributed reading materials, and teachers only provided a small amount of guidance for the reading rhythm, without any other intervention. Before the experiment, the students were given a 20-min pretest to establish a geometric thinking level baseline. In the reading activities, the three groups of students read the materials by themselves, and the reading duration was 4 h. EG1 students (n = 27) used AR-supporting software on tablet computers to scan the recognition map in the math picture book, and they could see the AR model related to the reading content and interact with it. EG2 students (n = 27) read mathematical picture books, while CG (n = 29) read traditional mathematical texts. After the experiment, a 25-min posttest (including the geometric thinking level test, flow experience scale, and cognitive load scale) was administered to the students, and EG1 (students who used AR mathematical picture books for reading) was interviewed. During the whole process, the administrators used unified activities and test instructions in strict accordance with the requirements. After the test results were recovered, we used SPSS 26 to sort and analyze the data. Two participant responses with abnormal data were eliminated, and 81 valid participant responses were obtained. Finally, conclusions were drawn through analysis.

Fig. 3
figure 3

Research procedure of the study

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3.4 Data collection instruments

The measurement tools used in this study include a geometric thinking assessment test on circles, a flow experience scale, a cognitive load scale and a student interview outline.

  • (1) Geometric thinking assessment test on circles

    Based on Van Hiele’s Geometric Thinking Level Scale (1999), we rewrote some topics to adapt to the knowledge base, life experience and circle-related geometric knowledge background of primary school students in China. The test paper was divided into two parts, which are used to measure the geometric thinking level about the circle before and after students participate in reading activities (see Appendixes A & B). The difficulty of the two test questions is equivalent, and the content is reasonable after the teacher's review. The induction and proof of geometric theory is classified at the geometric thinking level 5 stage, which is usually taught in high school geometry courses. Because the experimental object of our study is primary school students, the geometric thinking level test paper only involves the first four levels. Each geometric thinking assessment test paper has 12 questions, which are divided into four dimensions, corresponding to level 0 (visibility), level 1 (analysis), level 2 (informal deduction) and level 3 (formal deduction). The meanings of each level are shown in Table 1.

  • (2) Cognitive load scale

    The cognitive load scale compiled by Hwang et al. (2013) is used to measure the cognitive load of students in the process of reading. They divided cognitive load into two parts: mental load and mental effort. The scale uses a five-point scale with a total of 8 questions (see Appendix C) and has been tested with good reliability and validity.

  • (3) Flow experience scale

    The scale uses the flow experience scale compiled by Pearce et al. (2005) to measure students’ flow experience during reading. The scale uses a five-point scale with 8 questions (see Appendix D) and has been proven to have good reliability and validity.

  • (4) Student interview outline

    To understand the experience of students reading AR mathematical picture books, we conducted interviews with students in EG1 after the post-test. The interview outline included four dimensions, including interest, perceived usefulness, perceived ease of use and attitude toward using.

Table 1 The first 4 levels of Van Hiele’s geometric thinking
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4 Research results

Before the experiment, we conducted a pretest on the initial geometric thinking level of 83 participants; 2 participant responses with abnormal data were excluded, and 81 valid participant responses were obtained. The results of a one-way ANOVA showed that there was no significant difference in the level of geometric thinking of the three groups in the pretest (p = 0.226 > 0.05), and there was no significant difference among those who were assessed in level 0 (p = 0.288 > 0.05), level 1 (p = 0.288 > 0.05), level 2 (p = 0.828 > 0.05) and level 3 (p = 0.137 > 0.05) among the four levels of geometric thinking. Therefore, in the subsequent data analysis, the influence of the subject’s existing geometric knowledge on the dependent variable is not considered. Then, the data on the geometric thinking level, cognitive load and flow experience of the three groups of students in the posttest were analyzed by one-way ANOVA and multiple comparisons. The results are shown in Tables 2 and 3.

Table 2 One-way ANOVA of geometric thinking level, cognitive load and flow experience of the three groups in the post-test
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Table 3 Multiple comparisons of geometric thinking level 2, cognitive load and flow experience in the posttest
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4.1 Hypothesis 1

To verify hypothesis 1, we first conducted a paired sample t-test of three groups of geometric thinking levels pre-and post-test, as shown in Table 4. The results show that through reading activities, the geometric thinking levels 0–3 of EG1 students and EG2 students were significantly improved (p < 0.05). For students in CG, the first three geometric thinking levels were significantly improved (p < 0.05), but geometric thinking level 3 was not significantly improved (p > 0.05).

Table 4 Paired sample t-test of three groups of geometric thinking levels pre- and post-test
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Then, we used one-way ANOVA to explore the influence of three different reading media (AR mathematical picture books, mathematical picture books and mathematical texts) on the geometric thinking level of primary school students. As shown in Table 2, there was no significant difference in geometric thinking level 0 (F = 1.493, p = 0.231 > 0.05), level 1 (F = 1.768, p = 0.177 > 0.05) or level 3 (F = 0.085, p = 0.919 > 0.05) between EG1 students, EG2 students and CG students, but there was a significant difference in geometric thinking level 2 (F = 3.454, p = 0.037 < 0.05).

To further determine which reading medium had the greatest effect on improving geometric thinking level 2, this study made multiple comparisons among the three groups in level 2 in the posttest. As shown in Table 3, the score of EG1 students was significantly higher than that of EG2 and CG students, but there was no significant difference between EG2 and CG students. Compared with mathematical picture books and mathematical texts, using AR mathematical picture books in students’ math learning can effectively promote the development of students’ geometric thinking at level 2. Specifically, when students in EG1 read independently, AR mathematical picture books created more realistic situations for students and provided a good interactive experience, which made it easy for students to understand new knowledge and form correct geometric cognition, thus significantly improving geometric thinking at level 2.

4.2 Hypothesis 2

To verify hypothesis 2, this study used one-way ANOVA to explore the influence of three different reading media on the cognitive load of primary school students. As shown in Table 2, there were significant differences in cognitive load (F = 5.999, p = 0.004 < 0.01) among the three groups.

Then, this study conducted a single-factor multiple comparison of the cognitive load of the three groups, and the results are shown in Table 3. In terms of cognitive load, the score of EG1 students was significantly lower than that of CG students (p = 0.004 < 0.01), and the score of EG2 students was also significantly lower than that of CG students (p = 0.003 < 0.01). The results showed that reading AR picture books and paper picture books significantly reduced the cognitive load of primary school students in reading mathematics.

4.3 Hypothesis 3

To verify hypothesis 3, the study used one-way ANOVA to explore the influence of three different reading media on the flow experience of primary school students. As shown in Table 2, there were significant differences in the flow experience of the three groups of students (F = 4.445, p = 0.015 < 0.05).

Then, this study conducted a single-factor multiple comparison of the flow experience of the three groups. The results are shown in Table 3. The score of EG1 students was significantly higher than that of CG students (p = 0.004 < 0.05), which shows that the AR-based mathematical picture book can improve the students’ flow experience in the reading process compared with the traditional mathematics picture book.

4.4 Results of student interviews

The results of the interviews showed that the participants believed that AR could help them understand the content better and reduce the cognitive load. They believed that AR mathematical picture books present three-dimensional images, which enable them to see 3D shapes and help them better understand knowledge related to circles. Interviewee 1 said:

“We usually only have two-dimensional pictures when we read books, but with AR picture books we can see 3D shapes, which I think is very useful. I can understand the content of a picture book, but an AR picture book is better because I can understand the content better in 3D.”

Interviewee 2 commented,

“The AR picture book helps me to understand the text. For example, I don't understand how Kepler calculated the area of a circle, AR can give me a clear presentation of how the circle is divided into those small sectors and how it is formed into a rectangle.”

Participants also reported that the AR mathematical picture books provided a good experience and made learning more fun. Interviewee 3 said,

“I really like this AR picture book. In the software, we could go to the house and see how he made that thing. This kind of interaction makes me feel very interesting.”

Interviewee 4 stated,

“I'm actually interested in those electronics. When you use AR technology to teach a class, this product allows us to understand more deeply what we are learning in the course, so my interest in learning mathematics increases.”

Regarding the subsequent willingness to use the AR mathematical picture books, most of the students indicated that they liked the AR mathematical picture books and would be willing to continue to use them in the future.

The results of the interviews indicated that the mathematical picture book based on AR technology received highly positive feedback from the students. The results suggest that AR mathematical picture books can reduce cognitive load and enhance the mind-flow experience, which supports the quantitative data. The interview results also confirmed Liu et al. (2019) view that AR picture books make it easier for readers to understand more abstract and complex content by being more vivid, immersive, and imaginative. Chen et al. (2022) also confirmed the positive attitude of learners toward using AR.

5 Discussion

5.1 Impact on geometric thinking level

The experimental results show that the mathematical picture book based on AR technology significantly improves the level of primary school students’ geometric thinking, which is consistent with the conclusions of some studies (Corrêa et al., 2013; Kirner et al., 2012; Suherman et al., 2020). The development of the geometric thinking level is linear, and only after reaching a certain level can we continue to develop to the next level. In the post-test, the students in EG1 (reading AR mathematical picture books) scored significantly higher than those in EG2 (reading math picture books) and CG (reading math texts), and there was a significant difference in level 2 between EG1 and the other two groups. In contrast, there was no significant difference in scores between EG2 and CG students. Accordingly, AR mathematical picture books have a larger effect on improving pupils’ geometric thinking levels than math picture books and math texts.

Adding AR technology to picture books brings readers a brand-new way to read picture books, which is welcomed by readers (Dan & Park, 2019). First, situational geometry examples in picture books have a positive impact on geometry learning (Paksu & Ubuz, 2009). A good picture book can be used as an important teaching tool or learning resource to help children understand the basic premise of mathematics (Van de Walle et al., 2015). The mathematical picture book The Story of the Circle developed in this study allows students to learn about circles in the context of a story, which is beneficial to students’ geometry learning. In addition, AR technology also has many advantages. AR applications make it easier for students to learn that geometry is achieved through spatial visualization, and incorporating AR into math instruction can help students visualize how changes in structure affect certain attributes (Koparan et al., 2023). Liu et al. (2019) believe that AR picture books make it easier for readers to understand more abstract and complex content through more vivid, immersive and imaginative methods. Geometry teaching with mobile AR systems improves students’ spatial skills and ability to understand descriptive geometry (De Ravé et al., 2016). The AR software developed in this study can be used together with math picture books. Students can use tablet computers to view virtual content with this software and interact with virtual objects by touching the screen with gestures. The animation of virtual content presents the information in the picture book in a dynamic form, and students can carry out practical activities such as measurement and observation in AR software to deepen their understanding and application of geometric knowledge. In addition, the research of Fisher et al. (2012) showed that learning interest has a direct impact on mathematics learning investment and mathematics academic performance, which further shows that AR mathematics picture books can promote students’ geometric thinking level. In the interviews with students in EG1, some students mentioned that reading only picture books would be a little boring, but the interactive component of AR would make them feel interested. They stated that they could simulate the measurement of circles in AR and interact with the story characters, which made them feel the real experience. Students in EG1 thought that the interactivity of AR brought more fun and interaction, which had a positive impact on mathematics learning.

5.2 Impact on cognitive load and flow experience

The experimental results show that the students who read AR mathematical picture books have a lower cognitive load and higher flow experience than the other two groups, which is consistent with the conclusions drawn by Zhang et al. (2023). On the posttest, there were significant differences in cognitive load and flow experience among the three groups of students. The cognitive load of EG1 students was significantly lower than that of CG students, and the flow experience of EG1 students was significantly higher than that of the other two groups. The results of the semi-structured interviews indicated that students felt that AR picture books could help with math comprehension and provide a fun experience. Therefore, compared with math picture books and math texts, AR mathematical picture books have a more positive impact on reducing pupils' cognitive load and promoting pupils’ flow experience.

In the process of students’ independent reading of mathematical materials, the form of AR and picture books significantly reduces students’ cognitive load. Mathematical knowledge itself is complex, and the flat pictures in picture books can help to understand the content. Mathematical picture books based on AR present readers with a more intuitive and three-dimensional space. H. Wu et al. (2013) argued that the realistic environment supported by AR may reduce the complexity of learning materials and visualize unobservable objects or concepts. AR technology increases the readability of mathematical picture books, makes abstract geometric knowledge concrete and visualized, effectively promotes students’ understanding, and reduces students’ cognitive load in the process of mathematics learning. This study shows that the cognitive load of students in EG1 and EG2 is significantly lower than that of students in CG, but the difference between EG1 students and EG2 students is not significant. This shows that AR technology does not bring a higher cognitive load to students and responds to the criticism that AR will cause cognitive load to some extent. For example, Akçayır and Akçayır (2017) notes that AR technology may place an additional cognitive load on students. In the interview with the students in EG1, it was found that the operation of the software and the jump of the interface did not bring them any burden. They thought it was a very simple thing, so the use and operation of AR technology did not necessarily increase the cognitive load of users. Certainly, system design and procedures should also be considered in the practical application of AR technology to minimize the generation of additional cognitive load, such as understanding the operation of the AR system.

The form of AR mathematical picture books also significantly improves the flow experience of primary school students in the process of reading math materials independently. The integration of picture books into mathematics learning has a positive influence on students' mathematics attitudes (Zhang et al., 2023), which helps them understand mathematical concepts and improve their confidence in solving problems (Martinez & Martinez, 2001). With AR technology in math picture books, changes in the position, proportion, 2D and 3D rendering and animation effect of virtual content will bring readers different reading experiences (Dan & Park, 2019). AR picture books offer greater immersion to enhance learners' visual, auditory, and tactile senses (Ibáñez and Delgado-Kloos, 2018). AR-supported picture books enable readers to dynamically interact with virtual content in real environments, thus enhancing the reading experience with a magical feel (Cheng & Tsai, 2014; Danaei et al., 2020; Green et al., 2019). Dong and Si (2018) also considered that the application of AR technology in children's 3D interactive books can provide children with interesting, interactive, in-depth, and authentic learning experiences. In the process of using AR software for independent reading, students can interact with virtual content through electronic screens, and the corresponding behaviors can be responded to promptly, which is conducive to promoting a good flow experience for readers, while traditional mathematics picture books cannot give readers any feedback.

5.3 Practical implications

This research provides a successful pedagogical example of the use of AR/VR in the classroom, and the collaboration of AR technology and picture books in the study will provide some empirical references for future researchers, educational AR software developers, and teachers. Some studies have confirmed that it is difficult to learn geometric transformations and related mathematical concepts through common traditional methods (Gülkilik et al., 2015; Hollebrands, 2003). Widyasari and Mastura (2020) argued that the main factor causing students’ low geometric thinking ability is the medium. Zafirah et al. (2018) argued that mathematics teachers must be creative and skillful in using learning tools and media. Collaborating with the school's information technology (IT) teacher, subject teachers can gain insight into the nature, functions and applications of these technologies. Thus, we encourage subject teachers to creatively use various tools and learning media in the process of teaching mathematics, such as the AR mathematics picture book developed in this study. The use of math picture books based on AR technology allows students to interact with virtual content on the electronic screen, helps students understand math concepts, presents interesting, interactive and realistic learning experiences for students, and gives timely feedback, which improves the geometric thinking level of primary school students and brings higher flow experience and lower cognitive load. In addition, we found that teachers have some difficulties in independently designing and developing AR software, and that they often encounter technical problems (lack of equipment, unstable systems) in the development of tools for AR materials. Therefore, it is recommended that technical personnel provide help for teachers and jointly develop AR software to create an AR learning environment for students to improve their geometric thinking level. The time commitment to using AR mathematics picture books in the classroom and the challenge of developing AR software may appear discouraging, yet given all the benefits, teachers should consider and weigh all of the costs and benefits.

5.4 Limitations and future research

This study has certain reference significance for future research on the application of AR technology to mathematical picture books. However, there are still some limitations in this study. First, the sample size of this study was small, and only 83 students from a primary school participated in the experiment. Future research can include a larger sample size and obtain more quantitative and qualitative data to explore the effectiveness of AR mathematical picture books in assisting mathematics learning. Second, in the experiment, the three groups of students used different media to read independently for only 90 min. Future research will allow students to read independently many times and for a longer time, which will make the experimental data more accurate. Third, when the students in EG1 use the AR software on the tablet to support the math picture book to read independently, AR technology may make the students feel excited because of its novel effects. Finally, teachers in this study could not interfere with students’ equipment, and there was a lack of cooperative learning between teachers and students, which is also a limitation of AR teaching. Future research can further study how to better incorporate teachers with the use of AR mathematical picture books in collaborative learning between teachers and students. Besides, future studies should explore effective instructional designs to improve the effectiveness of AR picture books.

6 Conclusion

With the rapid development of new technology, AR picture books are becoming more and more popular as an innovative form of digital picture books. By exploring the influence of AR picture books on students’ geometric thinking, this study has contributed to bringing AR picture books into the primary school mathematics classroom environment. During the study, we independently developed a math picture book, The History of Circles, and an AR companion software for reading math materials. We conducted a quasi-experimental study in which students were divided into three groups and compared the effects of reading three different materials: AR mathematical picture books, mathematical picture books, and mathematical texts. The results of the t-test and one-way ANOVA showed that the students who read the AR mathematical picture book improved their geometric thinking the most, and had a higher flow experience and lower cognitive load than the students who read the math picture book and the math texts. The semi-structured interview results indicated that students had positive feedback about the AR picture book, which they felt could help with math comprehension and lead to an interesting experience. The results of the study reveal that reading AR mathematical picture books can improve elementary school students' geometric thinking, and bring higher flow experience and lower cognitive load. This study provides a successful teaching case for the use of AR/VR in the elementary classroom. The research offers a novel approach for the cultivation of primary school students’ geometric thinking, and provides practical insights for the application of AR mathematical picture books in primary school mathematics curriculum. The collaboration between AR technology and picture books in this study will provide some empirical references for future researchers, educational AR software developers and teachers.