Digital and Physical Interactive Learning Environments: Early Childhood Mathematics Teachers’ Beliefs about Technology through Reflective Writing

Abstract

In early mathematics education, the beliefs of the teacher are essential for facilitating the integration of technology into teaching mathematics. This study explores the influence of physical and digital interactive learning environments on the development of early childhood teachers’ beliefs about integrating technology into early mathematics classrooms. To understand the development of teachers’ beliefs, a half-year, content-based professional development program that incorporates interactive digital and physical environments was designed for this research on early childhood mathematics teachers (N = 58). We administered a questionnaire to measure teachers’ beliefs regarding employing an interactive technological environment in mathematics classrooms before and after engaging in an intervention program. In addition, a reflective writing strategy was implemented with the participants (N = 10) to understand the development of their beliefs about technology via an evaluation of their levels of reflection. In general, the research findings indicate that an interactive learning environment supports an improvement in teachers’ beliefs about technology. Furthermore, positive qualitative findings were drawn from the reflective writing essays of early childhood teachers. The qualitative findings indicate that an interactive environment enables teachers to be conscious of selecting effective math-specific technologies that facilitate children’s exploration and discovery of mathematics concepts.

1. Introduction

Over the last two decades, Saudi Arabia has concentrated on reforming its education system, with a focus on early childhood education. In 2007, a considerable budgetary allocation was assigned to technology for investment in learning environments geared toward technological advancement and elevating the standards for teacher qualifications [1]. Adapting educational systems to advances in technology is critical to ensuring sustainability through this dynamic process. With rapid advancements in every aspect of our lives—specifically, the proliferation of technology—change has become inevitable, with a considerable impact on early childhood education. In 2015, the Ministry of Education (MOE) of Saudi Arabia announced the Saudi Early Learning Standards framework, which addresses seven standards for children’s learning across all areas. Evidently, the standards comprise STEAM-related concepts—particularly general knowledge and cognition standards [2].

Researchers have highlighted the importance of exploring STEAM subjects during the early childhood years to provide children with a foundation for future learning and to predict later academic achievements [3,4,5,6,7]. In STEAM education, early mathematics is a rich field that utilizes learning environments enriched with activities and thrilling resources. The primary objective is to provide young children with opportunities to enhance their understanding of and proficiency in mathematical concepts and skills, thereby promoting their overall growth and learning potential [8].

To meet the requirements of this era of digital information, educational technologies must be utilized in early mathematics classrooms and learning environments. Consequently, educators must be capable of selecting suitable physical and digital technologies for mathematical learning to enrich children’s learning experiences. Because education using technological tools differs significantly from paper-and-pencil education, professional development is required to equip educators to identify and implement efficacious uses of technology-based educational materials [8,9]. In addition, implementing technological tools in teaching children mathematics is a critical endeavor. Such effort requires not only the teacher’s knowledgeability but also that the teacher possess positive beliefs regarding the importance of enriching the learning environment to facilitate children’s free exploration of mathematics concepts. Thus, teachers’ beliefs about integrating technology into their teaching have a tremendous impact on children’s mathematics learning.

Because of its crucial role, developing positive teacher beliefs is necessary for successful educational system reforms. Interactive learning environments that incorporate digital and physical technologies have a considerable influence on teachers’ knowledge and beliefs [10,11,12]. However, only a few studies have investigated how interactive mathematical learning environments influence teachers’ beliefs regarding the use of digital and physical technologies in teaching mathematics, and most of these studies focus exclusively on virtual environments [13,14]. Furthermore, most of these studies use survey assessment, with some combining survey assessments with interviews. This research investigates how immersion in interactive mathematical learning environments in which digital and physical technologies are combined contributes to belief change in teachers. Teachers’ beliefs were assessed using a questionnaire and reflective writing after the teachers underwent immersion in a professional program on digital and physical technologies. This study attempts to answer the following research questions:

• What is the impact of an interactive learning environment that incorporates digital and physical technologies on developing the beliefs of early childhood education teachers regarding teaching with technology?
• How does immersion in an interactive learning environment support the development of teachers’ beliefs about teaching with technology through reflective writing?

1.1. Theoretical Background

1.1.1. Digital and Physical Interactive Environments

An interactive learning environment that facilitates high-quality education in general—and education in STEM subjects, in particular—is crucial for laying a strong foundation for learning during early childhood. An interactive environment that incorporates digital and physical technologies into mathematics classrooms is needed to support mathematical learning and teaching because it facilitates an innovative pedagogy, teaching actions, and multi-representations [15]. Technology integration in the educational context in general, and mathematics in particular, is a long-standing tradition. In the past, technologies were simply physical and concrete tools that facilitated the construction of meaning. Since the appearance and blossoming of digital tools, the notion of technology has changed to include both physical and digital tools [16]. Physical technologies refer to concrete objects that students manipulate by hand. Physical mathematical tools have been used since 300 BCE, for example, the counting boards used by the Babylonians. Recently, in the twentieth century, many physical manipulatives have been developed for teaching and learning different mathematics concepts—Montessori materials are an example of such tools. Physical manipulatives used in mathematics include a wide range of materials such as dice, coins, spinner, balance scales, and analog clocks. Digital technologies include electronic devices and applications with digital screen displays, which have been developed since 1970 to enhance students’ learning environments [17,18]. In mathematics, many educational platforms and programming environments are designed to enhance exploration, sense-making, conceptual understanding, mathematical modeling, and problem-solving skills [19]. Examples of these digital tools include e-toys, robotics, digital stories, online mathematics games, digital manipulatives and counters, and computer algebra and geometry systems. These digital technology tools have been shown to aid learning and teaching and are used in various ways, for example, as tools for drills and practice and in discovery learning [20], as well as for self-learning activities and self-assessment [21].

There is extensive literature on the distinct influences of digital and physical environments on students’ learning and improvements in the teaching of mathematics [22,23,24]. Mathematics education researchers’ focus on studying environments is indicative of the powerful role that environments play in facilitating learning opportunities for young children [25]. On the one hand, numerous researchers have investigated how the affordances of technology encourage children to develop new ways of thinking about mathematics concepts either via learning in a digital environment [8,26,27,28] or physical environment [29,30]. These researchers conclude that both environments (i.e., digital and physical) have a considerable impact on children’s learning of mathematics. Recent studies investigating the combined use of both digital and physical environments conclude that the synergies between physical and digital technologies expedite comprehension of the meaning of mathematical concepts [10,11]. On the other hand, many researchers have investigated the factors that influence interactive mathematical learning environments and conclude that teachers are the most influential factor impacting students’ learning of mathematics and the learning environment [31,32,33,34], as teachers orchestrate and guide the use of physical and digital technologies in the classroom environment [35,36].

Because of the critical role teachers play in creating appropriate interactive mathematical learning environments, numerous researchers have investigated how teachers can make practical use of digital and physical technologies in classroom environments to provide children with activities that enhance their mathematical learning [37,38]. Researchers recognize that there are many factors that influence whether and how teachers provide students with appropriate interactive learning environments that incorporate digital and/or physical technologies [39,40,41]. These factors include the teacher’s mathematical knowledge, their perception of mathematical learning and teaching, and their attitudes toward and beliefs about digital and physical technologies. In addition, many studies have investigated how the affordances of technologies influence teachers’ mathematical knowledge while working in a digital environment [8,42,43] or a physical environment [29,44]. Ball, Steinle, and Chang (2015) [45] created a virtual learning environment that enhances the pedagogical content knowledge of teachers. Thomas and Palmer (2014) [46], in their paper on the pedagogical technology knowledge framework, highlight that, in addition to the knowledge that teachers need for technology implementation, beliefs play a crucial role in their teaching with technology because their beliefs act as “filters for interpreting their experiences, frames for addressing problems they encounter, and guides for actions they take” ([47], 2015, p. 49). Hence, teachers’ beliefs mediate between knowledge and practice [48], as these beliefs filter, frame, and guide intention, position, and action [47,48].

1.1.2. Teachers’ Beliefs

In the 1960s, mathematics education researchers considered teachers’ beliefs to be a critical factor in the teaching and learning of mathematics [49]. Philipp (2007) [50] defined beliefs as “psychologically held understandings, premises, or propositions about the world that are thought to be true” (p. 259). Many researchers conclude that teachers’ beliefs influence classroom environments, instructional decisions, teaching practices, and students’ attitudes and learning [51,52,53,54]. In addition, numerous researchers posit that teachers’ beliefs are essential for integrating technology into mathematics teaching [46]. Schoenfeld (1992) [55] researched teachers’ beliefs and reported that teachers’ beliefs about the nature of mathematics determine the type of classroom environment the teacher creates, and the environment contributes to shaping students’ beliefs about the nature of mathematics. With advancements in technology, some researchers have focused specifically on teachers’ beliefs about the role of technology use in learning and teaching, and they conclude that teachers’ beliefs about teaching with technology influence their use of technology in teaching [56,57]. Based on these interrelationships, changes in teachers’ beliefs regarding technology integration potentially influence students’ learning and their beliefs about technology use.

Developing positive teacher beliefs is a crucial aspect of reform efforts in general, and teaching and learning mathematics in particular. Therefore, researchers have attached particular importance to studying the phases of change in and development of teachers’ beliefs, the factors that influence this development, and the elements that may facilitate shifts in teachers’ beliefs. These researchers conclude that it is possible to change teachers’ beliefs through suitable interventions, such as teacher education programs [58,59], professional development programs [60], teaching experiences [48], and self-reflection [61]. Liljedahl, Rösken, and Rolka (2021) [59] found that immersing preservice teachers in courses designed around problem-solving and alternative learning methods bolsters the development of teachers’ beliefs. Thurm and Barzel (2020) [60] found that professional development programs based on teaching mathematics using multi-representational tools had a significant effect on teacher’s beliefs about teaching with technology. In addition, Speer and Eichler (2022) [12] studied the development of teachers’ beliefs through a seminar on learning mathematics using digital tools—the seminar had four phases: learning, designing, teaching experiment, and reflection. They found that positive teacher beliefs were developed through the program, although with slight individual deviations. Speer and Eichler also found that teachers’ beliefs progress through four phases: an initial situation, purely positive beliefs, disillusionment, and differentiated beliefs. Altogether, changing teachers’ beliefs about technology integration is a critical factor in mathematics education reform efforts.

2. Materials and Methods

This study addresses the impact of an interactive learning environment that incorporates both digital and physical manipulatives on the development of teachers’ beliefs about integrating technology into early childhood mathematics classrooms. The study population comprised female early childhood mathematics teachers taking a graduate program in early education at a university in the city of Alahsa, Saudi Arabia. In addition, this study follows a convenience sampling selection procedure. The members of both the experimental and control groups were registered for a core course in the graduate program called Teaching Mathematics to Young Children. All participants were early childhood teachers who had a range of two to five years of teaching experience.

The graduate course in which the teachers participated in this research had a 16-week duration. Thirty of the study participants were assigned to the experimental course, while 28 were assigned to the control group. Both experimental and control groups were taught by different professors. In addition, to understand and track the development of teachers’ beliefs through reflective writing, a convenience sampling of 10 participants from the experimental group was performed; these individuals were selected because they were willing to review and clarify their reflective essays.

The main goal of the content-based course for all participants (both experimental and control group) was to learn to teach students topics that are relevant to young children during their first years of life. These topics include number sense, addition and subtraction, multiplication and division, and geometrical concepts and spatial reasoning. In addition, as part of the course goal, both groups learned about technology integration in the mathematics classroom. Nonetheless, the control group followed direct instructions for learning about these educational topics. Similar to any educational graduate course, both groups engaged in writing assignments about teaching mathematics to young children.

The purpose of the experimental design of the graduate course was to teach teachers effective strategies for recognizing and promoting mathematical development among young children by enriching the learning environment with interactive tools such as digital and physical manipulatives. More specifically, the course is intended to facilitate teaching the meaning of mathematics concepts and to allow for the development of teachers’ beliefs in integrating interactive tools into the teaching of children.

In addition, the design of the experimental course took into consideration several principles developed by Guàrdia, Maina, and Sangrà (2013) [62] for empowering teachers to deliver impactful learning experiences in an interactive environment. These principles are employed primarily in courses that are blended in nature to enable effective teaching and learning. The guidelines are as follows: clear planning presented to the teacher participants, empowerment of learners through engagement in course activities such as mathematics tasks, collaborative learning among participants, support for social networking and discussions via online platforms, encouraging peer cooperation assessments and feedback, and enriching the learning experience with various digital applications, online tools, and hands-on manipulatives. Notably, for both the experimental and control groups, the graduate program broadly followed the guidelines of the Education and Training Evaluation Commission for course design in Saudi Arabian universities.

The experimental course was designed around three main sessions (Figure 1). The first session of the experiment in each lesson was the foundational stage, during which the teacher participants engaged in reading about new trends and publications on teaching specific mathematical concepts using Blackboard, an online platform. The second session involved a face-to-face session in which the teacher participants met with an instructor to discuss specific mathematical concepts, research thoughts, guidelines for teaching the mathematical concepts, and video examples with rich environments. The teachers were then presented with an example task, which they worked on in groups to solve using hands-on and digital manipulation. Through this process, they explored how children may determine the meaning of similar problems with the utility of an interactive environment. This was the third session, an online exercise in which the teacher participants engaged individually in writing their reflections on the entire experience of learning mathematics concepts via an interactive environment and how such settings can be effective in aiding children in learning mathematics concepts.

2.1. Instruments

This study used a mixed-method design to investigate the development of teachers’ beliefs regarding integrating interactive technology into their approaches to teaching children after taking the intervention course. We used two instruments to fulfill this goal. First, we implemented a teacher beliefs about teaching with technology instrument (BT) adapted from Thurm (2017) [63] that is designed to gauge the strength of different aspects of teachers’ beliefs regarding technology use in mathematics classrooms. The instrument comprises 25 statements, which are answered on a five-point Likert scale ranging from 1 (strongly disagree) to 5 (strongly agree). These statements assess six dimensions of beliefs: multiple representations, discovery learning, time consuming, skill gain, mindless working, and procedures first. The multiple representations dimension comprises items that assess the belief that multiple representations in mathematics can be enhanced using technology (4 items). The second dimension, discovery learning, assesses the belief that discovery learning can be embraced through technology (5 items). The next dimension assesses the belief that technology is time consuming (3 items). This category comprises negative beliefs about technology use in mathematics classrooms; however, the statements were inverted to align with the five responses (1 = strongly disagree to 5 = strongly agree), such that a high score on each scale item indicates strongly positive beliefs and vice versa. The skill gain dimension assesses the belief that technology has a positive impact on computational skills (4 items). In the original scale, this dimension was denoted by “skill loss” indicating negative beliefs about technology. This dimension was adapted to contain items that assess the belief that paper-and-pencil approaches are not impeded by the use of technology in mathematics classrooms. Mindless working (5 items) comprises scale items on the belief that technology leads students to “mindless button pushing” ([64], p. 3) and that working with technology is just a “substitute for thinking”. Procedures first comprises items that assess the belief that technology tools should be presented to students after they have mastered relevant concepts without using such tools (4 items). Complete information about the instrument and the scale items can be found in Thurm’s 2017 study.

Furthermore, to understand the development of teachers’ beliefs about integrating interactive technology into mathematics classrooms, the study participants engaged in a reflective writing activity. The participants were encouraged to demonstrate their writing skills by profoundly reflecting on the overall experience of learning the meaning of mathematics concepts using hands-on manipulation, digital apps, and a synthesis of both, as well as their beliefs about using interactive tools in their classrooms. After each writing session, the professors read the participants’ reflections, suggested several ways to improve the essays, and encouraged the participants to rewrite the reflective essays when it was unclear or not sufficiently deep. For instance, the professors can pose probing questions to participants struggling to articulate their ideas, such as the following: Why did you write this reflective essay? Could you explain your thoughts here? Do you have any evidence from your own experiences? For assessing the writing exercise, we adapted a reflective writing assessment protocol (RW) from Harland and Wondra (2011) [65] and Vogelsang, Kulgemeyer, and Riese (2022) [66]. The goal of RW is to provide an authentic assessment of qualitative data under standardized conditions; hence, it enables us to evaluate the degree of change in the writer’s beliefs about integrating technology into mathematics classrooms. Based on several elements of reflection, the RW model distinguishes between four levels of reflective thought: nonreflective writing, comprehension, alternatives, and critical reflection (

Table 1. Reflective writing rating protocol, RW.

Score	Level of Reflection about Teaching Early Mathematics Using Technology	Definition
1	Nonreflective	Habitual description of using technology in teaching early mathematics without thinking about how or why or exhibiting true understanding of the concept. Describing research results without any reflection.
2	Comprehension	Demonstrate an understanding of using technology in teaching early mathematics by drawing correlations between using technology and effective teaching and/or evaluating teaching situations with or without reasoning.
3	Alternatives	Formulate a personal philosophy, providing a strong connection between using technology and teaching mathematical concepts while mentioning alternative methods for improvement.
4	Critical reflection	Exhibit evidence of a transformation in perspective and fundamental teaching beliefs.

).

2.2. Validity and Reliability of BT Instrument

Several steps were taken to ensure the validity and reliability of the BT instrument. First, a pilot study was implemented with 45 teachers, and the data obtained were used to assess the validity and reliability of the quantitative instrument. In addition, the original instrument, which is published in English, was translated into an Arabic version and reviewed by three professors in the teacher education program. The initial version of the translated instrument contained multiple negative scale items of beliefs that were confusing to the Arabic participants in the pilot study. For example, the English instrument has a category labeled “skill loss”, which is a negative belief item. When directly translated into Arabic, it was caused confusion; thus, the item was inverted and labeled skill gain instead. In

Table 2. Reliability and validity coefficients of the research tool (n = 45).

Item	Cronbach’s Alpha If Item Deleted	Item–Total Correlation	Corrected Item–Total Correlation	Cronbach’s Alpha of Dimension
R1	0.868	0.78 **	0.61 **	Multiple Representations 0.868
R2	0.789	0.91 **	0.85 **
R3	0.807	0.88 **	0.78 **
R4	0.852	0.83 **	0.67 **
D1	0.857	0.76 **	0.75 **	Discovery Learning 0.885
D2	0.862	0.82 **	0.72 **
D3	0.825	0.94 **	0.90 **
D4	0.873	0.82 **	0.69 **
D5	0.885	0.77 **	0.62 **
T1	0.757	0.81 **	0.55 **	Time Consuming (Saving) 0.769
T2	0.644	0.84 **	0.65 **
T3	0.671	0.84 **	0.62 **
S1	0.751	0.96 **	0.92 **	Skill Gain 0.863
S2	0.842	0.81 **	0.67 **
S3	0.766	0.92 **	0.86 **
S4	0.863	0.73 **	0.49 **
M1	0.839	0.92 **	0.88 **	Mindless Working 0.888
M2	0.823	0.94 **	0.90 **
M3	0.845	0.89 **	0.81 **
M4	0.853	0.88 **	0.78 **
M5	0.888	0.56 **	0.38 **
P1	0.86	0.82 **	0.71 **	Procedures First 0.878
P2	0.824	0.89 **	0.79 **
P3	0.829	0.88 **	0.78 **
P4	0.861	0.85 **	0.70 **

** Sig. at (α ≤ 0.01).

, it can be seen that the overall Cronbach’s alpha values for the six dimensions are high and acceptable, ranging from 0.75 to 0.8, which is close to the values for the original instrument [63] (Thurm, 2017). In addition, these results indicate that all the Cronbach’s alpha coefficients for each subdimension—when deleting any of its items—are less than the alpha coefficient for the dimension if all its items are retained. In essence, the inclusion of any of the scale items under a dimension does not lead to a decrease in the total Cronbach’s alpha coefficients of that dimension, which indicates that each item provides a reasonable contribution to the overall reliability of the dimension they assess. In addition, all correlation coefficients of the total score of a dimension (i.e., the item–total correlation) are statistically significant (α ≥ 0.01), indicating the internal consistency and reliability of all the items. Furthermore, all correlation coefficients of the total degree of the dimension when the item score is omitted from the total score of the dimension it measures (i.e., corrected item–total correlation) are statistically significant (α ≥ 0.01), indicating the validity of all the items.

3. Quantitative Results: Impact of Interactive Digital and Physical Environments on Teachers’ Beliefs

This study utilized the BT questionnaire to measure teachers’ beliefs regarding the use of interactive technology environments in mathematics classrooms after engaging in an intervention program. To ensure that the experimental and control groups were equivalent, the independent sample t-test was employed before immersion in the intervention course. In

Table 3. Independent sample t-test results for the experimental and control group teachers’ beliefs regarding teaching using technology prior to the intervention.

Dimension	Experimental Group (n = 30)		Control Group		t-Test	Sig. (2-Tailed)
			(n = 28)
	Mean	Std. Deviation	Mean	Std. Deviation
Multiple representations	11.43	5.13	12.14	5.2	0.6	0.52
Discovery learning	14.1	6.16	14.93	6.38	0.62	0.5
Time consuming	7.9	3.29	8.11	3.15	0.81	0.24
Skill gain	11.43	5.06	11.93	4.96	0.71	0.38
Mindless working	12.7	5.21	12.79	4.78	0.95	0.07
Procedures first	9.97	4.41	11.14	3.84	0.28	1.08

, it can be seen that there is no statistically significant difference between the mean scores of the participants in the experimental and control groups with respect to the overall scores for the teachers’ beliefs and related aspects. This indicates that the experimental and control groups were homogeneous (or equivalent) in their beliefs regarding the use of technology in mathematics classrooms.

To uncover the impact of the interactive learning environment on the teachers’ beliefs about technology, the BT questionnaire was implemented before and after immersion in the interactive learning environment program. The descriptive statistics for the experimental group show that the mean for the multiple representation dimension ranged from 2.73 to 2.97 (N = 30, SD = 1.26–1.40) for the experimental group before immersion and ranged between 4.43 and 4.53 (N = 30, SD = 0.68–0.63) after immersion in the intervention. For the discovery learning dimension, the mean ranged from 2.60 to 2.97 (N = 30, SD = 1.16–1.43) before the treatment condition; after the intervention, the mean discovery learning dimension score was 4.37–4.60 (N = 30, SD = 0.93–0.77). For the time consuming and skill gain dimensions, the mean score ranged from 2.20 to 2.97 prior to the intervention (N = 30, SD = 1.03–1.43) and ranged from 2.90 to 4.70 after immersion in the intervention program (N = 30, SD = 1.32–0.60). For the mindless working dimension, prior to immersion in the intervention program, the mean score was 2.33 to 2.65 (N = 30, SD = 1.00–1.22); after immersion, it ranged from 3.93 to 3.18 (N = 30, SD = 0.90–1.30). The mean score for procedure first was 4.03–3.47 prior to the intervention (N = 30, SD = 1.13–1.25); after immersion in the intervention program, it was 2.20–2.6 (N = 30, SD = 0.93–1.25).

The first research question addresses the impact of interactive learning environments that combine digital and physical manipulatives on teachers’ beliefs about using technology in their classrooms. The independent sample t-test and paired samples t-test were used to calculate the impact of the intervention program. We also examined the eta squared value, η², to determine the effect size of the independent variable—the interactive environment in this study. The guidelines for interpreting the eta squared values are as follows: small effect = η² < 0.059, moderate effect = 0.059 ≤ η² < 0.138, large effect = 0.138 ≤ η² < 0.232, and very large effect = 0.232 ≤ η² [67,68].

The independent sample t-test was used to determine the difference between the mean scores of the experimental and control groups on the questionnaire after the intervention. The results of the independent sample t-test reveal that, at the 0.01 level, there is a statistically significant difference between the mean scores of the experimental and control groups. This indicates that there was a change in the strength of the beliefs of the members of the experimental group regarding teaching using technology after the intervention. Furthermore, the eta squared values (0.233–0.369) indicate that the intervention program had a very large effect size in terms of changes to the teachers’ beliefs about teaching using technology in their classrooms when the experimental group is compared to the control group. The value of the eta squared also indicates that the intervention program explains the percentages (23–36.69%) of the variance in the strength of teachers’ beliefs regarding technology use in teaching, which are significantly large amounts of variance (

Table 4. Independent sample t-test results for experimental vs. control groups for teachers’ beliefs about teaching using technology as reflected in the post-test.

Dimension	Experimental Group (N = 30)		Control Group		t-test	Sig. (2-Tailed)	Eta Squared
			(n = 28)
	Mean	Std. Deviation	Mean	Std. Deviation
Multiple Representations	18.23	2.25	14.25	4.48	4.32	0	0.25
Discovery Learning	23.37	2.66	17.5	5.48	5.24	0	0.329
Time Consuming	11.6	3.55	8.14	2.76	4.12	0	0.233
Skill Gain	18.8	1.95	13.75	4.39	5.72	0	0.369
Mindless Working	19.83	3.96	15.09	3.87	4.61	0	0.275
Procedures First	7.33	3.56	11.86	3.19	5.95	0	0.299

).

To understand the impact of the intervention program on the experimental group, a paired sample t-test was used to determine the difference in the mean scores before and after immersion in the program (

Table 5. Paired samples t-test results for the pre-test and post-test means of the experimental group for female teachers’ beliefs about teaching using technology (n = 30).

Dimension	Pre-test		Post-test		t-Test	Sig. (2-Tailed)	Eta Squared
	Mean	Std. Deviation	Mean	Std. Deviation
Multiple Representations	11.43	5.13	18.23	2.25	6.41	0	0.586
Discovery Learning	14.1	6.16	23.37	2.66	7.35	0	0.651
Time Consuming	7.9	3.29	11.6	3.55	4.16	0	0.374
Skill Gain	11.43	5.06	18.8	1.95	7.21	0	0.642
Mindless Working	12.7	5.21	19.83	3.96	5.52	0	0.512
Procedures First	9.97	4.41	7.33	3.56	2.56	0.05	0.184

). The results indicate that there is a statistically significant difference—at the 0.01 level—between the mean pre- and post-test scores of the teachers in the experimental group on their beliefs regarding technology use in teaching and on the six dimensions (multiple representations, discovery learning, time consuming, skill gain, mindless working, and procedures first) of the BT tool. In addition, the eta squared values (from 0.18 to 0.651) indicate that the program has a very large effect size with respect to the impact on the development of the teachers’ beliefs about technology use in teaching technology under the following dimensions: multiple representations, discovery learning, time consuming, skills gain, mindless working, and procedures first.

4. Qualitative Results: Level of Teachers’ Reflection in Relation to Improvements in Belief

To analyze the teachers’ reflective writing essays, a systematic and thematic approach was adopted to trace the development of the teachers’ beliefs while engaging with the interactive environment of the intervention program. This approach enables us to discover significant patterns and generate important themes about the development of teacher’s beliefs regarding teaching with technology. Four phases were taken into consideration in the thematic analysis:

(1)

Numerical phase: In the thematic analysis, we examined the reflective essays and rated each piece using the RW protocol. The data generated using this procedure are numbers that indicate the depth of reflection on the integration of technological resources into mathematics classrooms. For the rating process, each researcher read the same reflective essay independently and coded the writing based on the prescribed elements. The intercoder agreement was then assessed based on the number of agreements divided by the number of coding decisions; the agreement percentage was subsequently measured. Once the researchers reached a 90% level of agreement for each coding process, we admitted the a rating; when it was less than a 90% level of agreement, we inspected the disagreement and refined the analytic procedures to reduce them.

(2)

Signs: In this step, remarking signs or notes were produced for each written reflection essay. We used this step to generate meanings that were deduced in the numerical phase.

(3)

Grouping: In this phase, we produced groups by looking for similarities and differences around the signs produced in the preceding step. The grouping process was longitudinal (i.e., considering all the essays at once) and cross-sectional (i.e., considering individual essays and studying the developments in the writing).

(4)

Generating themes and recoding to record these themes: analyzing the reflective essays revealed two important themes, which are labeled as transformation in teachers’ beliefs and improvement in selecting digital and physical manipulatives.

4.1. Transformation in Teachers’ Beliefs

The analysis of reflective essays at the beginning, middle, and end of the intervention course revealed that the teachers exhibited a transformation in the level of their reflective writing, and this transformation was linked to changes in their beliefs about technology use in teaching early mathematics.

The results of the analysis show that 70% of the participating teachers (seven out of ten teachers) improved in their level of reflective writing—which reflects developments in their beliefs. Four of the ten teachers were at level 2 (comprehension) at the beginning of the intervention course, and their reflective writing improved to level 3 (alternatives) at the end of the course. Two of the ten teachers progressed from level 2 (comprehension) to level 4 (critical reflection), and one teacher improved from level 1 (nonreflective) to level 3 (alternatives) (

Table 6. Ratings of reflective writing essays.

Name of Participant	Reflective Writing Essay 1	Reflective Writing Essay 2	Reflective Writing Essay 3	Interactive Environments, as Acknowledged by Participants (Organized from the First, Second, to Last Reflective Writing Essay)
A	Comprehension	Comprehension	Alternatives	Electronic books, interactive app for math operations, YouTube channel, hands-on manipulatives
B	Alternatives	Nonreflective	Alternatives	Hands-on manipulatives, website with math puzzles and riddles for teaching fractions, a mix of hands-on and virtual environments
C	Nonreflective	Comprehension	Nonreflective	App for math operations, fractions virtual lab, Minecraft environment
D	Comprehension	Alternatives	Alternatives	WordWall platform, fractions virtual lab, hands-on activities for spital reasoning using sand
E	Nonreflective	Comprehension	Alternatives	No example provided, hands-on environment and electronic books
F	Comprehension	Alternatives	Alternatives	No example provided, Khan Academy, app for geometric shapes, hands-on environment, Montessori tools.
G	Comprehension	Alternatives	Critical reflection	Hands-on manipulatives, Montessori tools, virtual environment (Math Center)
H	Comprehension	Alternatives	Comprehension	App for creating games, math YouTube video, no example provided.
I	Comprehension	Alternatives	Critical reflection	WordWall platform, a mixing of hands-on and virtual environments, math center app.
J	Comprehension	Alternatives	Alternatives	No example provided, IXL platform, Math Playground website, mix of hands-on and virtual environments

).

For example, in the first reflection writing session, Participant F wrote, “I believe that technology is a facilitator for the education process, as it allows the child to learn in various ways that suit different learning styles: visual and auditory, and it is in line with the Saudi Arabia’s 2030 vision of supporting the digital transformation in education”. Such thoughts express the participants’ understanding of technology’s role in early mathematics classrooms and in the educational system in general. However, the reflections in this example do not touch on how specific technological environments may improve teaching a specific topic. In the last reflective writing session, Participant F wrote the following: “I see that teaching the children about geometric shapes, such as shape formation and the meaning of the sides and angles, through this application, BabyBus, contributes significantly to the development of creative thinking skills such as fluency, flexibility, originality, and imagination”. In this statement, the participant mentions digital tools and new alternative methods of teaching mathematics concepts in a way that improves the problem-solving skills of children.

At the beginning of the intervention course, Participant G wrote, “I believe that educational cubes and math manipulatives are effective and important for learning mathematics in the primary grades”. Midway through the study, she wrote, “I can use the Montessori Mathematics Decimal System Bank Game to teach division to kids because it focuses on their senses while learning”. Then, at the end of the semester, she wrote, “From my perspective, we can use the Math Center app in teaching fractions because it provides interactive games, videos, picture books, games, worksheets”. These three quotes highlight the improvement in her level of reflection, as well as the transformation in her philosophy about technology use in teaching and learning mathematics.

Participant J, in her first reflective writing essay, wrote, “It is dangerous to use technology with children at an early age… educational standards in Saudi Arabia advocates for using hands-on approaches with children when teaching mathematics and to connect math concepts with real life…” However, in her last reflective writing essay, she wrote, “We have to combine hands-on and virtual environments when teaching… it is okay to use technology at the icebreaker stage of the lesson and at the assessment stage… however, I will use hands-on manipulatives during the procedure part to facilitate understanding math concepts such as counting and quantity”.

The results of the analysis of the first theme indicate that the transformation and development reflected in teachers’ reflective writing are in accordance with the RW protocol. At the beginning of the course, Participating F seemed to believe in the role of technology in education in general, but her belief about technology use in teaching mathematics specifically was not obvious. Participants G and J seemed to indicate that they would avoid introducing a digital environment to children while teaching mathematics and that they would rely heavily on a hands-on environment. At the end of the semester, it appears that the program encouraged them to develop positive beliefs about technology integration in teaching mathematics.

In addition, the results of the analysis indicate that 30% of the participants exhibit vacillation in their level of reflective writing, which mirrors an instability in their beliefs about using digital and physical manipulatives in mathematics classrooms (Table 6). For example, at the beginning of the course, Participant B wrote, “I can develop problem-solving skills by giving kids fruits in numbers that exceed the quantity required for the problem, and then ask them to solve the problem. The kids might solve the problem by removing the extra fruits. I think this will help kids to improve their problem-solving skills and understanding of subtraction operations”. Midway through the study, she wrote, “Hands-on materials are better than learning that is based on abstract mathematical symbols”. In her final reflective writing essay, she wrote, “I think the puzzle and riddles virtual game is useful, but I suggest adding pictures to make it less complicated for kids. Also, we do not disagree that it is better for the games to be slightly higher than the child’s level in order to challenge the child’s abilities, but they should not be that difficult—which is in line with many learning theories like those of Piaget and Vygotsky”.

The example of Participant B demonstrates a transformation in a teacher’s beliefs about using technology in teaching mathematics to early childhood pupils. Participant B, who had a high rating (level 3) at the beginning of the intervention, was able to give a specific example of teaching mathematics concepts using an alternative method. Her essay reflects highly positive beliefs about using physical environments in mathematics classrooms. Midway through the intervention, her reflexive writing was rated low, as level 1. It appears that she evinced some confusion about which tools to use with her students, which reflects that her beliefs were inconstant. At the end of the intervention, her reflexive writing had reverted to level 3. The results of the analysis support the first theme (transformation in teachers’ beliefs) by explaining how participants exhibit vacillation as well as improvement in the overall level of their reflective writing.

4.2. Improvement in Selecting Digital and Physical Manipulatives

The analysis of the reflective writing essays also shows that the teachers improved their perspectives on selecting appropriate digital and physical tools that support teaching and learning mathematical concepts. Furthermore, making these selections contributed to deepening their reflective writing and clarifying their beliefs about integrating digital and physical manipulatives in teaching and learning mathematics. The results of the analysis show that 40% of the participating teachers selected general educational manipulatives at the beginning of the intervention course. They chose tools used by teachers in general—cutting across different subjects and disciplines—to produce printable worksheets, online quizzes, crossword games, and to interact with teacher communities. During the intervention, these participants gradually deepened their perspectives on selecting specific manipulatives that specifically support teaching and learning mathematics. It seems that the intervention helped them become conscious of selecting math-specific technological and hands-on environments to teach specific mathematical concepts, such as addition, subtraction, and fractions. For example, at the beginning of the course, Participants I and D selected a general educational app, WordWall, and their reflective writing essays were rated as being at the comprehension level. At the end of the intervention, both Participants I and D selected specific mathematical manipulatives that are effective for helping students grasp the meaning of mathematical concepts. Participant I wrote about the Math Center app in her reflective essay, while Participant D reflected on hands-on manipulatives, such as shapes and sands, for learning spital reasoning. The reflective essays of these two teachers were rated as being at the alternatives level. It seems that their selection of specific mathematical tools contributed to their developing positive beliefs about using interactive learning manipulatives in classroom environments.

In addition, the analysis of the last set of reflective writing essays reveals that all participants believed that both digital and physical environments play an important role in teaching mathematics and in learning mathematics in early childhood. Given that research participants currently serve as early childhood teachers, this perspective emerged from their previous understanding of children’s learning characteristics and how they learn mathematics best through a wide variety of interactive in-class activities such as coloring, role play, singing, block play, and other play-based classroom activities. However, this study supported participants to hold differing perspectives on what should be introduced first between digital manipulatives and physical manipulatives. Some of the participants preferred teaching mathematical concepts by beginning with a virtual environment and then progressing to a hands-on environment, while others preferred beginning with a hands-on environment and then progressing to virtual environments. For example, Participant J wrote, “I believe it is important to use multiple learning materials with children at the beginning of the lesson. For example, for teaching the concept of number 5, we have to start the lesson with electronic books, then move on to hands-on activities”. On the other hand, Participant D wrote, “We should use both virtual and hands-on environments in teaching mathematics concepts. For example, when teaching geometric shapes to kids, we begin using concrete material, then ask them to draw the shapes in the sand, and finally demonstrate shapes via virtual manipulatives”.

5. Discussion

In early childhood education, teachers’ beliefs are essential for facilitating the integration of technology into mathematics teaching [46]. This study explores the influence of physical and digital interactive learning environments on the development of teachers’ beliefs about technology use in early mathematics classrooms. To understand the development of teachers’ beliefs, a six-month professional development program that incorporates interactive digital and physical environments was designed for this research study. We utilized the BT questionnaire to measure teachers’ beliefs about the use of interactive technological environments in mathematics classrooms after engagement in the intervention program. In addition, a reflective writing strategy was implemented with the participants to understand the development of their beliefs about technology through the evaluation of their levels of reflection. In general, the results illustrate that interactive learning environments facilitate an improvement in teachers’ beliefs about technology. Although the changes in beliefs have slight individual deviations, they involves two important outcomes.

The results of the assessments using the BT instrument show that interactive digital and physical learning environments reveal significant differences between the experimental and control groups. The results show that the intervention program has the most considerable influence on the following dimensions: skill gain and discovery learning. This means that the teachers developed the belief that interactive technological environments can support children in learning mathematics through discovery and that they can more effectively gain math computational skills using technological tools. These results are in agreement with the findings of many studies on technological integration and that technology encourage children to develop new ways of thinking about mathematics concepts via digital or physical environments [8,25,26,27,28,30]. Furthermore, some research findings were also derived from the qualitative outcomes of a thematic analysis. For the theme of transformation in teachers’ beliefs, the participants’ reflective writing demonstrated that 70% of the participants improved in their level of reflective writing, which reflects the development of their beliefs. The discussion of quotations from the participants’ reflective writing essays reveal that the interactive environment facilitated their development of more positive beliefs about technology integration in teaching mathematics. These findings highlight the role of professional programs as interventions in changing teachers’ beliefs, as discussed in previous studies [58,59,60].

An important finding of this study pertains to teachers’ preferences regarding the type of technology they would choose when teaching mathematics to children. The study participants demonstrated consensus in selecting technology for the purpose of supporting the learning of mathematics concepts. Our analysis indicates that 40% of the participants exhibited a shift in their selection preferences from general technology to math-specific hands-on and digital manipulatives. The study results indicate that the intervention program facilitated a progression from general educational tools such as digital worksheets, online quizzes, and crossword games to interactive tools such as online mathematics teachers’ communities, interactive apps for addition and subtraction, Khan and IXL academies, dynamic geometric environments, and physical mathematics blocks and counters. Most of these tools have features that support and enhance discovery learning, creative thinking, and the exploration of mathematical concepts and their relationships. These findings correspond to the BT results, as participants developed positive beliefs about using technology to support the discovery process when teaching mathematics to young children. Items under the discovery learning dimension include statements such as “Using technology, it is possible to generate many examples so students can grasp relationships and structures, Technology supports tasks in which students can explore new content on their own, and Technology enables students to explore mathematical concepts on their own” [63]. In its position statement, the National Council of Teachers of Mathematics (NCTM) advocates for the strategic use of technology to enhance students’ sense-making, deepen their understanding of concepts, and stimulate mathematics interest by linking activities to authentic and relevant contexts [19]. Such powerful technological features can be generated through content-based interactive digital tools [19], which some of the teachers who participated in this study highlighted in their qualitative assessments.

Notwithstanding its many limitations, several recommendations for future research emerge from this study. First, this study focuses on one affective factor impacting technology use in teaching mathematics, i.e., belief, but does not take into account other affective factors that may enhance classroom practices. Future research may consider other affective factors that impact the teaching of mathematics using technology, such as confidence, motivation, and anxiety. Second, this study generated very limited qualitative data, as the reflective writing essays of only 10 participants were analyzed over one semester. The data on the reflective writing were not linked to classroom implementations, observations, or individual interviews. Thus, an analysis of further data over longer periods and the inclusion of classroom observations could potentially reveal more about the development of teachers’ beliefs. Incorporating classroom observations may provide further insights into how other variables, such as school culture, classroom norms, and administrative support, influence the development of teachers’ beliefs about technology use in teaching mathematics. In addition, the sample in this study comprised preservice early childhood teachers from only one university in Saudi Arabia. Further research is needed to determine whether the results can be generalized to various universities.

6. Conclusions

The development of teachers’ beliefs is critical to the success of mathematics education reforms. Summarizing the findings of this study, we can state that professional development programs may be effective for the development of positive beliefs about technology use in teaching. Analyzing teachers’ reflective writing is a dynamic way to understand the process of belief development and when and what type of technology early childhood mathematics teachers are willing to utilize in their classrooms. This research will positively inspire educators, professionals, and decision-makers to consider the cultivation of positive teacher beliefs by designing high-quality teacher preparation programs and professional development programs that incorporate effective interactive learning environments. In addition, this study’s findings call for the balanced integration of physical and digital technologies to support children’s sense-making and comprehension of mathematics concepts. A balanced integration of digital and physical environments is an effective tool for mathematics teachers to visualize mathematics concepts, making them more meaningful. In addition, considering the current shift in Saudi education toward a progressive digital transformation, this study recommends that practitioners collaborate to participate in appropriate digital technology integration. For example, they may collectively access digital platforms they can collaborate, interact, and design classrooms in which children can explore mathematics concepts with joy and deep understanding.