Effects of using mobile augmented reality for simple interest computation in a financial mathematics course

Planning

After the conversation with three financial mathematics professors, the planning stage began. The professors agreed with us about the three problems detected during the monitoring. However, they mentioned the barriers that students face when learning simple interest: (a) the problem is not analyzed, therefore, it is not understood; (b) they confuse simple interest with compound interest and vice versa; (c) the terms involved to solve the computation are wrongly cleared; (d) the concepts such as principal, amount, interest rate, and time are misinterpreted; and (e) conversions between time units are wrongly performed. Professors explained that around 70% of Mexican students commit at least one of the errors mentioned above. They also stated that simple interest knowledge is fundamental for mastering finances and understanding complex concepts such as compound interest, amortization tables, and annuities. Hence, students must comprehend the topic.

We ask professors for an explanation to understand how to compute simple interest. The explanation was based on the following example. When an individual borrows money, the lender expects to be paid back the loan amount plus an additional charge for using the money called interest. In contrast, when money is deposited in a bank, it pays the depositor to use the capital, also called interest.

Simple interest (I) represents the fee you pay on a loan or income you earn on deposits. In other words, simple interest represents the price of the money over a specific period. As shown in Eqs. (1) and (2), there are two ways to compute simple interest. Furthermore, notice the four terms involved: (i) Principal (P) is the original sum of money borrowed (also called present value); (ii) Interest rate (r) is a fraction/percentage of the principal (charged) per unit of time; (iii) Time (t) represents the time period over which the interest rates apply/are charged; and (iv) Amount (A) is the total accrued amount (principal plus interest), represents the future value of the financial operation (Hastings, 2015). (1)${\displaystyle I=Prt,}$ (2)${\displaystyle I=A-P.}$

The terms regarding principal, interest rate, time, and the amount can be cleared from Eqs. (1) and (2) as is depicted in Eqs. (3), (4), (5), and (6), respectively.

(3)${\displaystyle P=\frac{I}{rt}.}$ (4)${\displaystyle r=\frac{I}{Pt}.}$ (5)${\displaystyle t=\frac{I}{Pr}.}$ (6)${\displaystyle A=P+I.}$

In Eqs. (1) to (6), it is common to use years as the time unit. However, time could also be expressed in days, weeks, fortnights, months, bimesters, quarters, or semesters. For any calculation, if the period for r and t is defined in different units, then a conversion must be computed, which often causes mistakes.

To this end, we propose a prototype to support simple interest learning and design two surveys and two practice tests to assess the effects of using it with undergraduate students. The prototype is called “simple interest computation with mobile augmented reality (SICMAR)”.

Hypotheses development

Our study assesses students’ motivation when learning simple interest in traditional settings and with SICMAR. Also, we assess the students’ achievement when learning in both settings through a test. Finally, we consider obtaining insights about SICMAR technology acceptance and quality. Thereby, we pose twelve hypotheses.

Students motivation

Motivation affects what, how, and when the learners learn, and it is directly related to the development of students’ attitudes and persistent efforts toward achieving a goal (Lin et al., 2021). Motivation is an activity that must be performed to (i) attract and sustain students’ attention (A); (ii) define the relevance (R) of a content students need to learn; (iii) help students to believe they succeed in making efforts (gain confidence (C)); and (iv) assist students in obtaining a sense of satisfaction (S) about their accomplishments in learning (Cabero-Almenara & Roig-Vila, 2019). In this sense, Keller’s ARCS model provides guidelines for designing and developing strategies to motivate students learning (Li & Keller, 2018).

In previous studies, the ARCS model was used to observe if mobile augmented reality could be a resource that motivates students to learn anatomy and art (Cabero-Almenara & Roig-Vila, 2019), dimensional analysis (Estapa & Nadolny, 2015), and geometry (Ibáñez et al., 2020), obtaining promising results. Therefore, the present paper poses the following five hypotheses.

H₁: there is a significant difference in students’ attention scores in the pre-test and the post-test.

H₂: there is a significant difference in students’ relevance scores in the pre-test and the post-test.

H₃: there is a significant difference in students’ confidence scores in the pre-test and the post-test.

H₄: there is a significant difference in students’ satisfaction scores in the pre-test and the post-test.

H₅: there is a significant difference in students’ motivation scores in the pre-test and the post-test.

Students achievement

Academic achievement is the extent to which a student has accomplished specific goals that focus on activities in instructional environments (Bernacki, Greene & Crompton, 2019). In this paper, student achievement is related to how capable the students are when solving simple interest computation problems. The studies by Purnama, Andrew & Galinium (2014); Estapa & Nadolny (2015); Tobar, Fabregat & Baldiris (2015); Cascales et al. (2017), and Ibáñez et al. (2020) show how the use of MAR can affect mathematics academic achievement positively. Therefore, we propose the following hypothesis.

H₆: students learning with SICMAR achieve higher scores in simple interest tests than students exposed to traditional learning.

Technology acceptance

The technology acceptance model (TAM) was formulated by Davis (1989). TAM suggested that the perceived ease of use (PEU) and the perceived usefulness (PU) are determinants to explain what causes the intention of a person to use (ITU) a technology. The perceived ease of use refers to the degree to which a person believes that using a system would be free from effort. The perceived usefulness refers to the degree to which the user believes that a system would improve his/her work performance. The intention to use is employed to measure the degree of technology acceptance (Davis, 1989).

In previous research, TAM was used to examine the adoption of augmented reality technology in teaching using videos (Cabero-Almenara, Fernández & Barroso-Ozuna, 2019) and learning the Mayo language (Miranda et al., 2016). However, no studies related to the use of TAM in mathematical settings were detected. In this paper, the TAM is extended with prototype quality variable to explain and predict the SICMAR usage. The aim is to study the relationships between quality, perceived ease of use, and perceived usefulness and their positive effects on students’ intention to use SICMAR.

The family of statistical multivariant models that estimate the effect and the relationships between multiple variables is known as structural equation modeling (SEM) (Al-Gahtani, 2016). Therefore, we use SEM to test the following hypotheses.

H₇: quality positively affects students’ perceived usefulness of SICMAR.

H₈: quality positively affects students’ perceived ease of use of SICMAR.

H₉: perceived ease of use positively affects students’ perceived usefulness of SICMAR.

H₁₀: perceived ease of use positively affects students’ intention to use SICMAR.

H₁₁: perceived usefulness positively affects students’ intention to use SICMAR.

The words ”positively affect” mean that when the measured value of one variable increases, the related variable also increases.

SICMAR quality

Software quality is the field of study that describes the desirable characteristics of a software product. Establishing a measure for the quality of the software is not an easy task. However, attributes such as design, usability, operability, security, compatibility, maintainability, and functionality can be considered to define metrics (Dalla et al., 2020). When the quality of an AR product is evaluated, questions such as how fast the system responds, how difficult it is to manipulate the system and markers, and to which extent the illumination affects marker recognition must be answered (De Paiva & Farinazzo, 2014). In this paper, the quality was assessed considering the design and usability of SICMAR as recommended by Barraza, Cruz & Vergara (2015) and Pranoto et al. (2017).

In the literature, no MAR works that report a hypothesized minimal mean value of quality that serves for comparison were found. Therefore, we propose the following procedure: (i) determine the minimum and the maximum length of the Likert scale; (ii) compute the scale range by subtracting (5-1 = 4) and dividing by five (4/5 = 0.80); (iii) add the range to the least scale value to obtain the maximum. The ranges computed for a five-point Likert scale are 1-−1.8–2.6-−3.4–4.2–5. Results greater than 3.4 and less or equal to 4.2 are considered as good quality. Thus, the mean value of 3.8 was supposed to determine good quality. Moreover, as is explained in the results section, this value is the median obtained after experimentation. Hence, the following hypothesis is established.

H₁₂: the mean value evaluated by students regarding the quality of SICMAR is greater than 3.8.

Software development

We consider the cascade model to establish the stages to develop SICMAR. The cascade model is a linear procedure characterized by dividing the software development process into successive phases (Ruparelia, 2010). The model encompasses five phases, including (i) requirements; (ii) design; (iii) implementation; (iv) testing; and (v) maintenance. A visual representation of the SICMAR phases is shown in Fig. 1.

Requirements

According to Billinghurst, Grasset & Looser (2005), the physical components of the interface (inputs), the virtual visual and auditory display (outputs), and the interaction metaphors must be considered to build intuitive AR applications. Therefore, we determine five characteristics of the prototype to deal with the barriers faced by students: (i) a set of markers will be used to determine the term to compute and the parameters involved (inputs); (ii) 2D models will represent all the information needed for the calculations; (iii) markers’ movement will be used to observe the 2D models from different perspectives; (iv) the calculation to solve will be defined with a combination of markers (touch manipulation metaphor); and (v) we will employ virtual objects, such as text boxes, arrows, and images, to explain step-by-step calculations (outputs). A traditional computer application cannot offer all these features.

From the variety of information and communication technologies, PCs and mobile devices were considered to implement the prototype due to the high probability that a student has either one of them. The main differences between PCs and mobile devices are the display size, how it is manipulated, the processing power, bandwidth, and usage time. Portability, sensors included, and ease manipulation were considered to select mobile devices. Indeed, young users prefer mobile devices because they can be used anytime, carried from place to place, and connected to the Internet all day long. Moreover, recent studies have shown that almost 75% of AR works for educational settings were implemented on mobile devices obtaining satisfactory results (Bernacki, Greene & Crompton, 2019; Cabero-Almenara, Fernández & Barroso-Ozuna, 2019). AR applications are different from conventional applications that use a mouse and keyboard. By superimposing virtual information, mobile augmented reality increases perception (virtual objects can be observed from different perspectives) and user interaction (objects are manipulated with the fingers) with the environment; a non-AR application cannot offer that feature. Also, MAR can turn a classic learning process into an engaging experience because students perceive learning as a game (Arici et al., 2019).

Regarding mobile devices, Android and iOS-based devices are the leaders. Nevertheless, we selected Android because (i) it is the leading mobile operating system worldwide; (ii) the price for publishing an app in the play store is much lesser than posting an app in the apple store; (iii) the cost of Android-based devices is less than iOS-based devices; due to price, a student rarely has an iPhone; (iv) it possesses a good support architecture and functional performance; (v) the customization level offered makes it easy to use; (vi) the assortment of the batteries’ sizes overpowers the iPhone (Ivanov, Reznik & Succi, 2018).

Design

There are various alternatives to implement AR solutions, including Wikitude, ARToolKit, Augumenta, Easy AR, HP Reveal, and Vuforia, offering exciting characteristics. Considering the analysis presented in Table 1 and based on the authors’ experience, Vuforia Software Developer Kit (SDK) was selected. Vuforia is a robust platform that contains the libraries to implement the tasks related to AR, including real-time marker detection, recognition and tracking, and the computations for object superimposition. Unity 3D was employed to create the SICMAR visual environment and all the 2D virtual objects that will be superimposed on each marker.

SICMAR was designed based on the framework proposed by Barraza, Cruz & Vergara (2015). The framework comprises four subsystems (i) the rendering; (ii) the context and world model; (iii) the tracking; and (iv) the interaction, which works together to create the mobile application.

In the rendering subsystem, two main tasks are executed: (i) displaying the video acquired from the real world, and (ii) rendering the 2D models. We designed a touch-based graphical user interface (GUI) to display the components and the video acquired from the mobile device. At the top of the GUI, we inserted two sections: (i) input data and (ii) calculate (output). The first show the input terms (markers) detected inside the scene, and the second shows the term the user wants to compute (see the upper left corner in Fig. 2). We used the Unity sprite renderer for rendering all the photorealistic images of the 2D models that will be superimposed inside the real-world video stream.

The context and world model subsystem includes the design of image targets (markers), the data about the interest points, and the 2D objects that are going to be used in the augmentation. We used the Brosvision marker generator to design the markers to represent each of the five terms explained in (1) to (6). As shown in Fig. 3, the markers include lines, triangles, quadrilaterals, and at the center, a square with a letter corresponding to the simple interest term was added. Using Vuforia, we conducted a test of the contrast-based features (interest points) of the individual markers visible to the camera. All the markers earned five stars rating, which means they included excellent features for detection and tracking. Finally, four 2D objects were created for user interactions and augmentations, as shown in Fig. 2. (a) To display information about the detected marker (input term). (b) To capture the user inputs and determine if a term is handled as input or output. (c) To display information about the time conversions. (d) To display the calculation result (output term) or show an error.

Vuforia SDK was used to carry out the tracking subsystem. This subsystem exchanges marker tracking information with the rendering subsystem to superimpose the virtual 2D objects to the original scene displayed to the user.

Finally, the interaction subsystem collects and processes any input required by the user. A series of C# scripts were linked to the GUI objects. When a tap occurs on the screen, verification is carried out to determine if an element was touched. If the verification is valid, the search for a marker starts. If a marker is detected, then the corresponding method is invoked to carry out the task.

Implementation

The logic implemented to solve any of the Eqs. (1) to (6) is the following. The user taps the SICMAR icon to start the execution. The presentation screen is displayed, and the camera of the mobile device is turned on. When the user shows a valid marker in the front of the camera, it is recognized as the desired output. Then, the position, rotation, and perspective of the marker are computed, and the corresponding virtual object is superimposed accordingly to the view of the real scene. Next, the input checkbox is activated, and the prototype waits for the user to show the markers for input terms. When input markers are recognized, the text boxes to insert data are displayed, and the 2D objects are superimposed inside the real scene. Any marker different from the first selected can be used as input. The user must insert the data for each term with the keyboard of the device. Once the data was introduced, the input checkbox must be disabled to perform the computation. Immediately, verification is conducted to detect if the necessary data for the computation were inserted correctly. If there is any missing data, an error object is displayed, else the output calculated is presented. The process can be executed continuously.

Testing

An example of simple interest computation using SICMAR is shown in Fig. 2. If the user inserts r and t with different periods, then the associated conversions are computed. Notice that the result of simple interest computation is highlighted with the color blue. As shown in Fig. 4, the user selected quarters for r and fortnights for t. At the bottom of the screen, the value obtained from the conversion is displayed and explained for both periods. An example of students testing SICMAR is shown in Fig. 5.

Maintenance

Two experienced software developers tested our beta version of SICMAR. They recommended conducting modifications related to the color and size of the objects. We also performed modifications to the GUI, including object location changes and those related to interactivity. As explained in the discussion section, the students recommended performing additional modifications to SICMAR, which will be implemented soon.

The first survey (pre-test)

The first survey has two sections: the first includes items to collect students’ general information, such as name, gender, and age, and the second includes items related to Keller’s ARCS motivation model (Li & Keller, 2018).

The instructional materials motivation survey (IMMS) assesses students’ motivation based on the ARCS model that includes 36 items distributed as 12 items for (A), nine items for (R), nine items for (C), and six items for (S). Although IMMS was used and tested with a Cronbach α = 0.96, it is long, and not all items are necessary, especially those measured in a negative or reverse way (Chen, 2019). Therefore, the reduced IMMS (RIMMS) proposed by Loorbach et al. (2015) was employed. RIMMS comprises 12 five-point Likert scale items, three for each ARCS dimension. The original version was translated and adapted to the lesson of simple interest (see the left side of Table 2). The minimum score on the RIMMS survey is 12, and the maximum is 60 with a midpoint of 36.

The items about attention measure the degree to which the professor’s lesson attracts the learner’s attention. We consider the organization, quality, and variety of the materials employed. On the other hand, we use the content and style of explanations to measure the lesson’s relevance perceived by students. The items regarding confidence measure the degree to which the learner felt confident while completing the simple interest lesson. The final three items measure the degree to which the learner finds the lesson satisfactory and the intention to keep working.

The second survey (post-test)

The second survey comprises four sections. The first includes items to collect students’ general information. The second section includes the 12 RIMMS items of the first survey but adapted to assess students’ motivation using SICMAR (see the right side of Table 2).

The third section related to TAM comprises four items for perceived usefulness, five for perceived ease of use, and two for the intention to use (see Table 3). The 11 items used a five-point Likert scale and were adapted from Miranda et al. (2016). The minimum score for TAM is 11, and the maximum is 55 with a midpoint of 33. The four items regarding perceived usefulness measure the extent to which students believe that SICMAR would improve their performance in learning simple interest. The easiness that students perceived when using SICMAR is measured with the five items related to perceived ease of use (prototype manipulation employing the markers). The last two items measure the degree of acceptance when students use SICMAR.

The fourth section aims to gather information about SICMAR quality. The ten items based on the Likert five-point scale were adapted from Barraza, Cruz & Vergara (2015). We collect information about SICMAR design (colors, size of the objects, velocity) and usability (results obtained) that together determined quality, as shown at the bottom of Table 3.

The practical tests

Two financial mathematics professors helped us to design a set of practical exercises regarding simple interest computation. We divided the set of exercises to design two practical tests with five items each. The first test is applied after professor intervention, and the second after using SICMAR. Professors carefully reviewed both tests to ensure similar difficulty. In both tests, the first two items ask the students to compute simple interest. The last three questions are challenging because the terms to compute must be cleared from Eqs. (1) and (2). The third question deals with principal computation, while the fourth and fifth deal with interest rate and time calculation, respectively. An example of two pre-test exercises is shown on the left column of Table S1, while the post-test examples are shown on the right column.

Preliminary data analysis

Due to the restrictions imposed by the university, students were not divided into a control and experimental group. One hundred thirty-nine students enrolled in the financial mathematics course were surveyed. Data collected from the surveys was downloaded from Microsoft forms to create a database with IBM SPSS software. The responses obtained were minutely revised. The extreme values were not discarded, but registers with incomplete information were identified. The registers with incomplete information correspond to 36 students who did not attend the second session. Therefore, the final sample comprises data from 103 students.

The sample size was deemed valid due to (i) our sample almost doubled the mean (M = 58.2) from the fourth column of Table 1; and (ii) the section related to ARCS is the biggest of our surveys; therefore, the rule of thumb that a sample should have at least five times as many observations as there are variables to be analyzed was fulfilled (5x12 = 60).

Of the 103 participants, n = 59 (57.28%) were female, and n = 44 (42.72%) were male. The participants’ ages ranged from 18 to 30 years with a mean age (M = 19.74, SD = 1.93). We measure the internal reliability of the surveys with Cronbach’s Alpha (α). A summary of the results is shown in Table 4. Values greater than 0.7 are accepted (good-excellent). The total item correlation computed does not reflect the necessity of eliminating any item. Therefore, the α value for R in pre-test ARCS was also accepted.

Assessment of students motivation with RIMMS

This part of the study allowed us to assess if a significant difference in motivation is obtained when comparing the professor’s lesson and SICMAR. The mean and standard deviation for each item are displayed in Table 2. All scores exceed the central value of the scale. Moreover, the greater mean values were always obtained with SICMAR. The minimum difference is observed for attention (4.14−3.95 = 0.19) and the maximum for relevance (4.38−3.87 = 0.51). The difference for the whole study is (4.17−3.87 = 0.3). The results for both motivation studies are plotted in Fig. 6.

Also, it was necessary to determine if the differences obtained are statistically significant. The normality test indicated that data from the survey were normally distributed. Therefore, the paired t-test with a 5% level of significance was calculated (t =  − 1.761 for attention; t =  − 6.120 for relevance, t =  − 2.281 for confidence, t =  − 2.877 for satisfaction, and t =  − 3.613 for ARCS). P-values less than or equal to 0.05 are considered significant and values greater than 0.05 as non-significant. Considering the null hypothesis, ”there is no significant difference between pre-test and post-test scores”:

• H₁: is rejected. We obtained p = 0.081; therefore, the difference of 0.19 is not significant regarding attention (A).

• H₂: is accepted. There is statistical evidence (p<0.001) to support that with SICMAR, a significant difference of 0.51 on students’ relevance (R) is obtained.

• H₃: is accepted. The difference of 0.21 (4.08−3.87) is significant regarding the confidence (C) dimension with p = 0.025.

• H₄: is accepted. We obtained p = 0.005; hence, the difference of 0.3 is significant regarding students’ satisfaction (S).

The magnitude and significance of causal connections between variables can be estimated using path analysis. We perform a path analysis to compute total effects among ARCS four dimensions and determine students’ motivation. The diagram in Fig. 7 is the visual representation of the relationships between variables. The path coefficients (β) estimate the variance of the indicator that is accounted by the latent construct. The higher the value of β, the stronger the effect. The values calculated for the pre-test are shown above the arrows and the post-test values below the arrows. We also calculate the determination coefficients (R²) to measure how close the data are to the fitted regression line (values must be greater than 0.2). The pre-test values are shown in the upper right corner and the lower right corner for the post-test.

It is noted from Fig. 7 that a significant direct effect exists from A->R, from R->C, and C->S with a significance level of 5% for both tests. Hence, the hypothesis:

• H₅: is accepted. Students increased their motivation using SICMAR. The value M = 4.17 obtained with SICMAR is greater than M = 3.87 obtained with the professor’s lesson. The difference of 0.3 is statistically significant (p<0.001), representing a motivation increase of 7.75%. In summary, the mean values and the path analysis corroborate the motivation increase.

Assessment of students achievement in practice tests

The professor reviewed the students’ responses to emit the grade. An answer is correct only if the result and the procedure to obtain the response are good. Many students presented good results but a wrong procedure; these cases were qualified as incorrect. Since the test includes five items, each correct answer sums 20 points. Therefore, the final grade ranged from 0 to 100. A summary of the correct and incorrect responses for each test is shown in Table 5.

We obtained (M = 39.02 and SD = 28.88) for the pre-test and (M = 66.60 and SD = 29.02) for the post-test. Hence, an increase of 70.68% was observed on post-test grades when comparing with the pre-test. For the post-test, 25 students obtained the maximum grade (100), and only four in the pre-test. Thirteen students (13.59%) obtained better grades on the pre-test than post-test. Moreover, 72 students obtained better scores for the post-test than the pre-test, while 18 students obtained the same score for both tests. In both sessions, women obtained better grades, with pre-test values (M = 44.06, SD = 27.41) and post-test values (M = 76.61, SD = 20.41). The pre-test values obtained for men were (M = 32.27, SD = 30.56), and for the post-test (M = 53.18, SD = 31.38). The plot (box and whiskers) of the scores obtained by students is illustrated in Fig. 8.

The test of Kolmogorov–Smirnov was employed to select the statistical analysis tool accordingly to the data distribution. The results obtained with a 5% level of significance using SPSS for the pre-test were: Z = 0.162, p<0.001, skewness = 0.285, skewness standard error = 0.238, kurtosis = −0.885, and kurtosis standard error = 0.472. For the post-test the results were: Z = 0.192, p < 0.001, skewness = −0.675, skewness standard error = 0.238, kurtosis = −0.396, and kurtosis standard error = 0.472. For both tests (pre-test and post-test) the results were: Z = 0.109, p = 0.004, skewness = −0.329, skewness standard error = 0.238, kurtosis = 0.242, and kurtosis standard error = 0.472, meaning that normality is not satisfied. Thus, the two paired Wilcoxon signed-rank test was utilized to observe if grade difference is significant (Z =  − 6.129, p<0.001, and medium effect size d =  − 0.427). Therefore:

• H₆: is accepted. Students obtained an average grade of 66.6 with SICMAR and 39.02 with the professor’s material. The difference of 27.58 is statistically significant (p < 0.001).

SICMAR technology acceptance assessment

We use AMOS software to examine the effects between observed and latent variables and the validity of the proposed hypotheses. The variables and the relationships between them were established considering Miranda et al. (2016) and Hamidi & Chavoshi (2018). The model in Fig. 9 comprises four latent variables (spheres) and 21 observed variables (squares). The relationships are symbolized with unidirectional arrows. The latent variable of quality is independent because no arrow is connected to it, and the remainder are dependent (at least one arrow was connected).

In structural equation modeling, only the identified (over, just, or under-identified) models can be estimated. Identification is the act of formally stating a model. We conduct the identification by computing the degrees of freedom (DoF = 184). When the DoF is greater than 0, the model has more information than parameters to estimate. Therefore, our model is over-identified. Afterward, we calculate the sample variances and covariances to obtain the values that provide a reproduced matrix that best fit the observed matrix. A model fits the data well if differences between observed and predicted values are small. For this purpose, we employ the maximum likelihood method.

A summary of the values obtained is shown in Table 6. We expected that χ²/DoF ranged from 2 to 3, a GFI value near 1, and RMR closer to 0. Our model fulfills the conditions; therefore, we have a good-fitting model. Next, we compute the coefficients of determination (R²) to measure the percentage of variance explained by the independent variables. The results are shown in Fig. 9. Values higher than 0.5 are considered good.

Then, we compute the standardized factor loadings and p-values for the observed variables. A summary of the results is shown in the third and fourth columns in Table 3. All the relations between observed variables to latent variables are accepted with a confidence of 1%. For the case of quality, the variables Q9 and Q10 related to markers were the most important. For the perceived ease of use, PEU2 and PEU4, which address the familiarity with the technology and manipulation of the prototype controls, obtained the greater values. Regarding the perceived usefulness, PU3 and PU4 were the most important, which refers to the usability of SICMAR to learn and remember concepts. The highest value was obtained for ITU1, where students expressed their interest in keeping using SICMAR.

Finally, we compute the path coefficients (β), the p-values, and the direct, indirect, and total effects between variables (see Table 7). A direct effect is a relationship that exists between one variable to another. An indirect effect is a relationship between two variables mediated by at least one or more different variables. The sum of direct and indirect effects determines the total effect. Each direct effect is represented with a β in Fig. 9 and helps validate the hypotheses.

• H₇: is accepted. The quality effect on the perceived usefulness has β = 0.694 and p < 0.05. When the quality increases its standard deviation by one unit, the perceived usefulness goes up by 0.694 units, establishing a significant relationship with a confidence of 95%. Also, the quality establishes an indirect effect on the intention to use when it passes by the perceived usefulness.

• H₈: is accepted. The quality effect on the perceived ease of use has β = 0.902 and p < 0.001. When the quality increases its standard deviation by one unit, the perceived ease of use goes up by 0.902 units, establishing a significant relationship with a confidence of 95%.

• H₉: is rejected. The perceived ease of use effect on the perceived usefulness has β = 0.153 and p = 0.562. Therefore, the direct effect is not significant, with a confidence of 95%.

• H₁₀: is rejected. The perceived ease of use effect on the intention to use has β = 0.054 and p < 0.699. Therefore, the direct effect is not significant, with a confidence of 95%.

• H₁₁: is accepted. The perceived usefulness effect on the intention to use has β = 0.830 and p < 0.001. When the perceived usefulness increases its standard deviation by one unit, the intention to use goes up by 0.830 units, establishing a significant relationship with a confidence of 95%.

According to the results, the intention to use SICMAR is significantly affected by the quality and perceived usefulness. Students expressed their intention to use SICMAR due to the total effect of 0.738 encountered in the path Quality->PU->ITU.

SICMAR quality assessment

We conduct a study to determine if students considered SICMAR a good quality prototype. The scores obtained (M = 3.93 and SD = 0.62) demonstrate that students consider SICMAR a good quality prototype, as shown in Table 3. The minimum value obtained (M = 3.16) was regarding item Q5. Students considered that buttons are small, so we need to enlarge the buttons for better manipulation. The next minimum corresponds to Q10 (M = 3.56); hence, students could not easily manipulate the device and the markers simultaneously. The better results correspond to Q1 (M = 4.45) and Q6 (M = 4.40), which suggest that all the simple interest terms were included, and the velocity of response for computations was fast.

Data obtained from quality follow a normal distribution. Therefore, a one-sample t-test with a significance of 5% and a reference value of 3.8 was performed (t = 2.126, p = 0.036, and d = 0.20).:

• H₁₂: is accepted. A significant difference is obtained when comparing M = 3.93 with the reference value (3.8). Also, as mentioned in the TAM study, quality influences the students’ intention to use SICMAR.

Lessons learned

Our augmented reality educational prototype serves as an alternative tool to learn the simple interest topic, but it cannot replace the teacher. Professors will continue looking for tools to improve the teaching-learning process. However, many times, teachers are not willing to make the efforts to create the tools, and frequently they do not have the computer skills to develop them because a usable app is challenging to create. The software to rapidly create augmented reality experiences does not offer all the resources needed to explain complex science topics.

Augmented reality causes enjoyment in students and a desire to repeat the experience. Although not complex 3D models were needed to represent the augmented reality for SICMAR, this alternative representation of the real phenomena causes motivation to the students. Even when the literature has been asserted that augmented reality can be exploited in any field, we recommend choosing application areas where it is needed that 3D models show different views of the objects. Even though 3D models are the base of augmented reality, it is still difficult to explain how the computer-based models inserted into the real scene increase student achievement.

Some students expressed that prolonged use of SICMAR slows down and warm up the device. We know that this problem is common when a mobile device is used for a considerable time. However, we are not sure if this problem is accentuated due to the execution of our prototype’s complex routines. This leads to inviting developers to conduct a thorough review to detect routines that can optimize the processor usage, look for native development, or test another framework for coding.

Remarkably, we detected that students commit mistakes in handling the five markers to manipulate SICMAR. For example, they selected the principal marker when the correct one was the amount. Therefore, SICMAR cannot help students understand the problem stated and neither identify the concepts involved. The solution to the issue of problem understanding is still an open challenge. We recommend to developers avoid combinations of many markers to trigger augmented reality.

If professors and students disagreed with testing SICMAR, they would still be thinking that paper, blackboard, books, slides, or computer-based content are the unique resources to learn. With the findings obtained, we observed the potential of augmented reality for educational settings. The school administrators must be convinced that augmented reality is an educational tool that they should provide for the students. Moreover, schools must invest effort into implementing more resources based on augmented reality to the complete curriculum. With this, it will be possible: (i) to observe the real impact of augmented reality on students; (ii) have tracking about the usability of the resources; (iii) detect the moment when the interest is lost; (iv) establish if the impact was due only to the novelty; and (v) to know what happens with concentration, and cognitive load of the students.

Limitations

After experimentation, we note some limitations in our study. Because we conducted a quasi-experimental study, our data might be biased. Therefore, the reported findings should be replicated with an experimental study (using control and experimental groups). We cannot know if students change their behavior because they are aware of participating in a research study. Only one financial mathematics professor used SICMAR, so the positive comments regarding usability may change as more teachers are involved. Some students focused their attention on the application and not on the essential parts of the topic to learn. This fact is known as the attention tunneling effect, which can explain why some students scored lower using SICMAR. Also, not all students felt comfortable using SICMAR, which offered clues that for some person it could be challenging to use ICTs. Moreover, the issues related to gender were not analyzed in depth, which is currently a trend in the AR field.

Future research

Extensions of the proposed study include the improvement of the interaction environment, a larger sample of students, the measurement of cognitive load, to involve more financial mathematics teachers, and the implementation of other topics about financial mathematics. It is desirable to study in-depth the case of students which grade has decreased using SICMAR. The worst case is a student who obtained a grade of 80 with professor lesson and zero with SICMAR. Also, in-depth analyses of the individual answers to the tests and the questionnaires will be conducted. A critical review of the interface design should be performed. Further research is necessary to determine the content that must be added to SICMAR to keep students’ attention. Finally, it would be recommendable to run a pilot study with Microsoft Hololenses to observe if the possibility of not clicking on screens increases students’ motivation and achievement.