ARithmetic - KIT208 Assignment 4

Introduction

ARithmetic is a fun and interactive way for students to learn basic mathematics with the help of augmented reality. Students arrange playing cards to try to get the correct answer to mathematical problems that appear onscreen. Whenever the cards are rearranged, the answer updates in real time, so students get immediate feedback on their answers.

Description

Many education settings feature timed, high-stakes environments where students feel pressured to get the right answer. This phenomenon of ‘mathematics anxiety’ has long been identified as a cause of underperformance and poorer ability to learn, in particular one that disproportionately impacts disadvantaged students (Richardson & Suinn, 1972). It is perhaps not surprising then that in Australia, 30 per cent of year 4 students did not achieve the national proficient standard for mathematics (Thomson et al. 2019). Traditional approaches to teaching mathematics are highly abstract, typically making heavy use of exercise sheets, textbooks, and whiteboard diagrams. For students who are not naturally inclined toward this way of learning, this can mean falling behind in mathematics, and potentially, discouragement from pursuing a STEM career (Ashcraft & Moore et al. 2021).

However, new technologies offer the possibility of creating new, more engaging ways of teaching mathematics that make better use of a multitude of human ways of learning. Other augmented reality applications for teaching mathematics have been positively received by both students and teachers, who found them to be intriguing, playful, and non-stressful (Schutera et al. 2021).

This application tries to address these issues by using augmented reality to create an application that is a unique and engaging approach to teaching mathematics. Students are presented with a number onscreen which they attempt to make by arranging playing cards representing different numbers and operators. The current result of these is displayed onscreen, and updates dynamically as the cards are rearranged. Students can explore the use of different cards and operators to get different answers by moving the cards around, helping them to have a more tangible understanding of the numbers.

When a card is detected by the application, a 3D number associated with the card appears onscreen overlaid on the number. Each of these is a different colour to help further differentiate these to students in order to provide another avenue for learning. In future, a collection of objects of the given number will also be displayed above a card when detected. This will provide students with a visualisation of the number, and will also act as a way to assist the student with getting the correct answer if they are having difficulty, as they can manually count the number of objects.

The interaction of moving the cards around provides a novel way for students to learn mathematics. The goal of this approach is to take away the pressure of textbooks and exercise sheets, and instead to encourage students to be inquisitive and engage at their own pace. This reduces the level of anxiety associated with mathematics, which in turn helps students to understand the concepts better, as well as making the subject much more enjoyable and not like a chore or something that is stressful. With the additional features such as displaying 3D objects, it also makes the content more memorable. For these reasons, this approach offers a number of benefits over traditional ways of teaching mathematics.

Description of interface solution – Augmented Reality

The medium of augmented reality offers a number of benefits. It offers a way to bridge traditional methods of teaching mathematics combined with the benefits of technology. Having a virtual layer of information overlaid on the real world allows for real-time information to be displayed in ways that can be useful when learning mathematics. For example, in this application, moving around the cards and being able to explore the real-time updating value that they create is something not easily attainable with the use of exercise sheets and textbooks. This hands-on approach is also likely to benefit students who are kinesthetic learners. In addition, it also offers a way to add more explanatory visual information to a scene, for example by having a visual representation of five objects alongside the number five card. This helps students to associate the abstract number with a more tangible visual representation of the number.

Augmented reality also allows for natural interactions to take place (such as moving the cards around). For Furness (2001) this represents an important way of replicating humans’ natural way of perceiving the world. For the same reason, being able to have tangible interactions is also likely to lead to better recall of the subject matter. Bujak et al. (2013, p. 536) found that augmented reality applications can help students learn by ‘scaffolding the progression of learning, resulting in an improved understanding of abstract concepts’. In this way, these aspects of augmented reality combine to facilitate multiple types of learning simultaneously.

Given that mobile phones have become ubiquitous over the past decade, mobile augmented reality is relatively accessible. This is especially the case when compared to virtual reality, which requires the use of expensive headsets, which is likely not a viable option for many school students at home or in the classroom.

Interaction design

The main interaction in the application is the user moving around playing cards in order to solve the question on screen. The reason this method of interacting was chosen was to make the application more hands-on and engaging for users. Users can see the result of the mathematics calculation update in real time as they rearrange the cards. This may especially be of benefit for students who are having difficulty grasping the abstract nature of mathematics, as it makes it more tangible.

Another interaction that will be implemented in future is a ‘hint’ system that students can access if they are struggling with a question. This will likely involve having a card that is designated as a ‘hint’ card which, if the student flips it over and the application detects the front face, will display a hint around which cards can be used to solve the problem.

In future, the application will likely also feature a visual representation of the number itself, such as five objects being shown on screen when the ‘5’ card is in view. This would further help with the visualisation aspect being present alongside the numerical representation. In all, this interaction combines abstract, visual and physical/kinesthetic aspects of learning in order to make the application as effective as possible for users, who may each have different learning styles.

Also, it would be beneficial if more feedback could be given to the user, particularly when they do something successfully in the application. This would help to motivate users to continue playing the game and therefore to continue improving their skills.

Initial technical development

This application is developed for the Android operating system and currently does two major things. The first is the ability to detect the different cards and represents them in a 3D space, which helps by separating the augmented reality aspects of the application into something that can be seen at a glance for parents or teachers to assist with a certain puzzle, and to separate it into the actual game which helps makes this experience a lot more enticing to the younger users of this application.

The second feature is the calculation of the currently displayed formula as shown by the cards. This happens in real time, which further enhances the curiosity from an unexpected result. For example, adding a multiplier to a simple addition formula does not multiply the result, but whichever number the multiplier is interacting with. This can generate curiosity for young users, which further enhances the lessons and makes sure that they are able to memorise what each operator does.

In the future release of the software, the user experience will be improved by having a ‘theme’ for the application. The goal of this is to create a more cohesive application that is more engaging for the younger users, which may further help with improving learning and memorisation. This would include visual imagery, music, and sound effects that would further enhance the experience of the application.

In addition, more functionality could be added around tracking the user’s history, such as the number of questions answered, time taken to complete questions, or questions repeatedly answered correctly or incorrectly. These could then be used to optimise which questions users are asked to solve, in order to ensure the application is relevant to the skill level of each individual user.

Also, in future, users could be able to manually select the kinds of questions they want to answer (addition, multiplication etc.) rather than having completely random questions. This would make the application more tailored to each user’s ability and therefore make it a more effective and useful learning tool.

Initial 3D models

• 3D models of numbers and operators, created by Sophie
• Planned for next assignment: different objects to represent each card, based on theme

Conclusion

ARithmetic is an augmented reality (AR) card based mathematics game, where students are challenged to tackle mathematics problems by arranging playing cards in different combinations. ARithmetic provides a safe and fun way to enjoy the challenges of mathematics with real time calculations of the user’s current formula, showing the interesting interactions that math can produce to naturally spark curiosity.

The application provides a fun and interactive way for children to learn, making it more likely that they will engage with the material and retain what they have learned. It makes use of multiple types of interactions and visual cues to try and maximise learning for students of all abilities and learning types.

References

Ashcraft, M & Moore, A 2009, ‘Mathematics Anxiety and the Affective Drop in Performance’, Journal of Psychoeducational Assessment, vol. 27, pp. 197–205, available at https://www.semanticscholar.org/paper/Mathematics-Anxiety-and-the-Affective-Drop...

Bujak, KR, Radu, I, Catrambone, R, MacIntyre, B, Zheng, R & Golubski, G 2013, ‘A psychological perspective on augmented reality in the mathematics classroom’, Computers & Education, vol. 68, pp. 536-544, available at https://www.sciencedirect.com/science/article/abs/pii/S0360131513000560

Furness, TA 2001, ‘Toward Tightly-Coupled Human Interfaces’, in RA Earnshaw, RA Guedj, A van Dam & JA Vince (eds.), Frontiers of Human-Centered Computing: Online Communities and Virtual Environments, Springer, London, available at https://doi.org/10.1007/978-1-4471-0259-5_7

Richardson, FC & Suinn, RM 1972, ‘The Mathematics Anxiety Rating Scale’, Journal of Counseling Psychology, vol. 19, pp. 551-554.

Schutera S, Schnierle M, Wu M, Pertzel T, Seybold J, Bauer P, Teutscher D, Raedle M, Heß-Mohr N, Röck S & Krause MJ 2021, ‘On the Potential of Augmented Reality for Mathematics Teaching with the Application cleARmaths’, Education Sciences, vol. 11, available at https://doi.org/10.3390/educsci11080368

Thomson, S, Wernert, N, Buckley, S, Rodrigues, S, O'Grady, E, & Schmid, M 2021, ‘TIMSS 2019 Australia. Volume II : School and classroom contexts for learning.’ Australian Council for Educational Research, available at https://doi.org/10.37517/978-1-74286-615-4

Unity resources

macrovector, ‘Full deck of poker playing cards’ [image], available at https://www.freepik.com/free-vector/full-deck-poker-playing-cards_6086127.htm#qu...

Vuforia Engine Package for Unity, Vuforia Library, available at https://library.vuforia.com/getting-started/vuforia-engine-package-unity