Mobile learning appears to have an impact on education (Alden, 2013) and be considered as engaging and useful in many different contexts, with different target groups (Baya’a and Daher, 2009; Kalloo and Mohan, 2012). For instance, it is suggested that the integration of mobile technologies into mathematics teaching and learning could provide more meaningful, practical, and engaging learning experience (Bray and Tangney, 2016). Learning mathematics can be a struggle as well as challenge for many students, at which point effective use of technology by both teachers and students can help to increase students' motivation, bring out the inspiration to learn, and foster understanding of math. In addition, the use of technology in learning mathematics can reduce math errors as it helps students focus more and use their time efficiently (Wadlington and Wadlington, 2008). Hegedus et al. (2015) reported that their hypothesis was supported in their study such that the implementation of technology in a high school mathematics course improved student engagement, teacher-student interaction, and students’ test results. In recent years, a number of review studies have been conducted with regards to mobile technologies, in other words, mobile learning in mathematics. Crompton and Burke’s (2017) found out in their literature review study that there is a rising interest in mobile technologies supporting positive learning outcomes in mathematics. Moreover, Fabian et al. (2016) reviewed 31 studies, the majority of which reported mobile technologies improved students’ success. On the other hand, student success is affected by numerous factors (curriculum, students’ self-efficacy, parents’ socio-economic status, etc.) (Hattie, 2009) but teacher support including providing feedback and guidance to difficult math problems play a critical role in improving student achievement in significant ways (Cornelius-White, 2007; Roorda et al., 2011). Students perceive teacher support in a way that they receive their teacher’s care, respect, approval, and assistance (Klem and Connell, 2004; Ryan and Patrick, 2001).

 

Mathematics has been a problematic subject for students all over the world. It is not easy to develop skills, especially in solving mathematical problems and finding elegant and alternative solutions when faced with challenging conditions.

 

The quantitative multiplicity caused by the increase in the number of students in Turkiye every year, the placement of students in the educational institutions through examinations, and the supply-demand imbalance between the number of students and the number of schools make student selection exams mandatory (Gundogdu et al., 2010). The exam taken by students in the last year of secondary education to transfer to a higher education institution is a multiple-choice exam.

 

These exams in the education system lead students to solve more questions. In particular, high school students who wish to be placed in a university are expected to solve math problems regularly and systematically, and engage in meaningful analysis and comparison of those. The acquisition of mathematics knowledge and problem solving skills in high school is essential for students’ enrollment to a major at the university, and their career success in a progressively high-tech economy (Geiser and Santelices, 2007; National Mathematics Advisory Panel, 2008; Wang, 2013). However, traditional mathematics instruction may not be sufficient for improving problem solving skills. Besides, required to be solving many math problems can be burdensome for students.

 

In general, primary school children can solve math problems with the help of their parents. On the other hand, the ability of parents to support children in the following years of education becomes very limited according to their education level. Families seek various solutions according to their economic situation; however, they may not have the resources to support their children, for instance, on private lessons. In case of a math question that cannot be solved, students ask someone else, usually their teacher to solve the question. However, there are some limitations at this point.

 

In order to present the question, it is necessary to find a suitable time for the teacher during school hours and consult the teacher for a solution. This situation limits problem solving to school time. When students leave their questions blank to be solved later and continue with other questions, similar questions or questions on other topics are also left blank as the question at firsthand left blank was not answered. This leads to stacked questions that need to be resolved.

 

Therefore, the construction of semantic knowledge on the math subject remained unfinished, which possibly lead to a failure in math.

 

Being successful or failed in mathematics, particularly in the case of solving higher-order math questions, is profoundly reliant on in what way the students are provided with the feedback (Hattie and Timperley, 2007). Feedback hence can promote and support students to develop their mindset and go further in their learning experience to achieve desired success goals (Guskey, 2010). It  is  important  for students to have their teacher's solution to check for the "correct" solution(s) (Nicol and Macfarlane-Dick, 2006). Although it is accepted that being involved in the higher-order thinking process by solving math questions and getting teacher support for this may be factors for students' math academic success, there are fewer studies on these factors in the context of mobile platform.

 

High school students, in particular, need to have a continuous, and fast feedback and support by the teachers in solving mathematics questions, which might help them become successful at the university entrance exam. This process is significant especially for the students coming from a low socio-economic status. High school students try to find solutions and realize their shortcomings by asking their teachers about the problems they cannot answer. Being able to reach a solution by sharing the questions in a digital platform can provide an important convenience for the students. A digital platform where many students share only the questions they cannot solve among thousands of questions from different educational resources can provide important data in determining the learning outcomes that students cannot reach. Learning outcomes are decisive in teaching activities and the distribution of the questions shared by the students according to the learning outcomes is important. Since learning outcomes have an impact on students' learning processes, it is of great importance to determine learning outcomes correctly. Additionally, despite a growing body of research on mobile math learning, learning outcomes in high school using this mobile technology have rarely been studied.

 

Through such mobile learning platform, it can also be revealed that cognitive levels students have difficulty in reaching. A mobile learning platform to be developed for this purpose can contribute to the determination of the learning outcomes that can be reached and the cognitive levels of the students. In this study, a mobile application was developed in order to determine which mathematics questions that students have difficulty in solving are mainly distributed over which mathematics subjects and learning outcomes, and to reveal the cognitive levels of the questions sent. The present study both describes the design and development process of a mobile application and answers the following research questions:

 

1. In which mathematics subjects and learning domains did students have the most difficulty in problem solving and sought support for their solution?

2. At which cognitive levels are the learning domain questions that students have the most difficulty with?

3. What is the distribution of these cognitive levels among classes in high school?

4. In this learning domain, what math learning outcomes and associated cognitive level did students submit the most questions about?

3. What are the teachers' experiences and views on using the mobile learning application?

 

Task and content analysis

 

The math question submission, solution and feedback process were determined.

 

Design and development of the technological innovation - Mobile app

 

Interface design

 

Designing and creating math-specific mobile user interfaces to increase user friendliness according to user preferences. According to the user ergonomics of a mobile device, form factors such as screen size, minimizing keystrokes, offering image sharing and being task-oriented were taken into account.

 

Bidirectional system operation and pool system

 

This phase was about the design with regards to how the application would function, how its related elements would be arranged, and how users would fulfill their tasks. Designing the pool tool to enable registered users to reach and share all the questions and answers saved in the system.

 

Data labelling system

 

All questions (as in image files) sent by students were solved, labelled and submitted to the question pool by teachers according to specific mathematics topics. The categorization of questions based on labelling process helped learners to easily search the math topics in the pool and access the relevant questions and their solutions. The learning domains and sub-learning domains in the high school mathematics curriculum (Milli Egitim Bakanligi, 2018) (Table 1) were taken into consideration to create a list of math topics.  

 

 

In order to increase the effective use of mobile app, more math topics were included in the learning domains. For instance, Greatest Common Divisor (GCD), Least Common Multiple (LCM) and Absolute Value subjects which are in the sub-learning domain of "Equities and Inequalities" were presented separately in the app. Thanks to this topic classification, it tried to create a structure that is more useful for students and teachers in which they can access questions about a particular topic more easily. Thus, there were a total of 61 mathematics topics in the application (Table 2). While creating the topics, it was aimed that the students and teachers understand the content of the question more easily.

 

Integration of system user analytics

 

Considering system security according to determined criteria, this phase is about designing a mobile platform as well as an associated 'web platform' (http://math.dijitaladam.com/login.html) to manage user registration and analytics that provide statistical information. Table 3 and Figure 1 give some examples for statistical information, or findings. However, the purpose of the present study is different and will not focus on the findings indicated in the tables.

 

 

Testing and refinement

 

The following three procedures were carried out for mobile application product verification with user groups, and the formative evaluation was not limited to this process, but was applied continuously (Table 4).

 

Ethical principles

 

One of the principal design features of this mobile app focuses on the security of data within a closed platform where registration is required with the information (participants’ names, email addresses, ID numbers) obtained officially from schools. Communication and interaction among students via mobile devices may raise some ethical issues (for example, bullying, racism, and stalking), so it was essential to design a control mechanism and a closed platform for a learning community purpose to prevent unacceptable practices by users.

 

 

 

 

Students

 

The mobile application provides students with the opportunity to ask questions anytime, anywhere and to easily access the solutions of mathematics questions that they have difficulty in solving. Students also create a pool of questions by sending their unsolved math questions to this application (Figure 3).

In this question pool, students can access the questions categorized according to mathematics topics from any smart mobile phone or tablet with an Internet connection, and ask their questions without time constraints (Figure 4).

Students can access the answers to their own questions, as well as the questions and answers sent by other students (Figure 5).

 

 

 

Teachers

 

Teachers had a critical role in this mobile app, especially by providing support and feedback on students' math questions. It was believed that teacher support is an important predictor of students’ success. Students' perceived teacher communication and support was found to be the factor most closely related to their success in high school (Gregory and Weinstein, 2004). In order for teachers to provide a support and feedback to the students’ unsolved math questions, teachers, they were registered to this mobile application platform. Teachers were able to review all questions submitted by students in the system. They picked and took a math problem and submitted its solution as an image file, sometimes providing more than one solution, to the mobile platform. While sending the solution to the system, the teachers were required to match the related question with an appropriate mathematics topic from the given list and send it by labeling it.

 

Once a question was taken by a teacher to solve, other teachers could not see that question in the question pool unless it was reloaded by the teacher who did not want to continue working on it. However, the administrator had the right to warn the teacher to make a decision whether to work or not on a question in an appropriate timeframe. Not only could teachers have an access to their own solutions/answers in the system but also the pool including all questions and their answers. The following Figure 6 explains the procedure in visual.

 

Teachers generally provided students with one or more solutions of a math problem as much in detail as possible as shown in Figure 7.

 

With this application, students can become the managers of their own time without wasting time. In addition, it saves teachers and students from the trouble of stacked questions that are expected to be solved. In this way, teachers and students do not have to make a separate time plan for solving the questions. Since there is more than one teacher in the system, questions are solved and answered quickly, and a teacher's workload is lighter than normal and shared by other teachers in the mobile application.

 

 

 

 

 

 

While there are more questions at the level of remembering, understanding and application (n=156 in total) that require low-level thinking; there are fewer questions that require high-level thinking at the level of analysis, evaluation, and creation (n=24 in total).

 

According to this result, it can be concluded that students have problems in understanding or solving questions that require low-level thinking. It can be said that there are fewer questions that require high-level thinking  due  to   the  fact  that these  questions  may  be scarce in the source books they used. Sample questions can be seen in Figure 11.

 

 

According to Bloom's Taxonomy levels, it was determined that the most questions out of 162 questions were  at  the level of applying and understanding. For the 9th grade, 28 questions from the understanding level and 33 questions from the applying level were asked by the students, while for the 12th grade, eight questions from the understanding level and 35 questions from the applying level were asked (Figure 10). In line with these results, it was seen that the students in the 9th grade have deficiencies in understanding and applying the mathematical questions, while in the 12th grade they have more problems in applying rather than understanding the math questions.

 

 

According to the grade levels, it was determined that questions coming from the 9th and 12th grades were the most out of 162 questions. The reason for this may be that Numbers and Algebra domain takes up more space in the High School mathematics curriculum in the 9th and 12th grades compared to other learning domains.

 

 

What are the teachers' experiences and views on using the mobile learning application?

 

Thematic analysis was conducted under three core themes: general views on the use of the mobile application, its pedagogical and technological use, and students’ learning experiences.

 

General views of teachers on the use of the mobile application

 

Teachers stated that the mobile learning application is very useful, especially since it allowed them to solve many different math questions. In fact, it has been stated that the main purpose of using this application by teachers is to practice problem solving. It has been deduced that the teachers see the mobile application as a question bank containing alternative solutions from different perspectives. Example quotes with regards to this issue as follows:

 

“I benefit from solving questions and the solved questions in the question pool.” “It's a nice application to spend time in my spare time. When I'm tired, instead of picking up a pen and paper, pick up the phone and solve it over the phone.”

 

“We also see different perspectives from our own perspective.” “As a teacher, I see different questions and improve myself. A great resource as a question bank” “… at least I am useful in my spare time so I feel happy”

 

One teacher also indicated that she “began to see more clearly the subjects that students had the most difficulty with” by using this mobile learning app. Teachers stated that the most liked features of this application are that it resembles a private lesson, like a one-on-one lesson, and being a part of a learning community. Example quotes with regards to this issue as follows:

 

“…kind of one-to-one lessons... helps those who don't have the opportunity to ask questions in the classroom...”

“I think that the children who use the app and myself are also part of the learning community. I find the app very useful”

 

 “It definitely gives an experience, it's a privilege to even be a part of it, it is like a social network”

 

Pedagogical and technological use

 

Teachers reported that they were impressed with the student feedback process provided by the mobile app. Some responses stated that the mobile app as a feedback and support system has the advantage of increasing student engagement in the learning-teaching process by interacting with the platform and sharing their questions regardless of time and place. Example quotes with regards to this issue as follows:

 

“…it has positive effects. The student cannot find a teacher at home on issues that he or she is missing at home,  thanks   to  this  application,  they  can  reach  the  solution of questions from home and learn the technique of problem solving…”

 

“…they are definitely getting positive feedback and they say that this application adds a lot to them”

“The fact that the application answers the questions quickly increases the motivation of the students”

“At least she knows that if she has a question, there is a place where she can get an answer at any time, any hour”

 

Teachers also reported that they developed their teaching skills and methods by using this mobile app.

 

“The more questions we solve, the more different our instruction becomes”

 

“I didn't use an app like this, I used online applications in the classroom, I can help the individual student directly here through this app”

 

“…I also use the questions uploaded to the app in the classroom… interesting and good questions come up, for example, about the problems…”

 

Students’ learning experiences

 

When asked what effect the mobile application had on students' learning, teachers generally stated that it had a positive effect.

 

“Of course, there is an effect. Having learned the solution of the problem, the student can now solve similar questions”

“A useful application for children who use it for its intended purpose and for those who want to learn, it always provides the opportunity to learn...”

“It has a great effect when they receive feedback; it has positive effects as it allows them to make up for their shortcomings at home”

“Kids these days live fast. They want to solve the question that comes to mind immediately. It helps them with this”

“She solves the questions she cannot solve and learns the shortcuts”

“…absolutely helpful... I don't understand the opinions of those who didn't use it”

In contrary, some teachers stated that the effect felt was not as great as it seems.

“Students do not understand anything from the solution, sometimes they come with very simple questions”

“…some students' phones are not suitable”

 

According to the answers given to the question of how using this application improves students, teachers saw the application as a very helpful and useful tool.

 

“They may stop solving questions they have difficulty with, or they may stop working on them. So, they can give up. However, they know that they are not  alone  and they continue to take part in the process as long as they get the solution to their questions.”

“…they learn question techniques and how to approach the question”

“Solving those questions increase the self-confidence of the students”

“My students like the application; they are positively motivated when they see that it is useful”

High school students, especially students in their final year preparing for the university entrance exam, were solving a large number of mathematics questions. There is a need for teacher support regarding the solutions of those questions.

 

A mobile application was developed in this study with the purpose of providing this support at this point. According to previous research results, interactive mobile learning apps improve students' mathematical problem-solving skills (Amir et al., 2018; Amir et al., 2020).

 

Mobile devices along with an appropriate application can provide a learning context where students can create and share knowledge for better learning outcomes (Melhuish and Falloon, 2010; Haßler et al., 2016). Achieving learning outcomes has an impact on students' learning processes. For this reason, it is of great importance to determine the learning outcomes correctly. It is also important which cognitive skills and levels are included in mathematics teaching.

 

According to the results of the study, it was seen that the learning outcomes were mostly directed towards the low-level cognitive skills of Bloom’s Taxonomy. Although it was seen that the students were able to reach Evaluate level, it was observed that they mainly shared questions at the Apply and Analyze levels. This finding suggests that educational approaches or policies focusing on high-level cognitive skills should be taken as a basis. The positive impact of using technology throughout the curriculum can help students develop higher-order thinking skills that can help them learn math beyond the classroom (Murphy, 2016).

 

Mobile learning has been included in research literature as a developing topic in the context of teacher education (Kearney and Maher, 2013). It has been observed that teachers who solved questions in the system improved themselves in terms of different question types and alternative solution methods. In addition, it was observed that the teachers prepared new notes for the questions frequently asked by the students, contacted the students again on these issues, and made additional lessons. According to the findings of the qualitative part, it was observed that the teachers' use of the mobile application was high and they were willing to apply mobile technology in mathematics education, especially in providing their support for solving difficult math questions.

 

They stated that the mobile app has the potential to become an effective solution for supporting high school students in developing self-confidence and self-efficacy, which may lead to an academic success. This finding is in line with the research study by (Yu and Singh, 2018). The authors reported that teacher support through positive interaction between teacher and students has a strong and positive effect on students' self-efficacy and therefore indirectly affects students' mathematics achievement. Consequently, the teachers showed great enthusiasm and satisfaction in the use of this innovative application.

 

The educational capabilities of mobile devices offer learning activities for a better understanding, which were previously not possible (Cumming et al., 2014; Montrieux et al., 2016). This study is in line with the research by Jeng et al. (2010) showing that mobile apps provide a convenience in learning in the daily lives of student. Based on the results of the study, it can be concluded that the mathematics mobile learning application can be used as an alternative learning environment that can give an idea about the learning outcomes and cognitive levels of high school students.

Although the present study has important implications, there are some limitations as well. The sample of the study was limited to students studying at and teachers working in nine high schools in one district of Balikesir province. Therefore, future studies should be expanded to include more students and teachers from more high schools. This study did not investigate students' perception of the use of and engagement with the app. Moreover, the study did not take into account internet connection quality and students’ digital literacy and skills. It could be thought that not all students could afford the accessibility to mobile learning experience (Sabah, 2016). Moreover, the current study did not report any findings about whether or not all students benefitted from and enjoyed the developed mobile app. Therefore, future studies should conduct quantitative and qualitative methods to gain deeper understanding about the influences of the app on students’ mathematical problem solving and higher-order cognitive skills. Another limitation of the study was that it did not focus on whether the mobile app has an effect on students’ mathematics academic achievements. Factors related to the impact of mobile learning on student achievement can be identified and examined, so that the mobile application can be redesigned and developed accordingly. Further improvements of the application in terms of enhancing functionality and usability as well as ensuring long-term user engagement should be considered and tested.

 

The questions and answers in the system have created a question pool - a question bank. According to the statistical data available from this pool, it was determined which  mathematics subjects were asked the most questions. In this direction, it can be revealed what kind of deficiencies there are on the basis of subject in the lessons in schools. Hence, a mathematical map can be drawn about which subjects are not understood on the basis of schools and which subjects the mathematics teacher should focus on. Therefore, it can be determined which region is deficient in which subjects on the basis of districts. This could be an internal control and studies can be planned by investigating why the most difficult math topic is difficult, whether enough time is allocated, whether the necessary support is provided or whether it is due to the complexity of the topic. After these analyzes are done, the learning activities that need to be developed can be shared and discussed with the mathematics teachers working in the schools. As a result, it may be possible to determine and improve mathematical literacy on the basis of individual student, schools and districts.

 

Many teachers and students are now more experienced and willing to use mobile technology, which is more affordable and accessible than it was a decade ago. It is clear that students and teachers are already using mobile technologies to create their own time and space to practice a more flexible learning (Traxler, 2009).

We are only at the beginning of exploring the use of these promising mobile technologies in education. Technology that supports mobile learning is changing very fast. This study can be an initial study for designers, experts and teachers in mobile technology. The findings in this study are among the many topics in this rapidly evolving field. There are many opportunities and potentials waiting for us to realize. Finally, teachers are expected to continue to use ever-evolving mobile technologies in new ways, not just in the classroom, but outside the classroom anytime, anywhere to help students prepare for their future careers and lives.

The author has not declared any conflict of interests.

This work was supported by the Matematik Cepte project funded by the Karesi Municipality. The author gratefully thanks to Dr. Ikikardes and Dr. Ates from the department of mathematics at Balikesir University for their support during the design and development of the mobile application and for their helpful discussions in mathematics learning.