The Role of E-Mentoring in Mathematically Gifted Students’ Academic Life

Mentor’s role

The students revealed that the approach that the mentor took when he orchestrated the communication and guided them in thinking, contributing, and doing mathematics was one important motivational factor. The importance of the mentor’s approach was reflected in the data from the logs and interviews. For example, Tufan (all names used here are pseudonyms) wrote,

Our mentor provided us with explanatory information before each task. Instead of showing how to go step by step, he gave important clues during our work and allowed us to learn together through discussions. I think such clues were very helpful in our work. (L)

According to Alp, dividing the whole tasks into smaller parts enhanced their work on the tasks:

It was easier to understand what is going on; we were able to see the [whole] structure with all its [interrelated] parts. Working in this way motivated me . . . I thought I not only did what I was supposed to do, but also I learnt how complex problems can be solved thanks to our teachers’ [mentors’] help. (I)

Kaya and Mehmet also stressed the same point and argued that they could easily focus on solving these particular parts of the final product. Mehmet said that “our mentor taught us how to solve whole tasks by considering them as a collection of tiny pieces. I think, otherwise, the task would be too complicated” (I). Kaya added, “After we completed a task, I turned back and saw many steps we passed through. Of course, it was not easier. But, our mentor’s help and friends’ [contributions] motivated me” (I).

Online nature of e-mentoring

The second major factor that had a strong motivational effect on the students is the online nature of e-mentoring. Kaya said,

I do not like being forced by others into doing things; I like to be [involved in] doing something, especially if I am really interested and motivated. I loved to take part in this project when my teacher asked. I was very motivated, mostly because I was having an online experience. I realized that online learning is as interesting as other games, if there are interesting and instructive activities. (I)

Tufan stressed the same point as Kaya. Tufan pointed out that his parents allow him to use the computer for at most 2 hr. In these 2 hr, he is either playing computer games or chatting online with friends (L). He said that working on the project was very interesting (I). In the evenings, he preferred and enjoyed working on the project instead of spending time in other activities (I). In addition, Demet thought that online learning was a good and professional practice for students:

In this project I felt like a math teacher. I used to prepare some presentations on my computer by using Internet sources before. But this was the first time that I did something important for my academic development [using the Internet]. (I)

Nature of tasks

The nature of the mathematical tasks selected for this e-mentoring program was found to be one of the three most frequently mentioned factors that motivated students. The students revealed that the tasks were challenging and were rooted in real-world experiences. They further indicated that the stories used in the tasks were interesting and stimulating.

Kaya and Demet underlined the differences between the tasks in this program compared with those they solve in regular classes. Kaya pointed out that he loves to solve complex problems that stimulate in-depth thinking (L, I). He said that this program gave him the opportunity to solve such problems (I). Demet underlined the same point, expressing that the tasks had the potential to lead her in thinking deeply about the multiple solution processes (I). This type of task attracted her attention more than the type of task she works on in regular class (I).

In the interview, Alp said,

I do not enjoy solving easy problems, because you know what you are doing, and in each stage of your solution you see what you have expected before. But challenging problems with complex stories are not like that. It is like a puzzle, and you need to view it from different angles. I appreciate that the problems in this program were really challenging. They motivated me from the beginning to the end. (I)

He further revealed the challenging nature of the problems was an effective means that let him learn reasoning skills and effective problem-solving approaches (I). Tufan mentioned the challenging nature of the problems, as well (I, E, L), and indicated that these kinds of problems motivate them, develop their problem-solving skills, and help them excel in mathematics (L, I). He further commented on the stories that were part of the given tasks: “The problems were challenging and were given within the stories. The stories were interesting” (I).

Providing meaningful and real-world-related opportunities for gifted students is an essential means of meeting their learning needs. These opportunities have a potential to motivate them to achieve excellence. Embedding mathematical concepts or problem solving into interesting stories was found to increase student interest and motivation. This finding is supported by Baum, Cooper, and Neu (2001), indicating that the focus of the education on real-world experiences increase students’ motivation for learning.

Challenging tasks are very important, especially for gifted students’ mathematical learning (National Council of Teachers of Mathematics, 1998). Studies show that the challenging tasks trigger students’ high-level thinking and reasoning; thus, it facilitates their development of mathematical power as well as cognition (Henningsen & Stein, 1997). According to Lupkowski-Shoplik and Assouline (1994), students’ motivation increases while solving challenging tasks. Moreover, success in such tasks develops students’ self-esteem and self-efficacy (Bandura, Barbaranelli, Caprara, & Pastorelli, 1996).

To better motivate students and develop their self-esteem and self-efficacy through challenging tasks, instructors should be careful in guiding and directing students. This is the case too for a mentorship program. Daloz (1986) stated that in effective mentor–mentee relationships there should be a good balance of support and challenge. For instance, if a mentor is overly supportive without challenging mentees, the mentees do not grow professionally; however, challenging without providing a support may cause mentees to regress in their professional development. In this program, we aimed at balancing these two components and the findings revealed the program’s success in that sense. The role of the mentor was supportive and led students to successfully accomplish the tasks through effective communication and supportive interaction.

Numerical data

The number of posts to the discussion board can be considered as a way to observe the frequency of interactions. Table 3 shows the number of emails and messages sent to the discussion board. The total number of student posts to the discussion board was 334, excluding those that were just greetings and saying goodbye. Forty-four of these 334 were other off-task posts. The remaining 290 messages were coded based on Soller’s taxonomy. The language of all types was appropriate for a formal discussion environment. The content did not include any harassment, bullying, or provocations.

All students successfully completed the group and individual tasks. The number of emails indicates that the students and the mentor sent emails back and forth to complete the tasks. The mentor gave much feedback, and students were eager to ask and use this feedback through the problem-solving process. We did not observe any isolation or any other controlling behaviors during the group work.

Kaya was assigned as a group leader during the program. He sent 91 posts to the discussion board. This was the highest number among all students. In all three Level 3 categories, Kaya had the highest contribution to the group work. Although the mentor motivated the students during problem solving, Kaya too sent messages to reinforce and encourage group members. Mehmet also took similar responsibility in specific stages of problem solving. Mehmet’s contribution to the group discussions was at a high level. However, one interesting finding was that his interaction with the mentor in the individual tasks was more effective than other students’ interactions with the mentor. An evidenced in Table 3, Mehmet had the highest number of emails sent to the mentor over individual tasks. He asked questions to solve the tasks in more creative ways and had interesting approaches that he shared with the mentor and asked for the mentor’s thoughts and ideas. The number of Tufan’s posts to the discussion board was lowest (39). However, his contribution to the discussions and group work was very instructive and therefore valuable. We observed very effective creative conflict in student discussions. Observations and numerical data showed that the number of students’ posts that were coded under creative conflict was very high. The content of these posts was found to be meaningful and detailed. Some types of posts were rarely observed (e.g., Listening, Present, and Conciliate). One reason might be insufficient data due to the limited time of the e-mentoring program. Another reason might be that the CLCST was not developed for online interaction and might need further refinement.

Mentor’s role

In any case, teaching gifted students can be challenging for teachers. Teachers of gifted students usually point out that this experience can be both a joy and frustration. Mentoring, especially if it occurs in a virtual environment, becomes more complex than regular teaching, and the role of the e-mentor can be very demanding in terms of developing rapport and instilling trust in an online student group. Daloz (1999) set mentors apart from “regular teachers” (p. 21) and argued that mentors are more engaged and concerned with the individuality of their students.

Before the program, the researchers and the mentoring recommendation group (two university professors and one doctoral student in mathematics), as well as the school counselor and mathematics teachers, worked together toward the e-mentoring program goals related to students’ professional development and successful student outcomes. The group agreed that developing interpersonal and professional trust with mentees is a key element of a mentoring process in which each participant feels safe, confident, and appropriately challenged. Three weeks is a short time period to facilitate trust and openness, and to design and create appropriately challenging tasks. Therefore, the mentor visited the school several times and met with potential students who might participate in the program. During the student selection process and other visits, the school counselor arranged short meetings with these students so the mentor and students could get to know each other well. These meetings allowed the mentor to be supportive throughout the mentoring process and to create personal engagement with each student mentee.

During the e-mentoring process, the mentor used digital notes of encouragement and feedback such as questioning, giving praise, cognitive elaborations and explanations, pushing to explore, dialogue prompting, and scaffolding. He helped students to make conjectures, share their representations, reflect on their work, and make connections. Table 4 shows several examples of the feedback the mentor used in the individual and group tasks.

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Table 4.

Examples of the Feedback That the Mentor Used in the Program.

. . . you had a great discussion on finding the new ways of solution. But, it seems that you think we’d need some more information in order to choose one of these . . . I would like you to view the problem from his [Tufan’s] aspect.

We are in the second week and here we have the new task, I think you have already read the task. All you did a great job in the last week’s task! When I individually evaluated your contributions, I saw that you worked as professional team.

I was extremely pleased by your interesting suggestions in starting to solve this problem. At this point we all agree that Demet explained and supported her idea well. What you think, should we start with taking her ideas first?

Go ahead, and show your work, please. This is a good idea!

Mehmet’s example on these number patterns really impressed me. Should we ask him to explain how he came with this idea?

If you know all the distances between any two points, and the length of each side, what ways can you think of to figure out the shorter length between these two particular points?

You are in a right track. Take a minute and think about what we did in each step and why.

Let’s write all that we know about.

What would happen if we decided to go through Demet’s and my way of solution?

Besides giving helpful feedback in particular stages of problem solving, the mentor also had a critical role in the initiation of collective decision making and problem solving at the very beginning of group tasks. After the students read the first task, they all expressed that they understood the problem. However, they were not able to start collective problem solving. The mentor suggested that the students start sharing how they understood the problem first. The students wrote briefly what they understood. In the early stage, the first few messages were not systematic. A lack of effective group functioning was observed. Three of the students were disposed to direct the group through their own ways of solution. The mentor intervened to avoid confusion in the discussion. He reminded them of team responsibilities and rules. He further suggested they discuss ideas one by one and try working on behalf of the team. Kaya was selected as a team leader. He suggested reading Demet’s thoughts first. Some of the students revealed that it was a critical turning point for the creation of a healthy discussion environment that persisted throughout the project (I, L).

It should be noted that there appeared to be some irrelevant and off-task messages, but the quantity of these kinds of messages was quite small. The mentor’s role was important in those situations. The students indicated that the mentor’s way of intervention was effective, making them focus on the solution.

The role of the mentor in a discussion was to guide students in an appropriate way. He gave some clues to encourage students to think about the solutions from different angles and guarantee that the discussion was related to the topic. Demet had a complaint about one issue. She argued that some important messages in a group discussion board remained unanswered. She gave her message as an example and underlined that she believed the message had important content. She suggested that if there was an unanswered message, the mentor should ask students to respond to it (L). Alp, Mehmet, and Tufan did not agree with this idea (L). They stressed that the present role of the mentor in the group work was appropriate and there was no need for further intervention. Mehmet wrote, “Since this was a teamwork, the flow of the discussion should be related with majority’s thought. Thus, there might be some unanswered messages. If others saw these messages as relevant, they would certainly discuss on them” (L). Tufan argued that further intervention of the mentor would reduce their engagement in the tasks (L). The mentor’s role in the project was to monitor the students and provide necessary support to engage them in the practice. The advisors who were monitoring the program agreed that the mentor should only take part where the confusion in a discussion forum occurred. Students’ success in group task completion shows that the role of the mentor in a discussion forum was supportive overall.

Students’ views

The students believed that this 3-week program was a good example of successful teamwork. They mentioned communication, interaction, harmony, and respect having major impacts on team success. Alp said, “We are members of a group, so we need to support each other to achieve our goal” (I). Demet and Tufan had similar comments. Mehmet expressed his thoughts as follows:

We were informed that this study was designed to allow us to share our knowledge and to learn more about subjects we have seen at school. The knowledge of my friends who were real team players was important for this project. I have learned a lot from them. (I)

According to Demet, it would be difficult for them to solve these challenging tasks on their own: “We succeeded, because we were a team” (L, I). Alp shared his idea from a different perspective: “While sending messages [to the discussion board], I did not intend to criticize someone because of his/her meaningless solution, rather I tried to support their ideas, and clarify what they meant” (I).

Mehmet emphasized the importance of meaningful discussions while working on the tasks (L, I). He said that without the proper discussion environment they could not complete their missions (I). Tufan reported that

In a class, while working as a team, it is very hard to have an agreement on a lot of issues . . . It is hard to organize a team to have members listening to each other. Actually, teachers appoint a team leader, but it does not change the confusion. We did not have such problem here. Comments were meaningful and directly related to problem. Thanks to organized discussions, we could complete all tasks more easily than we expected. (L)

Demet completed all individual tasks and made significant contributions to the solution of the group tasks. She pointed out that this was her first experience with online mentoring (L). She found it interesting and helpful (L, I). Demet described herself as a student who loves to learn from others (I). Her comment about the group work was as follows:

The tasks were so interesting and challenging. All of us had different solutions. In the forum we presented our solutions and had discussions on them. I have read my friends’ blogs too. I have seen that we had different ways [of solving problems]. Their solutions helped me to understand the problems clearly and easily. (I)

The students indicated that using a virtual platform enhanced the quality of discussion (L, I, P). For example, Kaya explained, “While using the forum, we first read friends’ posts and then write comments.” He also added that group work in the regular class environment is different: “it is very hard to catch every single point because students talk [at the same time]” (I). Tufan reported that “the teamwork in this project was smooth and relevant; we were able to follow all previous messages in the board and also reply to whichever message we wanted” (L).

Quality of dialogue

Students worked in harmony. With only a few exceptions, they acted professionally and fairly while discussing one another’s arguments. For example, dialogue among the participants in “the bird and the train” task was very interesting. It shows how they collaboratively moved through the solution step by step (see Table 5). The mentor also gave guidance where misconception occurred.

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Table 5.

Example to the Discussion Board Dialogue Among the Students.

Tufan: Distance that the bird flew is twice the length of the train?

Demet: It had to be longer than that. But how can we find how much longer?

Demet: Take Point A where the train started.

Mehmet: But we don’t have such information, the train is already moving.

Kaya: Does it matter? We are interested with the distance between the starting and the finishing point, so we don’t have to know how much the train has traveled before.

Mehmet: I see. Velocity (the train) is constant. It confused me.

Tufan: Demet had a good idea, go on.

Kaya: And we need another point where the bird already finished its travel?

Demet: Yes, we know the time and we’ll find its velocity if we can know the actual distance.

Tufan: Demet, did you consider that the bird flew in both directions during its flight?

Demet: Yes, by the way, it would take less time during its return, because the train and the bird are going in opposite directions. But at the beginning, when they were moving in the same direction, it would take much more time for the bird to reach the front of the train.

Mehmet: So, we should consider both directions, and calculate them separately.

Tufan: Demet, but your idea about two points (starting and finishing) will not work. The total distance is not the length between these two points.

The Mentor: Very good ideas, but we have to be careful. Should we consider what Mehmet said? I think it was good point. (P)

Not only in this example, but also throughout all group tasks, it was observed that the students were advancing by having healthy dialogue with each other. This is consistent with the research findings that individuals facilitate each other’s learning through shared dialogue and negotiation (Bereiter, 1994; Brown & Campione, 1990; Vygotsky, 1962, 1978). Also, students’ attempts to clarify points were another way to share their ideas to establish a common meaning (Kuhn, 1993).

Two of the interview questions were “How did other members influence your participation to the group work?” and “Would it be better if you had the opportunity to choose the members with whom you worked? Why?” Students’ answers to these questions were similar. At the beginning of the project, the students indicated that they knew each other. Two of them were close friends. Alp’s comment to these questions was “The content of the forum was about our thoughts on mathematics. So, we did not need to have same ideas on each part. I do not think that being friends with members changes the quality of work” (I). Demet had a similar reaction: “I think the first feature of a participant to be selected into this project is his/her interest to mathematics. The major point is a participant interest. Otherwise, it wouldn’t work” (I). Tufan mentioned that in different courses they have classroom discussions on specific topics, most of which related to social issues. These topics drive students to share their own perspectives in the light of daily life problems. He said, “In such discussions I always want group members to be among my friends, but if the topic is related with mathematics, ‘being good at math’ becomes more important” (I).

Research shows that the relationship among community members is a very important factor for healthy group work. According to Donath (1999), “trust in the shared motivations and beliefs of the other participants is essential to the sense of community” (p. 31). In the group work within the e-mentoring program, trust becomes central to the development of a sense of shared community, too. Environments where the group members know each other well and feel safe encourage students and increase their involvement. However, as the students mentioned, this kind of environment is not seen as a necessary criterion for some specific domains. Axelrod (1990) argued that socializing and getting along with others is not always a necessity for successful cooperation.

Throughout the student discussions, we observed that they were eager to contribute to the teamwork toward successful completion of given tasks. They showed strong effort and great skill in cooperating with each other. They were respectful to the suggestions and critiques by group members. For instance, at the end of the solution of Group Task 3 Part 1, Mehmet explained his calculations and wrote his result (.12 mg). The answer was correct, and Mehmet was quite sure about that. Meanwhile, Kaya wrote that he was confused with one of the points in the previous discussion (P). Mehmet could insist upon his correct result and ignore the comment, but he provided explanation. For this age group, it looked like very genuine concern for each other.

Perhaps one reason behind the effectiveness of the e-mentoring program, especially in grouping these students, is the appropriateness of work for their characteristics and intelligence level. According to Benbow (1998), grouping gifted children has advantages for learning if the level of work is suitable to them. Moreover, providing challenging tasks enhances student cooperation in problem solving and knowledge construction. Working on challenging tasks, as discussed in the first theme, was also a factor in increased student motivation. From this point, we can argue that the factors that affected healthy cooperation might be correlated with student motivation too. Consequently, the researcher observations and interviews were consistent with each other regarding the point that student cooperation in the program was at an expected level and the reasons behind this result was the consideration of “norms, tasks, help giving, and group composition” (Blumenfeld, Marx, Soloway, & Krajcik, 1996, p. 38).