A case study of an experiment using streaming of ...

Teaching Mathematics and its Applications Advance Access published February 4, 2015 Teaching Mathematics and Its Applications Page 1 of 9 doi:10.1093/teamat/hru029

A case study of an experiment using streaming of lectures in teaching engineering mathematics HELGE FREDRIKSEN* Department of Technology, University College of Narvik, 8049 Narvik, Norway *Email: [email protected]

To support the possibility of taking an online engineering degree programme, Narvik University College has chosen to facilitate a streaming service of all lectures conducted by the college. At the Bod college campus, in the academic year of 2012/2013, these online lectures were used as a central component in a didactic innovation project. The aim was to test and evaluate the capabilities and limitations that web-based communication provides both academically and socially. This innovation was viewed within a Vygotskian theoretical framework linked to a social constructivist facilitation of students’ learning. A survey among the students was performed in the mid-semester. The results of the analysis show that the renewal of the teaching was well received by the students in the group. However, the social learning environment suffered, since students failed to participate in the sessions created in connection with the web lecturing. Thus, the social learning context that we initially sought to strengthen was fragmented and lacked momentum as a result of the change.

1. Introduction This article deals with an exploration of a teaching innovation tested in the first year of engineering studies at Bodø on the modules Mathematics 1 (autumn 2012) and Mathematics 2 (spring 2013) as part of a course delivered under the auspices of Narvik University College. The circumstances of mathematics modules in consecutive semesters with the same students provided ample opportunity to collect feedback from the students about the effectiveness of the teaching, to use this feedback to devise potential improvements and then to implement these improvements. At the end of the first term, an anonymous student survey was given in which students were asked to evaluate the teaching programme so far. The results from the survey highlighted the fact that many felt they had too little time with the teacher in a setting focused on problem-solving. It indicated that too much time was spent on the review of the theory on the blackboard, while the students would like to have example-driven teaching with a focus on problem-solving. To accommodate the wishes from the students, a radical change in the mathematics teaching was introduced. Narvik University College has considerable experience in the production of online learning resources, having been voted the best in the country on the use of podcasts in higher education (Arnstad, 2012). All courses taught in Bodø have the same syllabus and progression as in Narvik; ß The Author 2015. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved. For permissions, please email: [email protected]

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[Submitted December 2014; accepted December 2014]

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this facilitated an easy adoption of these podcasts, or streamed lectures. The idea was to use these presentations instead of tailoring a local version of them, and instead use the teaching resources in a more direct hands-on interaction with the students. This forms the background for the innovation. Thus, one could formulate a research problem as follows: In the perception of the engineering students involved, does a combination of online lectures and local tutoring lead to a better quality of the teaching of mathematics?

2. Theoretical foundations

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Learning strategies can roughly be divided into so-called teacher-centred or student-centred (Kember, 1997). In the teacher-centred strategies, the tutor will have more or less complete control over how the material is presented and processed, whereas in student-centred strategies, the student plays the central role. The teacher then has less direct control over how the learning occurs, and it will be more up to the students to direct their own learning process. Student groups will be comprised of different individuals with different learning styles, and one strategy may be more suitable to some individuals than others. However, there has emerged an understanding that in contexts where the teacher is able to facilitate so-called social learning (O’Donnell & O’Kelly, 1994), this usually increases engagement, motivation and capacity for deeper understanding of the material taught. This type of learning strategy is usually associated with a student-centred approach, meaning that group work, discussions and various activities have priority. This could be viewed in contrast to a more teacher-centred strategy that typically involves more lecture-based teaching, where the tutor presents theory in the form of theorems, proofs, methods and examples. In this sense, the students play a rather marginal role (Mascolo, 2009). This learning strategy places higher demands on both teacher and student. Teachers need to think more deeply about the discussion questions and activities that will encourage greater involvement of students. Students themselves have to be more active and responsive to these suggestions from the teacher, otherwise the dialogue-based learning would have less success. Having access to online lectures that presented the exact same curricula as that of the course in Bodø made it possible to use these as basis for the presentation. The teachers’ preparation time could then rather be used together with the students to facilitate learning in a more social constructivist manner. By using online lectures, the idea was to facilitate the students’ own participation in their education (Skott et al., 2010: 185–186). The intention was to create space for discussion, questions and cooperation based on the knowledge newly acquired from the online lecture. In this sense, the approach would contribute to more active student learning. Research on the effectiveness of this type of cooperative learning strategy as opposed to traditional classroom teaching is voluminous (Mascolo, 2009). An overwhelming majority of studies indicate better learning through such arrangements. However, there are many challenges if one chooses to use a more student-centred learning method. It is not intended to remove the teacher from teaching, rather the teacher is challenged to a greater extent both professionally and as a leader. Teachers need to facilitate tasks at the right level for the students, and the varying levels of mathematical understanding among the student body must be taken into account with training exercises adapted appropriately. The teacher also has to deal with students’ different levels of explanatory power when problems are to be formulated. In addition, the cooperative relationship between parts of the group may vary greatly. Some individuals may tend to dominate, which could have a negative impact on individual learning. Other individuals may have difficulty contributing in a social context. Others may have a tendency to want to talk too much about extra-curricular topics, which can also be disruptive to others in the

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group. Consequently, classroom management becomes a more important component than in a purely lecture-based context (Mascolo, 2009).

3. Methodology

 Use of reference groups to detect contrasts to the group in which the social experiment is taking place.  Large data set to ensure reliability.  Reproducibility or universality, which means that the results should be applicable in contexts other than where the data were collected. Using these principles, the researcher focuses to the greatest possible degree on certain objective knowledge that could be reproduced in new research. However, objective certainty in social sciences will nonetheless face clear limitations, and one must be careful to specify under what conditions and in what context this knowledge was obtained (Johannessen et al., 2011). Action research can assume a freer role in relation to these rigorous epistemological norms. In many ways the action researcher takes seriously the inherent uncertainty in the social sciences, and does not seek to have ambitions of timeless and global validity. Instead, one enters into an individual situation and seeks to have a participatory, actively changing role, where the reasons for these changes are crucial. The result of the action research should be an attempt to bring about a change for the better in society, or at least in one’s own practice (Coghlan & Brannick, 2001). Since this action research project lasted an entire academic year, we might classify this as a longitudinal study (Johannessen et al., 2011). Several surveys of a given student group were conducted; these were used to identify potential qualitative improvements in learning outcomes among the group. The surveys were anonymous and the focus was not on individual responses but rather on the whole group. Action research is often divided into two main groups, a responsive and proactive type (Schmuck, 1997). In the responsive version of action research, data are collected prior to making any changes or action. Naturally, this is performed to identify potential problems. The proactive version is a process of planning and executing an action without this initial step. Figure 1 shows the action research cycle as it was implemented in this project (Fredriksen, 2013). As can be seen, this research falls into the category of responsive action research. The various parts of the cycle are explained below. Point 1: During the autumn term, a standard course evaluation was conducted among the students, where they were prompted to give feedback on the course with respect to the teaching given.

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In this study, action research was chosen as the methodological framework. The appealing feature about action research as a framework for such studies is that it allows the researcher a more participatory role. It is not only allowed, but also encouraged, both to participate directly in the experiment as it evolves, as well as performing research in parallel. The term ‘‘research with’’ instead of ‘‘research on’’ might be a phrase that covers the main philosophy behind this approach (Schmuck, 1997). Action research can also be considered as a systematic way to describe/interpret one’s own interaction with a field of practice in which one might look for ‘‘improvements’’ after one or more operations are performed. Action research can be criticized for being too ‘‘subjective’’ in its form, in that it allows the researcher’s participation in the social experiment from which the data are obtained. In traditional social science research, emphasis is on factors like

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Point 1: Gathering of data about own teaching

Point 4:

Point 2:

Evaluate the response from the students upon the change

Considering actions to improve the teaching

Use the planned improvements and gather data

FIG. 1. Action research cycle in the project. This figure appears in colour in the online version of Teaching Mathematics and its Applications.

Point 2: Using the responses given in this feedback, a plan was laid out with the actions towards using the new form of teaching. These plans were put forward to the students at the start of the spring term at the start of the Mathematics 2 course. Point 3: The action was conducted until March 2012. Point 4: A survey was made to map out how well the new form of teaching was received.

4. Layout of the teaching before and after the change took place In the first term (autumn) running the Mathematics-1 module, a rather traditional setup of the teaching along the lines of the main college in Narvik was used. The teaching period followed the usual 20th of August to 1st of December time span and consisted of (1) 10 European Credit Transfer and Accumulation System (ECTS) study points of material on onedimensional calculus and introductory linear algebra. (2) Two to three lectures a week performed by an assistant professor, each about 1.5 h long, attendance rates would usually vary between 60% and 90%. (3) One group exercise a week, also 1.5 h long, accompanied by a student assistant. (4) Two obligatory submissions with the need to achieve 50% in order to pass. (5) Written examination, about 15th of December, 5 h long. The examination results from this course were that 17 students achieved an average mark of C and one student failed. In the second term (spring) the same student group took the Mathematics 2 module. The module had the same size, 10 ECTS study points, but a different syllabus consisting of (a) Introductory logic and proof by induction.

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Point 3:

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(b) (c) (d) (e)

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Series and sums. The Fourier and Laplace transform. Analysis of max/min problems for two-dimensional functions. Difference equations.

5. Results from the survey After having run this form of teaching during half of the spring term, a survey was conducted in which the students were asked for their opinions on the change of the education setup. In total 24 questions about this were posed, in which 21 were multiple choice questions, usually with a grading on the agreeability to each statement with five grading options. The class consisted of 19 persons, and a total of 14 responded to the survey, which corresponds to a response rate of 74%.

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For this module, it was decided to bring in the streamed lectures as a replacement for the campusbased lectures. It was arranged that the students should meet on campus to jointly watch the streamed lectures on a video projector as they were delivered live in Narvik. The reason for this was to simulate the ordinary lecture situation as closely as possible. The students would have the opportunity to ask questions to an assistant professor who was present during the lecture, and also to discuss the topic or otherwise socialize in the break. The students would then meet again, after having lunch together, to participate in a new group work session. The time schedule for lecture/group work would usually be organized in this way three times a week: Streamed lecture: 10:00–11:40, Lunch: 11:40–12:10 and Group work 12:10–13:50. The streamed lectures had the format of the lecturer in Narvik writing his presentation on ordinary paper accompanied with oral speech. The writing was captured in realtime by a document camera and projected onto a screen to the audience at the auditorium in Narvik. At the same time, the picture from the document camera was streamed live through the internet. This made it possible to watch the lecture via a web browser on an ordinary video projector in a classroom in Bodø. Remote locations were not able to communicate questions directly to the lecturer during the live session, but the lectures were recorded, so that they could be viewed later on. Thus, the lectures could be paused, and repeated if viewed afterwards. After the lectures, the notes from the lecturer were usually made available to the students via the online learning platform ‘It’s Learning’. The lecturer was not visible during the lecture, only the writing via the document camera. The complete set of lectures given at the main campus was in this way streamed to the classroom in Bodø. Furthermore (and most importantly), the streamed/recorded lectures could also be accessed from the students’ own personal computer. This possibility led many students to sit at home and watch the lecture and solve the tasks, as we will discuss later. Actually, the attendance rates dropped to about 25% of the student body, meaning that on average about five persons were there for the two consecutive sessions. The group work session followed the same form each time. The instructor usually started asking if they had any problems understanding the lecture. Sometimes this occurred, and the instructor did a quick walk-through of the principles, highlighting examples if possible. After having done this, the students usually worked on problems from the textbook. Most of the problems were accompanied by a suggested solution online. When the students got stuck on a problem, the instructor was asked for help, or they tried to find the answer using the solutions. Some of the students then chose to work on their own with the problems, while others usually worked with the same student colleagues every time. The form of assessment was the same as for the Mathematics 1 module: two obligatory submissions with a written examination in the end of the term. The results from the examination were that 15 students achieved an average mark of D and two students failed.

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The table below listed the most significant results from the survey. The results are presented in the form of mean and standard deviation of all collected answers on each question. All answers here are graded with options on a 1-2-3-4-5 scale: 1: 2: 3: 4: 5:

‘Strongly disagree’, ‘Disagree some’, ‘No conclusive opinion’, ‘Agree some’, ‘Strongly agree’.

Statement It was hard for me to understand the online lectures. Too much time was dedicated to activity after watching the online lectures. I felt well prepared to solve tasks after having watched the online lecture. I felt that watching the lectures online and concentrating the classroom activity on solving problems was a fruitful use of the course time. I believe that the learning outcome would gain from recapturing the material in the lecture via a quiz in the beginning of the group work session.

Mean

Standard deviation

Test

1.50 2.38

0.52 0.96

False False

4.29

0.91

True

3.93

1.07

True

2.57

0.65

True

Some of the statements that the test failed to give a clear false/true conclusion are listed below:  ‘I prefer to use the time in the classroom for problem-solving rather than listening to a lecture’.  ‘My understanding of the topic was enhanced by the additional time we spent working on problemsolving after watching the online lecture’.  ‘I prefer to listen to lectures face-to-face (‘‘live’’)’.  ‘I felt that more time could have been used to repeat the content of the lecture in the session afterwards’. A standard correlation analysis using Pearson correlation coefficient r was carried out, mapping the significant correlation between the individual answers (Johannessen et al., 2011). This analysis revealed a clear correlation between those students that reported little attendance in the group lectures, and those that liked the traditional course layout in the Math-1 module better (r = 0.819). On the other hand, there was also a correlation between those that were in favour of more group work, and those that recommended using this form of education in future courses (r = 0.825).

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A t-test was used to analyze the questions, since the population mean and standard deviation was unknown. The ordinal one to five data set was considered in a continuous fashion, extracting mean and standard deviation for each question (Lysø, 2010). The survey was designed in such a way that it should be possible to achieve a clear answer to the research question, namely if the new teaching method had led to a significant improvement for the students. Inspiration was found in a similar survey that was conducted among a group of architectural students from Pennsylvania State University, USA (Zappe et al., 2009). The experiment described in that article can be compared with this project in many respects: a transformation from traditional classroom tutoring towards watching video-lectures before the group work sessions. Many of the questions from that survey were used here, since they were found to be highly relevant. The table shows the results that falsified the H0 hypothesis in either positive or negative direction:

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In addition to these multiple choice questions, there were some open questions for the students. These questions were – ‘If you have participated to a small extent on the group work in the spring term, what would you say were the reason for this?’ – ‘If you didn’t participate much, what would have stimulated you to come more often?’ – ‘Is there anything you could point out that would have improved the teaching program of using a mixture of internet lectures and group work?’

6. Discussion As can be seen from the above results, there was statistically significant agreement among the students that it would be fruitful to run lectures online and work on assignments in groups. They felt well prepared to solve problems from watching the online lecture, a result that probably indicates that they thought the quality of the online lectures was good. Usually the students and the teacher met to see the online lectures before lunch, immediately followed by a working session after lunch. From the data, it seems a little more difficult to draw clear conclusions about this arrangement. They seemed to agree on the amount of time that was allocated to activity after the online lecture, but it cannot be concluded whether they think that this session increased their understanding of the topic. It is paradoxical that the same group of students gave these answers, given that much of the feedback in the previous term indicated a desire for more assistance on problem solving, and less on lectures. Quite rapidly it was seen that the students failed to meet on campus to follow the programme of teaching. On average, approximately 75% of the class were not present, meaning only four to six students were present, resulting in some loss of momentum in teaching. Since it was possible for the students to log on to the streaming service from their own PC, many chose to sit at their home PC, and work privately instead of participating at campus. Already early in the first semester, it was discovered that many of the students had difficulty in actively contributing to a social learning process. An attempt to remedy this was made by inviting them to social events to create better cohesion and acquaintance. However, it was difficult to get commitment for such activities. Many of the students had family obligations or a job in parallel to be able to fund their study. In addition, there was also a group of students from out of town. Many of them could not spare time for such activities.

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On the question of what was the reason for the low turn up on group exercises, the responses varied from idleness, through being satisfied with the online lectures and that they had too much work alongside their studies. Some also mentioned the priority of other subjects, and that they would rather do the problem-solving that was set up for the group exercise on their own. Thus, the results indicated that this form of teaching was given less priority by the students compared with other activities/studies. On the question of what could have stimulated the students to come more often, one student responded that a quiz with automatic evaluation of the responses would be motivating. Another one reported that less work besides the studies would make it easier to attend, and a third called for the teacher to circulate more in the classroom so that he would be easier to approach for an unsecure student. Finally, it was asked what could have been done better in this program, many then pointed out that a summary review of the topic in the lecture would have been helpful. In addition, a proposal emerged to reverse the order of the lectures/group work, and one also called for more mandatory assignments so that one became more motivated to come to the group exercise for help.

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7. Summary The starting point of this study was to undertake an innovative modification of mathematical education in engineering studies, by including online lectures as a key component. The survey showed that the majority of the student felt that the quality of the new teaching form was quite good. However, they were unable to conclude that the teaching had improved. Also, looking at the rather weak performance at exam, dropping from C to D in average, the students seem to have misjudged their own understanding of the quality of the teaching. So, their impression that they felt well prepared to solve tasks after having watched the online lectures is quite questionable. In addition, the socio-cultural learning style that the action research intended to improve did not succeed to any significant degree. This can be concluded from the fact that so many of the students chose not to attend the lessons. In this way, the classroom environment deteriorated, and the ‘‘pressure’’ in teaching waned. Several of the students became pure internet students, which was not at all the purpose. Informal talks with several of those who chose to study at home revealed that they lost motivation, and that their connections with the other students were deficient. A lesson to be learned from this experiment is how important a good class environment is for learning. It is not sufficient simply to emphasize the correctly conducted academic lecture, or optimal availability of learning materials. One must also ensure that arrangements are made for students to collaborate. If too much emphasis is put on online aids, it may lead to ‘‘lonely’’ students, who may also have difficulty getting help with problems that could have been easily solved in a social context. In this way, one can almost say that the experiment was counterproductive, that is, it provided less interaction in learning, not more! In conclusion, the reason this action research was initiated was to enhance the aspect of social learning in the teaching. However, this action turned the majority of students into pure internet-based student, a scenario that was not intended and which finally led to a complete loss of contact with as much as 50% of the students. Thus, one can state that this experiment acted against its primary objective which was an enhancement of the social-constructivist way of learning.

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It appears that the tasks set for the group work sessions were not engaging enough for students to want to attend these sessions. It may be that students had become accustomed in Semester 1 to working through problems from the textbook individually and so they did not perceive there to be significant value in undertaking these tasks in a group setting. The introduction of other activities where a group approach was more obviously beneficial might have resulted in a different outcome. Several students also showed early signs of falling behind in the review of the curriculum. The fact that many chose not to attend class could be interpreted to mean that this type of education sets higher demands on the students’ progress. It was no longer possible to sit back and passively receive lessons from the lecturer; one had to be up to speed on the topic, and to be prepared to actively work on it immediately after having it presented. There were statements from some of the students indicating that they felt uncomfortable not being updated adequately on the curriculum. Thus, they felt it was difficult to work effectively together with the other students. Mathematics as a field of learning is typically very cumulative in nature, each brick of knowledge usually resting on previous knowledge, thus making it difficult to step into a topic if sound progress on previous chapters has not been made. Usually, the engineering students also tend to give less priority to mathematics and physics subjects, compared with their main (engineering) subjects; this results in more burst-like progress, which was not very suitable for this model of teaching.

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REFERENCES

Helge Fredriksen is an Assistant Professor teaching mathematics, physics and statistics at the Bachelor of Engineering Studies in Bodø, Norway. His research interests is teaching and learning mathematics at university level with a particular focus on approaching flipped classroom as an instrument of active learning.

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