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SCAFFOLDINGARTICLE.pdf
Scaffolding in e‐Learning Environment
Antonín Jančařík Charles University in Prague, Faculty of Education, Prague, Czech Republic [email protected] Abstract: The paper focuses on the potential and possibilities of use of scaffolding in e‐learning courses. One of the key concepts the author works with and builds upon is the concept of zone of proximal development, which was introduced by Vygotsky. One of the key questions every teacher must ask is how to state the border between the current pupil’s knowledge and the horizon where it can be developed. Needless to say that determination of these limits may be of crucial importance for the educational process. The question becomes even more important in work with gifted pupils, in whose case the limit of what they can achieve under convenient guidance is very individual, as well as the teacher’s role very specific. The author presents various forms of scaffolding based on his longitudinal experience from work with mathematically gifted pupils in an e‐learning course Combinatorial Game Theory. This course is organized within the frame of the Talent project which is designated for gifted Czech upper secondary school students from all over the country. This course has been designed with respect to the principles of the method of problem‐based learning. Students are assigned problems that they solve either collaboratively or individually. Some of the problems are intentionally designed in such a way to bring students to situations in which they must overcome epistemological obstacles. In these situations scaffolding proves to be a very efficient method. However, its implementation in the environment of internet is specific and differs from its use in ordinary classrooms. As there is no face to face contact with the student, it is much harder to determine his/her real state of knowledge. Also the time lag in off‐line communication makes the process harder. The paper discusses different aspects of use of scaffolding in the internet environment in detail. This all is illustrated on specific examples of its use. The paper presents four forms of scaffolding realised by specific instructions. The aim of the paper is to illustrate by and demonstrate on concrete examples the benefits of the use of scaffolding in an e‐learning course for gifted students. Keywords: scaffolding, game theory, e‐learning, mathematical education
1. Introduction The concept of zone of proximal development, introduced by L. Vygotsky (1978), is defined as “the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance, or in collaboration with more capable peers.” However, this guidance does not have to be personified, it may also be provided e.g. by an e‐learning system. That is why Vygotsky introduced also the concept of “more knowledgeable other”.
1.1 Scaffolding The concept of scaffolding is close to the concept of zone of proximal development but is not used by Vygotsky. The concept refers to the help and support provided to a pupil or student while solving problems in order to allow him/her to achieve the desired goals (German, 2011, Saffkova, 2011). The methods of providing scaffolding are manifold. Saye and Brush distinguish between soft and hard methods (Saye and Brush, 2002). Soft, or also contingent scaffolding is based on a teacher’s discussion with their pupils, their reactions to the pupils’ needs and on offer of support and guidance with respect to the momentary needs (Simons and Klein, 2007). In contrast, in hard scaffolding the teacher analyses the problems that can be come across in advance, already when planning the lesson (Nováková and Novotná, 2011) and prepares supporting problems or hints to offer to the pupils or students when needed. Scaffolding can also be provided automatically (e.g. Wood, 2011) by the e‐learning system. However, this paper focuses predominantly on situations when guidance and support is provided by the course teacher, or more specifically the lecturer. Wood and Middleton (1975) define three categories of support that can be provided to pupils:
General encouragement
Specific instructions
Direct demonstration
The following text demonstrates and specifies the use of all these three categories of support within e‐learning courses. When introducing the category “Specific instructions”, four different forms of its use are distinguished:
Pushing the limits
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Confronting a counterexample
Providing the right answer but not the solving procedure
Experimenting using Trial and Error method
The advantages of each of the methods is classified with respect to the anticipated benefits of scaffolding into the following five categories (Wood et al., 1976):
Gaining and maintaining the learner’s interest in the task.
Making the task simple.
Emphasizing certain aspects that will help with the solution.
Controlling the level of frustration.
Demonstrating the task.
1.2 Course description The paper presents methods of scaffolding used by the author in e‐learning courses for mathematically gifted students. These courses for gifted students are opened repeatedly and the here reported research on scaffolding is still in progress. The paper therefore presents its interim findings and work in process. The courses are organized for small groups of students (5‐10 persons) from selected upper secondary schools from all over the Czech Republic. The syllabus of the course is Combinatorial Game Theory (Berlekamp, Conway and Guy, 2001, Nowakowski, 1998). The course is designed as assisted problem‐solving. There is almost no instruction, students are assigned a series of graded problems which they solve in open discussion forums. Students may also enter private discussion with the teacher but this option is seldom selected. The lecturer’s guidance has the form of his intervention into the discussion. This intervention has different forms, the lecturer uses both soft and hard scaffolding. The course is divided into two parts. In the first part students are introduced to different variants of the NIM game. The goal of this activity is to guide students to discovery of the winning strategy (Bouton, 1901). In the second part students get to know the game hackenbush. Their task is to find the value of given positions. The key moment of the course is discovery of positions with surreal values , a . Pupils must overcome
epistemological obstacles (Bachelard, 1940) connected to their existing understanding of real numbers, number line and the concept of infinity (Cihlár, Eisenmann, Krátká and Vopenka, 2008).
2. General encouragement in e‐learning courses It is often the case of e‐learning courses that pupils and students who find the presented problems too difficult stop being active. That is why the lecturer must observe activity of different participants of the course carefully and encourage the pupils and students as needed. It is much easier for a teacher to see that a pupil is not paying attention in the classroom – he/she starts disturbing, stares out of the window, reads something else. These evident signals are not present in e‐learning courses and the lecturer’s position is much more difficult. He/she may notice a participant’s lack of activity but may fail to interpret the reasons for this drop‐out. He must then carefully think what and how to do to encourage and motivate the student to get involved again. Sometimes it is very hard to discover the true reason of a student's drop‐out.
2.1 First example A student ceased to be active for several weeks during the course and did not even answer the lecturer’s messages. Only later was he able to find out that she had had a serious injury and had spent some time in hospital where she could not participate in the course. Having recovered she got involved in the course again and completed it successfully.
2.2 Second example The lecturer was facing the situation when several students fell silent for a longer period of time. He addressed them by personal e‐mails asking for reasons of their inactivity and offered help with difficult problems, including organizing a videoconference. The following are some of the replies he received:
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Student 1: I find the course very interesting and enjoy solving the problems. However, I’ve been a bit too busy recently and haven’t managed to do all the work in time. I apologize. Sorry.
My plan is to join in again at the end of the week. As soon as I finish other things that kept me occupied. I hope I will catch up on coursework. :)
Student 2: Hello, sorry for my activity but I have too many courses and am getting short of time. As it is I only have time to look at it at the weekend. But now I’ve been offered two scholarships :P so I won’t get to the coursework before the weekend. Honza
After the lecturer’s encouraging intervention the students joint in actively again.
Soft scaffolding in the form of general encouragement helps to gain and maintain the learner’s interest in the task. In some cases it may also help to control the level of frustration. It is advisable to make this encouragement very personal and to combine it with offer to help. This eliminates the potential risk of the student’s dropping out of the course for its difficulty.
2.3 Comparison to the situation when no scaffolding was offered In the first course, the teacher repeatedly used mail merge to alert to deadlines. Despite these alerts, some students did not join in and often sent excuses for having dropped out of the course. An analysis of individual cases showed that these students’ drop‐out was most often the consequence of a sudden increase in difficulty of the tasks and problems. Having discovered this, the lecturer now informs students in advance that they are about to proceed to a more difficult level and offers them additional help if they fall silent at this point.
3. Specific instructions – pushing the limits Pushing the limits is one of the forms of soft scaffolding. It may be in the form of lecturer’s reactions to the limiting conditions in a pupil’s or student’s reasoning and thinking. The lecturer tries to encourage the pupil or student to broaden and generalize his/her considerations. The aim of this type of guidance is predominantly to turn the student’s attention to those aspects of the assigned problem that he/she failed to notice or to deduction of consequences the pupil or student has been not aware of.
3.1 Example Lecturer: What is the relation between won and lost fields?
Student: Is their structure always regular?
Lecturer: A good question, but what do you mean by a “regular structure”? Try to find an answer, it is connected to the previous question.
Student: With the exception of the fields before finish, won and lost positions always repeat in the same numbers. In case one cannot use a move by one field they are always two blue and four red fields.
Lecturer: I thought you were asking whether a situation must necessarily have a regular structure regardless of the rules of the game. Is this not a more interesting question :‐)?
This example shows that the student uses the concept of “regular structure” spontaneously. This enables introduction of the general topic of periodicity of a solution to a problem. The lecturer takes the student’s concept which is yet not developed and hands it back to the student for further development. As the initial initiative was on the student’s part, the problem seems more real to the student and he/she is much more motivated to be solving it.
3.2 Comparison to direct task assignment Tasks in which students are asked to find a regular structure of won and lost positions can also be come across in the course but only if they follow a series of lead‐in tasks. In this case, reaction to the student’s spontaneous idea made it possible to skip these exercises and start solving a more demanding task before the student would have done if proceeding along the standard course trajectory. The idea of a regular structure had just moved into the particular student’s zone of proximal development, thus allowing the lecturer to make use of it.
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4. Specific instructions – confronting a counter example Another example of soft scaffolding is providing a counterexample to the presented hypothesis. Confrontation of the student’s strategy with a situation in which it does not work makes him/her reconsider the whole situation. Moreover, a conveniently selected counterexample may guide the student to the correct solution.
4.1 Example One of the games solved by the pupils in the discussed course is the game TIC‐TAC‐TOE (see fig. 1). In some cases students assess the game as won by the first player even though it is a draw. The counterexample is offered by playing the game with teacher.
Figure 1: TIC‐TAC‐TOE game (from Jancarik, 2007)
Providing a well‐chosen counterexample to the presented hypothesis helps to emphasise some aspects of the problem and may help with the solution. A counterexample may help the student realize where he/she is making a mistake and to correct his/her solution.
4.2 Analysis of use of counterexamples Providing a counterexample is in some cases far more efficient than looking for and uncovering of mistakes in students’ logical reasoning. The reasons are:
A student’s justification may be long and complicated. In some cases explanation of different separate ideas and deductions may require a lot of time. This of course implies that in an e‐learning course environment the effort to pinpoint the source of a mistake in reasoning is extremely difficult and time demanding. On the other hand, without any doubt in some cases this time and effort are worthwhile, especially in case of complex problems.
If a teacher or a lecturer points out a pupil’s or student’s mistake, it might demotivate the pupil or the student. In contrast providing a convenient counterexample enables the pupil or the student to succeed by discovering the source of his/her mistake in reasoning on his/her own.
5. Specific instructions – providing the right answer but not the solving procedure This form of help is based on the teacher’s provision of correct answer and student’s search for justification or explanation of this answer. This form of scaffolding may be situation based or planned in advance by the lecturer. It means this is a form of hard scaffolding.
5.1 Example The example comes from a discussion forum about the Cat and Mouse Game (Tapson, 1977, see fig. 2). The goal of the game is to have the cat capture the mouse. The game has a very simple winning strategy but every time most students defend the possibility that the mouse can always escape.
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Figure 2: Cat and mouse game (from Jancarik, 2007)
Student: Each hole neighbours at least with other two holes which means the mouse can never “be cornered”. The mouse can be escaping for ever. (This is the last of a number of comments expressing the same idea.)
Teacher: You all agree here that the mouse can be running away as long as it wants, you present supporting arguments, but are you sure about this? Are you sure there are not any mistakes in your considerations?
Teacher (after 4 days with no reaction): Well, nobody replied to my comment. So I am giving the right answer now: The cat, if it uses the right strategy, will catch the mouse quite fast, regardless of the mouse’s strategy. Will you find how the cat can do it?
Another student: Yes, this is a real Cat and Mouse game. The cat must not attack, it must lurk. If it wants to win, it must get the advantage of one move by cutting across the triangle. (If we leave any field A in a move, we get back to it by an even number of moves but if we take a shortcut via triangle, an odd number of moves will do.) So the position changes, the cat and the mouse can e.g. again get to the same position, but now the mouse will be in a trap as it is its move this time. Similarly the cat may get this advantage in a corner.
This example illustrates the use of this method in a situation when students “got stuck” while solving the problem and got lost what solution to be actually looking for. Once they were told the right answer they were able to justify the solution and find the correct solution of the whole problem.
6. Specific instructions – experimenting using trial and error method This form of support is also hard scaffolding. It is used for difficult problems where pupils and students can be expected to propose erroneous solutions. Scaffolding in this case is not provided by the lecturer. It is an automatic element which is integrated in the e‐learning course (see Wood, 2001). This enables the pupils and students to confront repeatedly their strategies with counterexamples, to test them and modify them.
6.1 Example The students’ task in the course was to find the winning strategy to a three‐pile NIM game. An automatic script was programmed in the game which runs according to the winning strategy. If a player makes a mistake in his/her solution, the computer wins. The game has the form of a car race. The player can select a car he/she wants to ace in and the number of fields (in accordance with the rules) by which he/she wants to approach the finish. The script enables setting different rules in respect to the needs of a given game. The winner is the player who first crosses the finish line (see Fig. 3)
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Figure 3: 3 heap NIM game with cars
The difference of this form of scaffolding and of providing one counterexample is that in case of one counterexample pupils and students cannot usually find the winning strategy. This form, in contrast, combines the advantages of confronting a counterexample and giving the right answer but not the procedure. The pupil or student sees the mistake he/she has made and the move he/she must make in the situation but does not know the reasons why it is so and must discover them.
6.2 Discussion of the problem In the first course, every single situation was discussed with the lecturer. This was unnecessarily too long. Automation using script made the process faster and more efficient. Students can now verify (or confront) their hypotheses before presenting them in public.
7. Direct demonstration Direct demonstration is the form of hard scaffolding which is used in this e‐learning course least often, which is the consequence of its focus. The goal of the course is not to introduce students to winning strategies but to teach them to look for them on their own. That is why they are expected to be looking for all solutions individually and none of the solutions is disclosed or directly demonstrated to them. Direct demonstration is used to make students familiar with a method they are subsequently expected to generalize and apply.
7.1 Example Students are expected to learn to use NIM numbers in order to employ them in search for strategies in other games. The lecturer demonstrates their application in the game The Silver Dollar Game With No Silver Dollar (Bogus Nim, see fig. 4). Subsequently students are asked to find the winning strategy for The Silver Dollar Game.
Figure 4: Bogus NIM game (http://www.cut‐the‐knot.org/, © 1996‐2013 Alexander Bogomolny)
Direct demonstration is very convenient when teaching algorithms. Its use in constructivist approaches is more problematic as it offers students very little space for their own observation, reasoning and deductions.
7.2 Discussion of direct demonstration Application of knowledge in new contexts is known to be very difficult in the long run. At the same time it is crucial. Students usually link their knowledge to knowledge from concrete situations they have experience with. Preceding full‐time courses showed that students had problems to apply NIM strategy in new situations unless they had had prior experience with this approach. That is why one sample of such use was presented to students in the e‐learning course. The lecturer’s experience shows that students then find it much easier to modify the winning strategy to other, more or less similar games.
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8. Conclusion Scaffolding is an important tool a teacher can use in their work. Scaffolding enables to push the limit of what pupils are able to achieve in their solving procedures. This implies that scaffolding is well justified not only in the classroom but also in virtual environment. E‐learning environments allow the use of most methods that a teacher would employ when working in the traditional classroom. However, it must be born in mind that work in a virtual environment rules out personal contact and face to face interaction between the pupil and the teacher. This may make it hard to predict the pupil’s reaction. Scaffolding, especially in the form of general encouragement, becomes increasingly more important. It can help the pupil overcome obstacles that would otherwise put them off from further work and would result in frustration and failure. However, students must not only be encouraged, they must also be offered stimuli and additional information needed for solution of the assigned problems and for drawing general conclusions. The paper presented and illustrated four forms of this support. The author presented concrete examples to demonstrate what forms scaffolding can take. As the same time he described his motivation for having used the described methods, or what their benefits were. The presented list is far from exhaustive. The aim of this paper is to document the chosen methods. Taking into account the course specialization and small number of respondents, the author decided to present his findings in the form of description of concrete examples. However, it does not mean the paper cannot be a source of inspiration for other authors of e‐learning courses. The presented methods can be applied in a variety of other contexts.
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Veronika Havelková is a PhD Student at Charles University in Prague and lecturer of seminars ‘Use the GeoGebra in the Teaching of Mathematics’, ‘Mathematical Software‘, ‘Computer as an Assistant (not only) in the Teaching of Mathematics’. Dissertation topic is The Phenomena Influencing the Efficiency of the Use of Dynamic Mathematics.
Michael A. Herzog is full professor for Business Management and IT at Magdeburg-Stendal University. His research is con- cerned with mobile systems, RFID-technology, knowledge management and e-learning. He founded several international operating IT-enterprises concerning media technology and software development. Michael holds a PhD in information sys- tems and master's degree in computer science from Technische Universität Berlin.
Jiri Hoffmann is currently in his second year as a PhD candidate at the Department of Information and Communication Tech- nologies at the University of Ostrava, Czech Republic. His main research activity is focused on technological competencies and out of school activities.
Jozef Hvorecky graduated PhD. in Computer Programming at the Academy of Sciences in Moscow. He is Professor of Com- puter and Information Sciences at School of Management in Bratislava, Slovakia. He is also Honorary Lecturer of the Universi- ty of Liverpool. His research interests cover introductory programming courses, university management, and knowledge management.
Gloria Otito Izu holds a Bachelor Degree in Biology Education, a Researcher with Colleges of Education Academic Staff Union, Nigeria. Her research focuses on e-learning and science teaching methodologies.
Antonin Jancarik works as a senior lecturer in the Department of Mathematics and Mathematics Education, Faculty of Educa- tion, Charles University in Prague. He is working in the areas of algebra, use of ICT in mathematics education and game theo- ry.
Amanda Jefferies is a Reader in Technology Enhanced Learning at the University of Hertfordshire, where she leads the Tech- nology Supported Learning Research group. Her interests relate to students’ experiences of using technology to support their learning and the development of supportive pedagogies. She was awarded a UK National Teaching Fellowship in 2011.
Cristian Jimenez Romero has a Degree in computer science and data systematization, University Antonio Nariño, Colombia. Further BSc-Honours degree with emphasis in biological psychology and artificial intelligence from the Open University, UK. Cristian has worked as software engineer at Nokia-Siemens-Networks. He is currently doing PhD, at the Complexity science department, faculty of computing and mathematics, OU. Thesis “Intelligent assessment systems applied to massive open online education"
Olga Kandinskaia is Assistant Professor of Finance and Director of Blended Learning at the CIIM (Cyprus International Insti- tute of Management). She has 20 years of experience in teaching F2F courses in Cyprus, UK and Russia, and 3 years of experi- ence with online/blended courses. Olga has an extensive record of publications, which include two books.
Elisabeth Katzlinger is assistant professor at the Department of Data Processing in Social Sciences, Economics and Business, Johannes Kepler University Linz (JKU), Austria. She has degrees in business administration and business education. Her re- search focus is in business education and technology enhanced learning. Early childhood education and game-based learning are another research interests
Carolyn King is the Understanding Dementia Massive Open Online Course co-ordinator, a lecturer in the School of Medicine at the University of Tasmania, and a Wicking Centre Research Associate. She has a PhD in Neuroscience and her research interests include the biology of dementia, therapeutic approaches in dementia, as well as the scholarship of learning.
Tomoko Kojiri received the B.E., M.E., and Ph.D. degrees from Nagoya University, Japan, in 1998, 2000, and 2003, respective- ly. From 2003 to 2007, she was a research associate at Nagoya University. From 2007 to 2011, she was an assistant professor in Nagoya University. Since 2011, she has been an associate professor at Kansai University, Japan.
Katerina Kostolanyova works in the Faculty of Education, Institute of Information and Communication Technologies, Ostrava in Czech Republic. She specializes in eLearning technology, especially adaptive eLearning. Her further professional growth focuses on students’ learning styles in the e-Learning environment. She is an author and co-author of almost forty profes- sional articles and ten e-contents.
Blair Kuntz has been the near and Middle Eastern Studies librarian at the University of Toronto library since 2003. Before this, he studied Arabic for Foreigners at the Balamand University in Lebanon and Birzeit University in Ramallah, Palestine. He has also studied Farsi and Turkish at the School of Continuing Studies of the University of Toronto.
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