+1443 776-2705 panelessays@gmail.com

Complete an Annotated Bibliography entry of a resource from this module that had the greatest impact on your learning and understanding of what it means to be an effective online instructor.


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 

Pushing the limits 


Antonín Jančařík 

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: 


Antonín Jančařík 

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 😛 
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 

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 


Antonín Jančařík 

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.  


Antonín Jančařík 

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? 


Sample Annotated Bibliography

Student Name

Program Name or Degree Name (e.g., Master of Science in Nursing), Walden University

COURSE XXX: Title of Course

Instructor Name

Month XX, 202X


Sample Annotated Bibliography

Autism research continues to grapple with activities that best serve the purpose of fostering positive interpersonal relationships for children who struggle with autism. Children have benefited from therapy sessions that provide ongoing activities to aid autistic children’s ability to engage in healthy social interactions. However, less is known about how K–12 schools might implement programs for this group of individuals to provide additional opportunities for growth, or even if and how school programs would be of assistance in the end. There is a gap, then, in understanding the possibilities of implementing such programs in schools to foster the social and thus mental health of children with autism.

Annotated Bibliography

Kenny, M. C., Dinehart, L. H., & Winick, C. B. (2016). Child-centered play therapy for children with autism spectrum disorder. In A. A. Drewes & C. E. Schaefer (Eds.), Play therapy in middle childhood (pp. 103–147). American Psychological Association. https://doi.org/10.1037/14776-014

In this chapter, Kenny et al. provided a case study of the treatment of a 10-year-old boy diagnosed with autism spectrum disorder (ADS). Kenny et al. described the rationale and theory behind the use of child-centered play therapy (CCPT) in the treatment of a child with ASD. Specifically, children with ADS often have sociobehavioral problems that can be improved when they have a safe therapy space for expressing themselves emotionally through play that assists in their interpersonal development. The authors outlined the progress made by the patient in addressing the social and communicative impairments associated with ASD. Additionally, the authors explained the role that parents have in implementing CCPT in the patient’s treatment. Their research on the success of CCPT used qualitative data collected by observing the patient in multiple therapy sessions.

CCPT follows research carried out by other theorists who have identified the role of play in supporting cognition and interpersonal relationships. This case study is relevant to the current conversation surrounding the emerging trend toward CCPT treatment in adolescents with ASD as it illustrates how CCPT can be successfully implemented in a therapeutic setting to improve the patient’s communication and socialization skills. However, Kenny et al. acknowledged that CCPT has limitations—children with ADS, who are not highly functioning and or are more severely emotionally underdeveloped, are likely not suited for this type of therapy.

Kenny et al.’s explanation of this treatments’s implementation is useful for professionals in the psychology field who work with adolescents with ASD. This piece is also useful to parents of adolescents with ASD, as it discusses the role that parents can play in successfully implementing the treatment. However, more information is needed to determine if this program would be suitable as part of a K–12 school program focused on the needs of children with ASD.

Stagnitti, K. (2016). Play therapy for school-age children with high-functioning autism. In A. A. Drewes and C. E. Schaefer (Eds.), Play therapy in middle cildhood (pp. 237–255). American Psychological Association. https://doi.org/10.1037/14776-013

Stagnitti discussed how the Learn to Play program fosters the social and personal development of children who have high functioning autism. The program is designed as a series of play sessions carried out over time, each session aiming to help children with high functioning autism learn to engage in complex play activities with their therapist and on their own. The program is beneficial for children who are 1- to 8-years old if they are already communicating with others both nonverbally and verbally. Through this program, the therapist works with autistic children by initiating play activities, helping children direct their attention to the activity, eventually helping them begin to initiate play on their own by moving past the play narrative created by the therapist and adding new, logical steps in the play scenario themselves. The underlying rationale for the program is that there is a link between the ability of children with autism to create imaginary play scenarios that are increasingly more complex and the development of emotional well-being and social skills in these children. Study results from the program have shown that the program is successful: Children have developed personal and social skills of several increment levels in a short time. While Stagnitti provided evidence that the Learn to Play program was successful, she also acknowledged that more research was needed to fully understand the long-term benefits of the program.

Stagnitti offered an insightful overview of the program; however, her discussion was focused on children identified as having high-functioning autism, and, therefore, it is not clear if and how this program works for those not identified as high-functioning. Additionally, Stagnitti noted that the program is already initiated in some schools but did not provide discussion on whether there were differences or similarities in the success of this program in that setting.

Although Stagnitti’s overview of the Learn to Play program was helpful for understanding the possibility for this program to be a supplementary addition in the K–12 school system, more research is needed to understand exactly how the program might be implemented, the benefits of implementation, and the drawbacks. Without this additional information, it would be difficult for a researcher to use Stigmitti’s research as a basis for changes in other programs. However, it does provide useful context and ideas that researchers can use to develop additional research programs.

Wimpory, D. C., & Nash, S. (1999). Musical interaction therapy–Therapeutic play for children with autism. Child Language and Teaching Therapy, 15(1), 17–28. https://doi.org/10.1177/026565909901500103

Wimpory and Nash provided a case study for implementing music interaction therapy as part of play therapy aimed at cultivating communication skills in infants with ASD. The researchers based their argument on films taken of play-based therapy sessions that introduced music interaction therapy. To assess the success of music play, Wimpory and Nash filmed the follow-up play-based interaction between the parent and the child. The follow-up interactions revealed that 20 months after the introduction of music play, the patient developed prolonged playful interaction with both the psychologist and the parent. The follow-up films also revealed that children initiated spontaneously pretend play during these later sessions. After the introduction of music, the patient began to develop appropriate language skills.

Since the publication date for this case study is 1999, the results are dated. Although this technique is useful, emerging research in the field has undoubtedly changed in the time since the article was published. Wimpory and Nash wrote this article for a specific audience, including psychologists and researchers working with infants diagnosed with ASD. This focus also means that other researchers beyond these fields may not find the researcher’s findings applicable.

This research is useful to those looking for background information on the implementation of music into play-based therapy in infants with ASD. Wimpory and Nash presented a basis for this technique and outlined its initial development. Thus, this case study can be useful in further trials when paired with more recent research.