Exploration

=Context = In order to address the social and cultural context for the design and development of my online learning activity I need to make explicit all the elements by following the Dabbagh & Bannan-Ritland’s Integrative Learning Design Framework encompassed by the circle.

Although my department within Juta and Co, is the Academic and Professional Division, also referred to as APD, which implies that we publish learning and teaching support material, as well as training materials for adult learning, my responsibility as a publisher. Some of these adult learning materials are developed for online learning.

As a publisher, my responsibility is to build and manage a publishing list for higher education textbooks within the fields of Engineering, Economics and Mathematical Sciences. Bluntly, the bottom line is to make profit. It is not to develop courses myself but to commission others to do that. If and when there is a need for any form of online course or support, I have to commission one of my colleagues to do that for me. I therefore do not have learners, or a setting to do this task. I basically depend on other settings and colleagues for collaborative problem-solving processes. Although we have QuestionMark for developing course material, I will need to acquire an extra licence to use it. I opted to use Moodle, an open source Learning Management System as a result.

This came with its own challenges. I have never used any form of online technology to teach, let alone develop a course using one. I am very much comfortable teaching mathematics, but now I have to develop a course with illustrations. The other challenge is that, because I travel often, I need to be able to use Moodle offline rather than online, in order to develop the course. I also do not have learners of my own, but I have asked two members from the Schools Development Unit to provide formative evaluation of the Activity. These colleagues have never used online learning interventions themselves.

=Content = The content for this intervention will be taken from the Curriculum and Assessment Policy Statement for Grade 7. The topic will be integers. A brief discussion on integers will be provided, followed by a set of questions, ranging from Multiple Choice Questions to Numerical one answer questions. Students will receive immediate feedback on their choice of answers, and sometimes will be provided with hints. The questions will be heaving scaffolded to encourage progression and understanding.

In this intervention the learners will be introduced to ways of working with integers and their properties. The assumption is that they have already developed an understanding of whole numbers, and will extend their knowledge by looking at integers, a set of numbers that includes positive and negative whole numbers including zero. They will use properties of operations to compare integers to be able to solve problems in authentic contexts.

**Learning outcomes **
After working through these activities, you should be able to:
 * Count, order and compare integers
 * Count forwards and backwards in integers for any interval
 * Recognise, order and compare integers
 * Add and subtract with integers
 * Recognise and use commutative and associative properties of integers
 * <span style="font-family: Georgia,serif; font-size: 120%;">Solve problems in contexts involving addition and subtraction with integers

<span style="font-family: Georgia,serif;">The Online Learner
<span style="font-family: Georgia,serif; font-size: 16px;">According to Dabbagh (2007), in order to determine the pedagogical implications for the online learning activity experience, I first need to better understand the characteristics and skills of the online learner, in terms of (i) who is likely to participate in online learning, (ii) what factors or motivators contribute to a successful online learning experience, and (iii) what are the potential barriers detering learners from participating in or successfully completing an online course.

<span style="font-family: Georgia,serif; font-size: 16px;">Who is the online learner
<span style="font-family: Georgia,serif; font-size: 16px;">These are Grade 7-9 teachers from the Western Cape Education Department registered for a one-year part-time course in Advanced Certificate in Education at the University of Cape Town's Schools Development Unit. These teachers attend a series of sessions during school holidays. They come from the rural areas of the Western Cape. <span style="font-family: Georgia,serif; font-size: 16px;">These teachers may have not been introduced to teaching using online courses. Their average age is 35 years; mostly males; none of them with a bachelor’s degree; their numeracy and literacy levels is average and over 70% of them are married. Their computer skills may be limited. Their teaching experiences vary, with the least qualified having about five-years and the most qualified twenty-five years, on average. They may be teaching other subjects other than mathematics at their schools. Their mathematical subject knowledge could be average to below average. Mathematics may not be their first subject choice. They could be mostly dependent on their textbooks and worksheets as their main resource, with limited or no access to the use of computers. The average class size could be about 40 learners per classroom in Grade 7. They may be teaching more than one mathematics class. <span style="font-family: Georgia,serif; font-size: 16px;">Their teaching style is mainly the traditional talk and chalk, with learners doing exercises and given homework, and working individually on tasks. Collaboration with other teachers in developing lessons could be considered non-existent. Assessment could be mostly formal.

<span style="font-family: georgia,serif; font-size: 16px;">In order to inform the Online Learning Activity, I have developed an [|Online Learner precourse questionnaire]in Google Forms to send to the learners before the class. This will help me determine student characteristics and expectations for the course.

<span style="font-family: Georgia,serif;">Lecturers
<span style="color: #000000; font-family: georgia,serif; font-size: 120%;">The prospective lecturers for this course would be from the staff of the Schools Development Unit. They are well experienced teachers of mathematics with more than five years teaching other teachers. They have been involved in some form of writing before, either as contributors to textbook writing or developing courses for their students. They are well aware of the school currulum and may have been involved in developing it. They have a lot of exprience implementing courses for mathematics teachers and are comfortable with it. They however may not have used online courses to teach mathematics.

=<span style="font-family: Georgia,serif;">Learning theories = <span style="color: #000000; font-family: Georgia,serif; font-size: 16px;">In this section I provide information on educational learning theories and theorists. I will discuss explain learning theory, and educational terms related to it in order to put forward my own understanding of how I have decided on the pedagogical and learning strategies discussed in the next section.

<span style="font-family: Georgia,serif;">** What is learning theory ** <span style="color: #000000; font-family: Georgia,serif; font-size: 16px;">There are many definitions of learning theory depending on one's epistemology. Learning theories come from the study of educational psychology as an attempt to describe how people learn. These theories include behaviourism, cognitivism, constructism, and connectivism.

<span style="color: black; font-family: Georgia,serif; font-size: 18px;">**Behaviourism** is attributed to the work of B. F. Skinner (1904-1990) and Ivan Pavlov (1849-1936). It is an approach to psychology based on the premise that human behaviour can be predicted and controlled. For a behaviourist human learning is objective and can be measured, with little emphasis on cognition - one learns through positive and negative reinforcements (see also Der-Thanq, et al., 2007)

<span style="font-family: Georgia,serif;"> **Cognitive theorists**<span style="font-family: Georgia,serif; font-size: 90%;">(Paivio, Gagne, Gadner, and Bloom) are opposed to the behaviourist theory and are concerned with thinking and remembering. For example, Paivio developed the Dual Coding Theory which assumes that one processes information in two distinctly different ways: (i) processing for images and (ii) processing for language. Another cognitive theorist is Robert Gagne, a psychologist and an educator. Gagne approach to teaching contends that learning tasks for intellectual skills can be organized in a ** hierarchy ** according to complexity. This is however too prescriptiveness.

<span style="color: black; font-family: Georgia,serif; font-size: 18px;">**Constructivist theorists** (Bruner, Piaget, and Vygotsky) is based upon the study of cognition. For Bruner, "learning is an active process in which learners construct new ideas or concepts based upon their current/past experiences". According to Bruner, for learning to take place, learners should be encouraged to construct hypotheses, through scaffolding, in order to go beyond what has been given to them. Piaget, also contends that learners construct their own knowledge through experiences. For Piaget, the expriences create schemas or mental models in their heads. These schemas are either changed, enlarged, or made sophisticated through two complimentary processes called assimilation and accommodation.

<span style="font-family: Georgia,serif; font-size: 16px;"> For this intervention, I have adopted the work of a Russian psychologist, Lev S Vygotsky (1896 - 1934). One of the major concepts in the Vygotskian theory is that mind is the product of our social history. In other words, mind is not merely a product of our biological evolution but more importantly for Vygotsky, it is a product of social life and social history (Vygotsky, 1978). Mind or consciousness is more than merely a recording device or reaction to stimuli from the environment. Vygotsky’s theory of mind and his emphasis on language tells us that mind is formed by the content and form of our human communication. Human communication is transmitted through language and our language is part of our ‘culture”. Language, for Vygotsky, is the “tool” or “vehicle” for making and creating meaning. Salomon, cited in Lim & Chai (2004: 216) alerts us that:

<span style="font-family: Georgia,serif; font-size: 16px;">“No tool is good or bad in itself; its effectiveness results from and contributes to the whole configuration of events, activities, contents, and interpersonal process taking place in the context of which it is [being] used”. This is Vygotsky’s model of learning and development, known as the zone of proximal development (ZPD). The ZPD is defined as:

<span style="font-family: Georgia,serif; font-size: 16px;">//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// (Vygotsky, 1978:86).

<span style="font-family: Georgia,serif; font-size: 16px;">Vygotsky (1992: 32) believes that in order to create fruitful learning, we need to determine the //actual developmental level// – “the level of development of a child’s mental functions that has been established as a result of certain already completed developmental cycles”. From this we can ask the child leading questions, show how a problem can be solved, offer a solution, or let the child solve the problem in collaboration with other children, until they reach their //“potential developmental level”//. <span style="font-family: Georgia,serif; font-size: 16px;">This is said better: <span style="font-family: Georgia,serif; font-size: 16px;">“From the very first days of the child’s development, his activities acquire a meaning of their own in a system of social behavior and, being directed towards a definite purpose, are refracted through the prism of the child’s environment. The path from object to child passes another person. This complex human structure is the product of a developmental process deeply rooted in the links between individual and social history.” (Vygotsky, 1978: 30)

<span style="font-family: Georgia,serif; font-size: 16px;">Gallimore & Tharp (2002) suggest six means of assisting performance, namely: //modeling, contingency management, feeding back, instructing, questioning, and cognitive restructuring.// For Gallimore & Tharp, teaching “//consists of assisting performance through the Zone of Proximal Development. Teaching can be said to occur when assistance is offered at points in the ZPD at which performance requires assistance.//” (Tharp & Gallimore, 1988 cited in Gallimore & Tharp, 2002:184).

<span style="font-family: Georgia,serif; font-size: 16px;">As Berg pointed out,

<span style="font-family: Georgia,serif; font-size: 16px;">"Just as the tools of labor change historically, so the tools of thinking change historically. And just as new tools of labor give rise to new social structures, new tools of thinking give rise to new mental structures. Traditionally, it was thought that such things as family and the state always existed in more or less their present form. Likewise, one also tends to view the structure of mind as something universal and eternal. To Vygotsky, however, both social structures and mental structures turn out to have very definite historical roots, and are quite specific products of certain levels of tool development.” (Berg in Vygotsky, 1978:132)

<span style="font-family: Georgia,serif; font-size: 16px;">It also assumes that one cannot expect children to approach an object and just extract meaning from it. Meaning is somewhat independent of the object - interaction needs to be mediated through the zone of proximal development by a capable other, such as the mother or teacher, for learning to occur. For Vygotsky, learning is only possible if it is located within the ZPD (Hedegaard, 1998). Concisely, the ZPD can be defined as the difference between what one could do alone and what one could do with assistance. This means that learning is socially constructed. Higher psychological functioning is then realised through mediation. According to Kuzolin (2003), Vygotskian theory stipulates that the development of the child’s higher mental processes depends on the presence of mediating agents in the child’s interaction with the environment. Vygotsky’s description of a two-stage psychological transformation that explains the way in which the child internalizes his or her social experience cannot be understood by studying the individual, we also need to examine the external social world. For Vygotsky,

<span style="font-family: Georgia,serif; font-size: 16px;">"every function in the child’s cultural development appears twice, on two levels. First, on the social, and later on the psychological level; first //between// people as an //interpsychological// category, and then inside the child, as an //intrapsychological// category” (Vygotsky, 1978:128).

<span style="font-family: Georgia,serif; font-size: 16px;">This means that when higher order functions move from the social or cultural plane to the psychological plane, an individual will gradually need less and less assistance, as the capacity to self-regulate increases.

<span style="color: black; font-family: Georgia,serif; font-size: 18px;">References
<span style="font-family: Georgia,serif; font-size: 16px;"> Dabbagh, N (2007). The online learner: Characteristics and pedagogical implications. //Contemporary Issues in Technology and Teacher Education//. 7(3), 217-226. Available: []

<span style="color: black; font-family: Georgia,serif; font-size: 16px;">Der-Thanq, C., Hung, D. & Wang, Y-M. (2007) Educational design as a quest for congruence: The need for alternative learning design tools. //British Journal of Educational Psychology.// 38(5), pp.876-884.

<span style="display: block; font-family: Georgia,serif; font-size: 16px; text-align: justify;">Gallimore, R & Tharp, R (2002) Teaching mind in society: Teaching, schooling and literate discourse in Moll (ed) //Vygotsky and education: Instructional implications and applications of sociohistorical psychology.// Cambridge: Cambridge University Press.

<span style="display: block; font-family: Georgia,serif; font-size: 16px; text-align: justify;">Hedegaard, M. (1998) Situated Learning and Cognition: Theoretical Learning and Cognition. //Mind, Culture and Activity.// 5: 114-126.

<span style="font-family: Georgia,serif; font-size: 16px;">Kozulin, A. (2003) Psychological tools and mediated learning. In Kozulin, A., Gindis, B. Ageyev, V. V., Miller, S. M. //Vygotsky’s educational theory in cultural context.// Cambridge: Cambridge University Press.

<span style="display: block; font-family: Georgia,serif; font-size: 16px; text-align: justify;">Lim, C. P. & Chai, C. S. (2004) An activity-theoretical approach to research of ICT integration in Singapore schools: Orienting activities and learner autonomy. //Computers & Education.// 43:215-236.

<span style="display: block; font-family: Georgia,serif; font-size: 16px; text-align: justify;">Vygotsky, L.S. (1978). //Mind in Society// (M. Cole, V. John-Steiner, S. Scribner, & E. Souberman, Eds. & Trans.). Cambridge, MA: Harvard University Press.