Learners interactions with Plato Pathways Learning Software, a qualitative analysis embedded in activity theory.

Mike Thiem

Abstract:

Computer Learning has an aura of invincibility; technology is seen as solution for many school issues. Certainly the author of this paper is convinced of its importance, but what do the users of the software feel about it? The study looks at the impressions of a group of learners, enrolled at a Western Cape FET college, of Plato Pathways math software. Data was collected through observation, conversations with both learners and teachers and an online survey. I have used Activity theory to provide an overarching structure to the essay. Two main tools are then used to achieve the object of this essay. Plato Pathways Math Software is analyzed through the lens of an activity system, helping to place the study in a larger context.  Survey data is examined using qualitative data analysis, helping to look at the embedded pedagogical assumptions of Plato Math. Conclusions are drawn that show the users of the software adapting it to fit their pedagogical comfort zone. Also the need for greater training of learners and teachers, examination and elucidation of expectations, and a greater involvement of stakeholders in the choice of learning software

Introduction and a bigger picture

This essay grew out of a) necessity, as a requirement for a Masters course and b) my observations and interactions with FET college students in my position as e-learning administrator at an FET college in the Western Cape.

Observations were carried out over the 12 weeks of the third term.

So I am writing this essay to understand more about teaching and learning with computers and the way in which students relate to the process. I am also interested in just how software is used to teach math and what link to theory there may be in the design of that learning software.

At the heart of this essay is students’ use of computers for the purpose of learning math. In that simple statement there are several important questions, viz. What is learning? (A big question?)  Is it different to learning with a computer? How does the software, constrain or open up the path to the goal of learning math?

Looking at the first question leads us naturally to a context and a framework in which to study the other questions.

“Activity theory (Leont’ev, 1978) gives us a framework, namely terms and ideas associated with those terms, that is useful for describing the interactions emerging in both the educational and training contexts as a result of ICT integration (ROSA-MARIA BOTTINO et al. 1999)

What is Activity theory and how can it help us?  This theory has its roots in the Vygotskian idea of learning being a mediated social activity, “For  Vygotsky (1978) humans use tools to change the world and are themselves transformed through tool use” (Hardman 2005). This idea gives us what is known as the first generation activity theory.

Engestrom in Daniels (2001) built on and extended this triangle by including the “macro level of the collective and the community” Daniels (2001)

In third Generation Activity theory “networks of interacting activity systems” (Daniels 2001) are conceptualized.

I will use the writing of this paper as an example of an activity and try to frame it within the theory, in the process, demonstrating how AT(activity theory) can be used at many levels depending on the focus of the researcher (Russell. D. 2002).

I am the subject, working towards the completion of this essay, the object. In order to reach the object I am using two major conceptual tools, Activity theory and qualitative data analysis. There are also the various software tools that enable me to write this. I am operating under the rules of academic research, constrained and helped through the need for accurate referencing, avoidance of plagiarism, and the necessity of presenting evidence or references for logical arguments. There are also rules embedded in the essay, namely a limit of 6000 words and a deadline which is rapidly approaching.

The community involves my fellow students to a limited extent and Joanne Hardman to a greater extent along with the external examiner as well as all who read this and choose to comment via my blog. (http://futurecollege.org/elearning). The community would also include all those researchers whose work has provided inspiration and references for my words.

As far as division of labor, in my own connected personal activity system is my partner, Wilma, who has provided more than her share of meals, freeing up time for me to research and write this. In the sphere of the Masters Course I play the role of the student, with Joanne Hardman in the position of Facilitator and Lecturer.

What makes the Activity theory more useful than just an examination and isolation of the various nodes of the activity, are the links between nodes. These links show the connections and the conflicts inherent in any activity system as “an activity system is constantly working through contradictions within and between its elements” (Engstrom 1987, in Russell 2002)

All parts of the system leading to the dual outcome of success in this course and a greater understanding of the issues around and pertaining to the use of ICT in learning.

This theory is seen as not a predictive tool but rather a useful heuristic, to tease apart the issues involved.(Kaptelinin, Nardi and Macaulay 1999).In this it seems to have synergies in my mind with ecosystemic view of things. Add to that a temporal perspective and this is a powerful exploratory tool.

	The Plato Activity System

The Mediating tool

From my own experience, I know that there is some great stuff out there in the virtual world that makes things very exciting and enabling for learning, personally I am completely enamored by possibilities of learning using computers, exited and overwhelmed by access to the biggest library and many levels of learning 24-7 . However it seems that the learners and indeed the teachers were less than excited with the software and the opportunity to learn with the computer as tool, and had to be administratively coerced into being there with a once a week requirement as part of the E-learning policy of the college.

Looking at this tension as a contradiction in our activity system, between Rules and Subject, and Rules and community, allows us to develop an understanding of the efforts at changing the subjects’ normal activity system (Russell and Schneiderheinze 2005). This elucidation of the context allows for a less judgmental evaluation of the Individuals involved and emphasizes the fact that once an innovation (use of Plato) enters the system it “becomes part of a complex system of social and pedagogical interaction” (Russell and Schneiderheinze 2005)

Reflectively reading the previous 2 paragraphs I notice how, although my primary intention was discussion of the mediating tool, the topic veered to tension in the use of the software. This I think shows just how connected the various issues are. So I am going to follow the train of thought and just change the heading.

Tensions in the Activity.

So just why did teachers or learners not take advantage of what I assume is a great opportunity?

Firstly lack of knowledge of the software specifically and computers in general.

Aaron Falbel in his essay ”The computer as convivial tool” (Papert and Harel ed 1993) uses Ivan Illichs phrase “convivial tool”  to describe a tool that can be used to enhance a persons “freedom and autonomy “, he states that there “is nothing inherent in the tool that makes it convivial or not” it is rather the peoples ‘attitude, relationship to, and use of he tool that make it convivial”.

Now a computer can be thought of a black box of mystery, requiring special techniques to enable its effective use leading towards its non-conviviality. Falbel also make the point that commercial software “suffers from opacity and non-conviviality”, our freedom toward the software is limited we must believe what the “experts” tell us, we are not free to make changes that would suit ourselves and by extension our learners. (Papert and Harel ed 1993)

So why should a tool be convivial, well to quote Illich in Falbel “Convivial tools are those which give each person who uses them the greatest opportunity to enrich the environment with the fruit of his or her vision” (Papert and Harel ed 1993). For the occasional user Computers can be anything but convivial.

Smerdon, Cronen, Lanahan, Anderson, Iannotti, and Angeles in Education Statistics Quarterly (2003) point out that “Teachers were generally more likely to use computers and the Internet when these technologies were located in their classrooms than elsewhere in the school”, Interesting that none of the Math teachers in the college have computers in their math classrooms, this can partially explain the relative lack of involvement or enthusiasm of teachers in the Plato Lessons.

So even though the teachers did have training on Plato, they did not have the opportunity during the time they were in class to play around with the program, a very necessary component of learning new software in my opinion. An opinion supported by a study of “ exemplary computer-using teachers ” that found that they “spent more than twice as many hours personally working on computers at school than did other computer-using teachers” (Becker, H.J. 2000)

An additional obstacle to using the software comes from the actual structure of the software. The topics available are predominantly derived from American syllabus, with a relatively small percentage of exercises being UK syllabus. For the South African market the fact that the topics can be rearranged into packages is used as a major selling point. However there is often still a mismatch between with is available as a topic and what the learners are doing in class. Or indeed what is required by the syllabus.

This would not be such an issue if the learners had more time to cover the syllabus. The relative obscurity of the questions coupled with the time investment needed by the teachers meant that they were not aware of what topics were exactly covered by the program or how.  None of the teachers used all of the required hour per week citing need to work the learners in class. Illustrating dramatically the belief that using the software was not a better way for them to teach math. This is reflected later in the essay with the responses to the survey where a learner explicitly remarks that the classroom is better.

This attitude is understandable for many reasons and maybe most importantly the fact that class contact time is fleeting and valuable in the college structure, and teachers struggle to finish the curriculum in the allotted time, so spending an hour a week involved with math that does not directly impact on what they need to do is de-motivating for both teachers and learners.

e Plato Maths software is arranged in a hierarchical system, main topic finally breaking down to sub topics, but it is only customizable down to just below the module level, which means that individual questions can not be picked and chosen, but the assignment, tutorial or mastery test must be used as a unit.

This means that for a teacher to go through the module is quite laborious as they have to actually enter into the module and work their way through it. All these issues constrain the “conviviality” of the tool negatively impacting on its ease of use, which in turn constrains the frequency of use.

“Our society places greater demands on educational systems to develop learners who can use knowledge in new areas and different situations” (Russell, and Schneiderheinze, 2005) An important issue arising from this is, given the research findings of Smerdon et al (2003) and Becker (2000), if the teachers feel un- comfortable with computer use then they will be less inclined to promote or facilitate successful access among the learners. Actively discouraging the use of knowledge in new areas and different systems.

The Mediating tool (PART2)

Back to this subsection after the examination of some contextual tensions inherent in the use of the Software.

How would I use activity theory to examine the design of Plato Software?

Firstly Activity Theory stresses the importance of context, i.e. the design of the mathware is not value free but embedded in the designers own Activity System, Secondly the design impacts directly on not just the subject but the community within a conjoined activity system. The whole thing then shifts around on an access of time.

In the design of mathware the designer and programmer should be aware that “inherent in the process of human comprehension and communication, there must be an approach that emphasizes the context in which stakeholders or users develop their activities and mediation tools” (Uden, and Willis 2001)

Plato software is one of the oldest learning applications (Anderson. M. 2003) and as a company has purchased other learning companies. This is seen in a range of types of exercises that are available. Plato software is basically constructed as a tutorial, revision, test structure with the tutorial being description of the problem followed by worked examples.

The learner then gets to try out a few worked examples and this is followed by a “mastery test” module. The learner “must earn a minimum score of 80% on mastery tests before proceeding to next the activity” (Plato Learning Users guide).

There is lots of software that supposedly helps with learning mathematics. Surely in order for software to promote learning it has to fit with the actual way in which people learn. So now the question becomes, how do people learn?

There are lots of different learning theories.

The Emerging technology site www.emtech.net/learning_theories.htm lists twelve main types of learning theories. Some theories such as  “brain based learning” and “right brain vs left brain”  were two ideas that always made sense to me. They seemed to link neuro-cognitive studies with pedagogy. That is they made sense to me until I read John T Bruer’s article on education and the brain, where he with clear research shows that “as educators, we should be wary of claims that neuroscience has much to tell us about education” (Bruer 1997). The take home lesson there is that assumptions about learning should be examined carefully and critically.

http://www.learning-theories.com/ has about 40 theories and a couple of paradigms for good measure. So There seems to be lots of choice in establishing just how people learn, in this regard I am with the Wikipedia that divides the learning theories into three big paradigms;  behaviorist, cognitive and constructivist (http://en.wikipedia.org/wiki/Learning_theory_(education))

In this mold the following table summarises those three paradigms very aptly.

Models of teaching and learning

	One-Sided Models		Sociocultural Model
	Curriculum-centred	Student-Centred	Teaching/learning Centred
Historical Roots	Skinner, Pavlov, Thorndike	Piaget, Chomsky, Geselle, Rousseau	Vygotsky, Rogoff, Bruner, Hillocks, Dewey: Child and Curriculum Experience and Education
Theoretical Orientation	Behaviourism	Progressivism Cognitivism	Coconstructivism Socioculturalism Constructionism
How learning occurs	Transmission of knowledge: Teaching is telling	Acquisition of knowledge	Transformation of participation
Implications for instruction	Both teacher and student are passive; curriculum determines the sequence of timing of instruction.	Students have biological limits that affect when and how they can learn; teachers must now ‘push’ students beyond the limits. Knowledge is a ‘natural’ product of development.	All knowledge is socially and culturally constructed. What and how the student learns depends on what opportunities the teacher/parent provides. Learning is not ‘natural’ but depends on interactions with more expert others.
Student’s role	‘Empty vessel’	Active constructor	Collaborative participant
Teacher’s role	Transmit the curriculum	Create the environment in which individual learner can develop in set stages-implies single and natural course	Observe learners closely, as individuals and groups. Scaffold learning within the zone of proximal development, match individual and collective curricula to learners’ needs. Create inquiry environment.
Dominant instructional activities	Teacher lectures; students memorise material for tests	Student-selected reading, student-selected projects, discovery learning	Teacher-guided participation in both small-and large-group work; recording and analysing individual student progress; explicit assistance to reach higher levels of competence
Who is responsible if student does not progress?	The student: He can’t keep up with the curriculum sequence and pace of lessons or meet the demands of prescriptive school program.	The student: He has a ‘developmental delay’, a disability, or is not ‘ready’ for the school’s program. Often, family or social conditions are at fault.	The more capable others: They have not observed the learner closely, problem-solved the learner’s difficulty, matched instruction to the learner, made ‘informed’ decisions, or helped the learner ‘get ready’.

Table from (Jeffrey Wilhelm, Tanya Baker, and Julie Dube 2001)

Personally, through experience I definitely associate good teaching and learning with the third column, social constructivism.  Following Davydov in Daniels, “Authentic teaching/learning and upbringing come through collaboration by adults with children, ……….The most valuable methods for students teaching/learning and upbringing correspond to their development and individual particularities, and therefore these methods cannot be uniform” (Daniels 2007), and later the statement that “Davydov’s Program advocates pedagogic responsiveness to an individual learner within a framework that is supported by the concepts of theoretical knowledge” (Daniels 2007).

This makes lots of sense to me however implementation of this in a 40 student classroom is hard, especially the individualistic thing. With the advent of computers in the classroom suddenly this particular grail of individualized response seems reachable. Indeed

Plato pathways is designed to make “individual prescriptions and assigns resources according to each learners path”(Rob Foshay and Corrie Bergeron 2000)

By individualized tuition I do not mean that the learner is left to fend for themselves, Again Daniels quotes Vygotsky in saying “we know that the child can do more in collaboration than he can independently” (Daniels 2007).

Perhaps, more importantly is Daniels (2007) quote of Vygotsky’s stating the impossibility of “direct pedagogic transmission of concepts” (Daniels 2007) “the transmission model , which still dominates classrooms of North America” (Elaine Kolitch and Ann V Dean 1999) It is not only teachers that are responsible for the transmission model but  “Students who are familiar only with transmission learning tend to believe that a `teacher [is] a knowledgeable authority for whose wisdom they are paying good money” Meaning that student expectations can negate changes in pedagogy (Shor, 1996, p. 67).(Elaine Kolitch and Ann V Dean 1999)

What else is there outside the transmission model?

“ In the Report to the President on the Use of Technology to Strengthen K-12 Education in the United States (1997), the committee of advisors recognizes the benefits of a constructivist theoretical framework” (Russell, and Schneiderheinze, 2005)

“The engaged-critical model, in contrast to the transmission model, is grounded in the assumption that educators need to take ‘a critical view of the existing society, The aim of mathematics education from the public educators’ perspective (Ernest, 1991) includes `the fulfillment of individuals’ potentials as human beings, a move to a greater awareness of social change, and the fight against injustice’ (p. 295).”(Elaine Kolitch and Ann V Dean 1999)

Why then does the transmission model seem to be the dominant mode of teaching either with software or without it. The preponderance of the transmission model helps to explain the learners inability to carry algorithms to novel concepts. This is supported by Palincsar and Brown in Daniels (2007) stating that “Pedagogies which do not attend to ways in which understanding develops, may, in practice, reconstruct the curriculum in such a way that makes real learning more difficult”

Bottino et al 1999  Vygotsky (1978) in Bottino et al 1999  “ pointed out that the development of high level cognitive functions” (aka learning? )” emerges through the interaction between a subject and the environment within an activity.” Not the use of the word emerge, it doesn’t come out complete and whole but is rather messy and unfinished but is a process , the interaction could be with another learned other or with software programmed by another or with other through the use of software.

Drilling down to real learning we find according to Vygotsky that

“The place where instruction and learning can take place is the zone of proximal development (ZPD). Learning occurs in this cognitive region, which lies just beyond what the child can do alone. Anything that the child can learn with the assistance and support of a teacher, peers, and the instructional environment is said to lie within the ZPD. “(Jeffrey Wilhelm, Tanya Baker, and Julie Dube 2001)

I like to think of the ZPD as the verb of social constructivism, it is the mental space where learning happens, as it is the doing thing, surely there needs to be emphasis on clearly establishing this space in the design of mathware. Now it does not necessarily have to be a teacher that leads the individual through the learning space, but could be a tool, however the tool would have to be well designed in order to adapt as the learner grasps some concepts and fails to understand others.

The “Pathways” approach in the Plato mathware does seem to implicitly try to achieve the repositioning of content based on the learners’ ability, thus promoting a ZPD. Unfortunately this is only seen if an educator chooses the “Fast-Track” option where the learner starts at a designated place then works forward through a range of activities. In the way the software was being used at the College, the lecturers wanted content that was specific to the syllabus at that time. This negated some of the potential in the software in setting up an individual ZPD for each learner. This tension once again related to time issues as was previously discussed.

If we look at this section of the above table on learning models and compare it to the use of Plato mathware there are several interesting observations to be made.

	One-Sided Models		Sociocultural Model
	Curriculum-centred	Student-Centred	Teaching/learning Centred
Dominant instructional activities	Teacher lectures; students memorise material for tests	Student-selected reading, student-selected projects, discovery learning	Teacher-guided participation in both small-and large-group work; recording and analysing individual student progress; explicit assistance to reach higher levels of competence

(Jeffrey Wilhelm, Tanya Baker, and Julie Dube 2001)

The software has the potential to operate in the Student centered

Cognitive space, if the learners are allowed to operate more ore less autonomously. This is problematic from a social-cultural point of view in that there is an observed lack of motivation to learn, coupled with the previously discussed “time for curriculum” constraints.

There is also potential for the software to be used with the socio-cultural model, given the ability of the software to record an individual progress. However group work in Plato system is problematic as there is no support yet for forums or discussion facilities. These problems could be overcome with careful use of alternative forum software. This would mean further innovation and as  Russell and Schneiderheinze (2005) point out that for a technological solution there are “both affordances and constraints that mediate the action of the agent” and  “When teachers attempt to implement a technology innovation in the classroom, they naturally face the  complex challenge of fitting together new ideas with deep-rooted pedagogical beliefs and practices.”(Russell, and Schneiderheinze, 2005)

Because of the constraints mentioned above the software is used primarily in a one sided curriculum centered approach, which closely replicates the dominant transmission pedagogy. This shows quite clearly that the solution is not in the software or the computer but in how the tool is used.

On the other side “The transmission model should not be disdained. It is not a bad characterization of such situations as learning arithmetic basics”(Tishman, , Jay, , and Perkins 1992).  They do however raise the caveat that in transmission “The teacher may well teach for understanding, not only communicating number tables but highlighting their logic and systemacity, …. check that these understandings have been adequately transmitted by calling upon students to explain back or to explain to one another how and why an algorithm works” (Tishman, , Jay, , and Perkins 1992). This caveat seems to imply quite an active teacher with a good grounding in the need for collaboration. Collaborative transmission??

To my mind by saying that “the transmission model is useful in some instances, particularly instances of direct instruction. But as a stand-alone model to guide teaching for thinking dispositions, it is simply too narrow” (Tishman, , Jay, , and Perkins 1992)The authors are implying the need for a diverse set of learning processes that will suit the subject matter. Not the Sock view ( one size fits all) Rogoff, Matusov, and White write  in (Jeffrey Wilhelm, Tanya Baker, and Julie Dube 2001) that learning is not about ‘transmitting’ or ‘acquiring’ knowledge, but is about ‘transformation’, namely about transforming the nature of one’s participation in a collaborative endeavor.

“Computers plus necessary pedagogical strategies facilitate development of higher order skills”(Ping Lim and Sing Chai 2004), (emphasis mine), and a very important emphasis because what are these strategies, Further they state that a primary motivation for including ICT is that the tools enable learner autonomy , leading to their ability to construct their own knowledge and engage themselves in “cognitive operations that may not be possible in the traditional classroom”(Ping Lim and Sing Chai 2004)

The above comment taken out of context could go a long way to justifying use of any ICT intervention, especially if quoted by unscrupulous salesman, but Lim and Chai do cover themselves by saying that
“ICt is not a panacea in schools , and care and experience are needed when using it”(Ping Lim and Sing Chai 2004)

In the same paper there is a useful division of ICT tools into “informative tools, situating tools,constructive tools and communicative tools. (from Chen Hsu and Hung in Lim, Chai). Having a focus on just one tool type in mathware would tend to limit the effectiveness of that tool in promoting learning.

The paper focuses on higher order skills as based on Marzano et al’s framework, they are namely focusing ,information gathering, remembering, organizing, generating, integrating, evaluating , few of which are present in the simple question answer interface seen in much mathware (Ping Lim and Sing Chai 2004)

Autonomy is promoted through learners own control of rate of learning and sequence of learning, in my observation autonomy did not lead to the stated goals of adopting a more favorable approach to learning but lead instead to opportunity to slack off. I think the reason for this in this western cape college are historical, in that given the current construction of the curriculum they had not been exposed to many situations where independent learning was required, they lack the specific skills of monitoring and making adequate judgments about their progress.

The structure of the software is also problematic in that learners can simply click through an activity, after three clicks the answer is provided for all but the mastery tests. The learners discovered this loophole quite early on, and would quite happily click through an assignment whilst engaged in other conversations.

Very few learners used a pen whilst doing the task which hampered their ability to complete the assignment and or work out an answers to questions that involved more than one layer of thought, The emphasis on steps in maths was then reduced and this led to an opacity in self analysis as to what the learner had got wrong and or why.

In terms of Assessment, the testing function of the software whilst seemingly democratic and learner centered does not offer particular standardized scoring, but only whether a topic was mastered or not. This further reduced the utilitarian aspect of the program. In that the use of the software as a testing tool is reduced. The lecturers can also not use the marks in a straightforward way in their assessment.

Looking closer at the subjects

In everyday use many negative comments from the learners towards the software were directed my way so to further examine the opinions of the students I set up an online survey using survey builder from http://chnm.gmu.edu/ .

I further hoped to get some opinions of learners that maybe were too shy to express them openly.  The survey was voluntary and of 40 learners 26 replied. The answers were then emailed to me. I then extracted them using Ditto as my primary tool into an excel spreadsheet.

The results were examined using a qualitative Data analysis process of (Seidel 1998) .

this approach seems logical to me, and when initially looking at the data and wondering how I was going to analyse it, I logically started ordering it into general themes and grouping the answers based on logical ideas. I also like Seidel’s (1998) model as

he describes QDA (qualitative data analysis) as “ Iterative and Progressive: …….In principle the process is an infinite spiral., Recursive and  Holographic” (Seidel 1998). These are all descriptions that emphasize QDA as a process and not a finite entity, reflecting my understanding of all activity systems as temporal systems

The questions were qualitative rather than quantitative as I wanted to tap directly into the learners feelings and not constrain their replies in any way. There was also a conscious attempt to try in some way to break down the power structure that would discipline them for saying something against authority.

Using a qualitative process of Noticing, Collecting and thinking (Seidel 1998) sheet I organized the answers into what I considered logical themes of common purpose. In trying to group common answers, something that struck me immediately that there was little reference to actual math topics and the concerns and answers had a lot to do with other issues. Looking at appendix 2, we find 15 out of 947 words were specific to math .015%. This can have several interpretations but one is that the math lexicon is similar to that of a foreign language for the learners.

I further analyzed the results with a simple lexical analysis inspired by Moscarola 2002 who explains that “Lexical analysis is driven by the calculation of word frequencies. Firstly the computer generates a “lexicon” of all words (graph forms) present in the text (corpus). By listing these in decreasing order of frequency and applying filters (e.g. removing “tool words”) we can quickly gain an idea of the main content”

Another theme to emerge was the idea that computers provide entertainment and learning on them should be more fun! This was highlighted by high frequency of “Games” ,“Fun” and “boring” With boring 10^th in the frequency list after the removal of most “tool words” (Jean MOSCAROLA 2002). My reading of that is that the learners were simply not engaged by the software.

During the lessons the central role of computer was revealed as none of the teachers stopped the lesson to point out something particularly difficult or challenging. Or reflect to the whole class some particular issue, but rather helped individuals out with questions. In the appendix two I noticed that the word lecturer and teacher had a very low frequency both on .22%, meaning their role did not impact in a major way on the learners.

M. Anderson (2003) in a major literature review of Plato Software

discusses “ instructor-as-tutor”  where as “a consequence of the self-pacing and self-mastery the instructor is freed by the students’ increased autonomy. With this freedom, teacher can act as facilitators of students’ learning “ (Anderson 2003) This shows the potential for division of labor in an activity system to change in time, this was also noticed with distributed learning by Russell (2002) where he “became more of a facilitator”.

This change is not a simple or small one in my experience; both teachers and students are habituated to the power dynamics of the transmission model, any movement out of this comfort zone is bound to bring tension. This shift in roles must be made explicit to both students and lecturers with training necessary on both sides.

Conclusion

ICT “may act as a mediator in the acquisition of important skills and competences), as well as on evolution of the education system.” Bottino et al 1999. Quite a responsibility for the digital tools. Then again the pen as tool and the printing press were remarkably powerful in evolving the education system. So much so that maybe it is difficult for us to imagine an education without them. A truly digital education !

It is puzzling to find that modern technology does not use modern methods of learning. Not that Vygotsky or Piaget are too modern. With the advent of the net there is the possibility of realizing learning idealized by Illich in a true social form.  However as we have seen in the small activity system that is the college where I work, it is the idealization of transmission pedagogy that has become formalized and co-opts the digital tools to its own devices.

This exploration of the nodes in this specific activity system, some more thoroughly than others, has led to an intriguing look at how a group of learners and teachers are coming to grips with a new technology, the activity system framework has proved a valuable tool to tease out connections and constraints that are part and parcel of learning and stimulated the asking of many more questions.

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on research projects based on ICT. Education and Information Technologies 4:, no. 3: 281±295.

Russell,, D, and A Schneiderheinze, 2005. Understanding Innovation in Education Using Activity Theory. Technology & Society 8, no. 1: 38-53.

Seidel, John V. 1998. Qualitative data analysis. Qualis Research, Qualis@qualisresearch.com, www.qualisresearch.com.

Tishman, , Shari,  Eileen Jay, , and D. N. Perkins. 1992. Teaching Thinking Dispositions: From Transmission to Enculturation. Harvard University (August 1). Harvard University.

Uden, Lorna, and Neil Willis. 2001. Designing User Interfaces using Activity Theory. In Proceedings of the 34th Hawaii International Conference on System Sciences - 2001.

Victor Kaptelinin, Bonnie A. Nardi, and Catriona Macaulay. 1999. Methods & tools: The activity checklist. interactions 6, no. 4: 27-39.

www.plato.com. Plato Users Guide. Plato .inc. www.plato.com.

Web 2.0 for the Classroom Teacher
an awesome list of stuff to try

Tags: web2

http://chnm.gmu.edu/tools/surveys/5106/
Used this tool out of many to set up a survey to examine what learners think about Plato tyhe chief learning tool we use, one that the kids find pretty boring, has dos pictures, and is a simple instruction- drill tool ?What do you think of the questions ?

Tags: onlinesurvey, maths software survey plato

Ok, so how do i go about this,

i have set up a ning site, got emails from learners so i can invite them to my ning site., generally click the pictures to go to the site.

,

i was needing ways of the learners actually working with the fractions, virtually manipulating them, I will be using the excel files, described in a previous post. And some virtual manipulatives that i found from Utah State University

I need the learners to be able to get to the manipulatives easily, and want to do it all from the ning site?

Ok sorted, they can click the link in the discussion and will get taken to the tool as i am calling it.

Added the link to a discussion, and sent to Wincina to test it? She did not get the mail, but Jacqui did?

Maybe the pre test done at teacher test or what i called it, no it is “that Quiz”  A Brilliant site that not only is free but gives grades and levels allows you to vary the questions, just wonderful?

so this is where the pretest will be done

In the process of looking for online testing i found UCCP, the univrsity of California, and some amazing online courses complete with well thought out multimedia, i love the net, not that this is exactly useful now..

back to the topic, one girl already completed the test, and got 5 % so so far my hypothesis that adding of unlike fractions is hard for our learners is true. I have reduced the test to 14 questions from 20, taking out any that were not unlike. see the test here (”http://thatquiz.org/tq/practicetest?JSVX1565″)

I have realised that the ning site might need an equation editor so off i go at 1:42, after some serious searching no real solution, but found http://www.sitmo.com/latex generates latex images on the fly, however you have to download the image then upload it  to the forum, wich is too much of a process i believe.

To prepare for my lessons on fractions, using excel as a constructionist tool, ifound out that Excel can represent fractions as a format of cell

www.microsoft.com/education/displayfractions.mspx

excell represents the fraction in simplest terms so off the top of my head i could imagine using it to demonstrate and simplify fractions

i then discover http://nrich.maths.org/,

The Project aims to:

• Enrich the experience of the mathematics curriculum for all learners
• Offer challenging and engaging activities
• Develop mathematical thinking and problem-solving skills
• Show rich mathematics in meaningful contexts
• Work in partnership with teachers, schools and other educational settings

which has ready made excel files that demonstrate fractions, the requirements for the one is the analysis addon  to excel so i learned to install addons as well

http://arcytech.org/java/fractions for java fractions

REGINALD RAYMON CEASAR  in his November 2005 minis thesis on using an integrated vs a compartmentalised approach in teaching mathematics  quotes a  Smith (2004) study that showed in a the results of a diagnostic test given by the University of the Western Cape in 2003 that only 8.8 % of learners were able to succeed in “multiplying and adding fractions according to the order of operation” Smith in Ceasar 2005.

Linked  to this is my own empirical experience of kids battling with fractions, and when i asked one of the math teachers about what topic i could possibly test the learners on. she said fractions.

I definately need to do more research into just why people find fractions particularily hard.

My idea is to use two types of Software, namely Plato Pathways which uses a predominately instructionist drill and test approach, and compare that with Excel,  that has the possibility of designing interactive constructive representations of fractions, indeed initially when i thought of designing the program myself, i looked for hints and help on the net and found several people already had designed working interactive fraction units and made them available to download. I love the net.

Creating a computer environment for the learning of mathematics must have cognitive growth of learners as its main consideration, (Papert 1980 in Caesar 2005). This then leads to the question. What computer environment will promote greatest cognitive growth and therefore learning. Well after Piaget with his constructivism and Papert with his constructionism, Vygotsky with Social mediation i would tend to say that a computer based learning product must take these into consideration. Despite these learning theories being around for a while a lot of the software i administer for learning such as Plato pathways seems built on instructionist, behavioural foundations. Why this should be is another good question. I Hypothesise that it is the technologists rather than than the educators that have most say in the design and implementation of a  program. I could be wrong?

the plato UK site http://www.platolearning.co.uk/view_product.php?prd_ref=PWLN-A003&type=3, has lots of benefits and features but doesn’t mention what theory the software is based on .

My plan is to administer a pretest on the four operations in fractions, non algebraic, to two classes of 15 year old students who are in math literacy. each of the two classes will be divided into two, half doing a plato tutorial, drill and test on fractions and half doing similar work but using excel .

I will then administer a post test and compare the results, i would also like to follow up the test a while later to see if there is a difference over time.

My hypothesis is that a) the constructive method will be more effective in teaching concepts on fractions.

through-the-interface , click for the silent movie that sort of goes with this text, and audio version should be coming not so soon as i is busy.

In the beginning we had Vygostky who said that human learning is mediated through cultural tools , this gave us triangle number one, then along came Engstrom who expanded his learning to expand, the triangle and he gave it a base, a base that allowed embedding of vygotsky into context and into the ecosystem of community , rules and division of labour. So the triangle grew and developed linkages. My hypothesis is that our thinking is as good as our representations. So taking yenka 3d i created a 3d image object of the triangle, showing it to be rather a pyramid or polygon, in doing this i expanded the surfaces so the nodes now can become surfaces, so now we can view community for example as a plane with expanded interactions. Or if the triangle is viewed as a prism, opening a face could illustrate a contradiction between two faces or nodes.

Even if we return to the original representation, i have found that working with the metaphor and theory in this way has allowed me to interrogate the theory and construct my own meaning that is coincident with the generally accepted theories. Besides it was fun working with three d objects and the process created a distinct zpd that had to be bridged. A self created ZPD, hmm is that possible ? Back to the readings

Math in education is of course a very wide field, my own interest lie with using technology to enhance learning, specifically E-learning and  mlearning, (I’m sure there needs to be one term for these fields, one term that then breaks down into components, a structured hierarchy of descriptors ? )

I am a 39 year old , white male ( race is relevant to my south African context as it neatly describes the possible education i had from the age of 7 in south Africa) I work at an FET college as an E-learning administrator, mainly focused on using Plato Pathways for math and language. The learners at the college show a diverse range of  culture and social background, but i haven’t been here long enough to make  a fuller description.

Before i started here i ran a small home school of max 12 learners. As i was the only teacher, the use of computers and the net as source of both content and exercises seemed obvious. The goal was eventually to become a fully online school, with the entire curriculum available online,  and face to face meetings serving for reinforcement or general discussions. Things did not quite work out as i had planned but more of that later.

So i am interested in the way people learn with computers, and how to maximise that learning as a teacher. I want to focus on math as that for me is a challenging/ rewarding area of study having just completed my ACE in FET maths at UCT ( got to love those acronyms… Advanced certificate in education, in the further education and training band at the university of cape town. )

Exactly what topic to explore in the incredibly wide range is the purpose of this essay, i suppose i am thinking on paper, or with electrons.  I was excited when i saw the course offered as i saw it as a chance to combine and investigate math and computers. Then i mentioned that i was a fan of Seymour Papert and especially constructivism and LOGO. It really makes sense to me as someone who has tried to get learners to move beyond rote learning to thinking for themselves.

I was given a range of books to read around the notion of digital learning, the wired world and a selection of essays on constructionism, edited by Seymour Papert and Idit Harel  ( an unfortunate name “Idit” in my opinion). I of course also tried to find some information around Elearning and math on line.  This search and research coupled with my starting another masters course on ICT and cognition, which is foccussing on learning theories under the tutelage of Joanne Hardman (sp). Oh yes i am finishing moving from Sunvalley ,where i had the old school to Muizenberg, and my car ended up running out of petrol on Tuesday Night, through my not giving the Petrol keys to carol when she borrowed it to go to Worcester because her car had run out of petrol.  I digress badly but the point is is that it has been a very intense week.

It seems that the more i read into Math education and the use of Computers, the broader become my choices of topics to examine.

Let me see if i get get some semblance of order out of my quite disparate and somewhat chaotic thinking.

Computers and technology are not going away soon.

Younger people who are maturing now seem to be very at home with all that they( comp and tech) offers, the digital natives as coined by Marc Prensky ?

Computers offer a very intellectually satisfying matrix of possibilities that has a richness beyond the walls of a tradition instructionalist classroom . OK so now i should go into what i mean by instructionalism. For me it means a learning environment where there is a more knowledgeable other who is to provide all the necessary learning input and determine what needs to be learnt and how.

Different to a constructionalist approach where learners have more autonomy to choose particular directions with material to be studied fulfilling both the needs of the learning objectives and the needs of the learner and teacher.  Yes i think that what we as teachers teach must be interesting to us, it must also challenge us to find out more . Of course we should have investigated the topic more thoroughly than the learner but we must always be open to new information.

Students are embedded in a media rich environment and a very social one, the notion that the use of technology is motivating and can lead to greater interaction and time on task has been borne out by personal observation and in lit ( m graph reading)

Use of free software, video for mobile

And then there is the other side. These results were from a huge study of 175 000 learners in 31 countries quoted in Christian Science monitor 2004 (By G. Jeffrey MacDonald | Correspondent of The Christian Science Monitor http://www.csmonitor.com/2004/1206/p11s01-legn.html)
“It seems if you overuse computers and trade them for other [types of] teaching, it actually harms the student,” says lead researcher Ludger Woessmann  “At least we should be cautious in stating that increasing [access to] computers in the home and school will improve students’ math and reading performance.”

On the other side of the spectrum Christopher Dede (prof of learning tech at Harvard) says in the same article
“There’s this sort of bizarre belief that computers cast a spell over students and teachers and schools,”  “Can you imagine what would happen if you had the same in business, asking if computers were interfering with performance? It would be a big joke.”

The article does go on to say that there needs to be understanding as to how to use the tech in the best way possible to promote learning.  G. Jeffrey MacDonald http://www.csmonitor.com/2004/1206/p11s01-legn.html)

Again in the article A Waldorf representative . Patrice Maynard says that “”priority lies with training students to think,  because problem-solving acumen and creativity lead to success and a joyful life.”

In my opinion he has never heard of Papert and constructionism. Idit Harel and Papert in Software Design as a learning Environment 1993) go into quite a lot of detail to show how using logo programming and a well thought out program is effective through many of the domains of learning not just the academic. “Computers cannot produce “good” learning, but children can do “good”  learning with computers” (Papert, Harel 1993)

In an essay in the same book(constructionism) Aaron Falbel makes a reasoned argument for the use of the computer as a “convivial tool”  using Ivan Illichs notion of a tool that allows the user to ” express his meaning in action” Illich 1973 (in Falbel 1993). Falbel talks about how we should be aware of “technocentrism” and instead understand that there are powerful educational ways in which a computer as tool can be used to encourage learning, namely through learning how to program it, through using it to make writing less labour intensive, and through use of it for networking( Falbel 1993) It would be interesting to hear his views now with the explosion of the social networking phenomena.

It has occurred to me now that i am interested in how to use computers to maximise learning especially in math. Thinking about my own journey with them. I now know that i can use a computer to learn just about anything, with information ranging from beginner to advanced. With forums archived and current to discuss solutions with people and or solve things together. Falbel, Papert and Harel argue against the use of simple instructionalist courseware, and argue for the use of constructionalist software such as LOGO, obviously they are biased in favour of constructionism model of learning, but it is a bias that i resonate with simply because it works for me!

My question then becomes “what software is available for the teaching of mathematics ?”

and thengo further to ask “what educational model (if any)  informed the development of that software ?”

Further questions could be “who is using what ?” and

“What effect is the use of the software having on teaching and learning ?”

I think it is important to include software for cell phones, as they are a very useful learning tool.

sjoe…

References

Papert, Harel ed  Constructionism, , Research Reports and Essays, Media Laboratory, 1993

By G. Jeffrey MacDonald | Correspondent of The Christian Science Monitor http://www.csmonitor.com/2004/1206/p11s01-legn.html)

Yay, back to bloggy, suffering a bit from blog withdrawl, just been a bit manic, what with setting up all the names in plato. The mission was the login. Found i couldn’t print the class lists without doing a screen capture. Then i found i had to change every learners password individually as there doesn’t seem to be a batch operation function.

When the learners are using the program you can not change any of there attributes, they must first log out

and then  log back in again.Frustrating…….

So Faldi Jackson’s math class was the first class, and a bit of an unmitigated disaster. I was running around trying to find plato signon names and clearing passwords. As a manager i could not see the users password, which is another mission and extra work for me or whoever.

In my opinion all the administration must be smooth and flawless to really lower the barriers to access. There is a real nervousness and uncertainty on behalf of the teachers using Plato, citing lack of PC knowledge as a limiting factor. Now also what would happen if i was not in the room, and a learner forgot their password, or other issue?

Hospitality level three, were the first math class and they did not seem to have nay patience, the ones who could log in used the frustration of those who could not in order to laze around and throw attitude all over. Attitude and disinterest. they were not evidently captivated at this oportunity .

After that i made sure that all the passwords were cleared, and that i had several printouts of all the classes.

There was also the requirement from the lecturer that the classes match what they are busy with at the moment. Big issue with plato is the lack of obviously South African Aligned material. I mean with measurement, it is hard enough throwing in area formulas without expecting learners to work in yards and inches. It is a learning event but does not make it easier for the learners to continue.

On that topic, although i can see the expediency of aligning what is happening in the class with the presented content, Plato does offer learners who need it the chance to brush up oon their basics which will stand them in good stead whatever they are doing. Some of the learners battled with reading a portractor for example. This led to discussions on degrees, straight lines etc. Some good math talk was generated. A real bonus in my eyes and one that should be promoted very visibly is students helping students. Hard to do when one is worried about control. And another good reason to have several facilitators in the class.

Needing to align the courses more closely, i felt the need to know exactly what courses are available, ther doesn’t seem to be any easy way to do this from the program, especially given the dificulty printing.

Dashed off e-mail to Sammy and am still waiting for the answer to batch change and printing question. However they did send me an exhaustive Excel spreadsheet with all the courses available, modules. Which has already proved useful with educator marking off on the sheet what course she would like to see .

So, that was my practice in setting up a course with specific information. I set up a course using all the modules on report writing. It will be tested next week in language classes.

So far i have had eight classes and my technique improves all the time. The learners showing that they could concentrate for over 30 minutes in a reading exercise, which is fabulous. I mean no talking, no activity, just pure unadulterated time on task. Just shows what they are capable of when they are engaged. That was at least 90 % of the class. There were some who were just not here, they were clearly on something, or had been recently. In some of the classes there was a very strong smell of dope around some individuals, this led me to muse on the futility of teaching an individual whose ability to focus and remember is even more reduced than normally. In teens it also leads to silly giggling about minor issues, anything to be disruptive or side tracked.

The teachers definitely need to be more involved at the level of the topics that are being covered, entering into discussion on what is being seen on the screen, stopping the class for a general comment, etc and generally showing an interest and not just letting the computer do the teaching. Wonder where there is some research which shows that having a teacher involved and active increases the learning of the kids.

Italc management software has proved its value with me catching several people, playing games, trying to see sexy woman or randomly googling.

live person.com

freeiq

mindbites

current.tv

revver

metacafe

skypeprime

wengo

learnhub

business of teach on line