Category Archives: Analytical Frameworks

Literature Review Introduction

Mood: d'oh d’oh
Now Playing: How sweet it is (James Taylor)

Yup, I’m still doing corrections. At the moment, I’m trying to get the literature introduction just right but I can’t seem to do it when I’m staring at the document, so I figured if I write it here it might be alright. Well, gonna start:

This chapter highlights and discusses the relevant literature in this thesis. In Chapter 1, the objective of this thesis was presented as understanding students mathematical learning when using the three software boxes. As shown in the reported studies highlighted in Chapter 1, students’ performance on set tasks was used as a measure for mathematical learning. Mathematical learning in these studies was operationalised by measuring students’ performance on conceptual and procedural knowledge. This chapter, firstly, elaborates on these knowledge types as a way for measuring mathematical learning.

This section is followed by discussing how both conceptual and procedural knowledge can be operationalise from which students’ performance is determined. This links with the three task types: mechanical, interpretive and constructive mentioned in Chapter 1. Thirdly, using the studies mentioned in Chapter 1 about the software boxes and measurement of conceptual and procedural knowledge, inferences are made on students’ expected performance on the three task types.

Whilst performance can show students achievement level in mathematical learning, it is unable to show the pathway for students eventual task solutions which relates to Research Question 2. Thus, three students’ approaches are next identified in the chapter: a) explanations, b) explorations and c) deep/surface processing level. These three approaches are not considered definitive of all the approaches that a student can undertake and neither are they mutually exclusive to each other.

The chapter then discusses each of these approaches on how they may influence performance, how they relate to each other and finally infers what approach students may take depending on which software box they have access to. These inferences should help in answering Research Question 3.

To account for attitudinal differences, self-efficacy is also considered for determining it’s influence on performance, approach and use of software boxes. Finally, an analytical framework is presented for understanding how performance is influenced by the approaches and self-efficacy. This analytical framework will be used for analysing any qualitative data that arose.

Yup, think that is the end of the introduction, this bit might go into the third section.

Again as noted in Chapter 1, research studies into glass-box and open-box software has been limited. The main concern on these research studies were determining whether these software  modes aided in procedural learning when compared to students using the black-box software or pen-and-paper. In the cases presented by Horton and Strickland, they each found that students who were trained with the glass-box (vs black-box) software and open-box software (vs pen-and-paper) outperformed their counterparts.  This is not a completely surprising result considering that in both the glass-box and the open-box software, students are presented with or trained to understand the steps, which is procedural learning. However, there are no studies indicating whether either of these software boxes may help in conceptual understanding.

Interestingly, in the studies involving only the black-box software, the main focus was on students’ performance for conceptual tasks by comparing student’s scores using the software versus a pen-and-paper method.  These studies with the black-box software included that of Palmiter, Heid and O’Callaghan and are discussed further to provide some insight into conceptual learning with software. Although, inferences made from these studies will be most relevant to black-box software, they will also be extended to the glass-box and open-box software.

This is just a point I have to remember to highlight in this section, i.e. why it is important to study intermediate steps (other than being under-researched).

Whether showing steps (glass-box software) or interacting with steps (open-box software) actually aids in conceptual learning is difficult to determine as these seem more geared towards ensuring procedural tasks are understood. However, as researchers have suggested that there is a conceptual-procedural link, there is a possibility that students having access to the open-box and glass-box software may outperform students using the black-box software in conceptual tasks. Drijvers found that some students like to know what is occuring and by showing these students the procedural steps, they will engage with the procedural steps. If there is a conceptual link, then those students who engaged with the procedural steps will then be more likely to perform better on conceptual tasks that is providing there is a conceptual-procedural link.

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Determining Literature Review Structure

Mood: chillin chilling
Now Playing: Ishq Hua Kaise Hua (Ishq)

I’ve been looking at my literature review – and I just don’t feel the structure is right. I am redrafting it – but still trying to figure out how’s the best way of presenting the work because I got so many ideas and topics I’m discussing but don’t know whether they fit in or I’m just blabbing about them because I should.

Let me list what I need to talk about:

  • Conceptual, procedural and declarative knowledge
  • Self-explanations
  • Bandura’s social cognitive theory – in particular to do with self-efficacy
  • Deep and surface approach
  • Linkages between learning, attitudes and deep/surface approach

Now additionally I have talked about previously in my literature:

  • Vygotsky’s instrumental method with respect to psychological tools
  • Internalization
  • Distributed cognition
  • Instrumental Genesis
  • A passing mention of activity theory
  • Linking working memory with internalization
  • Linking internalization to self-explanations

Now, I’ve been trying to determine whether I should even mention Vygotsky and all the other theories that came out from it (instrumental genesis, distributed cognition, and activity theory) – although initially I was mentioning it because when people learn with tools they often talk about one of these theories … although Mayer and Renkl’s work uses tools in the multimedia theories … they don’t usually rely on this but go straight into cognitive load theory. I don’t know what to do … I know my department likes Vygotsky (or a passing mention of him), so wanted to say something about that … but I am not analysing my work in a Vygotskian framework at all. I think my intention was to show that whilst I’m using an individual approach to analysis it could still be linked to Vygotsky’s work. So, what’s my structure? Still uncertain.

I think I’ve got to tell my reader that I’m approaching the thesis from an individual learning perspective – there is a paper on Bandura’s, Vygotsky’s and Piaget’s theories written by Tudge and Winterhoff, which indicates that all theories are linked – and that whilst Bandura and Piaget works with the individual as the unit of analysis and Vygotsky’s at a more social level of collaboration etc, it does not mean that they’re not inter-related.

So, let’s see how the structure should be. I should start with my introduction (always a good place :D) – ok what should my introduction say – I mean what I’m trying to do in this chapter – I should talk about that conceptual/procedural knowledge was introduced in the previous chapter which showed that self-explanations aided in helping the conceptual/procedural knowledge. Right, got that bit. Next up, the research focuses on the individual cognition and draws from cognitive psychology such as self-explanation and Bandura’s social-cognitive theory in particular work to deal with self-efficacy. Further, that self-efficacy is linked to high academic performance and that it may be linked to a deep/ surface approach to learning.

Ok here is where it gets complicated!. Most work with tools and learning (activity theory, distributed cognition and instrumental genesis) have developed via Vygotsky’s instrumental method, where the focus have been on the physical tool – however, this thesis would show to some extent that the cognitive tool such as self-explanations can join to Vygotsky’s instrumental method and it is a theory that can be linked to the same body of literature, thus, this work is not in isolation but indicates why the cognitive tool tack is taking instead. 

Now, should I put the Vygotsky bit first or last? That’s what has been bothering me – I mean I should end on a high not a low … so, thinking should talk about this bit first – probably could call it a “Different take on Vygotsky” and then move on to the bits that I want. Perhaps, in the introduction we should talk first that learning with tools have often derived from the Vygotskian framework and using several tools, however, this thesis takes the look of the individual and first indicates that this is not very different from putting the individual first. Then, we would move onto about the individual’s cognitive stuff such as conceptual/ procedural etc – but I need to discuss conceptual and procedural knowledge in depth before I moved onto Vygotsky … hmm, I could probably say before I can show the link, it is necessary to discuss conceptual and procedural knowledge in depth as it is through this that the links are being made. Sounds good – let’s go with that 🙂 .

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Chapter 6 and Conclusion

Mood:  not sure
Now Playing: I’d be lying (Chris Cagle)

Well, I sent off my Chapter 6 (not the greatest but a chapter!) – and John sent me back some comments – he wanted more information on my conclusions – ok my conclusion was woefully thin – so really got to bump that up, but I think I’ll be ok once I re-read everything and fix it up. He thinks it is broadly sensible … hmm … I wonder if he thinks that is enough for a discussion or whether I have to make a discussion separately, I’m getting confused.

At the moment trying to write a conclusion chapter to figure out what I really found out and how does this become original research. 

Oh well, this is just a short post in trying to sort my thoughts out.

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I just may have a theoretical framework!

Mood: spacey spacey
Now Playing: Tapping of keys in an Open Plan Office

Well, I’m back from holiday and my one week bout with dengue fever (not pleasant!) – still feeling a bit lethargic from it (energy levels are really low). Anywho, just had a meeting with Doug and it has cleared up some stuff I was wrestling on. I was trying to figure out how to explain my qualitative data and I was heading to nowhere land fast because I was already digging up work in the affordance literature and stuff to do with Krutetskii (with gifted students) – which come to think about it I can still use but more on why I can on that later.

Well, Doug said I should forget about trying to look for a new theoretical framework and just go back to something that I was familiar with and suggested using the deep and surface approach and once he said it just made complete sense – that was definitely something I could use in the explanations of what was going on.  And so, had to check and see what I could find on confidence and deep and surface approach because I think that is the key in analysing most of my data even those in the quantitative analysis. Thankfully, there is something. The RASI questionnaire has a scale for academic self-confidence and Duff (2004) have found that students’ academic self-confidence was related to a deep-approach – now this is good news because noted that students who had high maths confidence were using more of a deep-approach – well, not statistically speaking with respect to the ASI, but some of the high maths confidence students were using a more deep-approach.

Not quite certain how it might fit in with the boxes but Doug suggested that perhaps one will suspect with the open-box and glass-box, students with a deep approach may delve further in trying to understand what is going on, but also perhaps this is only limited to the procedural part, perhaps in the constructive parts students with the deep approach in all three boxes may approach it similarly or be hampered (??) – I have no idea what I’m saying now – I think I’m just bluffing 🙂 .

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Distributed Cognition

Mood: quizzical quizzical
Now Playing: I Have Nothing (Whitney Houston)

I’ve been trying to get my ahead around three concepts: Vygotsky’s idea of psychological tools, activity theory and distributed cognition as I think they’ll all form part of my literature review.

Anyway, yesterday I was reading Gavriel Salomon’s paper on “No distribution without individuals’ cognition: a dynamic interractional view” which he wrote in 1993. I thought this paper would help me understand things from my point of view. As I’ve noticed in activity theory and distributed cognition there seems to be more emphasis on the tools rather than the individual, at most times it seem as if the individual is incident to the fact rather than perhaps the person who is running the system. I think I’m a very individual cognitive person and hence my reasoning may be influenced from these thoughts.

Anyway, Salomon is saying something similar to what I’m thinking except it was very hard trying to make my way through the maze of different theories and considerations. One of the things that Salomon talks about is the way that Lave (1988) sees

person-acting-in-settings whereby cognitions are ‘distributed – stretched over, not divided among – mind, body, activity and culturally organised settings (which include other actors)'” 

It’s this stretching over that seems quite confusing – cognition is seemed to be divided between objects and people. Pea (1993) – in the same book – preferred to refer to it as ‘distributed intelligence’ since he didn’t believe that objects can have a cognition. So guess in Pea’s manner that cognition is a wholly human activity. However, in one of his earlier papers, Pea (1985) he talk about cognitive tools such as computers, pen etc. which acts as cognitive thinking reorganisers within a functional system (he was keen to debunk the word amplifier). I think in this case the functional system has evolved into the distributed system.

Anyway, although keen on reading Salomon paper I can’t say he has given me a strong argument for the individual (I really want one) – or perhaps I’m just too dense to understand what he is actually trying to say. One of the things, he does mention is cognitive residuenot certain it is something he coined or it comes from elsewhere. Basically, he says that in a distributed cognitive system when the individual is there he will learn something in that system and retain it (this is what is the cognitive residue) and apply or transform its application in a completely different distributed cognitive system, and thus it is the individual (and all other individuals) pool together their cognitive residue and causing it to redistribute and create more cognitive residue – and this is the individual cognition we cannot ignore, the learning is not all in the cultural/social chrysalis that the post-Vygotskian theorists seems to want to put the hold human race into (ok, probably the last bit is more me ranting rather than Salomon’s view :D).

Salomon seems also to ridicule (perhaps too strong a word) of Pea’s (1993) idea that the individual can off-load their “cognitive burden onto a a tool or onto human partners“. I haven’t read the full paper by Pea – so, not quite sure what Salomon is alluded to, but I don’t like the idea of saying we “off-load” our cognitive burden … when we give it to the other people – what do they do with it then? Do they off-load it back to us? Certainly, their is some individual cognitive thinking occurring there which is processed and then returned to us (or perhaps as Vygotsky says – internalised) – perhaps using their own conceptual and procedural knowledge which some may have acquired through a social/cultural heritage.

I feel ambivalent about saying some in the last sentence but this social/cultural heritage is very screwy – pretty much everything we do is within some environment, we live on earth our intelligence is  going to be shaped within that environment but does it mean that it is the main influence of our intelligence or we have some say in it as well? (I think I may be getting confused now :D).  

Anyway, what gets me, is that all systems are connected – how do you know where one ends and one begins, how do you define the boundaries, how do you know where your cognition has stop being distributed? Are we saying it is only the specific tools or person we are sharing it with? How about the environment – let’s say the ambiance helps in cognition being better? Which is true … if the temperature is conducive  the one is more likely to do work – but is that a product of the social/cultural history that we carry? Or something from our evolutionary history? And would this be part of the distributed system? You see the same thing happens in activity theory – where are the boundaries? At least in individual cognition the boundary is much more clearly defined. (I know although I’m doing this rant – I may just turn around and use distributed cognition or something of the same ilk in my literature review and be perfectly fine with it).

Anyhow, just one last statement from Salomon about having:

 “a search of effects of distributed activities to a search for the effects with them … the former pertain to cognitive residues in the mind of the individual, the latter pertain to the structure of the activity when the tools and social surrounds for distributed cognitions are available”

I’m not quite certain what all of that means conclusively but Salomon thinks it is something of importance because he keeps mentioning it, I’m not certain whether the prescribes to the notion of or with. I think it might be of but not certain, well I believe in the of rather than the with.

 Anyway, will list the four reasons why Salomon thinks we cannot ignore the individual (so I can for remember in the future):

  1. Some everyday experiences and observations do not require cognitions to be distributed (I think in this sense he means off-loaded to a person or a tool)
  2. Higher-order knowledge such as skills and operations may not be able to be distributed
  3. When representing the world as an activity, the individuals’ representation cannot be ignored (I think he is referring to activity theory triangles!)
  4. Using only situated and distributed cognitions provides “only frozen pictures of states that neither grow or develop” i.e. that is without incorporating the individual’s cognition.

One of the things that I’m wondering is how did one extend Vygotsky’s idea of a psychological tool (in which he meant mainly higher mental) into a physical tool such as computer etc or even a person. I’ve got to find the paper which does that – guess it must be Leon’tev (sp?).  Because basically what is being said is that the original psychological tools mentioned by Vygotsky are now external cognitive tools (which is a bit of a strange terminology since it gives the impression that the tool can think which we all know that it can’t!).

Anyway, gonna submit this now … I know sometimes I tend to ramble – but hoped it made logical sense in most places 🙂


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Theoretical Frameworks

Mood:  a-ok
Now Playing: Lovenworth (Roy Rogers)
Topic: Analytical Frameworks
Well, during the CALRG conference I was trying to put together the theories I’m using and how they relate to my research. So, just going to type up my ramblings on this.

First thing is that although I’m looking at individual learning there is no negation of the fact that social learning does help students to learn as well, however, initially particularly in a distance and e-learning context, a student will initially interact with materials/computers and this is the individual learning. Further in a information transmission mode of most lecture halls of universities the same may also occur.

Question: Which theories help to measure/ describe individual learning?

Well … not certain about but got some stuff here that students who do individual particularly in an e-learning context will tend to interrogate their material (perhaps!) and have some sort of interaction. I have a note here saying that is perhaps co-construction – but for the life of me I can’t think why? Could be that I think through the interaction of the software and they self-explain to themselves can start make meaning of what they’re doing and whilst this is not collaborative with a person it is collaborative with the computer.

So, I’ve been looking up individual learning theories on the internet as well and I came across these two websites: Theories of learning and Individual theories. I think those two web-sites might be useful.

Looking through the first website, the Sensory Stimulation Theory (Laird, 1985) seems to be linked to the computer-interaction learning and I’m guessing one of the basis for multimedia learning theory as effective learning occurs when the senses are stimulated. I can’t think of the boxes doing any effective sensory stimulation as there is mostly text and this is mostly visual. There is no hearing stimulation unless wants to count me prompting the student to do something. But I think whilst in the visual there is text, there can also be animation. Whilst the boxes don’t have high levels of animation or not one might consider animation, there is a sort of interactivity animation. I can see the glass-box being a full animation, the open-box a mixture of animation and interactivity and the the black-box with no animation or interactivity.

The second theory that strikes me is the adult learning (andragogy) (Knowles, 1990) in that adult learners need to see applications to new learning – I’m not quite sure if I’m interpreting this right but I’m thinking that adult learners need to make connections to real world applications. As I’m using undergraduate students is this something will be likely to exist – are they really adult learners? But I did notice in my pilot studies the more mature students liked to connect stuff to real world. But perhaps this comes from the social-constructivist theories that each learner is unique and has unique backgrounds and probably more likely to connect to things that are specifically related to them and this shapes what they find important or what knowledge they connect.

There is also the cognitive gestalt which I’m more keen in exploring and I quote from the first website:

The emphasis here is on the importance of experience, meaning, problem-solving and the development of insights (Burns 1995, p.112). Burns notes that this theory has developed the concept that individuals have different needs and concerns at different times, and that they have subjective interpretations in different contexts

This seem to incorporate my feelings on adult-learning and social-constructivism as this recognises that individuals have different needs and have different subjective interpretations and it is not beyond belief that everyone will have this based on their social culture.  Also, that the development of insights or problem-solving and finding of meaning can also be influenced in the way that the information is produced to the student – hence the reason for multimedia learning theory perhaps using cognitive load theory.

So, for me definitely cognitive theory is the way to go now don’t know how to make the jump to cognitive load theory but structured problems such as maths have been explained using cognitive load theory … so just going to skip to that and find out the connection later.

Well, there are several parts of CLT that may apply to my work and I think the two parts (which Sweller(2005) refers to as instructional consequences) that has the most influence are:

  1. Self-explanation – unfortunately don’t know which loads it affect – I think when a student self-explain the germane load perhaps increases? Got to check this
  2. Reversal-expertise effect – can’t remember which load this affects either but I think students using the open-box are more likely to experience this if they were able to figure out early what was going on – but not likely to happen if they still haven’t found out the rule for application – i think in this case initially the germane load increases but as their expertises increase their extraneous load increase and thereby decreasing germane load.

Right … so, I think those are the two things most likely to influence my research why I am not dealing with the rest don’t know … hmm … let’s list the rest based on Sweller (2005) paper from the Multimedia Learning Handbook:

  1. Worked example effect: students do better if there is a worked example provided. Works by reducing extraneous load
  2. Split-attention effect: attention split between multiple visual sources. Increases extraneous load
  3. Modality effect: similar to split-attention except this is reduced by incorporating verbal (said aloud) rather than as text. Decreases extraneous load
  4. Redundancy effect: Having several sources of the same information e.g. diagram with text rather than having to integrate mentally the diagram and then a textual explanation. Reduces extraneous load by removing the redundancy
  5. Expertise reversal effect: multiple/ dual sources of information lose their advantage as the learner because more of an expert. Guessing it increases extraneous load but not explicitly stated.

Alright, so that somewhat covers my cognitive load theory … how do I incorporate the multimedia learning theory? Sure we know that animation and text affects the way that students learn … that comes from the modality effect in cognitive load theory but what about interactivity. Can’t recall if Mayer did any work in that. I think that is perhaps where self-explanations come into it – with prompts? Is interactivity a prompt perhaps? Hmm … too lazy to look … was looking through the multimedia learning handbook and didn’t find anything so not going to go hunting at the moment.

We also have the problem-solving phenomenon of backward fading and forward-fading by Renkl and Atkinson but this is obviously linked to the worked example effect. There is no fading as far as I can see in the boxes … perhaps although in some way one can in a stretch propose that the open-box is acting as a forward fading problem – nah perhaps, if we were going from the black-box, glass-box to the open-box then one might claim that is a sort of backward fading but don’t think it would fit as well in this context

Updated: Thursday, 28 June 2007 3:29 PM

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Alternative theories

Mood:  a-ok
Now Playing: Sway (Dean Martin)
Topic: Literature Review
So, went to the OpenLearn reading group session on action research and whilst I was there whatever they were saying got me thinking about the writing of my literature review. So, I think these are some of the theories I’ll have to think off when I’m writing up as alternative theories that could have been used.

First, the first thing that struck me is that when the students are learning an activity is in the method I’m doing (single user in one episode of learning), learning may not be limited to that time or episode but instead continues (the concept of action research research – I think), and this learning here can be connected to future episodes of learning, although practically thinking this will be difficult to follow – but this is the way conceptual knowledge – linking up bits of knowledge – but isn’t this therefore a constructivist approach – although not necessarily a linear way as is suggested I think in earlier theories (as well as in cognitive load theory).

Also, in such an activity (as in my method) – students do not have time for reflection, they’re tested then and immediately – which I can live with – but why academically I can live with it … not sure. Is there truly any period of physical time that can be allocated for reflection. In a sense I’m hoping they would have more reflection occurring during the use of the software – perhaps an acceleration to the reflection they would normally have … ok, probably not an acceleration – but another medium for causing reflection. I’m thinking this reflection is the self-explanations that the students come up with.

Further, there are the social learning theories that I’ve ignored in this study, as students do discuss and share ideas and are then able to improve their concepts or develop a ‘community of learning’ – this doesn’t happen here as I’m looking at individual learning in a specific episode or moment. Whilst there is an agreement that there is merit in social learning or discursive types, perhaps what I’m trying to see is how a student learning in the first instance by themselves such as in distance learning or e-learning might be influenced or even in classrooms where discussion is not encouraged or where there is mostly a transmission mode. Whilst one do not want these modes of teaching (or may want it – if they’re a strategic/surface learner) it occurs quite regularly and hence nothing to ignore and this may more than likely be the way things are transmitted in undergraduate classes – as innovative learning methods are not often used at this level (well I think so!).

Anyway, what I’m saying is that although social learning may have its merits there are often cases where students do learn as an individual first and it is this is which we want to measure – the first instant of their learning what is occurring and if we can perhaps improve their first instant of learning perhaps their social learning might be more meritorious? Besides, I don’t think maths/ linear programming lends itself easily as a subject for discussion or to look at collaborative learning … well, perhaps it does – but perhaps I can look at that in my future research – does collaborative learning improve the conceptual knowledge which is elicited by these

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