Category Archives: Literature Review

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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Still fixing the literature!

Mood: crushed outcrushed-out
Now Playing: The typing of people still here at this time of night!

James told me I had to build on my previous Chapter 1 on why intermediate steps was such an important thing to study. Now, that stumped me as I thought I put forth everything there was about why I should study intermediate steps in chapter 1!!! So, now I’m racking my brains to figure what to say for that section.

So, here goes what I think I should include:

  • Drijvers have found that students using black-box wanted to see things that were happening in the white-box as well which may indicate that students do not feel satisfy doing something unless they know what is happening. I believe Heid speaks of this as well … and from my pilot studies some students said the same thing … so, that is reason 1! – but this may be influenced by the confidence of the students I think.
  • Star, Kadejevich etc. have said there is a link of procedural to conceptual therefore the software which shows the procedural part should help in the development of conceptual knowledge – but as found possibly not in the constructive problems
  • All the studies that have been done has indicated that CAS which is a black-box allows students to explore and have less cognitive load since that is taken away from them, if they are loaded with the same extraneous information does it make an effect on them, is it the process of automation that helps or is it not having the extraneous information
  • And lastly I probably could pull from Renkl’s work on using CASCADE which faded out steps – but that seems a bit lame … to use in this context – so think I would eliminate that

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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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Vygotsky and Self-explanations

Mood:  a-ok
Now Playing: Gill’s mobile ringtone 

I think this literature review is starting to make some more sense but not entirely sure. I think I’m going to see how well I can link Vygotsky with self-explanations, some guy called Schwarz had done some work in this area so, I’m going to have a read of his papers tonight and then quickly start typing up my literature review tomorrow – because definitely think I would be in the position to complete the right learning theory section. I’ve mostly talked about why the three boxes somewhat in the introduction so don’t think I need to go into that in quite so much detail but may have to give some literature on my thoughts on what is expected from these three boxes and my brain has just become sluggish on that since the literature seems to be dead in my mind right now – although a few months ago – I knew it perfectly – oh well guess I’ll be quoting Renkl etc and perhaps Sweller as well on steps – plus Renkl has done stuff on self-explanations.

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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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Restarting the literature review

Mood:  a-ok
Now Playing: If you leave me now (Chicago)

Right, I’ve decided to restart looking at my literature review – because the truth is I have no idea – and the weekend certainly didn’t make it any clearer. So, what I’m going to do without any pressure of looking at a word document is to write here instead (and I’m being very wordy about this part because I’m too scared to start – don’t know what is actually scaring me – but the literature review is starting to become like the monster in the closet!).

So, starting. I think what I need first is my research questions so I know what I’m doing, so going to copy them across – well the current research questions that I’m using obviously :D.

How does the use of software modes influence the learning of mathematics with respect to the three problem types?


Are self-explanations better promoted in different software modes depending on the questions types?

Ok, I’ve got the research questions … now what?I already know the answer to the first in terms of quantitative date … it doesn’t! Anyway, that is not what I’m here for, I’m here to dig up literature that would genuinely show me how I could have come with this question and why it is important and what would literature conjecture it would be.How to start? I have no idea *sob* *sob* – I’ve got some literature in the introduction which are just pertinent to the research questions – I think this is what is called writer’s block. I can’t be having it now – I’ve got at least 60,000 words to go :). I have some vague feeling I should start with Vygotsky but have no idea how. Although, Rebecca did mention that his scaffolding thing might be related to my research – hmmm – gonna have a brief look at it. Ok had a quick look at Vygotsky in several websites on scaffolding and zones of proximal development and some contrasts with Piaget. They all seem to apply to children’s learning. I just trying to determine to what extent this sort of theory can be applied to higher education or adult learning or if at all. Ok, I’ve just asked Rebecca and she has recommended I read a paper by Andrew Ravenscroft on  “Reclaiming thinking: Dialectic, dialogic and learning in the digital age“.  So, gonna add it to my endnote and give it a quick read to see if it makes any sense or has anything related to me.

Alright, thought I was onto something with this paper – but came up with nothing – well nothing right now it might prove useful later – anyway, the paper embarks on dialectic and dialogic which I had no clue of until I embarked on a search on wikipedia which revealed that dialetic is basically a logical argument (so just your plain old logics) and dialogic is as I gathered a dialogue – note here I mean a conversation between two  or more persons – but the dialogue is not synchronous or even near synchronous – because the dialogue could be a person interacting with the works of someone’s previous literature (who may or may not be dead and thus cannot contradict or illuminate the discussion – as I gather basically a literature review!) and moving on a discussion – although it is said a thought could be in some ways a form of the dialogic … I guess in that sense you’re having a dialogue between yourself and moving on the thought? Not sure if this interpretation is quite there – but will use if for myself in the meantime.

Anyway, so was expecting Ravenscroft et al. to explain to me why Vygotsky take on learning could be apply to higher education or to term it in Vygotskyian terms “a more learned other” (although a more learned other could just be someone in Form 3 versus someone in primary school so not sure that would count as higher education :P), but all they said was that it is widely accepted that it can be used. But by whom? And who made it acceptable? I hate these questions – need to find some recording of this in some literature – ok new literature research beginning. Gonna post this and perhaps make a new post or come back to it.

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Literature Review

Mood:  rushed
Now Playing: Little Old Wine Drinker, Me (Dean Martin)
Topic: Literature Review

Right, I’ve been trying to get my head around my literature review and have to say it has not worked! I have no idea what I’m writing or where to start. It seems like a bunch of words with no story with nothing really … wish literature writing were much easier and it came naturally to making a story etc. Oh well, think I’m going to give it a go again and see if I can tell it as a story – I tend to work well that way. I know it sounds a bit too narrative but I think only in that way I can feel as if I’m creating climaxes and anticlimaxes (i.e. gaps and arguments) – anyway, would see how this proceeds.

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