Category Archives: PhD

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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Thesis Feedback

Mood: quizzical quizzical
Now Playing: Mumblings of the JLB

On Wednesday I had feedback fro my supervisors … I’m not certain how to rate it … it certainly wasn’t fantastic feedback but neither was it “go back and do your whole thesis”. Doug commented that the thesis does appear to be a late draft of a thesis but had a feeling John was less thrilled with it.

Conclusion Chapter

My Conclusion chapter is bad (my wording!) – it really needs to be made better – in fact a lot more on the implications … and John really wants me to indicate to some extent what I’ve learned from this experience, and what I would have done differently if I had infinite resources or the same resources … still thinking about that one.

John wasn’t entirely sure what my contribution was (my Chapter 7 was woefully thin) – and indicated that if this was a cognitive psychology thesis, my one experiment with only 38 participants could not get me through my thesis. He perhaps suggested that I bring forth more information on the remote observation – but I felt a bit let down there since I really don’t care for the remote observation as much as everyone seem to – I’m more interested in the cognitive psychology side of the students learning mathematics.

Remote observation

Sure the remote observation was cool – I spent ages trying to perfect it but it is not what occupies my mind. John did suggest however that I put in all the ‘iterations’ I had to do in perfecting the remote observation model – I guess I should also indicate my reviews of other software such Netviewer, Morae, E-Slate and Wiredred – which I didn’t include and also reflect on the challenges associated with remote observation to some extent. Also, John indicated that perhaps I can suggest why I used remote observation (besides just because I have the students) – I guess what he is saying write it in a positive light … which I could do – not too difficult to do – but I think I was writing very critical when I did those sections – because I was reflecting on what was critically wrong with them. Doug did tell me to try and ‘big up’ my work more … so, got to make it appear great now (I mean it is great but really expand on how wonderful the technology is and the possibility of using the remote observation, the merits of collecting all these multiple data streams and the use of students from various and diverse populations).

Multiple Data Streams

Thankfully, Doug jumped in (when John suggested 38 was bit small) an indicated that this was an educational technology thesis with 38 students was more than sufficient since this was with multiple data streams  (software video, text, scores, and voice) not only relying on the marks of the students. I think I have to make this clear on the onset of the methodology that whilst 38 students and one experiment is not sufficient for a cognitive psychology experiment but because using the students to get additional information such as their think-aloud and video data it provides a more holistic view of what is occurring. Also, perhaps some literature on analysing multiple data streams. Doug said I needed to bump up my references section since I’ve read a lot of stuff but it is not reflected in my references section of my thesis.

Statistics

Also, John was not convinced about the power calculations – which although looked strange to me … this is what the programmes by Lenth and PASS said – anyway, I’ll await his detailed feedback on Monday to understand completely what the problem is. One other feedback was that according to John I wrote my statistical chapter as if I expected to Howell (the stats. guy) to read it and suggested dropping the more complicated statistics (well relegating it to the appendicies) because my findings were getting lost in the narrative. Considering I was taught how to do my statistical findings in the advanced experimental design based on Howell – not surprising I’ve modelled my work on that … so, again will await John’s comments on how exactly I should present these.

Proof-reading

Oh … and I will need to proof-read my work … which I knew to be true … since I tend to skip lots of words when I’m typing and never notice them until I get back to it … and less passive voice (which I actually hate – but so difficult to write active when you’re in the past tense – it just does not feel the same). And I do mix up my tenses all  the time.

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Research Questions … yes again!

Mood: rushed rushed
Now Playing: Baat Meri Suniya To Zara (Kuch Naa Kaho)

Well, James said I had to rephrase my research question. My current research question as it stands is as follows:

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

Well, first of all he didn’t like the word modes since I were referring to it as types before. But then him, myself and Doug came to a consensus that since I already introduced the term boxes then I could use the term boxes instead. Anyway, James problem with the research question as it is stated here was that to him it sounded as if I was going to do a survey of mathematics teachers to discover whether using software mode or not has an effect on how mathematics is learning. Instead he suggested a research question of the following format:

What are the differences between the software modes in their effect on the learning of mathematics with respect to the three task types?

However, I didn’t like the use of ‘what’ particularly as this indicated that I was comparing the three software specifically and as there were not very strong evidence to show that there is a specific difference I don’t want to use what.

I think perhaps if I developed the hypothesis or what I’m trying to do maybe it might be easier to determine the appropriate research question. Ok the first hypothesis is that:

  1. Students perform differently depending on task type (this is not actually a hypothesis Galbraith and Haines found this out)
  2. Students’ performance/approach to solving different task types would vary depending on the software used

I think the second hypothesis is what I’m trying to do … but one word that could combine performance and approach … because performance to me only indicate the scores but I also want to look at the approach they are taking but I want to be careful with the word approach because then I might get into tool appropriation when I am more concerned with their cognitive processes. Hmm, but I have a slight problem with the term solving since interpretive tasks do not seem to be really solving but rather a sort of reasoning of what might be happening although I guess in some sense that is solving – but supposed the students did not solve the problem but yet gave an answer so probably answering might be better. Maybe I could put them as two questions (that might make James a bit antsy :D)!

But I think the research questions could be:

“Do students’ performance when answering the three task types vary depending on the software box used?”

and if so or not

“Do students’ approach to answering the three task types vary depending on the software box used?”

and if so or not

“Why do students’ approach to answering the three task types vary depending on the software box used?”

Yup I think I could work with that since the first would use the scores, the second one would use the explorations and explanations to answer these questions since these could be quantitatively based. And I could see the third question being answered qualitatively.

Ok just to send this off to Doug and James.

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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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Reviewing Thesis

Mood: don't ask don’t ask
Now Playing: Hum Ko Tumse Pyaar Hai (Ishq)

So, write now I’m reviewing my thesis … I don’t like doing it … I don’t mind creating new work or writing that- but I hate trying to make it perfect … because it takes so much effort. But writing new sections are alright … I did that yesterday and it was fun. Today, I’ve just got to polish up the stuff and it feels like pulling teeth!

I also got to prepare a presentation for Thursday on my quantitative and qualitative methods and my rational for it – and I seemed to feel woefully unprepared – we’ll see how it goes …

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Rereading my thesis

Mood: blue blue
Now Playing: Listen to the Band (The Monkees)

Last week I put together all my chapters together (even the conclusion which John gave me some bad feedback too 😀 ) … anyway, I’m starting to read it. Now, I thought in about 3 days I should finish reading it – but it is taking forever. My first chapter took the first day … now, I’m on the second – hopefully, I could finish read the literature review pretty quick – I have set aside two days to fix it – hopefully that works.

I am working to a tight schedule at the moment, since I want to send off a corrected draft to some readers to get some feedback before I leave to go to Trinidad (for Mama’s 40 days) … although, I told my supervisors it would depend on my thesis, I really think I should go because my state of my mind won’t be good.

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