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.