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**Chapter 4 Research Method**

** Introduction**

Data collection was organized in three phases. The first phase established students‟ expectations of the role of mathematics in physics; the second determined what mathematical approach 1^{st} year students use when solving electricity problems; and the third determined types of understanding that emerge when 1^{st} year students solve electricity problems.

To provide data to answer the first research question, two instruments were used namely: a survey administered to students, and focus group interviews, both of which students‟ expectations on the use on mathematics in physics were explored. The survey was given pre-instruction with respect to the topic of interest (electricity) and focused on students‟ views on their use of mathematics-in-physics, in general. The interviews were conducted during the period when the topic of electricity was being taught. The interviews focused on students‟ views on their use of mathematics in physics; starting broadly and eventually narrowing to the specific topic of electricity.

Copies of students’ scripts were made to answer the second and third research questions. Previous studies on and related to students‟ use of mathematics in physics were coalesced to come up with a theoretical framework for this study (MATHRICITY) (see section 3.5). MATHRICITY was subsequently used to explain students‟ use of mathematics in the physics topic of electricity, when analyzing their test scripts. The analysis was also done in the context of what emerged from the survey and interviews.

**Research Design**

This study is based on an intepretivist research paradigm. Interpretation is about giving meaning to data, developing insight, making inferences, refining understanding and offering explanatory lessons (Hatch, 2002). The study approach is mainly qualitative but also makes use of quantitative methods in analysing some of the data. Qualitative research has been chosen because of the richness of the data that it produces as well the in-depth information that results from the analysis (Hoepfl, 1997). Qualitative research focuses on the idiosyncratic as well as the pervasive, with an attempt to find the uniqueness of each case (Chenail, 2000) and emphasizes open – mindedness and curiosity of both the participants and the researcher.

The specific nature of this qualitative study is both descriptive and explanatory. Descriptive studies focus on what is going on, while explanatory studies focus on why something is going on (Otero & Harlow, 2009). Qualitative studies are appropriate for this research since there is need to uncover, characterize and interpret what is observed. How students view the use of mathematics in physics; how students with those types of views eventually apply mathematics in physics; and the meaning (why) that may be derived from all these results, are fertile qualitative research fields.

**Instruments**

The three instruments that were used to collect all the data for this study are; the expectation survey, students‟ test scripts as well as focus group interviews. Data from these three were deemed appropriate to explore the boundaries of the research problems.

**Expectation survey**

Surveys are important evaluation tools that help in understanding a social or cognitive practice like pedagogy. Redish (2003) states that a cost-effective way to determine the approximate state of class knowledge is to use a carefully designed research-based survey. As baseline, an expectation survey was designed and administered to students, to find out “*What* *are the students’ expectations of role of mathematics in physics*?” The survey was conducted at the end of the first semester, in the form of a questionnaire.

the survey was developed by coalescing selected items from three established science education questionnaires, namely: Maryland Physics Expectation – MPEX (appendix A) developed by Redish, Saul and Steinberg (1998); Views Assessment Student Survey –VASS (appendix B) developed by Halloun and Hestenes, (1998) and Epistemological Belief Assessment Physics Survey – EBAPS (appendix C) developed by Elby, Frediksen, Schwartz and White (1998).The chosen items from these three questionnaires were those deemed relevant to the study as they addressed particularly the first objective of the study; *Establish* *students’ expectations of the role of mathematics in physics *.

MPEX could not be chosen as a whole as most items addressed students‟ expectations on introductory physics in general. Item (19) from MPEX, “the most crucial thing in solving a physics problem is finding the right equation to use” is an example of an item used in the construction of SERMP item 11 where it reads exactly the same. Item 18 from SERMP, “the first thing that I do when solving a physics problem is to search for formulae that relate givens to unknowns” was derived from VASS, from where it was item 35 and initially read “The first thing I do when solving a physics problem is: (a) represent the situation with sketches and drawings (b) search for formulas that relate givens to unknowns”. EBAPS contributed to the construction of SERM item 25 “I treat equations as representations of reality” where the original item (12) was “when learning science, people can understand the material better if they relate it to their own ideas”.

The resultant questionnaire was then named Student Expectation of the Role of Mathematics in Physics (SERMP) (appendix D).SERMP consisted of thirty (30) items put along a 5 point Semantic scale of; strongly agree, agree, neutral, disagree and strongly disagree. The items were parsed from categories that would depict students‟ perceptions on the “interrelationships, connections and generalities” between mathematics and physics.

Surveys only measure what students think they think (Redish, 2003). To really see how students think about mathematics in physics, their actual work during problem solving will provide that critical information. Accordingly, copies of students‟ test scripts when working on electricity questions were made for analysis.

**Test scripts**

A key source of data was the students‟ work in their test scripts. Two sets of students‟ test scripts were collected for the duration when the students were doing the electricity topic, which was the second semester. The first test consisted of questions mainly from the electric force and electric field subtopics while the second test covered the electric circuits subtopic.

Copies were made of students‟ scripts submitted for marking, with their informed consent. Students work from the electric force; electric field and electric circuit subtopic were evaluated. The particular students‟ solutions identified for even more detailed analysis were scanned and stored to make up this report. Data from the documents were analyzed in a bid to answer the two research questions; “*What are the mathematical approaches students use in **solving electricity problems*”, and “*What patterns of understanding emerge when students use certain mathematical approaches to solve electricity problems”?*

**Focus group semi – structured interviews**

According to Wilson (1997) focus group discussions in educational research are normally employed in concurrence with other qualitative methods. The major advantage of focus group interviews is their capacity to produce “concentrated data on precisely the topic of interest” Mogan (1996). Being interviewed in a group gives informants a sense of security and comfort that may lead to more candid and reflective responses than in individual interviews (Gorrad, 2001).

Focus group semi – structured interviews were conducted with the students. The interviews were audio recorded and later transcribed (appendix H). Each tutorial group was interviewed about 2-3 times during the semester. Overall, 7 episodes of interviews covering approximately 7 hours were conducted. This was a period when the topic of electricity was being taught. The time interval between interviews of the same group was about 2-3 weeks. GST concepts were used in aiding the design of the interview questions. Questions were also framed along the continuing analyses filtered from students‟ responses to the SERMP as well as from their work on tests scripts. The interviews intended to further elicit “*students’* *expectations of the role of mathematics in physics*”, with particular emphasis to the topic of electricity.

**Validity and Reliability of the Instruments**

Validity, an essential quality in research data, has to do with whether the data are, in fact, what they are believed or purported to be (Bless & Higson – Smith 1995; Charles, 1998). Reliable information in qualitative studies simply means that the information has to be consistent, that similar results will be obtained in a similar environment. This is done with the understanding that individuals are different, and that a student‟s state of mind may be influenced by many external factors, but also that the fluctuations in individual responses tend to average out over a large enough class.

**Declaration**

**Abstract**

**Acknowledgements**

**List of Tables**

**List of Figures**

**List of Abbreviations**

**Language Editing Certificate**

**Turn it In Report**

**Turn it in Receipt**

**Chapter 1 Introduction and Background**

1.1 Introduction

1.2 Study context

1.3 Problem Statement

1.4 Rationale for the Study

1.5 Objectives and Research Questions

1.6 Operational definition of key terms

1.7 Dissertation overview

**Chapter 2 Literature Review**

2.1 Introduction

2.2 Contrasting mathematics and physics

2.3 Problem solving in physics

2.4 The dichotomy in students‟ use of mathematics in physics

2.5 Students‟ learning outcomes on electricity as a topic in physics

2.6 MPERG and related studies on students‟ use of mathematics in physics

2.7 Mathematical thinking in physics

2.8 Summary of the observations

**Chapter 3 Conceptual Framework**

3.1 Introduction

3.2 General Systems Theory (GST

3.3 Extended Semantic Model (ESM)

3.4 Some relevant approaches for students‟ use of mathematics in physics

3.5 Design of the conceptual framework

3.6 Application of MATHRICITY through analysis of a typical first year electricity question

3.7 Chapter summary

**Chapter 4 Research Method**

4.1 Introduction

4.2 Research Design

4.3 Instruments

4.4 Validity and Reliability of the Instruments

4.5 Participants

4.6 Analytical Framework

4.7 Ethics

4.8 Summary

**Chapter 5 Students‟ Expectations on the Use of Mathematics in Physics**

5.1 Introduction

5.2 Students‟ response to the SERMP

5.3. Emergent responses from the SERMP

5.4. Students‟ Epistemological Frames

5.5. Epistemological frame: What students think it takes to learn physics

5.6. Epistemological frame: What Students think about the Use of Mathematics in Physics

5.7 Summary

**Chapter 6 Students‟ test scripts**

6.1. Introduction

6.2 Analysis of students‟ work on Electric Force

6.3 Analysis of students work on Electric Field question

6.4 Analysis of students‟ work on Electric Circuit question

6.5 Chapter Summary

**Chapter 7 Summary of Study and Findings**

7.1. Study summary

7.2 Discussion of findings

7.3 Conclusion

7.4 Limitations of the study

7. 5 Implications and further studies

REFERENCES

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The Role of Mathematics in First Year Students’ Understanding of Electricity Problems in Physics