Data collection methods

Consistent with an interpretive approach, data collection and analysis had complementary roles with each activity informing the other “as an iterative and reflexive process” (Tolich & Davidson, 1999, p. 108). Data collection

instruments appropriate for this study are the questionnaire, interviews and focus group interviews, and the researcher.

3.5.1 The questionnaire

The questionnaire is a common qualitative data collection tool. It asks set questions and the responses are assessed. Questionnaires can cover a wide range of data, such as descriptive data using close questions or open- ended questions which seek to extract ideas and beliefs. The use of the questionnaire allows efficiency and timeliness as it is easy to administer and can produce a large number of responses (Burns, 1997). It allows the same questions to be posed to a number of participants whilst guaranteeing the participants confidentiality, which encourages more honest responses. In this study, participants were offered the choice of a postal questionnaire or an Internet-based questionnaire, which allowed participants to set their own timeframe for answering questions, albeit that the researcher asked for returns before a due date. Interestingly, all participants completed the online questionnaire, which may indicate their comfort levels with ICT-based surveys or their perception of the time needed to complete the questionnaire.

A questionnaire (Appendix C) was designed to provide data on principals!

self-perceptions and on their mathematical identity, their leadership of mathematics in their schools, and issues relating to professional development in mathematics. A second questionnaire (Appendix D) was designed to provide data on teachers! views on their school leader!s mathematical capabilities, their own mathematical identity, and the provision of professional development in mathematics. Both questionnaire designs offered both closed and open-ended items. The questionnaire was self- administered and designed to elicit information about the Principals! role in the provision of effective mathematics professional development and the teachers! perceptions of that provision and the effectiveness of the Principal!s leadership in mathematics education. In particular, the questionnaire provided information on:

• Personal details, in terms of age, time in role and experience as a Principal or teacher, and mathematical qualifications.

• The self-perception of participants in terms of mathematical identity • The self-perception of the respondents in the mathematical context • The nature and extent of mathematics professional development

offered to staff

Additional areas that were addressed were:

• Perceived effectiveness on professional development methods

• The type of leadership of mathematics utilised by the Principal from their own point of view and that of their staff.

• Barriers to the provision of professional development

Gathering information on the participants! self-perception in terms of mathematical identity initiated a search on several methods of relevant data collection that could be used in a questionnaire format. The widely used Mathematics Anxiety Rating Scale (Richardson & Suinn, 1972; Suin & Winston, 2003) measures students! mathematics related anxiety but fails to assess other relevant dimensions of mathematics value and is cumbersome in the context of a wide-ranging survey. Subsequently, the Mathematics Value Inventory (Luttrell, et al., 2010), was selected and adapted for as a self-report inventory that measures individual differences in perceptions participants hold of mathematics interest, utility, need for achievement, and personal cost. The Mathematics Value Inventory (MVI) reveals positive and negative feelings towards mathematics, giving indications of strong or weak mathematical identity or anxiety to be further investigated in interview.

Exclusive use of questionnaires has limitations: The length of the questionnaire and the depth of answers required can affect the response rate in respect of each question; responses cannot be followed up due to the confidentiality of the questionnaires; the participant must understand each question; the honesty of responses may or may not be trustworthy, and; the manner in which the question is posed must be assumed to be the same as that in which it is read.

3.5.2 Interviews

The interview, as an investigative tool, was applicable within the constructivist paradigms of this research project. Interviews allow for collecting data that would be inaccessible through the pure use of questionnaires as they enable the researcher to question more deeply and clarify issues raised in the questionnaires. Interviews were recorded with a digital audio recorder and wholly transcribed.

The use of interviews offers flexibility for the researcher to delve deeper for richer meanings than can be obtained purely by questionnaire. Kvale (1996) says that an interviewer should be a "miner! (p. 3) or "wanderer! (p. 5) and should use a conversational approach to elicit participants! “stories of their lived world” (p. 5). However, the balance of talk in an interview is different to a conversation in that the interviewer needs to listen more closely and promote participant talk (Babbie, 2010). This was an important consideration in this research as the interviews supported the researcher!s intention to understand the Principals! and teachers! mathematical identities from their own perspectives.

(Kvale, 1996)

The reliability and validity of interviews is in dispute due to the open-ended nature of questioning techniques (Truran & Truran, 1998). Truran and Truran also argue that reliability and validity “must be assessed in terms of the way the information is used and the nature of knowledge claims made” (p. 63). It is proposed that this research project has used interviews correctly under this argument.

The researcher chose to interview individual principals and to interview teachers in groups, using focus groups. A focus group brings together a number of individuals to discuss a common topic (G. Anderson, 1990). The interview is semi-structured because, although the interview centres on a topic, it is conducted in a setting that is comfortable for the participants and allows flexibility on the progress of the discussions. It allows an individual a

choice to explain or clarify their point of view or to make no response at all. It also allows other members of the group to develop issues that others have raised. This is an advantage when working with teachers as interactions lead to a wealth of ideas and increases flexibility whereby the parties “generate and answer research questions” (Morgan, 1997, p. 18). The data collected from focus groups complement the data collected from the individuals through questionnaires. Morgan (1997) notes that a focus group interview is limited to verbal behaviour and leads to difficulty in identifying interactions within the group. The interaction between the researcher and the group may also lead to bias. Another limitation is the time it takes to conduct the interview and the expense in time and resources of arranging focus group interviews when compared to a questionnaire (Burns, 1997).

This research project use both interviews and focus group interviews to develop the issues that have been raised in the questionnaires (Appendix E).

3.5.3 The researcher!s role

Although the perspective of principals and teachers were central to this study, the researcher, as the primary instrument for collecting and making meaning of that data, was central in its outcome and any potential bias should be stated explicitly (Merriam, 1998). Current experience of teaching mathematics to students in the primary sector and developing personal mathematical knowledge through in-house and tertiary professional development meant that the researcher had realistic expectations of effective professional development in mathematics. He also had expectations of the Principal as lead learner and knew that the Best Evidence Synthesis on school leadership and student outcomes (Robinson, et al., 2009) showed that the highest effect size a school leader could expect was from promoting and participating in professional development opportunities.

By its very nature, qualitative analysis incorporates subjective assessments by the researchers who can never honestly be neutral (Creswell, 2009). Through the conscious awareness that this may be so, this researcher did what Tolich and Davidson (1999) describe as metaphorically wearing two hats. The identity of a teacher needed to be consciously replaced with the clearly defined role of the researcher in order to remain objective.