Interviews

In Phase 2, open-ended interviews were conducted as a means of elaborating on responses given through the ATMI (Schackow, 2005). Further, the interviews assisted in the identification of factors contributing to each teacher‟s attitude formation. These qualitative interviews were characterised by the conversational manner in which they were conducted (Rubin & Rubin, 2005). According to Rubin and Rubin (2005), the interviewing process should have three organisational components to ensure depth, detail, and vivid answers. These components are: (a) the main questions, (b) the follow-up questions, and (c) the probes.

The main questions were created from the research topic (Rubin & Rubin, 2005).

The wording of these questions contained terms used in the research questions. The following open-ended questions were available to guide the conversation with each participant:

Your results from the ATMI (Tapia, 1996) suggest that you have a strongly positive/neutral attitude towards mathematics. Can you tell me more about your attitude to mathematics?

Can you tell me about how or when this attitude formed?

Can you recall specific incidences which might have contributed to the formation of your attitude towards mathematics?

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How does your attitude towards mathematics affect your teaching of mathematics?

Whilst these questions were used as a guide, they were altered or omitted depending on the progress of the interview (Moustakas, 1994). However, leading questions were avoided because they would have influenced the responses and the direction in which the conversation went (Seidman, 2006).

Follow-up questions related directly to what the participant had stated during the conversation. Answers to follow-up questions provided depth and detail as they encouraged elaboration and nuance (Rubin & Rubin, 2005). Some of these questions related back to specific responses given in the ATMI (Shackow, 2005). If a participant, for instance, answered a follow-up question, with a contradicting response, additional follow-up questions were used to clarify and expand the participant‟s response. For example,

Your attitude was identified as positive yet you have recounted experiences in a negative manner which contradicts your survey responses. Can you explain the difference between your survey response and your interview response?

The probes were used to extend the conversation, ensuring that enough detail and clarification was obtained throughout the conversation. Probes were used to seek in-depth responses when participants may have responded without detail or with a general statement. For example,

I noticed that you mentioned particular teaching methods in your preservice course as contributing to the formation of your attitude towards mathematics. Can you elaborate further?

Seidman (2006) argues that individual interviews should not be rushed in order to gather an adequate amount of information from each participant. In accordance with this, the length of the interview was determined largely by the participants‟ responses, but on average lasted approximately fifteen minutes. The interviews were audio recorded and later transcribed.

47 3.3.4 Data analysis

The following sections outline the procedures used in the analysis of the ATMI (Schackow, 2005) and the interview data. The first section discusses the scoring protocols used in the analysis of the survey data (Section 3.3.4.1). The second section outlines how themes were identified within the interview data (Section 3.3.4.2).

3.3.4.1 Analysis of the Attitude Towards Mathematics Inventory

The question of What attitudes do early years teachers hold towards mathematics?

was explored through the ATMI (Schackow, 2005). This survey contains four attitudinal components: value, enjoyment, self-confidence and motivation (see 3.3.3.1). Consistent with the scoring protocol for this instrument, scores were calculated for each of the 20 participants on each of these components as well as an overall attitude score which combined all four components. To allow summation of attitude components, total scores were calculated. This set of scores informed the question of What attitudes do early years teachers hold towards mathematics? Five levels of attitude were created for this Master‟s project using the scores for ease of attitude identification. These levels were strongly positive, positive, neutral, negative and strongly negative.

Comparative analysis (Ragin, 1994) was conducted using the survey data. In this way, similarities and differences were identified within the results. A table (see Table 4.3) and bar graph (see Figure 4.1) were used to present the findings and provide a visual interpretation for ease of data comparison. The data were analysed in three ways: total scores, subscale scores and attitude group (positive and neutral) scores. First, the teachers‟ total scores were calculated. In doing so, the teachers were assigned their attitude level of strongly positive, positive, neutral, negative or strongly negative. These data were primarily used in the selection of the six teachers to interview. Second, the survey results from the six teachers identified to participate in the interviews were analysed in terms of the four subscales: value, enjoyment, self-confidence and motivation. The subscales are considered to be the underlying dimensions of attitude (Tapia, 1996). The data provided critical information used in the analysis of the interviews by identifying the influence of each dimension of attitude (subscales) in the formation of the teachers‟ attitudes. Third, the total scores and subscale scores from the positive group were compared to those of the neutral

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group. These scores were used in conjunction with interview comments made by teachers, during the analysis of process (see Chapter 4) to provide possible explanations. They also allowed for trends to be identified amongst the teachers.

3.3.4.2 Analysis of interview data

The question of How did these attitudes form? was investigated through an analysis of six representative teachers‟ responses to the open-ended interviews. Data on the attitudes teachers hold were used to triangulate the survey data. Credibility was improved through the use of triangulation, whereby two sets of data, being the ATMI (Schackow, 2005) and the interviews, were used to answer the research questions (Creswell, 2008). These data provided an insight into how teachers perceived their attitudes towards mathematics formed. The analysis of the interviews followed Yin‟s (2003) explanation building format, where the data collected was used to create a theory about attitude formation in early years teachers. In this way, experiences leading to each participant‟s attitude formation were explained.

In order to identify themes from the interview data, the process of pattern coding was adopted. Pattern coding identifies themes within the data. This process pulls together large amounts of data into more workable sets (Miles & Huberman, 1994). Within the data, pattern coding (Miles & Huberman, 1994) identified three stages of education influencing the teachers‟ attitude formation being experiences recalled from primary school, secondary school and tertiary studies. The identified themes acted as a way to collate a lot of material into smaller and more meaningful units to analyse (Miles & Huberman, 1994). Within these stages of education, teachers‟ comments were further explored using the four dimensions of attitude:

value, enjoyment, self-confidence and motivation. Further, within the dimensions of attitude, comments made by teachers containing similar content were grouped.

Analysing the teachers‟ comments according to these dimensions provided a clear picture of the importance of each dimension during the three stages of education identified by the teachers as well as the importance of each dimension for the differing attitudes. Survey data were referred to where comments matched ATMI (Schackow, 2005) scores or where disparity was evident between scores and interview responses.

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3.4 Quality and Rigour of the Study

The quality and rigour of the study was addressed in three ways. First, through the reliability of the survey (Section 3.4.1); second by the trustworthiness of the data collection methods (Section 3.4.2); and third by the ethical conduct of the study (Section 3.4.3).

3.4.1 Reliability

The reliability of a survey or its ability to produce similar scores across multiple administrations is an important consideration when selecting a survey (Burns, 2000).

Reliability of the results may have been compromised due to particular wording used in the statements (De Vaus, 2002). For example, if the participant did not understand a statement or interpreted it differently from the researcher‟s purpose then the results might not reflect the participant‟s true attitude. However, using a well-established survey with high internal validity addressed the issues of reliability. The previous uses of ATMI (Schackow, 2005; Tapia, 1996; Tapia & Marsh, 2002) have shown that measures of internal consistency were high, indicating high reliability.

3.4.2 Trustworthiness

Throughout the research process, issues of trustworthiness (credibility, confirmability and generalisations) were observed. Credibility, in terms of the open-ended interviews involved establishing that the results were credible or believable from the participant‟s perspective. To ensure credibility, participants were invited to read through the transcripts of their interview to ensure that a true and accurate account was reported (Burns, 2000).

Confirmability was assured through the use of a peer reviewer (i.e., supervisor) to independently analyse and interpret some of the data. Any discrepancies between the researcher‟s and the peer reviewer‟s coding was resolved through discussion. Adopting this strategy ensured that interpretations and conclusions were questioned (Burns, 2000).

Statistical generalisations or transferability for the study was inappropriate due to the method of participant selection because convenience sampling does not provide a group of individuals representative of the population (Creswell, 2008).

Therefore, results cannot be transferred to the general population (see Section 5.3).

50 3.4.3 Ethical considerations

Ethics approval was sought and approved for this study from Queensland University of Technology and the study was conducted in accordance with the National Statement on Ethical Conduct in Human Research (2007) (Approval # 0900001179).

This was a low risk research project as there was only one identified risk being discomfort during or following the interviewing process as participants were asked to discuss their attitude towards mathematics. Some teachers may have felt that by identifying themselves as having a negative attitude their professionalism would be compromised. All participants completed surveys (see Appendix A) and took part in interviews voluntarily. Issues concerning the participants‟ right to withdraw from further participation at any time were discussed with them prior to commencement.

All teachers and the school principal and junior school principal were provided with information about the study and informed consent was obtained from each participant (Rubin & Rubin, 2005). Participants were provided a consent form regarding the banking of their data for possible future projects. Consent for the teachers‟ participation was also obtained from the junior school principal who was the teachers‟ supervisor. A copy of the information pack and the consent form for the teachers and the principals is provided in Appendix C. Ethical considerations for this study include anonymity for the teachers and school. This was addressed by using pseudonyms in all reporting (Burns, 2000).

3.5 Chapter Summary

This study adopted an explanatory case study design (Yin, 2003) in order to identify teacher attitudes to mathematics and the formation of these attitudes. The design consisted of two sequential phases of data collection. Quantitative data were collected in Phase 1 and qualitative data were collected in Phase 2, as per explanatory case study design. Phase 3 consisted of data analysis in which both the quantitative and qualitative data were analysed separately and also compared.

Participants were selected through convenience sampling. They all taught at Lower Creek School, a Brisbane southside school, from a middle socio-economic area approximately 25 km from central Brisbane. Data from participants were collected through the ATMI (Schackow, 2005) and open-ended interviews. The ATMI (Schackow, 2005) identified each teacher‟s attitude towards mathematics. From

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these data, six teachers with varying attitudes were invited to participate in the interview process. The interview identified consistencies and inconsistencies between the survey results about the attitudes that teachers hold and investigated how the teachers‟ attitudes formed.

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4 Results

4.1 Chapter Overview

This study investigated early years teachers‟ attitudes towards mathematics and how these attitudes were formed. Data were collected through an attitude survey (Schackow, 2005) (Appendix A) and open-ended interviews (Appendix D). Twenty early years teachers completed the Attitude towards mathematics inventory (ATMI) (Schackow, 2005) to identify their attitudes towards mathematics. Six teachers representing a range of attitudes were then selected to participate in open-ended interviews (see Section 3.3.2).

This chapter has five parts. The first part of this chapter presents the survey results and identifies the six teachers who were interviewed (Section 4.2). The second part presents the data collected from the open-ended interviews conducted with the teachers along with the themes identified within the data (Section 4.3). The third part focuses on teachers with positive attitudes and presents the experiences that these teachers attribute to the development of their attitudes towards mathematics (Section 4.4), a comparison of the survey and interview data (Section 4.5), and how the results of this study relate to the existing literature (Section 4.6). The fourth part focuses on teachers with neutral attitudes and presents the experiences that these teachers attribute to the development of their attitudes towards mathematics (Section 4.7), a comparison of the survey and interview data (Section 4.8), and how the results of this study relate to the existing literature (Section 4.9). The fifth part compares the findings of the positive teachers and neutral teachers (Section 4.10) and the long-term impact of schooling experiences on the teachers interviewed (Section 4.11).

4.2 Survey Results

Phase One of this study used a survey instrument to investigate the research question, What attitudes do practising early years teachers hold towards mathematics? The ATMI (Schackow, 2005) is a 40 item instrument that measures attitude through the four subscales of value, enjoyment, self-confidence and motivation (Section 3.3.3.1).

Results from the ATMI (Schackow, 2005) were used to identify the types of attitudes existing amongst the 20 teachers participating in this study (Section 4.2.1). The teachers‟ scores were then used to identify six focus participants, representing a

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range of attitudes, who would be interviewed in order to investigate how their attitudes formed (Section 4.2.2).

4.2.1 Overall survey results

The ATMI (Schackow, 2005) was completed by 20 teachers employed at Lower Creek School. This inventory was administered and a total score was calculated for each teacher based on their responses to the 40 statements. Teachers responded to each of the 40 statements by indicating their level of agreement with each statement.

Schackow‟s (2005) scoring scheme was implemented (see Section 3.3.3.1). Just as Schackow (2005) calculated summative scores, scores were calculated for each interview participant. The teachers‟ total scores on the ATMI (Schackow, 2005) were used to infer how positive their attitudes were towards mathematics.

For the purpose of this Master‟s study, teachers‟ attitudes were categorised into five levels for ease of attitude identification: strongly negative, negative, neutral, positive and strongly positive (see Table 4.1). These categories were assigned by identifying the possible range of each participant‟s score by five. A range of 160 was identified with the lowest possible score of 40 (rating of 1 on each of 40 statements) and the highest possible score of 200 (rating of 5 on each of 40 statements). Divided the range of scores as evenly as possible by the five levels, each category cumulatively increased by 31 points:

Table 4.1

Scoring Ranges on the ATMI

Scoring Range Attitude

40-72 Strongly negative

73-104 Negative

105-136 Neutral

136-168 Positive

169-200 Strongly positive

The attitude scores of each of the 20 teachers surveyed can be found in Table 4.2.

The six focus teachers for interview are also identified on this table. Their selection is discussed shortly. After the 20 teachers‟ survey responses were scored, only three categories of teacher attitude were identified. These were strongly positive, positive

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and neutral, with no teachers identified as having negative or strongly negative results (Table 4.2). No teachers were found to have negative or strongly negative attitudes towards mathematics. This is in contrast to the findings of Kolstad and Hughes (1994) who reported that 34% of Kindergarten to Year 4 teachers held strongly negative attitudes towards mathematics. This discrepancy between Kolstad and Hughes‟ (1994) findings and the outcomes of this study suggests that further investigation of this topic is warranted. A possible reason for the absence of negative and strongly negative attitudes found amongst the participants of this study, may relate to the fact that the surveys were not anonymous. Further, the teachers may have been hesitant to divulge their true feelings due to their collegial relationship with the researcher.

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A key purpose of the survey was to select six teachers for indepth interviews.

The purpose of the interviews was to identify how they perceive their attitudes formed (Section 4.3). The original intent was to identify a representative group of teachers with a range of attitudes in order to interview two teachers with positive attitudes, two teachers with neutral attitudes and two teachers with strongly negatives attitudes towards mathematics. However, the results from the 20 surveys revealed the absence of a single teacher with a negative or strongly negative attitude (see Table 4.2). Further, the strongly positive teacher (Teacher 1) and the two teachers scoring highest in the neutral range (Teacher 14, Teacher 15) declined to be involved in the interview process. Therefore, to reflect maximum variation in attitudes, the two

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teachers with the closest scores to the strongly positive range (Bianca, Mary) were selected for interview. The interview group containing neutral teachers was represented by Linda and Yvonne as they were the top two teachers with neutral attitudes who agreed to participate in the interview process. Lily and Sandra were included in the absence of teachers with negative or strongly negative attitudes. The reason for including the two additional neutral teachers was that they would seem more likely to give some insight into negative views as opposed to adding either strongly positive or positive teachers in the interview cohort. Unfortunately, the neutral teacher (Teacher 20) with the lowest attitude score was unavailable for interview. Thus, using the positive and neutral teachers it was hoped to obtain insight into the broadest range possible of teacher attitudes within this cohort.

4.2.2 Subscale scores

The ATMI (Schackow, 2005) has four subscales: value, enjoyment, self-confidence and motivation. These subscales are considered to be underlying dimensions of attitudes towards mathematics (Schackow, 2005; Tapia, 1996). For example, the following statement is found within the category of enjoyment: I have usually enjoyed studying mathematics in school (see Appendix A). Subscale scores were calculated for the six selected teachers and are presented in Table 4.3. Due to different numbers of items per subscale, both total scores and percentages are presented.

58 Table 4.3

Subscale Results from the ATMI (Schackow, 2005)

TOTAL SCORE/200 TOTAL SCORE % Value/50 Value % Enjoyment/50 Enjoyment % Self-confidence/75 Self-confidence % Motivation/25 Motivation %

Positive teachers

Mary 167 83.5 45 90.0 42 84.0 61 81.3 19 76.0

Bianca 161 80.5 45 90.0 36 72.0 64 85.3 16 64.0

Neutral teachers

Linda 119 59.5 41 82.0 28 56.0 32 42.7 18 72.0

Yvonne 118 59.0 40 80.0 24 48.0 43 57.3 11 44.0

Lily 117 58.5 42 84.0 21 42.0 42 56.0 12 48.0

Sandra 114 57.0 40 80.0 22 44.0 34 45.3 18 72.0

The teachers‟ subscales scores on the ATMI (Schackow, 2005) provide some indication of the contribution of value, enjoyment, self-confidence and motivation towards their mathematics attitude. The six teachers‟ subscale percentages are presented in Figure 4.1 for comparative purposes. The results for value, enjoyment, self-confidence and motivation were later compared with their interview responses relating to these dimensions of attitude (Section 4.5, 4.8).

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Figure 4.1. Teachers‟ ATMI total and subscale scores.

Value statements refer to mathematics being worthwhile and necessary (Hannula, 2002). Valuing mathematics also relates to a desire to develop mathematics skills as well as valuing the role mathematics plays in our everyday and professional lives. The percentage scores relating to the value statements in the inventory are similar across all teachers with a range of 80.0% to 90.0% (Figure 4.1, Table 4.3), suggesting that, although their overall attitudes vary, all six teachers valued mathematics.

Enjoyment statements refer to feeling satisfaction when solving problems and enjoying challenges (King, 2006; Ma, 1997; Thorndike-Christ, 1991). They also relate to the feeling of happiness experienced as well as the level of interest held for the subject. The enjoyment scores varied greatly between the positive teachers Mary and Bianca (average 78.0%) and the neutral teachers Lily, Linda, Sandra and Yvonne (average 47.5%). In contrast, the scores relating to value showed little variation (90.0%

average for positive c.f. 81.5% average for neutral). The enjoyment scores suggest that the teachers with positive attitudes enjoyed mathematics where the teachers with neutral attitudes enjoyed it less.

Self-confidence statements relate to expectations about doing well, solving problems without difficulty and how easily new concepts are learnt (Goolsby, 1988;

Self-confidence statements relate to expectations about doing well, solving problems without difficulty and how easily new concepts are learnt (Goolsby, 1988;