Mathematics Course and Students’ Professional Vision

Methodology

Introduction

The purpose of this research was to examine how the specific course in mathematics could change the students’ visions of their professional competence. In order to examine how experiences in learning the aspects of the mathematics methodology course and in teaching mathematics could affect teachers’ self-efficacy, both quantitative and qualitative methods of data collection and analysis were employed throughout the investigation. The study was conducted involving students of Indiana University of Pennsylvania. The study was carried out in two phases in order to receive the accurate information regarding the students’ efficacy beliefs during different stages of learning aspects of the mathematics methodology course.

Specific methodology, research strategies, and approaches discussed in this chapter were used to provide a research framework in order to answer the following research questions:

  1. How do the teaching efficacy beliefs of elementary pre-service mathematics teachers differ between the beginning and end of a mathematics methodology course?
  2. What are the pre-service teachers’ understanding of their skills, competence, and ability to teach mathematics?
  3. What features of teaching context affect the self-efficacy beliefs of pre-service educators?

The questions were answered with the help of both qualitative and quantitative research designs. The first question aimed to discuss the relations between variables, and the second and third questions were important for understanding the experiences and beliefs of pre-service teachers.

Research Design

The study adopted a mixed-methods research approach in its attempt to not only examine pre-service elementary teachers’ sense of self-efficacy in relation to teaching mathematics but also to analyze how experiences in teaching mathematics could affect self-efficacy. The advantages of the mixed-methods research are in possibilities to use quantitative and qualitative research methods sequentially in order to research a certain phenomenon in detail (Lampert, 2001; Creswell & Clark, 2011). Mixed-methods studies have evolved from the paradigm debates on the effectiveness of qualitative and quantitative research studies (Creswell & Clark, 2011). These approaches were discussed as important to be used in educational research due to their capacity to yield informative and valuable data in order to generate a cumulative body of knowledge (Creswell, 2007; Creswell & Clark, 2011).

Quantitative research not only underscores the measurement and analysis of causal relationships between isolated variables within a framework which is value-free, logical, reductionist and deterministic, but it also endorses the perspective that psychological and social phenomena have the objective reality that is independent in relation to the subjects being studied (Creswell, 2009). According to Gay and Airasian, quantitative data are used to describe certain conditions, and quantitative research is used to analyze the link between various variables (Gay & Airasian, 2000). Thus, the current study utilized quantitative methods in order to work with the descriptive quantitative data. It is important to note that the use of quantitative descriptive data allowed the researcher to assess the current condition of beliefs held by mathematics teachers in relation to self-efficacy (Creswell & Clark, 2011; Gay & Airasian, 2000). The participants were able to assess themselves using the survey sheet, and such self-assessment helped them rate their ability to teach mathematics. Additionally, the quantitative research approach provided the researcher with the leverage to use objective means of the data analysis to investigate the ability of teachers to teach mathematics and also to investigate the relationship between components of mathematics methodology course and its impact on the teachers’ self-efficacy related to mathematics.

The qualitative research approach was important in determining the opinions of the participants in relation to variations in the methodologies used to teach mathematics. The correlational data were analyzed to understand the relationship between learning the components of mathematics methodology and its impact on teachers’ mathematics self-efficacy (Bandura, 1993; Hall & Ponton, 2005). An interpretation of the qualitative research findings along with the quantitative research findings provided information on the teaching methods that produced the best results for teachers (Johnson & Onwuegbuzie, 2004). The argument for using the mixed-methods research approach was the necessity to assist the researcher in discussing the relationships between various variables of interest through quantitative means, and also to understand the experiences of pre-service teachers using the qualitative means (Brown, 2012; Creswell, 2009; Creswell & Clark, 2011).

The used mixed methods are described as the specific class of the research when it is possible to combine different research techniques and concepts in a single study in order to achieve the desired result (Creswell, 2009; Creswell & Clark, 2011; Hall & Ponton, 2005; Johnson & Onwuegbuzie, 2004). In this research, the mixed method approach was used with focusing on a survey and face-to-face interviews with the participants. First, the quantitative data was collected and analyzed in order to increase the quality of the research (Creswell, 2009; Creswell & Clark, 2011; Johnson & Onwuegbuzie, 2004). Thus, the stages of the quantitative survey were conducted before the administration of the qualitative survey in the form of interviews.

Quantitative Research

Quantitative research was used to test objective theories through the examination of the relationships between the measurable variables. The quantitative data was used to provide the broader understanding of the research problem through the data collected from the participants (Creswell, 2009). Following Creswell and Clark, the quantitative approach added such strengths to the research as 1) a possibility to use the numerical data; 2) independence of the results of the research; and 3) a possibility to focus on the deductive and explanatory statistical analysis (Creswell & Clark, 2011; Johnson & Onwuegbuzie, 2004). The quantitative approach was used in this research in order to provide a numerical array of the elementary mathematics teachers’ opinions through a study of a sample of the population (Creswell & Clark, 2011; Hackett & Betz, 2009; Johnson & Onwuegbuzie, 2004). It is important to state that the quantitative approach is effective in order to provide the most accurate data regarding the observed and studied phenomenon that can be used in order to conclude about the certain relationship between the variables.

Qualitative Research

The qualitative research was used in order to explore and understand meanings that the future pre-service teachers associated with or added to their vision of self-efficacy and mathematics methodology (Creswell, 2009). The qualitative research provided the important qualitative data to analyze with the help of coding and identifying themes. The qualitative research was chosen because it 1) offered an understanding of personal experiences of the subjects, 2) provided participating teachers with the opportunity to describe their experiences in detail, and 3) made it possible to focus on cross-case comparisons (Creswell & Clark, 2011; Johnson & Onwuegbuzie, 2004). In this study, the qualitative data was collected through face-to-face interviews based on a moderated questionnaire. All participants responded a set of eight questions. Additionally, the systematic and thematic analyses were used for the work with the interview data (Creswell, 2009; Hackett & Betz, 2009; Johnson & Onwuegbuzie, 2004). In this study, the qualitative data collection aimed to present the personal information from the participants.

Selection of Research Participants

Pre-service early childhood teachers taking the course in mathematics methodology at Indiana University of Pennsylvania were invited to participate in the study. In order to obtain the faculty agreement regarding the participation of 30 students in the study, the researcher provided the department chair with a consent letter, and a study began when the consent was obtained from the department chair and the faculty members via email. Pre-service teachers were recruited as participants for the study in the class after the approval from the department chair and the faculty members was received.

Purposeful Sampling

A purposeful sampling approach was used in the research (Creswell & Clark, 2011). Purposeful sampling enables the researcher to focus on the population which characteristics address the research’s needs. According to this technique, participants were selected according to certain inclusion and exclusion criteria (Creswell, 2009). Following the inclusion criteria, only students who were majoring in the early childhood education and who were enrolled in a mathematics methodology class at Indiana University of Pennsylvania were invited to participate in the study. Those future pre-service teachers who were not taking the mathematics methodology course were excluded from the participation in the study. This approach allowed the researcher to focus on studying how students enrolled in a mathematics methodology class can evaluate their self-efficacy in relation to teaching.

Population Characteristics

While focusing on the specific population’s characteristics, it is important to state that 30 students of Indiana University of Pennsylvania studying the mathematics methodology course were invited to participate in the study because they were selected according to the inclusion criteria. There were 70% of the female students and 30% of male students involved in the study because of the particular features of the population studying the early child education courses at the university. The participants’ age was determined to be between 20 years and 30 years.

Study Site

The site selected for the study is Indiana University of Pennsylvania. Thus, Indiana University of Pennsylvania is a large public university that serves more than 12,000 undergraduates and about 3,000 graduate students. Indiana University proposes two courses in Mathematics as requirements for students majoring in early childhood education. The courses prepare future teachers to using mathematical concepts effectively while teaching young learners (Enochs, Smith, & Huinker, 2000). One of the key courses at Indiana University of Pennsylvania for elementary teachers is the course in Mathematics for Early Childhood Education. The course incorporates concepts and studies used in school mathematics programs. Teachers learn how to help children understand basic mathematical concepts using manipulative materials. The topics covered in this course form the foundation for the student’s understanding mathematical concepts. Another offered mathematical course examines the contemporary curriculum and methods of instruction used in school mathematics. Topics covered in this course include statistics, problem solving, probability, and geometry. These courses were the target because of the topic of the research.

Instruments for Data Collection

Quantitative and qualitative instruments were used in this study in order to received the complete information regarding the per-service teachers’ self-efficacy beliefs and experiences in teaching. The quantitative data were gathered with the help of the Mathematics Teaching Efficacy Belief Instrument (MTEBI) that was developed by Enochs, Smith, and Huinker (Enochs et al., 2000). This instrument was used during the first phase of the survey, including two stages of the quantitative research. The qualitative data were obtained through conducting face-to-face interviews with the participants that were based on the use of a questionnaire developed by the researcher to address the important aspects associated with the investigation.

The Mathematics Teaching Efficacy Belief Instrument (MTEBI)

The Mathematics Teaching Efficacy Belief Instrument (MTEBI) developed by Enochs, Smith, and Huinker was used in the research in order to determine the students’ self-efficacy rating regarding their successes in teaching mathematics at the beginning and final stages of taking the mathematics methodology course (Enochs et al., 2000). Thus, the MTEBI scale was used in order to determine the possible development in the pre-service teachers’ beliefs regarding their success in teaching mathematics. The used MTEBI is a modification of the Science Teaching Efficacy Belief Instrument (STEBI-B) developed by Enochs and Riggs in 1990 (Bleicher, 2004). The instrument employs a five-point Likert scale and includes 23 items divided into two subscales (Enochs et al., 2000). The first subscale is Personal Mathematics Teaching Efficacy (PMTE) subscale which has 13 items. The second one is the Mathematics Teaching Outcome Expectancy (MTOE) subscale which includes 10 items (Enochs et al., 2000). The two subscales of the MTEBI were adapted to become understandable for teachers in order to guarantee accuracy of answers regarding the self-efficacy beliefs at different stages of the survey (Enochs et al., 2000).

The validity and reliability of the MTEBI is supported with many studies. The MTEBI was often used in studies involving the assessment of the self-efficiency of teachers (Bandura, 1993; Enochs et al., 2000). Enochs and the group of researchers conducted the reliability analysis according to which the alpha coefficient for the first subscale was 0.88, and it was 0.75 for the second subscale (Enochs et al., 2000). As a result, it is possible to speak about the high level of the instrument’s reliability. Furthermore, the confirmatory factor analysis was indicated to state the high level of the MTEBI’s validity.

The Interview Questionnaire

The interview questionnaire was designed in order to conduct the follow-up interviews and gather the information regarding the participants’ opinions on taking the mathematics methodology course and its effectiveness for their teaching practice. Nine open-ended questions were developed by the researcher to include in the interview questionnaire (Appendix A). The interview questions were constructed in correspondence to the research questions so that the participants could provide more detailed information and express their opinions and experiences completely. The questions asked about observed changes in the teachers’ experience, helpfulness of the course, and about possible changes in teachers’ strategies and vision of their success. Thus, the questions helped establish the relationship between the mathematics methodology class and teachers’ vision of self-efficacy (Creswell, 2007). All participants responded to the same questions. In order to contribute to the reliability and validity of the used instrument for conducting interviews, the questions were revised according to the experts’ commentaries

Data Collection Methods

The researcher obtained the approval to conduct the study from the coordinator chair of the Mathematics Department at the university and got permission from all faculty members in order to administer a survey in students’ classes. The students’ participation in the study was voluntary. The researcher organized the appropriate schedule for the data collection while cooperating with the Mathematics Program coordinator at Indiana University of Pennsylvania. The class periods for collecting the quantitative data were determined during the second and last weeks of the semester. The collection of the quantitative data was discussed as the first phase of the research. A graduate research assistant was invited to help in distributing the survey in the class, organizing the work, and collecting materials. A research assistant was identified by the faculty member supporting the study to decrease suspicion or possible coercion related to the researcher and professor.

The quantitative data were collected as a result of two stages of the survey. During the second week of studying the mathematics methodology, students were asked to participate in the first stage survey. The determined time for completing the first stage of the survey was 15 minutes. The research assistant distributed a survey packet for students including the survey informed consent letters, the Mathematics Teaching Efficacy Belief Instrument (MTEBI) survey, mathematics worksheets for those students who chose not to complete the survey, and the interview consent forms for participants. Mathematics worksheets were distributed to avoid the identification of participants by peers in the class. The assistant explained the instructions provided in the forms. The participants were informed about the voluntary character of participating in the study and completed the consent forms. The participants completed the MTEBI survey worksheets and put them into an envelope near the entrance in the classroom. Participants who chose not to participate in the study put their worksheets into the same envelope as the other students. The participants of the survey were also involved into a drawing to win a gift certificate to visit a restaurant after the survey. The participants’ names were not used after the drawing.

The second survey was conducted before the end of the course. The determined time for completing the second stage of the survey was 15 minutes, as it was during the first stage. The students filled in the MTEBI worksheets and put them into an envelope. The research assistant provided students with the voluntary consent letter for the interview and with a contact information form for those students willing to be interviewed. After the students have completed the consent forms and the second survey, they deposited them into an envelope near the entrance to the classroom.

During the second phase, the researcher interviewed the students willing to participate in the study. Focusing on the information provided in the consent forms and letters, six volunteers were determined to participate in the interview. The researcher contacted students via email using the previously provided contact information. The details regarding the place and time of the interview for all participants were arranged individually. The interviews were conducted during the final week of the semester, after the students have completed their mathematics methodology course. Each participant was answering the interview questions during the period of 25-30 minutes. The interviews were recorded using a digital voice recorder after the participants permission had been received (Turner, 2010). The researcher stored the personal information and data safely in the researcher’s house. Confidentiality and anonymity of the participants were guaranteed (Turner, 2010). The interviewees were involved into a drawing to win a gift certificate to visit a restaurant. To compensate the spent time and efforts, the participants were offered a $10 gift card.

Analysis Methods

In order to analyze the quantitative data effectively, statistical analysis tools were utilized. There are two types of statistical analysis methods that are descriptive and inferential statistical analyses. Descriptive statistics refers to the determination of frequency, mean, and standard deviation of the data collected (Creswell, 2009). Inferential statistics is used to determine significances. This statistical method is used when one variable is in a statistically significant relationship with the other variable (Creswell, 2009). In order to conduct the statistical analysis correctly, the researcher used a computer program (Creswell, 2009). As a result, the researcher received the opportunity to interpret the received the quantitative data effectively and formulate appropriate conclusions.

The results of the quantitative survey were analyzed with the help of such a statistical tool as the SPSS (Creswell, 2009; Creswell & Clark, 2011). This program allowed the researcher to conduct the complete descriptive and inferential statistical analyses. The use of the computer software was necessary in order to be able to present the most accurate results and to state the relationship between the variables in order to conclude about the observed correlations (Cohen, 1988; Creswell, 2009; Creswell & Clark, 2011). The frequency, mean, and standard deviation related to the Likert scale questions were determined as the part of the the descriptive statistics (Creswell, 2009; Creswell & Clark, 2011). The focus was on discussing the variances of the participants’ responses that revealed general trends in the data (Cohen, 1988; Creswell, 2009; Creswell & Clark, 2011).

The analysis of the qualitative data was based on the process of coding and identification of thematic patterns in the participants’ answers to the interview questions. First, the researcher focused on transcribing the recorded interviews and reviewed the data in order to pay attention to all the details mentioned in the participants’ responses (Cohen, 1988; Creswell, 2009; Creswell & Clark, 2011). The material was read several times in order to code different segments of the qualitative data according to the determined themes (Turner, 2010). Having coded the data, the researcher organized the qualitative material using the themes (Turner, 2010). The emergent and main themes characteristic for the qualitative data were identified as a result of the qualitative data analysis stage.

Summary

The purpose of this research was to examine how the specific course in mathematics could influence the changes in the students’ visions of their professional competence. A mixed-methods approach was selected for conducting the research as effective to examine how experiences in learning the aspects of a mathematics methodology course can influence the teachers’ self-efficacy. Quantitative and qualitative methods of data collection were employed throughout the investigation in order to examine the visions of students of Indiana University of Pennsylvania regarding self-efficacy. The quantitative research was realized in two stages during which participants completed the surveys with the help of the Mathematics Teaching Efficacy Belief Instrument (MTEBI). The qualitative research involved those students who agreed to participate in the follow-up interviews. To explore the teachers’ self-efficacy beliefs, the researcher asked six participants to answer the open-ended interview questions prepared in correspondence with the topic of the research. The quantitative data were analyzed with the help of the SPSS software appropriate to calculate the statistical variances. The qualitative data was analyzed with the focus on coding the participants’ responses and identifying the themes regarding the participants’ self-efficacy beliefs and visions of their successes in teaching after completing the mathematics methodology course.

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