Abstract The central research question of the study asks: how do middle school students experience learning mathematics in middle school mathematics class? The additional research questions that guide the study ask: what are some of the barriers to learning mathematics in middle school mathematics class and what causes students to understand certain mathematics concepts in middle school mathematics class?
The purpose of the study is to discover and understand middle school students’ experiences learning mathematics in middle school mathematics classes. Qualitative methods are utilized, and a basic design is employed that uses the interview, document collection, and field notes in order to gather data.
The results of the study show repetitive themes communicated by the participants related to how hard middle school mathematics is, how students have to work on mathematics problems by themselves, the fast pace at which middle school students have to work, student disruptions in the mathematics classroom, students playing and talking in the mathematics classroom, and that there are many skills, tools, and resources within the middle school mathematics class that help middle school students learn mathematics.
It is concluded that learning mathematics in middle school mathematics classes can be an intimidating experience especially in light of the fact that some of the teachers give little help and that the pace at which some teachers move may be a little too fast for some students. It is also concluded that middle school mathematics students cannot learn mathematics effectively in the presence of competing stimuli such as students talking about things other than mathematics or students simply playing in class.
Conversely, however, it is concluded that students have positive experiences learning and understanding mathematics in middle school mathematics classes as a result of certain skills, tools and resources being in place. Based off of the findings of the study, it is recommended that the study be replicated using other American sub-cultures, the “new” findings of the study be tested as hypotheses, the data from the study be rereviewed, and that the study be completed using observations as the primary means of data collection. Dedication I thought long and hard about to whom (or what) this work should be dedicated.
The list would be too many if I were to dedicate to the many possible prospects. As such, I finally remembered who was there with me—unconditionally—up to and through this point in my 44 years on this earth. So, I dedicate this work to myself. Selah. iv Acknowledgments To me, it would make no sense whatsoever if I did not acknowledge my Lord and Savior, Jesus Christ. It would be almost just as nonsensical if I did not acknowledge my wife and children who endured the time I took away from the family as I completed this dissertation—for the former, all praise is due, and, for the latter, thanks for hanging in there with me.
This work represents the culmination and expression of a journey I began many years ago. Beyond the journey, the completion of this dissertation is the truest of paradoxes in that it is the beginning of the end. Yes, the acknowledgements already made go without saying; however, and unbeknownst to many, acknowledgement must be made to an individual who is responsible for the impetus and motivation that is and has been an integral part of my journey from having no high school diploma to completing a terminal degree.
This individual was the only person who had the effect on me that engendered a desire to embrace education, so (just under God—smile), one of my greatest acknowledgments go to (the then) Lieutenant Michael Evans (during our tour at the Anti-Submarine Warfare Operations Center [ASWOC] at Guam). I can say with an utmost of certainty I would not be making this acknowledgment if it were not for all of his positive words about the importance of education and the related encouragement about why I should embrace it—Thanks Lieutenant Evans. v Table of Contents Acknowledgments List of Tables CHAPTER 1.
INTRODUCTION Introduction to the Problem Background of the Study Statement of the Problem Purpose of the Study Rationale Research Questions Significance of the Study Definition of Terms Assumptions Limitations Nature of the Study Organization of the Remainder of the Study CHAPTER 2. LITERATURE REVIEW Theoretical Framework of the Study Mathematics Achievement Mathematics Underachievement In the United States Factors that Impact Mathematics Achievement—the Child Other Factors that Effect a Child’s Achievement in Mathematics Factors that Impact Mathematics Achievement—the Teacher vi v ix 1 1 2 5 6 8 11 11 13 14 16 17 18 20 20 21 24 26 33 37.
Other Problems Linked to the Teacher that may Impact Student Achievement in Mathematics Factors that Impact Mathematics Achievement—School Climate Summary CHAPTER 3. METHODOLOGY Statement of the Problem Research Questions Research Methodology Research Design Population and Sampling Procedure Panel of Experts Sources of Data Validity Reliability Data Collection Procedures Data Analysis Procedures Ethical Considerations Summary CHAPTER 4. DATA COLLECTION AND ANALYSIS Descriptive Data Data Analysis Results Summary vii 42 43 52 57 59 60 60 61 63 65 67 70 72 73 80 86 92 94 95 95 103 105.
CHAPTER 5. RESULTS, CONCLUSIONS, AND RECOMMENDATIONS Summary of the Study Summary of Findings and Conclusion Recommendations Implications REFERENCES APPENDIX A. INTERVIEW QUESTION GUIDE/PROTOCOL APPENDIX B. COMPLETE LIST OF CODES AND THE FREQUENCIES IN WHICH CODES OCCURRED ACROSS ALL CASES/PARTICIPANTS 107 107 109 121 124 127 142 144 viii List of Tables Table 1. Student Demographic Data and Student Dynamics Data for the School District During the 2011-2012 School year 96 Table 2. Participant Descriptive Data Table 3. Participant Responses to Research Question Three 96 119 ix CHAPTER 1.
INTRODUCTION Introduction to the Problem Within American schools, the current standards-based reform prompts school districts to use standardized tests to account for and highlight the academic progress of its students. In short, these standardized tests emphasize core content areas of learning. Of these core areas, mathematics and reading are the subjects upon which most states report (No Child Left Behind [NCLB] Act of 2001, 2002). Between mathematics and reading, today’s American youth experience lower achievement in mathematics than in reading (Boe & Shin, 2005; Ketterlin-Geller, Chard, & Fien, 2008).
Researchers highlight a myriad of factors that have a potential for contributing to why students experience lower achievement in mathematics to include both cognitive and affective explanations (Koutsoulis & Campbell, 2001). However, American mathematics underachievement, at least from grades three and four to grades seven and eight, cannot be explained by a number of important factors since factors that impact mathematics achievement have been shown to be consistent across grade levels through much of the research (Boe & Shin, 2005).
As a result and because little research has been found related to student perceived experiences in mathematics, it is the intent to listen to what the much ignored student in educational research has to say about his or her experiences in mathematics classes. In previous studies, when getting information about or directly from the student, much of the research involves post-secondary students (Anthony, 2000; Moody, 2003). Therefore, the current study attempts to directly garner the collective voices of a small 1
group of regular education middle school students. The study is accomplished by using a qualitative research methodology and a basic research design (Creswell, 2009; Merriam, 2009). Consequently, students participate in face-to-face semi-structured interviews in order to gather data about the experiences they have had in mathematics classes. Incidental to the interview process, documents offered by participants or asked for by the researcher are collected.
Additionally, as suggested by Miles and Huberman (1994), field notes are collected as a third source of data. In turn, in an attempt to “make sense out of text and image data” (Creswell, 2009, p. 183), a systematic process is used to analyze collected data from student participants so as to identify some themes, patterns, and relationships that emerge between the participants’ experiences in mathematics classes and the actual phenomenon of being a part of the middle school mathematics class.
Background of the Study Student learning of mathematics has been characterized as being either cognitive or affective (Singh, Granville, & Dika, 2002; Winstead, 2004). For a long time, researchers have only considered the cognitive aspects of the student when providing explanations for student learning and academic achievement; however, recent research has considered the affective component of the student when providing explanations for learning and academic achievement (Singh et al. , 2002).
Despite the explanation for how students learn, it is now known that there are a number of factors that play a role in student learning and achievement both in general, and more germane to this study, in middle school mathematics classrooms (Stevens, Olivarez, Lan, & Tallent-Runnels, 2004). 2 In a study conducted by Singh et al. (2002), a number of important factors were pointed out as salient pieces to students’ learning of mathematics.
Within middle school mathematics classrooms, a student’s achievement is a behavioral outcome that is impacted by other factors within that environment (Schweinle, Meyer, & Turner, 2006).
More specifically, the researchers of the above mentioned study observed how a mathematics teacher’s instructional practices greatly impact a student’s impetus and subsequent achievement within that environment. Other researchers support the idea that student mathematics achievement is an outcome response that stems from factors such as test-taking, the level of mathematics, task difficulty, self-perception, and utility or intrinsic value (Eklof, 2007; Trautwein, Ludtke, Marsh, Koller, & Baumert, 2006; Watt, 2006).
In the case of test-taking, evidence points towards students taking low-stakes test less serious than high stakes tests (Eklof, 2007). In one study, it was found that a positive correlation existed between providing eighth grade students with a monetary incentive and their subsequent effort and test achievement (O’Neil, Abedi, Lee, Miyoshi, & Mastergeorge, 2004). However, in the same study, it was found that a similar incentive had no effect on twelfth graders and their respective effort and test achievement (O’Neil et al., 2004).
Karmos and Karmos (1984) found that the level of motivation to achieve in mathematics was stronger in boys than in girls, but, in a study conducted by Brown and Walberg (1993), no correlation was found between the level of motivation to achieve in mathematics and the sex of the child. All of the aforementioned research has made it known that test-taking is a factor that impacts student mathematics achievement in both negative and positive ways. 3
Other research has shown that there is a connection between the level of mathematics (i. e. , Pre-Algebra, Algebra, or Geometry) and how difficult the mathematics task is and student mathematics achievement (Trautwein et al. , 2006; Watt, 2006). Both studies conducted by the aforementioned researchers showed that despite the level of mathematics or the difficulty of the mathematics task, boys were still more motivated and displayed higher levels of achievement within higher level mathematics classes.
The level of mathematics was shown to impact student mathematics achievement in the case of middle school students who show a decline in their ability to obtain success in mathematics courses (Eccles et al. , 1993). Another study showed this same diminished achievement ability in mathematics at the high school level (Chouinard & Roy, 2008). A study conducted by Watt (2006) showed, although indirect, the difficulty of mathematics tasks impacts a female student’s mathematics achievement, choices in advanced mathematics classes, and choices in mathematics related career choices.
In similar fashion, student achievement in mathematics has been impacted by such things as the student’s own self perception of mathematics as well as the student’s intrinsic and extrinsic values. Students’ achievement at higher levels of mathematics courses dwindles as they get into higher grades as these higher levels of mathematics are perceived by students as being more challenging (Eccles et al. , 1993; Chouinard & Roy, 2008). In this same vein, Skaalvik and Skaalvik (2004) found that boys may perceive themselves as being better at mathematics than girls.
Other literature suggests that mathematics achievement can be an outcome construct of one’s intrinsic and extrinsic value (Ryan & Deci, 2000). Andrews and Hatch (2002) clarify that intrinsic value is the desire to do something that is self-satisfying while extrinsic value is the desire to do 4 something to get an outside reward (such as pay). Unfortunately, factors that deal with the student and teacher are not the only variables impacting student performance within the United States.
Other researchers have pointed towards the climate of the school as yet another piece that effects mathematics achievement for students within the United states with the brunt of the effects of diminished mathematics achievement being felt by students at the middle school level (Cohen, Pickeral, & McCloskey, 2009; Good & Weinstein, 1986; Kuperminc, Leadbeater, Emmons, & Blatt, 1997; Rutter, 1983). According to Boe and Shin (2005), data from the Program for International Student Assessment (PISA) presents a larger problem that involves American students lagging behind other industrialized nations in mathematics achievement at all grade levels.
For American students in the middle school, 31 percent of included industrialized nations scored better in mathematics. For many of these American students, there are a myriad of factors that come into play that impedes access to and achievement in mathematics; many of these factors have been proven to negatively impact a student’s overall success in mathematics (Center for Teaching/Learning of Mathematics, as cited in Newman, 2008; Pustjens, Van de gaer, Van Damme, Onghena, & Van Landeghem, 2007; Fuchs et al. , 2008;
Newman, 2008; Walsh, 2008; White-Clark, DiCarlo, & Gilchriest, 2008). As for middle school mathematics students, providing some explanations of the phenomena of learning mathematics has become a continued priority of research (Singh et al. , 2002). Statement of the Problem There is a gap in literature regarding regular education middle school students’ experiences learning mathematics in mathematics classes.
This gap in literature 5 perpetuates a practice problem for administrators of education as administrators focus more on the needs and wants of the administration instead of the needs and wants of the student (Armstead, Bessell, Sembiante, & Plaza, 2010). For many of the studies completed concerning today’s youth, the research does not taken into account the perceptions of the student except in cases in which the research involves post-secondary students (Angier & Povey, 1999; Anthony, 2000; Moody, 2003).
Armstead et al.(2010) suggest that when soliciting information directly from the student, a clearer picture of what has and has not changed in the classroom is garnered. Furthermore, DeFur and Korinek cite the importance of getting information directly from students and state that, overall, getting information directly from the student is the equivalent of a “powerful tool for school improvement” (2009, p. 15). Preble and Taylor (2008) put it succinctly by stating the voice of the student is a valuable source of information.
As a result of the aforementioned absence of the much ignored student in educational research and because little research has been found that asks middle school students about their experiences learning mathematics within the mathematics classroom, it is the goal of this dissertation to investigate those experiences as perceived by this group of students. Purpose of the Study Ultimately, the purpose of this study is to discover and understand middle school students’ experiences learning mathematics in mathematics class.
Collected data regarding these experiences will more than likely have spoken to the larger problem that involves American students lagging behind other industrialized nations in mathematics achievement at all grade levels (Ross, 1992; Tschannen-Moran et al. , as cited in Charalambous, Philippou, & Kyriakides, 2008; Chouinard & Roy, 2008). In American 6 schools, underachievement in mathematics has placed us far behind other industrialized nations (Boe & Shin, 2005).
Much research has been done in an attempt to explain possible causes to mathematics underachievement, and this study is completed in order to provide further contributions to that body of research. Research on mathematics at the middle school level is important as achievement in mathematics at the middle school level may determine course enrollment and mathematics choices in high school (Singh et al. , 2002). Additionally, mathematics achievement at the middle school level is an indicator of other things such as students’ abilities to handle advanced mathematics courses that are predicated on middle school mathematics skills.
Moreover, mathematics achievement at the middle school level makes available or limits postsecondary and occupational opportunities for students as they move from childhood to adulthood (Gonzales et al. , 2008; Singh et al. , 2002). Unfortunately, while there is a great deal of literature on mathematics that highlights such things as mathematics achievement as well as other mathematics phenomena, little is done in terms of interviewing the middle school student directly when it comes to mathematics research (Angier & Povey, 1999).
To date, when students are involved directly in mathematics research, the participants are postsecondary students (Anthony, 2000; Moody, 2003). As a result, the purpose of this dissertation is to listen to sixth, seventh, and eighth grade middle school students from one middle school within a large school district in the eastern United States regarding their experiences learning mathematics in mathematics classes. In a few past studies, getting information directly from the student provided for an assessment of the needs and wants of the student as opposed to the needs and wants of 7 the administration (Armstead, Bessell, Sembiante, & Plaza, 2010).
In the same fashion, by soliciting the thoughts and experiences of the student, a clearer picture of what has and has not changed in the classroom can be ascertained (Armstead et al. , 2010). Having provided a collection of experiences pertaining to learning mathematics in mathematics classes, data students share about such experiences should resonate in the form of their beliefs, attitudes, likes, dislikes, motivation, lack of motivation, etc.
when it comes to being a part of a middle school mathematics class. By gaining this type of information, the proposed study is also meant to contribute to mathematics instruction by providing teachers, principals, superintendents, and curriculum specialists with data that highlights both impediments and compliments to middle school students’ acquisition of and overall achievement in mathematics courses.
Simultaneously, the intent of this study is to yield data that may also help school administrators to determine whether or not the proper resources are available for students to learn mathematics as well as to train school personnel and teachers in matters regarding the presentation of mathematics concepts. Rationale A study such as this one requires the view of the participants being studied—the students. Accordingly, a Social Constructivist philosophical stance has been undertaken that follows under the assumption that “individuals seek understanding of the world in which they live and work” (Creswell, 2009, p.8).
For many of the studies completed concerning today’s youth, the research does not taken into account the perceptions of the student (Angier & Povey, 1999). When gathering information directly from the student, much of the research involves post-secondary students (Anthony, 2000; Moody, 2003). Therefore, the current study takes the Social Constructivist stance in an attempt to 8 construct some meaning from what middle school students have to say concerning their experiences in mathematics classes.
In many studies, listening to what the student has to say about his or her own experiences pertaining to a specific phenomenon provides for an assessment of the needs and wants of the student as opposed to the needs and wants of the administration (Armstead, Bessell, Sembiante, & Plaza, 2010). In the same fashion, listening to what students have to say about their own experiences provides a clearer picture of what has and has not changed in the classroom (Armstead et al. , 2010).
Although little has been gathered in the way of actually interviewing and listening to the middle school student concerning mathematics in general, the research suggests the importance of considering that actual words of the student as, in the case of the current study, listening to the experiences of the middle school student regarding their experiences learning mathematics in mathematics class can be the equivalent of a “powerful tool for school improvement” (DeFur & Korinek, 2009, p. 15).
Preble and Taylor (2008) conclude that the voice of the student is a valuable source of data. Mertens (1998) suggests that qualitative research usually dictates a Social Constructivist approach. In identifying the phenomena as described by middle school students, such a stance should provide for the collection of qualitative data surrounding their experiences in mathematics classes through “multiple stages of data collection and the refinement and interrelationship of categories of information” (Creswell, 2009, p. 13).
As part of a larger basic design, the collection of data within this study is accomplished through face-to-face interviews (of which middle school students are the participants), the collection of report card documents, and the collection of field notes. Collected data is constantly compared with emerging categories of information (i. e. , relationships between 9 the students’ experiences and their actual beliefs, attitudes, likes, dislikes, motivation, and/or lack of motivation when it comes to being a part of a middle school mathematics class (2009).
In short, the Social Constructivist, qualitative, basic approach of this study provides for the most complete investigative and exploratory coverage of the phenomenon experienced by middle school students in the form their collective experiences in middle school mathematics classes. Because little research has been found that asks the middle school student directly through interviews about his or her experiences within the mathematics classroom, this study is a rational choice and contributes to current mathematics practices used in America with the overall goal being to get children to do better in mathematics.
Additional rationale behind conducting a study such as this one evolves from following recommendations for further research by previous researchers surrounding motivation and mathematics.
Such recommendations include (a) “further research on the relationship between test-taking motivation and test achievement” (Eklof, 2007, p. 311), (b) how different aspects of affect interact with each other (Hannula, 2006), (c) the “need for more research regarding the measurement of affective and motivational variables” (Singh et al., 2002, p, 331), or, in the case of this study, (d) what are the learning experiences of middle school students in mathematics classes.
The reason behind conducting a study dealing with students’ perceived experiences in learning mathematics is to contribute to a body of knowledge in which a gap exists.
Ultimately, this dissertation is closely linked to providing educational practitioners and educational law makers with some understanding of the phenomenon at hand that could be used to further fine tune teacher quality and selection, modify school—based as well as educational 10 policy in general, create relevant, appropriate, and applicable curriculum, and/or create appropriate placements for students during their matriculation through middle school.
In this sense, doing a study such as this one is worthwhile. Research Questions The central research question that guides the dissertation is as follows: R1. How do middle school students experience learning mathematics in middle school mathematics class? The additional research questions that guide the dissertation are as follows: R2. What are some of the barriers to learning mathematics in middle school mathematics class? R3.
What causes students to understand certain mathematics concepts in middle school mathematics class? Significance of the Study The current standards-based reform is largely predicated upon education being conducted utilizing research-based ideals (Deshler et al. , 2001). The reform has been occurring in order to provide some cohesion and consistency across local and state educational lines. Engaging in research-based educational practices also provides for a standardization of such practices that is the sounding board and foundation for our current standards-based educational practices and the larger No Child Left Behind (NCLB) policy.
In this same vein, the current study is significant. At a federal level, there are many boards and councils that attempt to document mathematics achievement as well as provide suggestions to improve such achievement (Gonzales et al. , 2008; National Mathematics Advisory Panel [NMAP], 2008; National 11 Council of Teachers of Mathematics [NCTM], 2000). In an attempt to continue to contribute to the larger body of research that mandates proven ideas and practices, mathematics research has become a major priority (McKinney, Chappell, Berry, & Hickman, 2009).
As such, the current study is being offered in order to augment research that seeks to contribute to current mathematics practices used in America. Of course, the overall goal is to get children to achieve at higher levels in mathematics. In terms of mathematics learning and achievement, much has been written about mathematics achievement as an outcome variable that is preceded by a multitude of factors that impact the subsequent behavioral response of students in mathematics classrooms (Schweinle et al. , 2006; Singh et al. , 2002).
As a result, doing a study such as this one is in keeping with recommendations for further research by previous researchers. Within the realm of identifying the experiences of middle school students learning mathematics in mathematics classes, a gap exists in the literature when it comes to such experiences as perceived by these students that necessitates that further research be conducted. Studying this area in mathematics contributes to an area of research that has not taken into account what the actual middle school students say about their experience learning mathematics in the middle school mathematics classroom.
Overall, the significance of conducting this study is closely linked to providing educational practitioners and educational law makers with some scientific information that could be used to further fine tune teacher quality and selection, modify school—based as well as educational policy in general, create relevant, appropriate, and applicable curriculum, and/or create appropriate placements for students during their matriculation through school. 12 Definition of Terms The following terms are used operationally in this dissertation according to the definitions provided: Affective learning.
The dimension of learning that is concerned with the reactions, feelings, and emotions of the learning (Buchanan & Hyde, 2008). Attitude. A predisposition to think or act in a particular way in response to a specific stimulus (Fitzsimmons & Barr, 1997). Child. An individual who has not attained the age of consent for medical care or for research activities in the jurisdiction in which the research will be conducted (Jonsen, 1978). Coding. The process of organizing qualitative research information in chunks or segments before ascribing any interpretation or meaning to the collected information (Rossman & Rallis, 1998). Content standards.
Broad, measurable statements about what students should know and be able to do (MSDE, n. d. d). Cross-sectional. A process used to gather data over the course of a few weeks as opposed to over several months as with a longitudinal process (Creswell, 2009). Mathematics Belief. Describing what students see as true in mathematics, in the classroom, and within themselves (Op ’T Eynde, De Corte, & Verschaffel, 2002). Middle school. A school configuration in the United States, which in recent decades, includes students in grade six through eight, or occasionally grade five through eight (National Center for Education Statistics [NCES], 2000).
13 Middle School Mathematics. Middle school mathematics is a specific set of learning expectations for the middle school level that emphasizes the learning, development, and strengthening of computational fluency with fractions, decimals, and integers, measurement, statistics, problem-solving, reasoning and proof, communication, connections, representation, and, the ability to represent ideas algebraically and geometrically (NCTM, 2000). Nuremberg Code.
A set of standards established for the conduct of human research as a result of Nazi leaders committing and conspiring to commit war crimes against humanity during World War II (Byerly, 2009). Social constructivist philosophical stance. A basic set of beliefs that guide a researcher’s actions during research. A Social Constructivist stance is a stance that follows under the assumption that “individuals seek understanding of the world in which they live and work” (Creswell, 2009, p. 8). Standardized test.
A tool used (either in paper and pencil or on the computer) to measure student academic achievement (Higgins, 2009). Standards-based reform. “An attempt to boost the academic achievement of all students by establishing rigorous educational standards for all, aligning instruction with those standards, and using accountability assessments to measure progress toward meeting those standards” (Voltz & Fore, 2006, p. 331). Assumptions The following assumptions, based off of the characteristics of qualitative research outlined by Creswell (2007), are present in the study: 14.
1. Data is collected in the students’ natural setting where students experience the phenomena. 2. In qualitative research, the researcher is the primary instrument. In this sense, although data is collected by conducting face-to-face interviews, gathering documents, and taking field notes, that data is mediated through the researcher (Patton, 2002). 3. Multiple sources of data (the interview, documents, and field notes) are collected. 4. A variety of procedures are employed in order to check the accuracy of findings within the study (Gibbs, 2007). 5.
In an attempt to “make sense out of text and image data” (Creswell, 2009, p. 183), a systematic process is used to analyze collected data from student participants so as to identify themes, patterns, and relationships that emerge between the participants’ experiences in mathematics classes and the actual phenomenon of being a part of the middle school mathematics class. 6. The research follows under the assumption that themes and categories emerge as the research process progresses. 7. An inductive form of data analysis is used. 8. The study uses a Social Constructivist lens. 9.
The researcher makes interpretations of what research participants reveal in each interview as well as what the researcher collects in terms of documents. It is assumed that such interpretations cannot be separated from the researcher’s own background, history, context, and prior understanding (Creswell, 2009). 10. A holistic account of the phenomenon under study is reported. Additionally, 15 11. The sample size is large enough to provide an understanding of the experiences of middle school students learning mathematics in mathematics classes.