Students Experiences in Mathematic
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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. 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.
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
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
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).
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 (Eklöf, 2007; Trautwein, Lüdtke, Marsh, Köller, & Baumert, 2006; Watt, 2006).
In the case of test-taking, evidence points towards students taking low-stakes test less serious than high stakes tests (Eklöf, 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).