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 Title
 Calculus III Students' Analytic and Visual Understanding of Surface Areas of Spheres, Cylinders, Pyramids and Prisms.
 Creator

Meadows, Yelena A., Shaw, Kenneth, Huckaba, Sam, Aspinwall, Leslie, Jakubowski, Elizabeth, School of Teacher Education, Florida State University
 Abstract/Description

Calculus is often viewed as a gateway to more technical college majors, such as engineering, computer science and teaching of mathematics. The majority of existing research in college calculus classes has been focused on reports and studies that were conducted within the singlevariate calculus content. Some researchers explain the high rate of students changing their majors from scienceoriented to less mathematically rigorous majors due to students' struggles with passing multivariate...
Show moreCalculus is often viewed as a gateway to more technical college majors, such as engineering, computer science and teaching of mathematics. The majority of existing research in college calculus classes has been focused on reports and studies that were conducted within the singlevariate calculus content. Some researchers explain the high rate of students changing their majors from scienceoriented to less mathematically rigorous majors due to students' struggles with passing multivariate content of the calculus college sequence (calculus I, II, and III). A qualitative case study of one section of a calculus III class was undertaken in order to obtain descriptive data on students' visual and analytical understanding of surface areas of familiar shapes of spheres, cylinders, prisms, and pyramids in the context of multivariate calculus. Specifically, this research focused on application of the surface area formula of surfaces described by a function of two variables. In the course of semesterlong study, observed students divided into three distinct groups according to their mathematical visualization preference and mathematical accuracy characteristics. The three cases are: (1) students who prefer analytical method of solving mathematical problems with above average mathematical accuracy; (2) students who prefer visual method in solving mathematical problems with above average mathematical accuracy; and (3) students who prefer visual method of solving mathematical problems with below average mathematical accuracy. There was no group of students with below average mathematical accuracy preferring analytical methods of solving mathematical proeblems. The results were analyzed through the theoretical frame of Krutetskii (1976); Presmeg's (1985) mathematical visualization instrument and types of imagery, Guzman's (2002) types of visualization; and Donaldson's (1963) classification of errors. In short, the best demonstrated understanding was observed in the case of mathematical visualization preference and above average mathematical accuracy. Observed finding of the other two cases provide evidence of limitations in understanding surface areas. Students preferring analytical solutions struggled with graphing, students who preferred visual mathematical solutions with below average mathematical accuracy showed deviations from traditional understanding of basic shapes. A "left" cylinder and a starshaped prism are examples of such discrepancy. This study is the beginning of research of how students learn multivariate calculus and what specific struggles they encounter. More research is encouraged to follow up on trends that emerged in this study.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd2512
 Format
 Thesis
 Title
 Cognitive Processes during Problem Solving of Middle School Students with Different Levels of Mathematics Anxiety and Self Esteem: Case Studies.
 Creator

Jones, Vivian Olivia, Aspinwall, Leslie, Shaw, Kenneth, Jones, Maxine D., Fernandez, Maria L., Department of Middle and Secondary Education, Florida State University
 Abstract/Description

This qualitative case study examined the cognitive processes used during problemsolving tasks of two middle school students with different levels of mathematics anxiety and selfesteem. One student had low selfesteem combined with low mathematics anxiety, while the other had high selfesteem and high mathematics anxiety. These two students were administered the Rosenberg SelfEsteem Scale (RSE) and the Mathematics Anxiety Rating Scale for Adolescents (MARSA). They participated in task...
Show moreThis qualitative case study examined the cognitive processes used during problemsolving tasks of two middle school students with different levels of mathematics anxiety and selfesteem. One student had low selfesteem combined with low mathematics anxiety, while the other had high selfesteem and high mathematics anxiety. These two students were administered the Rosenberg SelfEsteem Scale (RSE) and the Mathematics Anxiety Rating Scale for Adolescents (MARSA). They participated in taskbased interviews speaking their thoughts aloud as they completed each task. Both participants were in grade 8 at the time of this study. The findings of this research study led to the following recommendations. (1) Educators must make reading comprehension a priority in their curriculum, (2) Curriculum writers must make problemsolving more of a priority giving teachers more opportunities to teach and enforce application of cognitive processes in the classroom., (3) Reflection must be monitored and driven in our children's classrooms, (4) Those writing textbooks and designing curriculum must incorporate using cognitive processes, (5) Students must be taught "what" cognitive processes are as well as "what" they mean, and "how" to use them, (6) Teachers need to be aware of those students having issues with mathematics anxiety and selfesteem so that they can implement meaningful strategies to reduce mathematics anxiety and selfesteem in their students.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd3446
 Format
 Thesis
 Title
 Describing Students' Pragmatic Reasoning When Using "Natural Mathematics Computer Interfaces (NMI)".
 Creator

Nold, Erich, Flake, Janice, Dancy, Russell, Jakubowski, Elizabeth, Aspinwall, Leslie, Department of Middle and Secondary Education, Florida State University
 Abstract/Description

The researcher characterized the pragmatic reasoning of students' mathematics learning using certain technology. A "Natural Mathematics computer Interface" designation, NMI, was introduced and predicated on its virtual use of things like compassrule, or pencilpaper traditional mathematical inscriptions. The NMI provided capacities for manipulative geometric constructions and transformations, or symbolic interfacing to a Computer Algebra System. Two separate case studies facilitated...
Show moreThe researcher characterized the pragmatic reasoning of students' mathematics learning using certain technology. A "Natural Mathematics computer Interface" designation, NMI, was introduced and predicated on its virtual use of things like compassrule, or pencilpaper traditional mathematical inscriptions. The NMI provided capacities for manipulative geometric constructions and transformations, or symbolic interfacing to a Computer Algebra System. Two separate case studies facilitated empiricallybased characterization and reflection concerning students' explorations, experimentations, and deductions in this NMI use setting. Over the course of a semester, one student studied Geometry proof (an elementary education major), and one Markov Chains (a lower division mathematics major). Four distinctive types of perceived mathematical embodiments were observed to be used by the students. These abstract embodiments, and related reasoning acts were described in the context of C. S. Peirce's Pragmatic Reasoning theory. NMI interactivity, and the means of a mathematical semantics level organization (via interface layout), were seen to be important contributors to the students' pragmatic reasoning. The abstract types of mathematical embodiments revealed were named: i) Interfaceprocedural, ii) Natural Mathematics Computational, iii) Applications, and iv), Generic. These mean, respectively, (i) interpreted merely as memorized interface procedures, (ii) resultant from interactive computation, interpreted as mathematical in a (sometimes) surface sense, as the student may not understand the underlying mathematics directing the computation, (iii) resultant from a student's interest in a realworld application used to analogously consider a mathematical model and its interpretation, and (iv) clearly abstracted and generalized, internal or mentalesque mathematical explanations or systematizations.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd2554
 Format
 Thesis
 Title
 Exploration of Metacognition and NonRoutine Problem Based Mathematics Instruction on Undergraduate Student Problem Solving Success.
 Creator

Nancarrow, Michael, Jakubowski, Elizabeth, Milton, Sande, Aspinwall, Leslie, Fernandez, Maria L., Department of Middle and Secondary Education, Florida State University
 Abstract/Description

The purpose of this research was to examine and attempt to influence the problem solving processes used by typical undergraduate mathematics students. A structured problem solving methodology designed to foster a heuristic way of reasoning was introduced and a study of how this treatment affected the participants' nonroutine problem solving styles and abilities was performed. An approximately equal mix of male and female student participants selfselected into three sections of precalculus...
Show moreThe purpose of this research was to examine and attempt to influence the problem solving processes used by typical undergraduate mathematics students. A structured problem solving methodology designed to foster a heuristic way of reasoning was introduced and a study of how this treatment affected the participants' nonroutine problem solving styles and abilities was performed. An approximately equal mix of male and female student participants selfselected into three sections of precalculus algebra at a private southeastern institution. Each section consisted of approximately 15 students. The researcher and one other professor instructed the three sections. All sections were instructed using the same set of notes, were given the same assignments, and covered the same mathematical topics in the same order. The research model consisted of the following elements. 1. Testing students in treatment and control sections for routine algebra skills necessary to successfully find solutions to specific nonroutine problems. 2. Testing students in treatment and control sections for ability to solve nonroutine problems that can be handled using the routine algebra skills on which they had previously been tested. 3. Providing metacognive control practice and instruction in the treatment section using a combination of weekly homework and inclass assignments. 4. Conducting pre and posttreatment videotaped interviews of four treatment section students engaged in nonroutine problem solving. 5. Analyzing interview records in an attempt to determine if any changes in metacognitive control occurred. 6. Examining statistical evidence gathered from the pre and posttreatment examinations. Results of the study were mixed. A significant increase in the statistical correlation between resources (mathematical facts and procedures) and nonroutine problem solving success indicated that students may have benefited from the treatment by improving their metacognitive control of resources. However, analysis of the videotaped interviews did not reveal any significant change in the way students approached nonroutine problems. Group statistical evidence comparing treatment to control sections seemed to substantiate most of what was observed during the interviews
Show less  Date Issued
 2004
 Identifier
 FSU_migr_etd2772
 Format
 Thesis
 Title
 Faculty Perceptions of A Calculus Reform Experiment at A Research University: A Historical Qualitative Analysis.
 Creator

Windham, Douglas M. (Douglas Macarthur), Aspinwall, Leslie, Driscoll, Marcy, Shaw, Ken, Jakubowski, Elizabeth, Department of Middle and Secondary Education, Florida State...
Show moreWindham, Douglas M. (Douglas Macarthur), Aspinwall, Leslie, Driscoll, Marcy, Shaw, Ken, Jakubowski, Elizabeth, Department of Middle and Secondary Education, Florida State University
Show less  Abstract/Description

From 1999 through 2004, the mathematics department at Research University experimented with using a reform text, HughesHallett et al.'s Calculus, to teach the undergraduate calculus sequence. A historical qualitative analysis was undertaken involving three linked case studies to determine, from the perspective of the professors in the classroom, the success of the experiment in reform. Three professors, one a selfidentified reform advocate, one an archtraditionalist who vehemently opposed...
Show moreFrom 1999 through 2004, the mathematics department at Research University experimented with using a reform text, HughesHallett et al.'s Calculus, to teach the undergraduate calculus sequence. A historical qualitative analysis was undertaken involving three linked case studies to determine, from the perspective of the professors in the classroom, the success of the experiment in reform. Three professors, one a selfidentified reform advocate, one an archtraditionalist who vehemently opposed reform, and one who professed himself to be in between, gave insight into the results of the switch and the departmental atmosphere that led to the return in 2004 to a more traditional calculus instruction. The results of these case studies include a picture of a department in transition, trying to better serve its students but having difficulty adjusting to the changes in instruction coincident with reform. Each of the participants admitted using the textbook as little more than a delivery vehicle for homework assignments; none of the three participants changed their lecture style or teaching methods to respond to the demands of the reform movement. Calculus reform's founders and those who have inherited the movement and brought it into the 21st century advocate technological exploration, real world applications, group projects, and conceptual understanding. Each one of the participants admitted to applying some of these in their teaching style, but each in turn rejected other tenets of the reform movement as unusable, or unwieldy. As the department did not change any other aspect of calculus instruction at the university other than the text used, this experiment could have been dismissed as naïve, insincere, or halfhearted. But in fact, the department may have benefited indirectly from the move by even the more traditional text they embraced postreform, as all participants acknowledged that even traditional texts now contain elements of reform themselves. However, the case studies analyzed in this research would indicate that any reform effort conducted in a research university should expect to meet some resistance of the type exposed at this university. Anyone attempting to reform the teaching of calculus at their college can benefit from reading the perceptions of these professors and addressing them, either with seminars and research that can convince faculty that a change is needed, or at the very least by adjusting curricular structure and pacing so the reforms have a chance to succeed. Also, educational researchers could benefit greatly from a nationwide qualitative/quantitative research focus on the acceptance of calculus reform at mainstream colleges and universities that do not have a vested interest in proving the reforms a success to maintain funding levels. Finally, those educational researchers interested in the perceptions of college math professors at research institutions could further analyze how those professors' perceptions could impede or enhance efforts at reform, and how those perceptions differ from those predominant at teachingfocused institutions.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0938
 Format
 Thesis
 Title
 How Graphing Calculators and Visual Imagery Contribute to College Algebra Students' Understanding the Concept of Function.
 Creator

Lane, Rebekah M., Aspinwall, Leslie, Rice, Diana, Fernández, Maria L., Jakubowski, Elizabeth, Department of Middle and Secondary Education, Florida State University
 Abstract/Description

The purpose of this study was to answer the following research questions: • What is the role of graphing calculators in understanding functions? • How does visual imagery contribute to visual and nonvisual College Algebra students' understanding of functions? Interviews and document reviews were the data sets used in this study. The data were analyzed by using two theoretical frameworks: O'Callaghan's (1998) translating component for understanding functions and Ruthven's (1990) role of...
Show moreThe purpose of this study was to answer the following research questions: • What is the role of graphing calculators in understanding functions? • How does visual imagery contribute to visual and nonvisual College Algebra students' understanding of functions? Interviews and document reviews were the data sets used in this study. The data were analyzed by using two theoretical frameworks: O'Callaghan's (1998) translating component for understanding functions and Ruthven's (1990) role of graphing calculator approaches. The investigation utilized the qualitative case study method. The findings of one of the case studies of the two College Algebra students were reported in chapter 4. The findings of the second case study were reported in this chapter. The two participants in this study were presented with mathematical tasks to complete over the course of a semester. Each task was given to the students individually. In order to thoroughly understand the students' responses, taskbased interviews were conducted and videotaped. In addition, each participant was interviewed based on his or her response to the mathematical tasks. The tasks captured different types of mathematical functions. These included linear, quadratic, cubic, absolute value, and exponential functions. Furthermore, prior to receiving the tasks, the students' preference for processing mathematical information visually or nonvisually were determined using Presmeg's (1985) Mathematical Processing Instrument and Questionnaire. These tools were chosen because they measured how a student preferred to process mathematical information, i.e., visually or nonvisually. In this investigation, O'Callaghan's (1998) translating component was present during the completion of linear, quadratic, cubic, absolute value, and exponential functions. One of the participants used the graphing calculator during the completion of all of the mathematical tasks and exhibited Ruthven's (1990) approaches. The other participant used the graphing calculator during the completion of five of the tasks and exhibited Ruthven's (1990) approaches. In addition, one participant relied on visual imagery during the completion of five of the mathematical tasks. The second participant relied on visual imagery during the completion of three of the tasks.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd3297
 Format
 Thesis
 Title
 Identification and Analysis of Pedagogical Techniques in Decartes' La Géométrie.
 Creator

Dean, Amanda Saxon, Clark, Kathleen M., Jakubowski, Elizabeth, Aspinwall, Leslie, School of Teacher Education, Florida State University
 Abstract/Description

Much research has been conducted about the philosophy and mathematical writings of René Descartes, but that which focuses on pedagogy does so in a holistic manner. The present study uses a systematic approach to identify pedagogical techniques within each sentence of Descartes' La Géométrie. Next, the study provides an analysis of La Géométrie based on the techniques identified, their frequencies, and patterns of use within the text. The results of this analysis indicate that Descartes placed...
Show moreMuch research has been conducted about the philosophy and mathematical writings of René Descartes, but that which focuses on pedagogy does so in a holistic manner. The present study uses a systematic approach to identify pedagogical techniques within each sentence of Descartes' La Géométrie. Next, the study provides an analysis of La Géométrie based on the techniques identified, their frequencies, and patterns of use within the text. The results of this analysis indicate that Descartes placed a high value on the use of demonstration, particularly in conjunction with deductive reasoning and multiple representations; that Descartes believed his method of approaching mathematical problems was superior to other methods; and that Descartes was in fact concerned with whether his readers understood his ideas or not.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd0062
 Format
 Thesis
 Title
 The Influence of Curiosity and Spatial Ability on Preservice Middle and Secondary Mathematics Teachers' Understanding of Geometry.
 Creator

Unal, Hasan, Jakubowski, Elizabeth, Keller, John M., Aspinwall, Leslie, Milton, Sande, Department of Middle and Secondary Education, Florida State University
 Abstract/Description

The objectives of this study were to investigate and characterize the geometric thinking of preservice middle and secondary mathematics teachers while taking account into their curiosity types and spatial ability levels, and to examine the relationship between the students' curiosity types (perceptual and epistemic) and their motivation, and to examine the relationship between students' spatial ability and motivation. The study used the van Hiele model of the development of geometric thought...
Show moreThe objectives of this study were to investigate and characterize the geometric thinking of preservice middle and secondary mathematics teachers while taking account into their curiosity types and spatial ability levels, and to examine the relationship between the students' curiosity types (perceptual and epistemic) and their motivation, and to examine the relationship between students' spatial ability and motivation. The study used the van Hiele model of the development of geometric thought to examine description of geometric thought in preservice middle and secondary teachers and the ARCS model of motivation to examine students' motivation. Both quantitative and qualitative methods were employed. The van Hiele levels of students were identified by using, clinical interview protocol, designed by Mayberry (1981). Four preservice teachers were interviewed. To investigate the difference, if any, exist between preservice middle and secondary teachers with different spatial ability levels and understanding geometry, pre and posttest design were employed by using Mayberry's (1981) protocol. Preinterview results showed three groups of levels of understanding were identified with the preservice middle and secondary mathematics teachers. One teacher whom very low in spatial ability indicated a level II, one teacher low in spatial ability indicating levels II/III, one teacher with medium spatial ability indicating level III/IV and one teacher very high in spatial ability a Level III understanding. Post interview results showed a gain among all three preservice teachers, only one teacher who were very low in spatial ability did not demonstrated such gain in geometric understanding. Correlation design were employed examine relationships among motivation, curiosity and spatial ability. This study looked at following relationships having motivation as a dependent variable, curiosity types (epistemic and perceptual) and spatial ability as independent variables. The Pearson productmoment correlation was utilized to investigate these relationships. There was a significant correlation between perceptual curiosity and motivation.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd1461
 Format
 Thesis
 Title
 Instructional Implications of Social Justice Pedagogy on the Teaching of Mathematics.
 Creator

Johnson, Jason D., Jakubowski, Elizabeth, Bower, Beverly, Aspinwall, Leslie, Shaw, Ken, Department of Middle and Secondary Education, Florida State University
 Abstract/Description

The epidemic of African American and Latino students' lack of success in mathematics has been puzzling researchers (Gutstein, Lipman, Hernandez, and de los Reyes, 1997; LadsonBillings, 1991, 1995, 2000) in the field of mathematics education. Many researchers have identified that a problem does exist, however, solutions have yet to resolve the emerging problems for the African American and Latino student. Such a pedagogy as social justice has attempted to address the crisis of low achievement...
Show moreThe epidemic of African American and Latino students' lack of success in mathematics has been puzzling researchers (Gutstein, Lipman, Hernandez, and de los Reyes, 1997; LadsonBillings, 1991, 1995, 2000) in the field of mathematics education. Many researchers have identified that a problem does exist, however, solutions have yet to resolve the emerging problems for the African American and Latino student. Such a pedagogy as social justice has attempted to address the crisis of low achievement of African American and Latino students in mathematics. The current study will use a nontraditional mathematics education research structure, situated cognition theory, as a theoretical framework, that was most appropriate for the implementation of the social justice activity. The purpose of the research was to investigate the instructional implications of social justice pedagogy on the teaching of mathematics. How does social justice pedagogy impact African American and Latino preservice teachers' views of the important of mathematics? How does social justice pedagogy influence African American and Latino preservice teachers' positions about mathematics? The results indicated that social justice activities provided a way for students to solve real world issues related to African Americans and Latinos. The preservice teachers also pointed out that they would consider implementing social justice activities into their classroom. Also, the questionnaire and the audiotape represented consistent data regarding the research questions. The participants in the study indicated that due to the social justice activity, they have gained an understanding of the importance of mathematics and they have established a fondness for mathematics due to the social justice activity.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd3560
 Format
 Thesis
 Title
 An Investigation of College Students' Covariational Reasonings.
 Creator

Koklu, Onder, Jakubowski, Elizabeth, Milton, Sande, Aspinwall, Leslie, Shaw, Kenneth, Department of Middle and Secondary Education, Florida State University
 Abstract/Description

Present study investigates college students' covariational reasoning in light of five mental actions described in covariation framework introduced by Marilyn P. Carlson. More specifically, this study focuses on college students' understanding and reasoning about simultaneous changes of two variables when they interpret a functional situation and use their interpretations to demonstrate simultaneous changes of two variables in graphical representations. Two high performing college students'...
Show morePresent study investigates college students' covariational reasoning in light of five mental actions described in covariation framework introduced by Marilyn P. Carlson. More specifically, this study focuses on college students' understanding and reasoning about simultaneous changes of two variables when they interpret a functional situation and use their interpretations to demonstrate simultaneous changes of two variables in graphical representations. Two high performing college students' reasoning was investigated in a multiple case study design. Data was obtained from a detailed examination of students' thinking and reasoning processes through the task based indepth clinical interviews. Data obtained from students' verbal expressions and graphical representations were analyzed in light of the theoretical lens. Carlson et al.'s (2002) covariation framework provided a skeletal structure for the description and interpretation of findings in each case. Specifically, five mental actions defined in the framework were used to describe each student's covariational reasoning. Analysis of data disclosed that functional situations are conceived as static rather than dynamic. This static approach prevents students from evaluating the whole process as it is happening at once. In other words, students have difficulties to represent continues changes of two variables in a functional situation and coordinate the simultaneous changes of two variables on entire domain. In addition, students' difficulties in graphical representations produce inconsistencies between interpretations and representations of simultaneous changes of two variables. It is also revealed that Students' strong procedural tendency hinders reasoning and meaningful interpretations about change in functional situations.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd2848
 Format
 Thesis
 Title
 An Investigation of How African American Community College Students with Different Levels of Mathematics Anxiety Engage in Problem Solving Tasks.
 Creator

Moorman Walker, Calandra, Aspinwall, Leslie, Jones, Ithel, Clark, Kathy, Shaw, Kenneth, Department of Middle and Secondary Education, Florida State University
 Abstract/Description

This qualitative case study examined the strategies and thinking processes used during problem solving tasks with African American community college students with varying levels of mathematics anxiety. Two students had high mathematics anxiety, while the other two students had low mathematics anxiety. These students were administered the Mathematics Anxiety Rating Scale – Shortened Version (MARS). They participated in taskbased interviews that included six problem solving tasks while...
Show moreThis qualitative case study examined the strategies and thinking processes used during problem solving tasks with African American community college students with varying levels of mathematics anxiety. Two students had high mathematics anxiety, while the other two students had low mathematics anxiety. These students were administered the Mathematics Anxiety Rating Scale – Shortened Version (MARS). They participated in taskbased interviews that included six problem solving tasks while thinking aloud. After completion of the problem solving tasks the students completed a mathematics anxiety symptom survey and participated in a short interview. The study was completed in order to answer the following questions: (1) What strategies and thinking processes do students with low mathematical anxiety use when they engage in problem solving tasks? (2) What strategies and thinking processes do students with high mathematical anxiety use when they engage in problem solving tasks? (3) What differences and similarities are there, if any, in the strategies and thinking processes of students with high mathematical anxiety and low mathematical anxiety when they engage in problem solving tasks? Using the frameworks of Malloy (1994) and Montague (2003), I was able to make the following recommendations. (1) Exhibiting mathematics anxiety symptoms may not completely hinder student performance. (2) Drawing pictures or diagrams maybe important for high mathematics anxiety students when solving problems, but not necessarily meaningful. (3) Mathematics anxiety may lead to an inability to recall previously studied material which hinders student performance. (4) Failure to use all of the thinking processes described by Montague (2003) does not hinder the student's ability to successfully solve mathematical problems. (5) Difficulty with reading skills may hinder the problem solving process. (6) Students must be able to check their calculations and check for the use of correct procedures. (7) Mathematical anxiety symptoms can be visibly present even if a student does not notice the symptoms himself.
Show less  Date Issued
 2007
 Identifier
 FSU_migr_etd2281
 Format
 Thesis
 Title
 A Longitudinal Analysis of Science Teaching and Learning in Kindergarten and FirstGrade.
 Creator

Olgan, Refika, Jones, Ithel, Aspinwall, Leslie, Lake, Vickie E., Piazza, Carolyn, Department of Childhood Education, Reading and Disability Services, Florida State University
 Abstract/Description

This study attempted to determine how often science is taught in the early grades as well as the science topics taught in these grades. A related purpose of the study was to determine the relationship between science teaching and students' science achievement. In doing so, the analyses took into consideration the influence of gender, socioeconomic status (SES), and race/ethnicity on children's academic performance in science. By using the Early Childhood Longitudinal Study Kindergarten class...
Show moreThis study attempted to determine how often science is taught in the early grades as well as the science topics taught in these grades. A related purpose of the study was to determine the relationship between science teaching and students' science achievement. In doing so, the analyses took into consideration the influence of gender, socioeconomic status (SES), and race/ethnicity on children's academic performance in science. By using the Early Childhood Longitudinal Study Kindergarten class of 199899 (ECLSK) kindergarten and firstgrade data files, children's science Item Response Theory Scores (IRT) and Academic Rating Scores (ARS) were examined to measure the relationship between children's early science experiences in schools and their achievement on the "General Knowledge Assessment Battery". According to this study's findings science teaching and learning in kindergarten level is somewhat limited. Additionally, the science content taught in kindergarten is narrow. The results of crosssectional and longitudinal multilevel analyses revealed that several student and school level factors can influence young children's science achievement in kindergarten and firstgrade. Although there were inconsistent conclusions about male and female students' science achievement as assessed by direct and indirect assessment batteries, there was no association between children's science scores and their gender and the amount or degree of science practices in school. While results of the analyses clearly showed that socioeconomic status (SES) had the most influence on both kindergarten and firstgrade children's science achievement, the findings related to the effects of different science practices on science achievement were inconsistent. The results showed that science instruction effects some children's science achievement more than others. The findings have important implications for policies governing the teaching of science in the early grades. A clear demand exist for extension of science resource materials to include broader topics, more childselected activities, integration with other subject areas, and more quality time for science teaching and learning in the early grades.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd2295
 Format
 Thesis
 Title
 Making Sense of Students' Understanding of Fractions: An Exploratory Study of Sixth Graders' Construction of Fraction Concepts Through the Use of Physical Referents and Real World Representations.
 Creator

Stewart, Veon, Jakubowski, Elizabeth, Bunea, Florentina, Aspinwall, Leslie, Fernandez, Maria L., Department of Middle and Secondary Education, Florida State University
 Abstract/Description

This study was an investigative, whole class descriptive research, on the development of twenty sixth graders' understanding of fractions as they interacted with physical referents, handson taskbased activities and activities that model real life situations during eight weeks of a teaching sequence. The study was conducted in a metropolitan school situated in southeast Florida. The teaching sequence consisted of 12 taskbased activities that spanned 20 sessions with each session lasting for...
Show moreThis study was an investigative, whole class descriptive research, on the development of twenty sixth graders' understanding of fractions as they interacted with physical referents, handson taskbased activities and activities that model real life situations during eight weeks of a teaching sequence. The study was conducted in a metropolitan school situated in southeast Florida. The teaching sequence consisted of 12 taskbased activities that spanned 20 sessions with each session lasting for approximately 60 minutes. Data was collected through audio and videorecording, in addition to the numerous written tasks. The taskbased activities that the students were involved with during this study were analyzed to gain an insight into their understanding of fractions in the context of subdividing, comparing and partitioning of continuous and discrete models and the connections they made with the fraction ideas generated through these activities. The study also examined how these students make sense of fractions and investigated how their performance differed when fractions were presented using different models. Herscovics and Bergeron's (1988) extended model of understanding, and the partitioning strategies identified by Charles and Nason (2000) and Lamon (1996) provided the theoretical framework through which the investigation was explored. Results from the study revealed that the participants exhibited an understanding of unit and nonunit fraction based on the components of the abovementioned model of understanding. The students also displayed a number of different partitioning strategies. The knowledge growth that was evident in the whole class confirms earlier studies as to the significant role that partitioning plays in the basic development of the fraction concept. Although discrete models were used by the students, a majority of the students exhibited a preference for using continuous models as forms of reference for given fractions. The students appreciated working with fractions that model real world situations. Preliminary findings from this study seem to indicate that students should be introduced to fraction concepts via partitioning activities. The partitioning activities should be introduced in grades earlier than sixth grade. Further research can be undertaken to investigate the role partitioning activities play in the development of students' ability to add, subtract, multiply and divide fractions.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd0390
 Format
 Thesis
 Title
 The Nature of Pedagogical Practices Influenced by an Instructor's Beliefs in an Online Mathematics Education Course.
 Creator

Lynn, Apryl Charelle, Aspinwall, Leslie, Jones, thel, Clark, Kathleen, Jakubowski, Elizabeth, Shaw, Kenneth, Department of Middle and Secondary Education, Florida State University
 Abstract/Description

This qualitative case study evaluated an instructor's practices and decision making in the online course, Seminar in Teaching Geometry. The focus of the data analysis was to understand and evaluate the instructor's decisions as they were influenced by the association of belief dimensions and learningcentered orientations. The results were coded based on my interpretation of the framework presented by Samuelowicz and Bain (2001). This framework explains that there are nine belief dimensions...
Show moreThis qualitative case study evaluated an instructor's practices and decision making in the online course, Seminar in Teaching Geometry. The focus of the data analysis was to understand and evaluate the instructor's decisions as they were influenced by the association of belief dimensions and learningcentered orientations. The results were coded based on my interpretation of the framework presented by Samuelowicz and Bain (2001). This framework explains that there are nine belief dimensions and four learningcentered orientations. The data collection involved one case (the instructor), examining the relationship between this instructor's decision making, class activities, and responses from two students. At the conclusion of the study I presented a model that detailed the findings of this instructor and this online mathematics education course. The model identifies belief dimensions and learningcentered orientations associated with this online mathematics education course. This model will help educators, institutional administration, and students understand the dynamics of an online environment, in hopes of enhancing the experiences for the students and the instructors.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0969
 Format
 Thesis
 Title
 Performance, Motivation and Gender with Two Different Instructional Approaches in Geometry.
 Creator

Halat, Erdogan, Jakubowski, Elizabeth, Blumsack, Steve, Shaw, Kenneth, Aspinwall, Leslie, Department of Middle and Secondary Education, Florida State University
 Abstract/Description

The purpose of this quantitative study was to compare performance and motivation of sixthgrade students engaged in instruction using a van Hiele theory based curriculum with sixthgrade students engaged in instruction not using a van Hiele theory based curriculum. While the instruction following the van Hiele theory used the curricula, CMP's Shapes and Designs and Key Curriculum's Discovering Geometry: An Inductive Approach, the comparative group's instruction used Scott Foresman's Middle...
Show moreThe purpose of this quantitative study was to compare performance and motivation of sixthgrade students engaged in instruction using a van Hiele theory based curriculum with sixthgrade students engaged in instruction not using a van Hiele theory based curriculum. While the instruction following the van Hiele theory used the curricula, CMP's Shapes and Designs and Key Curriculum's Discovering Geometry: An Inductive Approach, the comparative group's instruction used Scott Foresman's Middle School Math Course I. Two hundred seventythree sixthgrade mathematics students – 123 in the control group, and 150 in the treatment group – were involved in the study. The researcher employed a geometry test, Van Hiele Geometry Test (VHGT), used to measure students' geometry performance and a questionnaire, Course Interest Survey (CIS), used to measure students' motivation toward the geometry instruction. The VHGT and CIS were both administered to the students by the researcher before and after a fiveweek period of instruction during a single class period. The paired samples ttest, the independent samples ttest, and ANCOVA with á = .05 were employed in the analysis of the data. The study indicated that there was no statistically significant difference with respect to students' performance between the treatment and control groups, and that there was a statistically significant difference in regard to students' motivation between the two groups favoring the treatment group instructed with the van Hiele theory based curricula. However, no statistical difference was indicated by gender in regard to students' performance and motivation.
Show less  Date Issued
 2003
 Identifier
 FSU_migr_etd4327
 Format
 Thesis
 Title
 A Qualitative Study: Algebra Honor Students' Cognitive Obstacles as They Explore Concepts of Quadratic Functions.
 Creator

Eraslan, Ali, Aspinwall, Leslie, Shargel, Emanuel I., Jakubowski, Elizabeth, Fernández, Maria L., Department of Middle and Secondary Education, Florida State University
 Abstract/Description

With the paradigm shift from a behavioral to a constructivist perspective in teaching and learning of mathematics, students' thought processes have become a major focus for learning and students' learning of the specific subject matter has been analyzed and approached more qualitatively. In parallel to this development, the present study attempted to describe two algebrahonor students' cognitive obstacles in the learning of quadratic functions. In particular, along with students' concept...
Show moreWith the paradigm shift from a behavioral to a constructivist perspective in teaching and learning of mathematics, students' thought processes have become a major focus for learning and students' learning of the specific subject matter has been analyzed and approached more qualitatively. In parallel to this development, the present study attempted to describe two algebrahonor students' cognitive obstacles in the learning of quadratic functions. In particular, along with students' concept image and definition for the quadratic function (Tall & Vinner, 1981), five other aspects of quadratic functions were examined to identify students' cognitive obstacles surrounding quadratic functions. These five aspects, adapted by Wilson (1994) who identified the most important aspects of the function concept for deep understanding, were as follows: translating, determining, interpreting, solving quadratic equations, and using quadratic models. A multiple case study involving two algebra honor students was designed and implemented. Two honor students under the pseudonyms of Richard and Colin were purposely chosen and voluntarily participated in this study. Data were obtained from oneonone clinical interviews, students' written work (a test, quiz, and questionnaire), and classroom observations. The analysis particularly focused on identifying students' cognitive processes as they worked on quadratic tasks during the interviews. The whole data were analyzed through the lens of an integrated framework using Schoenfeld's (1989) level of mathematical analysis and structure and Tall and Vinner's (1981) framework of concept image and concept definition. The study revealed the cognitive obstacles that Richard and Colin encountered during the study of quadratic functions. In light of these obstacles, the following four assertions were made in this study: (1) one of the obstacles arises from a lack of making and investigating mathematical connections between algebraic and graphical aspects of the concepts, (2) another cognitive obstacle arises from the need to make an unfamiliar idea more familiar, (3) a third cognitive obstacle arises from the disequilibrium between algebraic and graphical thinking, and (4) the image of the quadratic formula or absolute value function has a potential to create an obstacle to mathematical learning. This study has important applications for classroom teaching. By identifying the students' cognitive obstacles based on the six aspects of quadratic functions, the study indicates which obstacles are associated with certain aspects of quadratic functions. Moreover, in light of these obstacles, it emphasizes the interrelation and complementary aspect of algebraic and graphical thinking in an ongoing backandforth process in learning and teaching of quadratic functions.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd0557
 Format
 Thesis
 Title
 Teacher Knowledge of Students and Enactment of Motivational Strategies in Teaching the Concept of Function.
 Creator

Nguyen, GiangNguyen T., Clark, Kathleen M., Chicken, Eric, Aspinwall, Leslie, Jakubowski, Elizabeth, Schrader, Linda, School of Teacher Education, Florida State University
 Abstract/Description

This research linked educational psychology and mathematics education to investigate how a teacher used his knowledge of students in designing and implementing mathematical tasks related to piecewise function and composition of functions. The study revealed that the teacher ("Mr. Algebra") faced many challenges in the implementation of mathematical tasks because students had not mastered early algebra concepts. Additionally, students carried with them some incomplete formal learning about...
Show moreThis research linked educational psychology and mathematics education to investigate how a teacher used his knowledge of students in designing and implementing mathematical tasks related to piecewise function and composition of functions. The study revealed that the teacher ("Mr. Algebra") faced many challenges in the implementation of mathematical tasks because students had not mastered early algebra concepts. Additionally, students carried with them some incomplete formal learning about function evaluation, constant functions, and domain and range, which made learning piecewise functions and composition of functions more difficult. The study employed various frameworks of mathematical tasks, SelfDetermination Theory, and motivational design approaches. Additionally, this research employed Keller's (2010) ARCS Instruments, Course Interest Survey and the Instructional Materials Motivation Survey. On these instruments, students were asked to give their teacher a score based on how the teacher: (1) captured and maintained student attention; (2) established that material is relevant to their lives; (3) built their confidence using such strategies as scaffolding and feedback; and (4) provided satisfaction for students to know that the material will be useful to their lives after the course ends. The analysis based on these ARCS Instruments showed that students were not fully motivated to learn mathematics because they perceived the course material irrelevant to their lives. Moreover, the analysis of student motivation based on SelfDetermination Theory showed that there were differences in student motivation that required flexibility in teaching strategies. Even though students had lost their motivation to learn mathematics at an earlier grade the teacher played a role in renewing their motivation. Also, the study revealed that mathematical tasks the teacher created were of high cognitive demand but students were willing to perform their best because they felt the teacher related to them. However, they did not perform well because they had not mastered previous course materials. Students at the college level continue to encounter difficulties with the concept of function such as those documented in earlier research. Therefore, intervention in Algebra (prefunction concepts) in teaching and learning is beneficial to help students be success at that level and move students to learning and application within and beyond Algebra.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd2614
 Format
 Thesis
 Title
 What Is the Nature of African American Teachers' Beliefs About Mathematics and How Do These Beliefs Relate to Their Beliefs About the Performance of African American Mathematics Students?.
 Creator

Howse, Mark, Jakubowski, Elizabeth, Shargel, Emanuel, Aspinwall, Leslie, Foulk, David, Department of Middle and Secondary Education, Florida State University
 Abstract/Description

Recent measures of educational progress indicate that student performance is on the rise. More students are taking advanced placement courses and attending college. However, the performance of African American students, particularly in mathematics, continues to lag behind that of white students. Several studies have examined various factors that influence the performance of African American students. Of particular interest are the beliefs of teachers and the impact of those beliefs on student...
Show moreRecent measures of educational progress indicate that student performance is on the rise. More students are taking advanced placement courses and attending college. However, the performance of African American students, particularly in mathematics, continues to lag behind that of white students. Several studies have examined various factors that influence the performance of African American students. Of particular interest are the beliefs of teachers and the impact of those beliefs on student performance. The purpose of this study was to explore African American teachers' beliefs about the nature of mathematics and the relationship between these beliefs and their beliefs about the performance of African American students. The study focused on thirty teachers that were employed in high schools where African American students made up 40% or more of the population. The research is based on the results of a survey instrument that was designed to capture and categorize teachers' beliefs on mathematics, mathematics students, and strategies for mathematics teaching. Bourdieu's construct of cultural capital served as the primary theoretical lens used to evaluate the teachers' beliefs about students. Ernest's conceptualization of a hierarchy for describing teacher views on the nature of mathematics was employed to place the teachers into three math definition categories. Symbolic interactionism was used as a context for evaluating the impact of the teachers' beliefs on classroom interaction. Data analysis revealed that the majority of the teachers held views of mathematics that were inconsistent with views that are endorsed by the National Council of Teachers of Mathematics. Evidence also shows that the majority of the teachers held relatively low beliefs about the performance of African American students. The study found that, contrary to the relationships described in much of the literature, the teachers' beliefs about mathematics had no associations with their beliefs about African American student performance or the strategies that the teachers employed in the teaching of mathematics. The results of the study provided information that is useful to mathematics educators and researchers who are interested in understanding the factors that impact the performance of African American students. By examining teachers' beliefs within the context of race, this study sheds new light on the critical role of teachers' beliefs in classroom dynamics.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd3707
 Format
 Thesis