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Articles 31 - 60 of 60
Full-Text Articles in Education
Teachers' Decisions To Use Student Input During Class Discussion, Heather Taylor Toponce
Teachers' Decisions To Use Student Input During Class Discussion, Heather Taylor Toponce
Theses and Dissertations
One of the most vital decisions that teachers make during classroom discussion is whether to and how to validate the thinking that students present to the class. In this thesis I describe a study that addressed the issues that are associated with the decisions that teachers make in regards to validating students' ideas. Through qualitative research I explored these issues through videotaping an expert teacher, taking field notes, and conducting interviews. I share a description of what it looks like for one middle school mathematics teacher to make different decisions to use student input during class. The expert teacher in …
How Student Positioning Can Lead To Failure In Inquiry-Based Classrooms, Kelly Beatrice Campbell
How Student Positioning Can Lead To Failure In Inquiry-Based Classrooms, Kelly Beatrice Campbell
Theses and Dissertations
In an effort to improve mathematics instruction, I studied how the positions students choose or are pressed to take on can lead to failure in an inquiry-based classroom. Positioning refers to the temporary roles that a student or a teacher can place each other in or take on in a given classroom environment. Since positions are constructed and maintained by language use, I drew from positioning theory and discourse theory for my theoretical framework. From analyzing transcripts of classroom episodes and interviews with the teacher and a student, I identified common positions that the teacher and the student took on. …
Thinking On The Brink: Facilitating Student Teachers' Learning Through In-The-Moment Interjections, Travis L. Lemon
Thinking On The Brink: Facilitating Student Teachers' Learning Through In-The-Moment Interjections, Travis L. Lemon
Theses and Dissertations
In order to investigate ways pre-service student teachers (PSTs) might learn to teach with high-level tasks and effectively incorporate student thinking into their lessons a teaching experiment was designed and carried out by the cooperating teacher/researcher (CT). The intervention was for the CT to interject into the lessons of the PSTs during moments of opportunity. By interjecting a small question or comment during the lesson the CT hoped to support the learning of both the students of mathematics in the class and the PSTs. This in-the-moment interjecting was meant to enhance and underscore the situated learning of the PSTs within …
Understanding Teachers' Change Towards A Reform-Oriented Mathematics Classroom, Linnae Denise Williams
Understanding Teachers' Change Towards A Reform-Oriented Mathematics Classroom, Linnae Denise Williams
Theses and Dissertations
Within the current mathematics teacher population there are teachers that want to change from traditional teaching styles to become more reform-oriented (i.e. focusing on student understanding rather than procedures). Many of these teachers do not know how to begin this change. This research looks into the tools that are most valuable for teachers as they change from traditional teaching practices to include more reform-oriented teaching practices. Through this phenomenological study, six successful reform-oriented teachers were interviewed to understand what tools they found to be most valuable in their process of change. The interviews uncovered a common guiding principle that facilitates …
Growth In Students' Conceptions Of Mathematical Induction, John David Gruver
Growth In Students' Conceptions Of Mathematical Induction, John David Gruver
Theses and Dissertations
While proof and reasoning lie at the core of mathematical practice, how students learn to reason formally and build convincing proofs continues to invite reflection and discussion. To add to this discussion I investigated how three students grew in their conceptions of mathematical induction. While each of the students in the study had different experiences and grew in different ways, the grounded axes (triggering events, personal questions about mathematics, and personal questions about a particular solution) highlighted patterns in the narratives and from these patterns a theoretical perspective emerged. Reflection, both on mathematics in general and …
Contextualized Motivation Theory (Cmt): Intellectual Passion, Mathematical Need, Social Responsibility, And Personal Agency In Learning Mathematics, Janelle Marie Hart
Contextualized Motivation Theory (Cmt): Intellectual Passion, Mathematical Need, Social Responsibility, And Personal Agency In Learning Mathematics, Janelle Marie Hart
Theses and Dissertations
Student motivation has long been a concern of mathematics educators. Here, I characterize motivation, defined as an individual's desire to act in particular ways, through analysis of students' extended, collaborative problem solving efforts. Grounded in a longitudinal research project in calculus learning and teaching, Contextualized Motivation Theory (CMT) offers a means for understanding the complexities of student motivations in mathematics learning. Students in this study chose to act upon various intellectual-mathematical motivations and social-personal motivations, existing simultaneously, within a supporting "web" of motivations. Students exhibited intellectual passion in persisting beyond obtaining correct answers to build understandings of mathematical ideas. CMT …
The Influence Of Risk Taking On Student Creation Of Mathematical Meaning: Contextual Risk Theory, Erin Nicole Houghtaling
The Influence Of Risk Taking On Student Creation Of Mathematical Meaning: Contextual Risk Theory, Erin Nicole Houghtaling
Theses and Dissertations
The primary concerns of mathematics educators are learning and teaching mathematics. It is, therefore, natural to ask "what implications and benefits might there be if learning were perceived as a risk-taking event?" (Atkinson, 1957, p. 266). The underlying motivation of this study is to analyze the risks students take in the mathematics classroom and how risk influences student creation of meaning and development of understanding. I define risk in the mathematics classroom to be any observable act that entails uncertain outcome. The research presented here focuses on a table of four students: Andrew, Carina, Kam, and Mark as they grapple …
A Comparison Of Mathematical Discourse In Online And Face-To-Face Environments, Shawn D. Broderick
A Comparison Of Mathematical Discourse In Online And Face-To-Face Environments, Shawn D. Broderick
Theses and Dissertations
Many studies have been done on the impact of online mathematics courses. Most studies concluded that there is no significant difference in student success between online and face-to-face courses. However, most studies compared "traditional" online and face-to-face courses. Mathematics educators are advocating a shift from traditional courses to student-centered courses where students argue and defend the mathematics under the guidance of the teacher. Now, the differences in online and face-to-face student-centered mathematical courses merit a more in-depth investigation. This study characterized student mathematical discourse in online and face-to-face Calculus lab sections based off of a framework derived from an NCTM …
Uncovering Transformative Experiences: A Case Study Of The Transformations Made By One Teacher In A Mathematics Professional Development Program, Rachelle Myler Orsak
Uncovering Transformative Experiences: A Case Study Of The Transformations Made By One Teacher In A Mathematics Professional Development Program, Rachelle Myler Orsak
Theses and Dissertations
Effective professional development is vital for improving mathematics teaching (National Council of Teachers of Mathematics [NCTM], 2007), so studying effective professional development programs is important to the field of mathematics education. This case study presents findings on one teacher, Rebecca, and her experiences in a five-semester mathematics professional development for elementary teachers. The participants in this professional development engaged in collaborative problem solving of challenging mathematical tasks over extended periods of time. I used qualitative research methods based on grounded theory methodology (Charmaz, 2006) to analyze Rebecca's entrance and exit surveys, video data of Rebecca's individual interviews, and video data …
Mathematics Student Teaching In Japan: A Multi-Case Study, Allison Turley Shwalb
Mathematics Student Teaching In Japan: A Multi-Case Study, Allison Turley Shwalb
Theses and Dissertations
Nearly all research that seeks to assist in reforming mathematics student teaching in the United States has been limited in that it (1) does not consider student teaching models in non-Western cultures, and (2) has not sufficiently studied the unique context of mathematics in student teacher-cooperating teacher interactions. This multi-case study addresses these issues by analyzing the interactions between three cooperating teachers and two student teachers in the mathematics student teaching setting in Japan. Four conclusions are presented to generate a coherent picture of the principles of teaching and learning to teach that are emphasized during this Japanese student teaching …
Student Teacher Knowledge And Its Impact On Task Design, Tenille Cannon
Student Teacher Knowledge And Its Impact On Task Design, Tenille Cannon
Theses and Dissertations
This study investigated how student teachers used their mathematical knowledge for teaching and pedagogical knowledge to design and modify mathematical tasks. It also examined the relationship between teacher knowledge and the cognitive demands of a task. The study relied heavily on the framework in Hill, Ball, and Shilling (2008), which describes the different domains of knowledge in mathematical knowledge for teaching, and the framework on the cognitive demands of mathematical tasks in Stein, Smith, Henningsen, and Silver (2000). Results of the study indicated that the student teachers used their common content knowledge when they lacked sufficient knowledge in other domains, …
Choose Your Words: Refining What Counts As Mathematical Discourse In Students' Negotiation Of Meaning For Rate Of Change Of Volume, Christine Johnson
Choose Your Words: Refining What Counts As Mathematical Discourse In Students' Negotiation Of Meaning For Rate Of Change Of Volume, Christine Johnson
Theses and Dissertations
The purpose of this study is to describe how university honors calculus students negotiate meaning and language for conceptually important ideas through mathematical discourse. Mathematical discourse has been recognized as an important topic by mathematics education researchers of various theoretical perspectives. This study is written from a perspective that merges symbolic interactionism (Blumer, 1969) with personal agency (Walter & Gerson, 2007) to assert that human choice reflects, but is not determined by, meanings that are primarily developed through social interaction. The process of negotiation of meaning is identified, described, and analyzed in the discourse of four students and their professor …
Similar But Different: The Complexities Of Students' Mathematical Identities, Diane Skillicorn Hill
Similar But Different: The Complexities Of Students' Mathematical Identities, Diane Skillicorn Hill
Theses and Dissertations
We, as a culture, tend to lump students into broad categories to describe their relationships with mathematics, such as ‘good at math’ or ‘hates math.’ This study focuses on five students each of whom could be considered ‘good at math,’ and shows how the beliefs that make up their mathematical identities are actually significantly different. The study examined eight beliefs that affect a student's motivation to do mathematics: confidence, anxiety, enjoyment of mathematics, skill level, usefulness of mathematics, what mathematics is, what it means to be good at mathematics, and how one learns mathematics. These five students' identities, which seemed …
How Eighth-Grade Students Estimate With Fractions, Audrey Linford Hanks
How Eighth-Grade Students Estimate With Fractions, Audrey Linford Hanks
Theses and Dissertations
This study looked at what components are in student solutions to computational estimation problems involving fractions. Past computational estimation research has focused on strategies used for estimating with whole numbers and decimals while neglecting those used for fractions. An extensive literature review revealed one study specifically directed toward estimating with fractions (Hanson & Hogan, 2000) that researched adult estimation strategies and not children's strategies. Given the lack of research on estimation strategies that children use to estimate with fractions, this study used qualitative research methods to find which estimation components were in 10 eighth-grade students' solutions to estimation problems involving …
Discovering The Derivative Can Be "Invigorating:" Mark's Journey To Understanding Instantaneous Velocity, Charity Ann Gardner Hyer
Discovering The Derivative Can Be "Invigorating:" Mark's Journey To Understanding Instantaneous Velocity, Charity Ann Gardner Hyer
Theses and Dissertations
This is a case study using qualitative methods to analyze how a first semester calculus student named Mark makes sense of the derivative and the role of the classroom practice in his understanding. Mark is a bright yet fairly average student who successfully makes sense of the derivative and retains his knowledge and understanding. The study takes place within a collaborative, student-centered, task-based classroom where the students are given opportunity to explore mathematical ideas such as rate of change and accumulation. Mark's sense making of the derivative is analyzed in light of his use of physics, Mark as a visual …
Probing For Reasons: Presentations, Questions, Phases, Kellyn Nicole Farlow
Probing For Reasons: Presentations, Questions, Phases, Kellyn Nicole Farlow
Theses and Dissertations
This thesis reports on a research study based on data from experimental teaching. Students were invited, through real-world problem tasks that raised central conceptual issues, to invent major ideas of calculus. This research focuses on work and thinking of the students, as they sought to build key ideas, representations and compelling lines of reasoning. This focus on the students' and their agency as learners has brought about a new development of the psychological and logical perspectives, as well as, highlighted students' choices in academic and social roles. Such choices facilitated continued learning among these students.
The Main Challenges That A Teacher-In-Transition Faces When Teaching A High School Geometry Class, Greg Brough Henry
The Main Challenges That A Teacher-In-Transition Faces When Teaching A High School Geometry Class, Greg Brough Henry
Theses and Dissertations
During a semester-long action research study, the author attempted to implement a standards-based approach to teaching mathematics in a high school geometry class. Having previously taught according to a more traditional manner, there were many challenges involved as he made this transition. Some of the challenges were related to Geometry and others were related to the standards-based approach in general. The main challenges that the author encountered are identified and discussed. A plan of action for possible solutions to these challenges is then described.
Applying Toulmin's Argumentation Framework To Explanations In A Reform Oriented Mathematics Class, Jennifer Alder Brinkerhoff
Applying Toulmin's Argumentation Framework To Explanations In A Reform Oriented Mathematics Class, Jennifer Alder Brinkerhoff
Theses and Dissertations
This study looks at conceptual explanations given in a reform-oriented mathematics class for preservice secondary mathematics teachers and extends Toulmin's argumentation framework to account for some of the complexities of the explanations given by these students. This study explains the complexities that arose in applying Toulmin's framework to explanations and extends the framework by accounting for the features of conceptual explanations. The complexities of these explanations are that they are made up of multiple arguments that build on each other to reach a final conclusion and that they are also dependant upon the social aspects of the class in which …
What Are Some Of The Common Traits In The Thought Processes Of Undergraduate Students Capable Of Creating Proof?, Karen Malina Duff
What Are Some Of The Common Traits In The Thought Processes Of Undergraduate Students Capable Of Creating Proof?, Karen Malina Duff
Theses and Dissertations
Mathematical proof is an important topic in mathematics education research. Many researchers have addressed various aspects of proof. One aspect that has not been addressed is what common traits are shared by those who are successful at creating proof. This research investigates the common traits in the thought processes of undergraduate students who are considered successful by their professors at creating mathematical proof. A successful proof is defined as a proof that successfully accomplishes at least one of DeVilliers (2003) six roles of proof and demonstrates adequate mathematical content, knowledge, deduction and logical reasoning abilities. This will typically be present …
The Importance Of The Riemann-Hilbert Problem To Solve A Class Of Optimal Control Problems, Nicholas Dewaal
The Importance Of The Riemann-Hilbert Problem To Solve A Class Of Optimal Control Problems, Nicholas Dewaal
Theses and Dissertations
Optimal control problems can in many cases become complicated and difficult to solve. One particular class of difficult control problems to solve are singular control problems. Standard methods for solving optimal control are discussed showing why those methods are difficult to apply to singular control problems. Then standard methods for solving singular control problems are discussed including why the standard methods can be difficult and often impossible to apply without having to resort to numerical techniques. Finally, an alternative method to solving a class of singular optimal control problems is given for a specific class of problems.
One Problem, Two Contexts, Danielle L. Gigger
One Problem, Two Contexts, Danielle L. Gigger
Theses and Dissertations
In this study, a group of students were presented with two mathematically isomorphic problems but in radically different contexts. Analysis of their thinking and reasoning as they worked to solve and explain each problem demonstrates that the thinking and reasoning that emerged in each problem responded to clear purposes that the problems elicited in these students. The first problem was posed in a context that relied on experience and intuition rather than a formal mathematical description. The second problem was posed in a formal, set-theoretic context. While the analysis offered here reveals similarities in the students' final reasoning in the …
How A Master Teacher Uses Questioning Within A Mathematical Discourse Community, Omel Angel Contreras
How A Master Teacher Uses Questioning Within A Mathematical Discourse Community, Omel Angel Contreras
Theses and Dissertations
Recent scholarly work in mathematics education has included a focus on learning mathematics with understanding (Hiebert & Carpenter, 1992; Hiebert et al., 1997; Fennema & Romberg, 1999; National Council of Teachers of Mathematics, 2000). Hiebert et al. (1997) discussed two processes that they suggested increase understanding and that are central to this study: reflection and communication. Learning mathematics with understanding requires that the students create a deeper knowledge of mathematics through reflection and communication. The environment in which such learning can take place must include patterns of behavior, known as social norms that promote deeper thinking. When the social norms …
Second Graders' Solution Strategies And Understanding Of A Combination Problem, Tiffany Marie Hessing
Second Graders' Solution Strategies And Understanding Of A Combination Problem, Tiffany Marie Hessing
Theses and Dissertations
I inquire about second graders' capabilities of developing solution strategies and the original variety of strategies they bring forth while solving a combination problem. Based on analysis of the data presented in this paper, students developed five different general strategies. After analyzing what the second grade students were capable of developing, we can conclude that young children are capable of developing powerful systematic strategies grounded in their personal experiences. This research shows that even when the teacher does not foster personal agency, children will still exercise agency. The social interactions in the classroom helped students learn to propose mathematical ideas, …
The Nature And Frequency Of Mathematical Discussion During Lesson Study That Implemented The Cmi Framework, Andrew Ray Glaze
The Nature And Frequency Of Mathematical Discussion During Lesson Study That Implemented The Cmi Framework, Andrew Ray Glaze
Theses and Dissertations
During a year-long professional development, the faculty members at an elementary school received instruction on mathematics and how to use the Comprehensive Mathematics Instruction framework. The instruction and the framework were consistent with the standards suggested by the National Council of Teacher of Mathematics (2000). This thesis analyzes the mathematical language used by three fifth-grade teachers who participated in lesson study to create a research lesson based upon the Comprehensive Mathematics Instruction framework.
Determining High School Geometry Students' Geometric Understanding Using Van Hiele Levels: Is There A Difference Between Standards-Based Curriculum Students And Nonstandards-Based Curriculum Students?, Rebekah Loraine Genz
Theses and Dissertations
Research has found that students are not adequately prepared to understand the concepts of geometry, as they are presented in a high school geometry course (e.g. Burger and Shaughnessy (1986), Usiskin (1982), van Hiele (1986)). Curricula based on the National Council of Teachers of Mathematics (NCTM) Standards (1989, 2000) have been developed and introduced into the middle grades to improve learning and concept development in mathematics. Research done by Rey, Reys, Lappan and Holliday (2003) showed that Standards-based curricula improve students' mathematical understanding and performance on standardized math exams. Using van Hiele levels, this study examines 20 ninth-grade students' levels …
What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses?, Matthew M. Webb
What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses?, Matthew M. Webb
Theses and Dissertations
Lesson study is a form of professional development for teachers adopted in recent years from Japan. Introducing lesson study to U.S. teachers and researchers has been the focus of most of the literature on this subject. Much of the literature outlines how lesson study works and describes its essential features. One of the features of lesson study is anticipating student responses, also known as anticipating student thinking. Anticipating student responses is passingly described in lesson study literature. This research was conducted to understand what it means to anticipate student responses for preservice mathematics teachers in a lesson study group. Lesson …
An Examination Of The Role Of Writing In Mathematics Instruction, Amy Jeppsen
An Examination Of The Role Of Writing In Mathematics Instruction, Amy Jeppsen
Theses and Dissertations
This study uses qualitative methods to investigate the use of writing in a content course for elementary education majors in which writing was considered an important part of mathematical learning. The study differs from previous studies by investigating the role of writing in the everyday instructional activities, rather than investigating writing as a separate mathematical activity. An analysis of the instruction and class discussions that took place in this class reveals that components of writing that were addressed implicitly and explicitly in classroom instruction were developed simultaneously with conceptual understanding, suggesting a much stronger and more integral relationship between writing …
Fraction Multiplication And Division Image Change In Pre-Service Elementary Teachers, Jennifer J. Cluff
Fraction Multiplication And Division Image Change In Pre-Service Elementary Teachers, Jennifer J. Cluff
Theses and Dissertations
This study investigated three pre-service elementary teachers' understanding of fractions and fraction multiplication and division. The motivation for this study was lack of conceptual understanding of fractions and fraction multiplication and division. Pre-service elementary teachers were chosen because teachers are the conduit of information for their students. The subjects were followed through the fractions unit in a mathematics methods course for pre-service elementary teachers at Brigham Young University. Each subject volunteered to participate and were interviewed and videotaped throughout the study, and they also provided copies of all work done in the fractions unit in the course. The data is …
Reasoning About Motion: A Case Study, Tiffini Lynn Glaze
Reasoning About Motion: A Case Study, Tiffini Lynn Glaze
Theses and Dissertations
Several dance and industrial design students were given the opportunity to attend a non-traditional mathematics course. The nature of this course prompted student interaction and expected collaboration. My research focuses on one dance student, Sara, who did not consider herself a strong mathematics student, but who understood physical motion very well. This paper explores the evolution of Sara's representations for physical motion in a given task, and discusses her reasoning for keeping or dismissing various parts of her representations during the course of this task. I examine first how Sara learns mathematics with understanding in this task, and second how …
An Analysis Of The Influence Of Lesson Study On Preservice Secondary Mathematics Teachers' View Of Self-As Mathematics Expert, Julie Stafford
An Analysis Of The Influence Of Lesson Study On Preservice Secondary Mathematics Teachers' View Of Self-As Mathematics Expert, Julie Stafford
Theses and Dissertations
This research seeks to investigate the influence of lesson study on preservice secondary mathematics teachers' view of self as mathematics expert. The study acknowledges the commonly held belief that prospective mathematics teachers have that they know and understand secondary mathematics. The purpose in engaging the preservice teachers in lesson study is to dislodge this belief. In particular, this research report focuses on one preservice teacher and her experiences during lesson study. Using the data collected, the researcher reports on the baseline beliefs that the preservice teacher held toward her knowledge of secondary mathematics, her mathematical experiences during the actual lesson …