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Articles 1 - 10 of 10
Full-Text Articles in Education
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 …
A Study Of The Impact Graphing Calculators Have On The Achievement In High School Pre Calculus, Marsha Brumberg
A Study Of The Impact Graphing Calculators Have On The Achievement In High School Pre Calculus, Marsha Brumberg
Theses and Dissertations
The use of graphing calculators in high school mathematics has long been debated. The transformation of function, in particular, parabolas, was studied and it was shown that there was no loss of achievement in Pre-Calculus classes with the use of graphing calculators. Assessments examined the impact of the graphing calculator on the conceptual knowledge of the topics by testing the students without the graphing calculator and with the graphing calculators. Five classes of pre calculus students (two classes who used graphing calculators and three who did not) were used in the study. The same students were used in the before …
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 …
A Study Of New Jersey Middle School Mathematics Teachers' Qualifications And Beliefs On Certification, Stephanie Marone
A Study Of New Jersey Middle School Mathematics Teachers' Qualifications And Beliefs On Certification, Stephanie Marone
Theses and Dissertations
The purpose of this research was to assess New Jersey middle school mathematics teachers' qualifications and beliefs on certification. To research this topic, teachers from South Jersey middle schools were contacted and asked to respond to a survey. The survey was created by the researcher to obtain information on the qualifications of respondents and their beliefs. The survey used a Likert scale to measure teachers' beliefs on their qualifications and comfort level teaching New Jersey Core Curriculum Content Standards. It is clear from previous research that middle school mathematics teachers should be educated specifically to teach both mathematics and young …
Professors' Perceptions Of Student Readiness For College-Level Mathematics, Tara L. Pedrick
Professors' Perceptions Of Student Readiness For College-Level Mathematics, Tara L. Pedrick
Theses and Dissertations
Students are not performing well in their freshman year in college mathematics classes. More incoming college freshman are being required to take remedial mathematics coursework. The purpose of this research is to determine if professors feel that traditional incoming freshmen students are prepared for college-level mathematics, and what factors they feel contribute to this level of preparation. To research this topic, professors from chosen two- and four-year colleges were contacted and asked to respond to a survey. The researcher created a survey using a Likert scale to obtain information on the views of college professors pertaining the topic. The instrument …
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 …