# Education Commons™

2007

Science and Mathematics Education

Brigham Young University

Articles 1 - 7 of 7

## Full-Text Articles in Education

Discovering The Derivative Can Be "Invigorating:" Mark's Journey To Understanding Instantaneous Velocity, Charity Ann Gardner Hyer Jul 2007

#### 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 ...

Jul 2007

#### 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.

Probing For Reasons: Presentations, Questions, Phases, Kellyn Nicole Farlow Jul 2007

#### 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.

Applying Toulmin's Argumentation Framework To Explanations In A Reform Oriented Mathematics Class, Jennifer Alder Brinkerhoff Jul 2007

#### 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 ...

#### 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 ...

Mar 2007

#### 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 Jan 2007

#### 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 ...