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Full-Text Articles in Education
A Psychometric Analysis Of The Precalculus Concept Assessment, Brian Lindley Jones
A Psychometric Analysis Of The Precalculus Concept Assessment, Brian Lindley Jones
Theses and Dissertations
The purpose of this study was to examine the psychometric properties of the Precalculus Concept Assessment (PCA), a 25-item multiple-choice instrument designed to assess student reasoning abilities and understanding of foundational calculus concepts (Carlson et al., 2010). When this study was conducted, the extant research on the PCA and the PCA Taxonomy lacked in-depth investigations of the instruments' psychometric properties. Most notably was the lack of studies into the validity of the internal structure of PCA response data implied by the PCA Taxonomy. This study specifically investigated the psychometric properties of the three reasoning constructs found in the PCA taxonomy, …
A Validity Study Of The Cognitively Guided Instruction Teacher Knowledge Assessment, Debra Smith Fuentes
A Validity Study Of The Cognitively Guided Instruction Teacher Knowledge Assessment, Debra Smith Fuentes
Theses and Dissertations
This study reports the development of an instrument intended to measure mathematics teachers' knowledge of Cognitively Guided Instruction (CGI). CGI is a mathematics professional development framework based on how students think about and solve problems and how that knowledge guides instruction for developing mathematical understanding. The purpose of this study was to (a) analyze and revise the original CGI Teacher Knowledge Assessment (CGI TKA), (b) administer the revised CGI TKA, and (c) analyze the results from the revised CGI TKA. As part of the revision of the original CGI TKA, distractor analysis identified distractors that could be improved. Experts in …
How Teacher Questions Affect The Development Of A Potential Hybrid Space In A Classroom With Latina/O Students, Casandra Helen Job
How Teacher Questions Affect The Development Of A Potential Hybrid Space In A Classroom With Latina/O Students, Casandra Helen Job
Theses and Dissertations
Questions have been shown to aid in student understanding of mathematics, particularly "novel" questions (Mesa, Celis, & Lande, 2013) that do not have a predetermined answer. However, students do not always understand what is intended by questions posed by teachers, particularly those students who come from different cultural and lingual backgrounds than those dominant in the classroom discourse. This project investigated the relationship between how a mathematics teacher acknowledged students funds of knowledge in her questions and how Latina/o students responded. It shows some research based questioning techniques that allow Latina/o students greater opportunity to participate in the mathematical problem-solving …
Teacher Graphing Practices For Linear Functions In A Covariation-Based College Algebra Classroom, Konda Jo Luckau
Teacher Graphing Practices For Linear Functions In A Covariation-Based College Algebra Classroom, Konda Jo Luckau
Theses and Dissertations
Graphing is a fundamental topic in algebra that is notoriously difficult for students. Much of the past research has focused on conceptions and misconceptions. This study extends past research by looking at the mathematical practices of a practitioner, specifically one instructor of a function-based covariation-focused algebra class in the linear functions unit. Considering practices in addition to conception adds dramatically to our understanding of mathematical activity because it leads to explicit descriptions of normative purposes that are connected to particular situations or problems and also specifies how tools and symbols are coordinated to achieve these purposes. The results of this …
Academic And Peer Status In The Mathematical Life Stories Of Students, Carol Ann Wise
Academic And Peer Status In The Mathematical Life Stories Of Students, Carol Ann Wise
Theses and Dissertations
Mathematics students often define themselves by their grades, test scores, how they compare to other people, how comfortable they feel in mathematics class, and so on. These experiences are all part of a student's mathematical life story. Students assume positions with particular rights and duties for themselves and for the actors in the stories they tell. Those positions reflect certain types and levels of status. Those types and levels of status have been shown to either inhibit or open a student's access to learning mathematics. Thus, a student's status in mathematics education is an issue of equity. Mathematics educators and …
Student Evaluation Of Mathematical Explanations In Aninquiry-Based Mathematics Classroom, Ashley Burgess Hulet
Student Evaluation Of Mathematical Explanations In Aninquiry-Based Mathematics Classroom, Ashley Burgess Hulet
Theses and Dissertations
Students do not always evaluate explanations based on the mathematics despite their teacher's effort to be the guide-on-the-side and delegate evaluation to the students. This case study examined how the use of three features of the Discourse—authority, sociomathematical norms, and classroom mathematical practices—impacted students' evaluation and contributed to students' failure to evaluate. By studying three pre-service elementary school students' evaluation methods, it was found that the students applied different types of each of the features of the Discourse and employed them at different times. The way that the features of the Discourse were used contributed to some of the difficulties …
Supporting An Understanding Of Mathematics Teacher Educators:Identifying Shared Beliefs And Ways Of Enacting Their Craft, Joseph S. Rino
Supporting An Understanding Of Mathematics Teacher Educators:Identifying Shared Beliefs And Ways Of Enacting Their Craft, Joseph S. Rino
Theses and Dissertations
For many preservice elementary and secondary teachers, the first time they encounter the notion that mathematics can be taught in ways other than what they experienced is in their teacher preparation program. Therefore, the potential impact of the mathematics teacher educator on the understanding and development of preservice teachers is immense, especially as that impact is considered in connection to the various reform efforts related to mathematics education that have spread across the country for the past three decades. Given the scarcity of systematic research focused on mathematics teacher educators, the author sought to understand defining characteristics of that role. …
Parents And The Common Core State Standards For Mathematics, Rebecca Anne Roberts
Parents And The Common Core State Standards For Mathematics, Rebecca Anne Roberts
Theses and Dissertations
As the majority of the nation has adopted Common Core State Standards for Mathematics (CCSSM), studying parents' resistance to these standards becomes vital in improving parental involvement and support of school mathematics reforms. Using Schoenfeld's (2011) model for decision making as a framework, an online survey and six interviews were conducted. The results of the survey showed that parents' resources related to student experiences and the mathematical methods students are performing are affecting their resistance toward CCSSM. The survey results also showed that parents' orientations related to the difficulty of the standards and politics affects their resistance toward CCSSM. The …
Online Student Discussions In A Blended Learning Classroom: Reconciling Conflicts Between A Flipped Instruction Model And Reform-Based Mathematics, Lewis L. Young
Theses and Dissertations
Two ideas are prevalent in teacher professional development today. Teachers are finding new and innovative ways to incorporate technology into their classroom. The use of video and social media is increasing. One type of pedagogy that has emerged among the blended learning pedagogies is flipped instruction, where students participate in some of the instruction outside of the classroom. Another prevalent idea is the focus on inquiry learning and reform-based mathematics instruction. This pedagogy adheres to the idea that students can use their problem solving skills to understand complex mathematics. This qualitative content analysis outlines how one researcher sought to find …
It Takes A Village: Investigating The Critical Role Clinical Faculty Play In Mathematics Teacher Education, Damon L. Bahr
It Takes A Village: Investigating The Critical Role Clinical Faculty Play In Mathematics Teacher Education, Damon L. Bahr
Faculty Publications
The dispositions of preservice elementary education teachers toward reform-oriented mathematics education were surveyed before and after an extended pre-student teaching practicum. During the practicum, university and school-based personnel served a "clinical faculty" as they supported the preservice teachers' practicum experiences. The preservice teachers' perceptions of the clinical faculty's dispositions were also surveyed. Relationships between changes in the dispositions of the preservice teachers and their perceptions of the clinical faculty were discovered thus highlighting the important influence clinical faculty wield as mathematics teacher educators.
The Adoption Of Open Educational Resources By One Community College Math Department, John Hilton Iii, Donna Gaudet, Phil Clark, Jared Robinson, David Wiley
The Adoption Of Open Educational Resources By One Community College Math Department, John Hilton Iii, Donna Gaudet, Phil Clark, Jared Robinson, David Wiley
Faculty Publications
The high cost of textbooks is of concern not only to college students but also to society as a whole. Open textbooks promise the same educational benefits as traditional textbooks; however, their efficacy remains largely untested. We report on one community college’s adoption of a collection of open resources across five different mathematics classes. During the 2012 fall semester, 2,043 students in five different courses used these open access resources. We present a comparison between the previous two years in terms of the number of students who withdrew from the courses and the number that completed the courses with a …
A Conceptual Framework For Student Understanding Of Logarithms, Heather Rebecca Ambler Williams
A Conceptual Framework For Student Understanding Of Logarithms, Heather Rebecca Ambler Williams
Theses and Dissertations
In the past, frameworks for what it means for students to understand elementary mathematical concepts like addition have been well-researched. These frameworks are useful for identifying what students must understand to have a good grasp of the concept. Few such research-based frameworks exist for secondary mathematical topics. The intent of this study was to create such a framework for what it means for students to understand logarithms, a topic that has been under-researched up to this point. Four task-based interviews were conducted with each of four different preservice secondary mathematics teachers in order to test a preliminary framework I had …
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 …
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 …
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 …
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 …
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.
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 …
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 …